Exponential growth on a logarithmic graph looks like a straight line. On a regular graph, the line would appear to be curved, but when plotted on a logarithmic graph, the line appears to be a straight line.
Exponential growth on a logarithmic graph appears as a straight line. This is because the logarithmic scale is a compressed scale, meaning that it takes a large range of values and compresses them into a smaller range. This makes the data easier to read and understand. The straight line occurs because the logarithmic scale is designed to fit the data points more closely, making the line appear linear. This is in contrast to the regular scale, where the line appears curved due to the large range of values being plotted. Thus, exponential growth appears as a straight line on a logarithmic graph.
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How do you graph a parent graph?
This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola. For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.
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What percent of 48 is 16?
Answer:
Step-by-step explanation:
hello follow me on zepeto if this helps
16 is 33.3333% of 48. 33 is the whole number hope you get a
A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet
The provided solution says that
The cylinder can be "unwrapped" into a rectangle, to get a stripe that is a parallelogram with base 3 and height 80.
However, I don't understand how the height of the stripe can be eighty. The distance from the top of the cylinder to the bottom is 80 feet as given, so how can a winded stripe that goes around be also 80 feet? Isn't the shortest distance, 80 ft, simply from the top to the bottom? How does a winded spiral also become 80 feet ?
The stripe's area in square feet is 240 square units.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.
Here,
The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base 3 and height 80.
area=3*80
=240 square units.
the area of the stripe in square feet is 240 square units.
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Is Y =- 2 vertical or horizontal?
y = − 2 is a horizontal line that crosses the -axis at -2.
Now, According to the question:
Let's know:
What is Horizontal lines?
If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.
The given equation is Y = -2
y = 2 is a horizontal line that crosses the -axis at 2.
=> y = − 2 is a horizontal line that crosses the -axis at -2.
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Question 3 A student solved a quadratic equation as shown here
Answer:
Didn't move the 12 on the other side of the equal sign to make
2x^2 + 5x - 12 = 0
the other steps error city.
Step-by-step explanation:
2x^2 + 5x - 12 = 0
(2x - 3)(x + 4)= 0
2x - 3 = 0
2x = 3
x = 3/2
x + 4 = 0
x = -4
On a coordinate plane, the center of dilation is at (0, 0). Triangle A B C is dilated to create triangle A prime A C prime. The points of A B C are (negative 3, 3), (negative 1, 1), and (negative 3, 1). The points of A prime A C prime are (negative 9, 9), (negative 3, 3), and (negative 9, 3).
The dilation DO,3 (x, y) → (3x, 3y) is performed on the pre-image △ABC to make a similar triangle. Which statements are true? Check all that apply.
∠A corresponds to ∠A'.
∠A'AC' corresponds to ∠B.
CB corresponds to C'A.
Segment A'A is parallel to segment C'C.
△ABC ~ △A'AC'.
The true statements after a dilation of scale factor 3 are,
∠A corresponds to ∠A' and Triangle ABC is similar to triangle A'B'C'.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, The points of ABC are (negative 3, 3), (- 1, 1), and (- 3, 1).
The points of A'BC' are (- 9, 9), (- 3, 3), and (- 9, 3) after a dilation of 3, (x, y) ⇒ (3x, 3y).
We know dilation maintains the similarity of the dilated figures.
Therefore, The statements that are true,
∠A corresponds to ∠A' as dilation maintains similarity.
Triangle ABC is similar to triangle A'B'C'.
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Answer:
Options A,B,C,E
Step-by-step explanation:
A bookstore owner has 15 different books to arrange on the shelves in a display case. Each shelf can display 3 books.In how many different ways can the owner arrange 3 books on the top shelf of the display case
There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.
How many different ways can you arrange3 books on a shelf?different bundles of novels, and we have to put this bundle and other 3 books onto the shelf. So the total number of ways is 3! × (3 + 1)! = 144.How many ways can you arrange 3 books on a shelf from a group of 7?= 5040 arrangements. Three books that we want together have 3!Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways.A trilogy is a set of three distinct works that are connected and can be seen either as a single work or as three individual works. They are commonly found in literature, film, and video games.When using three shelves, place the middle shelf higher or lower than the one on either side. Five shelves can be staggered with two or three higher than the others, alternating every other shelf for a horizontal groupingTo learn more about arrange3 books on a shelf refers to:
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Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens
The expanded form in terms of the sums of powers to tens of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]
As per the given data the given decimal number is 237.45.
Here we have to determine the expanded form in terms of the sums of powers to tens.
Expanded Form: In its extended sense, A number is divided up into its place values, then expanded to represent the value of each digit.
Then N can be written in expanded in for terms of 10 is
[tex]$$\Rightarrow N=a \times 10^2+b \times 10^1 + c \times 10^0+d \times 10^{-1}+e \times 10^{-2}$$[/tex]
Let the given number 237.45 is denoted by N.
N = 237.45
First, write the expanded form of a number before the decimal place.
Then using [tex]$\circledast$[/tex], we have
[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times \frac{1}{10}+5 \times \frac{1}{10^2} \\[/tex]
[tex]& N=2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2} \\[/tex]
237.45 = [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex]
Therefore the expanded form of 237.45 is [tex]2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}[/tex].
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Which of the following expressions represents 237.45 written in expanded form in terms of the sums of powers to tens
A. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0+4 \times 10^{-1}+5 \times 10^{-2}$[/tex]
B. [tex]$237 \times 100+45 \times 1 / 1000$[/tex]
C. [tex]$2 \times 10^2+3 \times 10^1+7 \times 10^0-4 \times 10^1-5 \times 10^2$[/tex]
D. 200+30+7+0.4+0.05
HELP 50 points :D
1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.
2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.
3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.
__/__
4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.(1 point)
$___ for each silver ticket and $___ for each gold ticket
5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.
1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.
To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.
To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.
Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.
How calculate the cost?2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.
To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player
3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.
The reciprocal of the fraction 2/3 is 3/2
4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.
Let's call the cost of a silver ticket x.
The cost of a gold ticket is x + 8.
We know that Patrick spent 10x + 10(x+8) = $140
We can simplify that: 10x + 10x + 80 = 140
Then we have 20x + 80 = 140
Then we have 20x = 60
And x = 3
Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11
5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.
If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.
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Why do we use similarity transformation?
The goal of using similarity transformations is to make the evaluation of a matrix's eigenvalues less complicated. In fact, the computation of the eigenvalues would be instantaneous if a given matrix could be translated into a similar matrix in diagonal or triangular form.
A geometric similarity or a matrix transformation that produces a likeness are both covered by the term "similarity transformation."
A conformal mapping with a similarity transformation is one whose transformation matrix A' has the formula A'=BAB⁻¹, where A and A' are referred to as similar matrices.
Space-based items are converted to equivalent objects by similarity transformations. Fractals and iterated function systems have a lot to do with similarity transformations and the idea of self-similarity.
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The scores on the last math quiz are summarized in the following frequency table:
Score
10 9
8
7
6
4 3 2 1 0
7
5
3 2
1
0
0
10
0
Frequency 6
The information is then put into the following histogram:
Frequency
5
4
3
210
1 2 3 4 5 6 7 8 9 10
5
1
Score
Therefore , the answer to the above problem is 5.75 for the mean and 9 for the median.
What is mean?Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the amount of values present in the dataset by its total number of values in the data. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the integers in a data set and dividing the total by the total number of numbers. For example, in the data below
Here,
Spread it all out here first:
4, 5, 6, 7, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10
The mean is calculated by dividing total total by the total number of scores. Add up each number.
There are 16 numbers total, and they add up to 92. 92 / 16 = 5.75
To get the median, identify the middle number among all the other numbers.
Sadly, there is no "center number" given that there are 16.
Add the ninth and eighth numbers together, then divide by to find the middle.
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Graph the line with slope of 3/4 passing through the point (-1, 2)
Answer:
Step-by-step explanation:
Water leaking onto a floor forms a circular pool. The circumference of the pool increases at a rate 24 cm/min. How fast is the area of the pool increasing when the radius is 5 cm
The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm
How quickly does the pool's area grow when the radius is 5 cm?Given:
radius of the pool increases at a rate of 24 cm/min
To Find:
How quickly does the pool's area grow when the radius is 5 cm?
Solution:
we are given with the circular pool
hence the area of the circular pool =
A = πr²-----------------------------(1)
The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t
so differentiating eq (1) with respect to t , we have
dA/dt =π 2r dr/dt
we have to find dA/dt with dr/dt = 24 cm/min and r = 5cm
substituting the values
dA/dt = π 2(5)24
dA/dt = π 26*8
dA/dt = π 240
dA/dt =240π
dA/dt = 753.98
The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm
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a form of reasoning called is the process of forming general ideas and rules based on your experiences and observation
A form of reasoning called induction is the process of forming general ideas and rules based on your experiences and observations.
What is the Induction?The process of welcoming newly hired employees and assisting them in adjusting to their new positions and working surroundings is known as induction. Beginning a new work can be stressful, so new hires require assistance adjusting to their new environment.
The action or process of inducting someone to a position or organization.
We have given that,
A form of reasoning called is the process of forming general ideas and rules based on your experiences and observations.
As a result, the process of formulating general hypotheses and rules based on your observations and experiences is known as induction.
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18 points ! The shape of Gretchen's data can be described as 1) skewed left 2) skewed right 3) symmetrical.
Because of this, the 1) mean 2) median would be the best measure of center for this data set. The actual value for the best measure of center is 1) 7, 2) 9, 3) 9. 1, 4) 9. 6
The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.
What is skewed left?A distribution that is left-skewing has a lengthy left tail.
Distributions that are negatively skewed are also known as left-skewed distributions.
This is due to the number line having a significant negative tail.
Additionally, the peak is to the left of the mean.
The right tail of a right-skewed distribution is lengthy.
It's a widespread misperception that "peakness" is defined by the distribution's peak.
To put it another way, a peak that leans left indicates a left-skewed distribution.
Hence, The first blank is skewed left, the second blank is median, and the third blank is 9 is correct options.
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The diameter of the cylinder barrel was 20 in. When the barrel was lifted away it left an imprint of a circle on the ground. What is the area of the circle?
The area of the circle is 1256.64 square inches.
What is a Circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
A closed 2D form that isn't a polygon is a circle. It has one face that curves.If two circles have the same radius, they are said to be congruent.Equal chords are always located equally from the circle's center.The center of the circle is the perpendicular bisector of a chord.The line joining the points of two overlapping circles will be perpendicular to the line joining the points of the circles' centers.The tangents drawn at the diameter's endpoints are perpendicular to one another.One of the most fundamental curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its basis in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
The diameter of the cylindrical barrel is 20 in
So the diameter of the circular base is 20 in = 10 inches in radius.
Area of the circle = [tex]\pi\ r^{2}[/tex] = π*20*20 = 1256.64 square inches.
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A line has a slope of 2 and a y-intercept of 0. What is its equation in slope-intercept form
Answer:
y = 2x
Step-by-step explanation:
y = mx + b
m = 2
y-intercept = b = 0
y = 2x + 0
y = 2x
WZ and XR are diameters of circle C. The diagram is not drawn to scale.
Circle C is shown.
Radii are drawn from point C to point R at the right, point Z at the upper right, point Y at the upper left, point X at the left, and point W at the lower left.
Angle Y C Z measures 112 degrees.
Angle X C W measures 63 degrees.
Points X, C, and R are all on the horizontal diameter of the circle.
What is the measure of convex arc upper Z upper W upper X?
A. 355º
B. 5º
C. 292º
D. 243º
The measure of convex arc upper Z is 243⁰ Option D
How to find the measure of the angle?We should be aware that a convex angle is the angles that are irregular in nature
Assume that the radius of the given circle is r.
The central angle of the lower arc ZWX = 41+180 = 221⁰
Note that then central angle of the upper arc ZWX = 360- 221⁰
This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰
Recall that Lenght of arc = A/360 *2*π*r
Where A is the angle made by the radii, r= radius of the circle
Arc length of upper ZWX:
Arc length of upper ZWX = 139π/180*r
Arc length of upper ZWX = 139πr/180
The lenght is (139*22)/ 180*7
= 3058/2360
= 245⁰
In conclusion the measure of the convex upper is 245⁰
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Is 8 15 17 a right angle triangle?
No, 8 15 17 is not a right angle triangle. A right angle triangle is a triangle in which one of the three angles is equal to 90 degrees.
To determine if a triangle is a right angle triangle, we can use the Pythagorean theorem. This states that in a right angle triangle, the sum of the squares of the two shorter sides (a and b) will equal the square of the longest side (c).
In this case, the length of the sides are 8, 15 and 17. We can calculate the sum of the squares of the two shorter sides, which is 8² + 15² = 144 + 225 = 369. However, the square of the longest side (17²) is 289. Since 289 is not equal to 369, this means that 8 15 17 is not a right angle triangle.
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can someone please help me ( check the link for the question
The equation of the line that passes through the point (3, 2) and is perpendicular to 3x + 5y = 15 is y = (5/3)x - 3
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is y = m(1)x + c
The line passes through (3, 2) and is perpendicular to 3x + 5y = 15.
This means,
3x + 5y = 15
5y = -3x + 15
y = (-3/5)x + 3
m(2) = (-3/5)
Now,
m(1) x m(2) = -1
m(1) = -1 / ((-3/5)
m(1) = 5/3
Now,
(3, 2) = (x, y)
y = m(1)x + c
2 = (5/3) x 3 + c
2 = 5 + c
c = 2 - 5
c = -3
Thus,
The equation of the line is y = (5/3)x - 3.
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Please help
Solve the rational equation: 1/x+1 - 1/x+2 = 1/5
A. There is no solution.
B. x = −0.64, x = 1.44
C. x = −3.79, x = 0.79
D. x = −1, x = −2
The solution for the rational equation (1/(x + 1)) - (1/(x + 2)) = 1/5 is specified by the option C.
C. x = -3.79, x = 0.79
What is a rational equation?A rational equation consists of a fraction that has a polynomial numerator denominator.
The specified equation can be expressed as follows;
[tex]\dfrac{1}{x + 1} - \dfrac{1}{x+2} = \dfrac{1}{5}[/tex]
Finding the common denominator for the right hand side expression, we get;
[tex]\dfrac{ (x + 2) - (x + 1)}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]
[tex]\dfrac{1}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]
[tex]\dfrac{1}{x^2+ 3\cdot x+ 2} = \dfrac{1}{5}[/tex]
Inverting both sides of the above equation, we get the following quadratic equation;
x² + 3·x + 2 = 5
x² + 3·x + 2 - 5 = 0
x² + 3·x - 3 = 0
The quadratic formula indicates that we get;
x = (-3 ± √(3² - 4×1×(-3))) ÷ (2 × 1)
x = (-3 + √(21)) ÷ 2 and x = (-3 - √(21)) ÷ 2
x ≈ 0.79 and x ≈ -3.79
The correct option is option C
C. x = -3.79, x = 0.79
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A guy wire attached to the top of a radio antenna
is bolted to the ground 48 m from the base of
the tower. If the wire makes an angle of 14°
with the ground. What is the length of the
guy wire? Round your answer to the nearest
hundredth of a meter.
1
The length of the guy wire is 48.87 m.
How to find the length?To find the length of the guy wire, you can use the formula for the length of a side of a right triangle (the Pythagorean theorem): [tex]c = sqrt(a^2 + b^2)[/tex]. In this case, c is the length of the guy wire, a is the distance from the base of the tower to the point where the guy wire is attached to the ground (48 m), and b is the distance from the point where the guy wire is attached to the ground to the top of the antenna.
To find b, you can use the tangent function: [tex]tan(14°) = b / 48.[/tex]
Solving for b gives b = 6.78 m
Then, length of wire can be calculated as
[tex]c = sqrt(48^2 + 6.78^2)[/tex]
[tex]c = 48.87 m (approx)[/tex]
Rounding it to the nearest hundredth of a meter, the length of the guy wire is 48.87 m.
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Boxplots are NOT recommended for use with which of the following types of? distributions?
Choose the correct answer below.
a. Symmetric
b. Unimodal
c. Skewed
d. Bimodal or any multimodal distribution
Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.
Which distributions are unimodal?The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).
Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.
There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.
Therefore, the correct answer is option b) Unimodal.
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The required correct option for the given question is uni-modal.
Which distributions are uni-modal?The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).
Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.
There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.
Therefore, the correct answer is option b) Uni-modal.
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The function f(x) = 225(1.29)", represented in the table, shows the number of people (in thousands) who own a cell phone device in a certain country where x is the number of years after 2010.
Year
Number of Cell Phone Owners
(in thousands)
2010 2012 2014 2016 2018
225 375 623 1,037 1,725
Find the average rate of change from 2012 to 2018 and interpret its meaning in terms of the context. (1 point)
-225; represents the average depreciation in cell phone owners from 2012 to 2018
225; represents the average growth in cell phone owners from 2012 to 2018
-37.5, represents the average depreciation in cell phone owners from 2012 to 2018
37.5, represents the average growth in cell phone owners from 2012 to 2018
Therefore , the solution of the given problem of function comes out to be f(x) = 2871 thousands.
What is meant by the word function?A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.
Here,
Given :
=> f(x) = 225(1.29)×
After 10 year number of years x =10
=> f(x) = 225(1.29)¹⁰
=> f(x) = 12.76 * 225
=> f(x) = 2871 thousands.
Therefore , the solution of the given problem of function comes out to be f(x) = 2871 thousands.
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Homer Simpson left an estate of $2.4 million. He left 10% to Springfield University, 15% to the First Church of Springfield, $600,000 to his wife Marge, and the remainder to be divided among his three children. How much did each child receive?
Hello there!
Answer:
$400'000
Step-by-step explanation:
Estate -- $2.4 million or $2'400'000
Springfield University will receive: 10% * $2'400'000 = 0.1 * $2'400'000 = $240'000
First Church of Springfield will receive: 15% * $2'400'000 = 0.15 * $2'400'000 = $360'000
Wife will receive $600'000
Total: $240'000 + $360'000 + $600'000 = $1'200'000
Children will receive at total: $2'400'000 - $1'200'000 = $1'200'000
So each child will receive: $1'200'000 / 3 = $400'000
Answer: Each child of Homer Simpson gets $400000.
Step-by-step explanation:
Homer Simpson left 10% of his estate, or (10/100) x $2.4 million
= $ (10/100)x2400000= $240000
$240,000 to Springfield University.
He left 15% of his estate, or (15/100) x $2.4 million = $(15/100)2400000
= $360000
So 360,000 to the First Church of Springfield.
So in total, he left $240,000 + $360,000 + $600,000 = $(240000+360000+600000)
=$1200000
$1,200,000 to organizations and his wife.
That means the remainder of the estate, $2.4 million - $1,200,000
= $2400000-1200000
= $1200000
1,200,000, was divided among his three children. So each child received $1,200,000 / 3 = $1200000/3
=$400000
Answer: $400000.
Which of the following are irrational numbers?
Choose two correct answers.
3.05
√17
√27
√81
Answer:√17
√81
√27
This 3 numbers are irrational number
Answer:
17 and 27 are irrational
Step-by-step explanation:
A certain psychological test measures empathy and
emotional intelligence. The score, S, of a randomly
selected senior student at a large university has a mean
of 123 and a standard deviation of 29. The score, F, of a
randomly selected first-year student at a large university
has a mean of 104 and a standard deviation of 34.
Suppose we randomly select one senior student and one
first-year student. We can consider Sand F to be
independent random variables.
As per the given standard deviation, the probability that the first-year student shows a higher emotional intelligence test score in a randomly selected senior/first-year pair is 0.72
Here we have given that the score, S, of a randomly selected senior student at a large university has a mean of 123 and a standard deviation of 29.
And the score, F, of a randomly selected first-year student at a large university has a mean of 104 and a standard deviation of 34.
Then the probability is calculated as,
=> 123/104
=> 1.182
Where as the based on the standard deviation, the value is calculated as
=> 29/34
=> 0.852
Then the total probability of the given situation is calculated as,
=> 0.852/1.182
=> 0.72
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pls help with question image is linked
The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg
How to determine the amount sold each dayFrom the question, we have the following parameters that can be used in our computation:
Day 2 = Day 1 - 25
Day 3 = 2/7 * (Day 1 + Day 2)
Total weights = 315
Next, we use the following representations
x = Day 1, y = Day 2 and z = Day 3
So, we have the following equations
y = x - 25
z = 2/7(x + y)
x + y + z = 315
Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315
z = 2/7(x + x - 25) = 2/7(2x - 25)
x + y + z = 315 ⇒ x + x - 25 + z = 315
So, we have
z = 2/7(2x - 25)
2x + z = 340
Substitute z = 2/7(2x - 25) in 2x + z = 340
2x + 2/7(2x - 25) = 340
So, we have
7x + 2x - 25 = 1190
Evaluate the like terms
9x = 1215
Divide by 9
x = 135
So, we have
y = x - 25 = 135 - 25 = 110
z = 2/7(x + y) = 2/7 *(135 + 110) = 70
Hence, the amounts are 135 kg, 110 kg and 70 kg
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Farmers Lirn and Rew both bought gespils and alabers for their farms. Lirn bought 8 gespils and 9 alabers for $117. Rew bought 3 gespils and 8 alabers for $67. Write a system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y).
The system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -
8x + 9y = 117
3x + 8y = 67
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Farmers Lirn and Rew both bought gespils and alabers for their farms. Lirn bought 8 gespils and 9 alabers for $117. Rew bought 3 gespils and 8 alabers for $67.
We can write the system of equations as -
8x + 9y = 117
3x + 8y = 67
Where -
cost of gespils → (x)
cost of alabers → (y).
Therefore, the system of equations, in standard form, modeling the relationship between cost of gespils (x) and cost of alabers (y) is -
8x + 9y = 117
3x + 8y = 67
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Ason is organizing the silverware drawer. He has 8 spoons. There are twice as many forks as spoons. There are 34 as many knives as forks. How many knives does Jason have
The result of two Newton's technique iterations to approximation a function's zero using the provided starting guess is 1.5262!
What is a formula that is iterative?Iteration describes carrying out a process repeatedly. To get a new value, start with an initial value and enter it into the iteration formula. To solve an equation using iteration, apply the new value for the subsequent substitution after that, and so on.
By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1, and by using the previous guess, xn, like so-
xn+1 = xn - f(xn)/f'(xn)
and herethe case is [tex]f(x) = cos(x), and so f'(x) = -sin(x).[/tex]
Also, furthermore, [tex]cos(x)/(-sin(x)) = -cot(x).[/tex]
here, we have to simplify the formula to get a better guess for a zero to: xn+1 = xn + cot(xn)
[tex]x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...\\And x3 = 2.06170... + cot(2.06170...) = 1.52615...\\Ans = 1.5262![/tex]
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