The length of the line YZ is 26 units
The Y is the mid point of the line XZ
The length of the line XY = 20 + 2a
The length of the line YZ = 8 + 6a
When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ
The length of the line XY = The length of the line YZ
Substitute the values in the equation and find the value of a
20 + 2a = 8 +6a
Rearrange and group the like term
6a - 2a = 20 - 8
4a = 12
a = 12 / 4
a = 3
The length of the YZ = 8 +6a
= 8 + 6×3
= 8 + 18
= 26 units
Hence, the length of the line YZ is 26 units
The complete question is:
Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.
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Beatrice makes a jar of dry soup mix. The ingredients are:
1 3/4 = 7/4cups uncooked rice
1/2 cup dry lentils
1 2/3 = 5/3 cups uncooked pasta
1/3 cup beef bouillon
1/4 cup dried onion flakes
1/2cup dried peas
How much soup mix does this recipe make?
Answer the questions to find out.
The sum 7/4+ 1/2+5/3 +1/3 +1/4 +1/2 gives the amount of mix.
1. Which property could you use to change the grouping of the addends?
The soup mix that this recipe makes is 5.
The property could you use to change the grouping of the addends is the associative property of addition.
How to calculate the value of the mix?From the information, the following can be deduced:
7/4cups uncooked rice
1/2 cup dry lentils
1 2/3 = 5/3 cups uncooked pasta
1/3 cup beef bouillon
1/4 cup dried onion flakes
1/2cup dried peas
The soup mix that this recipe make will be the addition of all the values. This will be:
= 7/4+ 1/2+5/3 +1/3 +1/4 +1/2
= 5
The associative property of addition can change the grouping.
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for each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points on graph paper and drawing the line thoruhg them wiht a ruler
The slope of points (1,3) and (4,5) will be 2/3.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise and the run of the line.
Given that the line is passing through points (1,3) and (4,5). The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 5 - 3 ) / ( 4 - 1)
Slope = 2 / 3
Therefore, the slope of points (1,3) and (4,5) will be 2/3.
The complete question is given below.
Find the slope of the line that passes through both points (11,3) and (4,5).
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What is the angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow?
O
The angle of elevation is
(Simplify your answer. Type an integer. Round to the nearest degree.)
***
The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127
What is the angle of elevation ?At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."
The "tangent" trig function includes the following variables:
Tan = (opposite side) (elevation angle) (adjacent side).
In this case, tan (angle of elevation) equals opposing side / adj opposing side.
is used for
radians, or tan (angle of elevation)
= 47/14 = 3.3571
3.3571 is equal to 73.4127 degree.
The angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow 73.4127 degree
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What are the coordinates of the point on the directed line segment from (-9, -10)
to (1,5) that partitions the segment into a ratio of 2 to 3?
The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)
The end points of the line segment = (-9, -10) and (1, 5)
The partition ratio = 2 : 3
According to the partition rule
The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]
A = 2
B = 3
Substitute the values in the equation
The x coordinate of the point = -9 + [2(1--9) / 2+3]
= -9 + [2×10 / 5]
= -9 + [20/5]
= -9 + 4
= -5
Similarly,
The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]
= -10+[2(5--10)/2+3]
= -10+[2×15/5]
= -10+[30/5]
= -10 + 6
= -4
Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)
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STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one deviation of the mean have IQ scores that are 15 points higher or lower than the mean.
An absolute value equation that can be used to find the maximum and minimum scores within one standard deviation of the mean is |x - 20.9| = 5.3.
The minimum score that is within one standard deviation of the mean is equal to 15.6.
What is an absolute value function?In Mathematics, an absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0).
Mathematically, an absolute value function can be represented by this mathematical expression:
|x| = x, x ≥ 0.|x| = x, x < 0.Since the standard deviation is 5.3 and the mean is 20.9, an absolute value equation for the scores that is within one standard deviation of the mean is given by:
|x - 20.9| = 5.3.
x - 20.9 = ±5.3
Evaluating the absolute value function, the maximum score is given by:
x - 20.9 = 5.3
x = 20.9 + 5.3
x = 26.2.
Evaluating the absolute value function, the minimum score is given by:
x - 20.9 = -5.3
x = 20.9 - 5.3
x = 15.6.
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Complete Question:
The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the data are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one standard deviation of the mean have IQ scores that are 15 points higher or lower than the mean. One year, the mean mathematics score on the ACT test was 20.9 with a standard deviation of 5.3. Write an absolute value equation to find the maximum and minimum scores within one standard deviation of the mean. Use your equation to find the minimum score that is within one standard deviation of the mean
Greg mow and rakes lawn to earn extra money He makes 45 for every lawn he mows and an extra 15 for raking his goal is to earn at least 250 per week
The inequality is 45m + 14 n ≥ 250.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
He makes 45 for every lawn he mows
and an extra 15 for raking
His goal earning= at least 250 per week
let the number of lawn he mow is m and the number of lawn rakes is n.
Then the inequality is
45m + 14 n ≥ 250
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On a math quiz, Tatiana earns 5 points for each question she answers correctly. She wrote this
equation to find how many points she earns (p) based on how many questions she answers
correctly (g):
p = 5q
Identify the dependent and independent variables.
Points earned (p)
Questions correct (g)
Dependent variable Independent variable
Answer:
For points earned (p), the button should be on the left, and for questions correct (q), its on the right.
Step-by-step explanation:
me not know how to speak English!
In the given equation p = 5q, p is the dependent variable and g is the independent variable.
Given that Tatiana earns 5 points for each question she answers.
So, the equation is p = 5q
The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.
The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.
From the above explanation, we can conclude that p is dependent variable and q is independent variable.
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What is the next fraction
in this sequence?
Simplify your answer
5/14, 3/7, 1/2, 4/7 …
rohit studies 5⅖ hrs daily. He devotes 1¼ hrs of his time for English abd 1½ hrs for Mathematics. How much time does he devote for other subjects
Answer:3 1/2 hours
Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2
if -3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
Answer:
-3 - i
Step-by-step explanation:
This is true, because when solving for an imaginary solution through a polynomial, the form A ± Bi will always be adhered. A and B are both constants.
(Constants are just any real number, like 1, 2.35, or [tex]\frac{1}{2}[/tex].)
3. What linear equation models the relationship between the values in each table?
a)
P
t
0
11
1 2 3
16
21
26
b)
C
r
1
-2.1
2
-0.6
3
0.9
4
2.4
The linear equations that can satisfy the values given in tabular form are
t = 5d +11 c = [tex]\frac{2}{3}[/tex] r + 2.4How to form line equation using values given in tabular form?
A line equation is of the form y = mx + b where x and y are the coordinate values, m is the slope of the line and b is the y intercept.
Follow these steps to find the line equation:
Write the standard form of the line equation according to the variables given.Find the value of slope m by the formula [tex]m = \frac{y - y'}{x - x'}[/tex] where (x, y) and (x',y') are the given values.Find the value of y-intercept by substituting value of y,x and m in standard form.According to the given data:
Table I)
Standard form: t = md + b
Slope: m = [tex]\frac{16 - 11}{1 - 0}[/tex] = 5
y-intercept: t = 5d + b
Substituting (d, t) = (1, 16) as given in the table
16 = 5x(1) + b
∴ b = 11
Hence linear equation in terms of d and t is t = 5d +11
Similarly, for Table II)
Standard form: c = mr + b
Slope: m = [tex]\frac{2 - 1}{-0.6 + 2.1}[/tex] = [tex]\frac{2}{3}[/tex]
y-intercept: c = (2/3)r + b
Substituting (r, c) = (-2.1, 1) as given in the table
1 = 2/3 x (-2.1) + b
∴ b = 2.4
Hence linear equation in terms of r and c is c = [tex]\frac{2}{3}[/tex] r + 2.4
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A car moves at a speed of 80km/h from P at 0800 hours and reaches Q at 0930 hours. A lorry takes the same route from Q at 0800 hours to P at a speed of 70km/h. At what time do both vehicles meet?
The vehicles will meet at 0845 at a distance of 64 km from P when they move at the respective speeds.
The car moves at a speed of 80km/h from P to Q and it takes time t
t = 9.30 - 8.00 = 1 hour 30 minutes or 1.5 hours
Distance covered = speed × time
Distance = 80 × 1.5 = 120 km
Now et the cars meets at a distance of x km from P.
times taken by the car to cover x km = x/80 hours
The lorry travels 120 - x in that same time.
time taken = 70/(120 - x)
Now the time taken must be equal.
Therefore we will form an equation to calculate x.
(120 - x) / 70 = x / 80
or, 960 - 8x = 7x
or, 15x = 960
or, x = 64
Therefore the cars will meet at 64 km from P.
Now time taken by the car to cover 64 km = 64/80 = 0.8 hours = 48 minutes
Hence the cars will meet at 0845 hours.
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Solve this system of equations using the SUBSTITUTION method, then answer the questions below.
x + 2y = 4
3x + 6y = 18
What did you get for the (x, y) solution to this system? If you were to graph these equations, would their lines cross? Explain why or why not.
The x and y do not have the values in the equation because both the equations don't intersect each other.
given that the equation,
x + 2y = 4 ..........i
3x + 6y = 18 ...........ii
now multiply i with 3 and subtract with from ii,
3x + 6y = 18
-(3x + 6y ) = 12
0x + 0y = 6
which is not possible so x and y do not have the values at the intersection of the both equations which states that both the equation do not intersect at each other.
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8x1 4* 28 × +8 help me
Answer:
8x1 4* 28 × +8 = 28x + 12
8x^1 + 4 times 28 + 8
Add common Factors which are 8x and 28x added they equals 36x and 4 and 8 which equals 12 so now we got 28x + 12 and that is the answer
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each of 14 mothers-to-be received 3d ultrasound scans, which showed that 7 of them will give birth to girls. assuming that simultaneous births do not happen (i.e., babies are born one after another), what is the probability that the first two babies that are born happen to be boys? g
Probability that first two babies born are boys is 0.23
Number of Mothers to be received ultrasound = 14
Number of mother giving birth to girl = 7
Number of mother giving birth to boy = 14 - 7 = 7
P(giving birth to girl) = P(G) = 7 / 14 = 0.5
P(giving birth to boy) = P(B) = 7 / 14 = 0.5
Probability that the first two babies that are born happen to be boys =
favorable outcome / total outcome
here, favorable outcome = ⁷C₂
Total outcome = ¹⁴C₂
Required probability = ⁷C₂ / ¹⁴C₂
= (7×6 / 2×1) / (14×13 / 2×1)
= 7×6/14×13
= 42 / 182
=0.23
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Between which two integers does the square root of 92 lie?
The square root of 92 lies between 9 and 10.
According to the question,
We have the following information:
Square root of 92
Now, we have to find the two integers between which its square root lie.
So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.
Perfect squares are given below:
1 = 1
2 = 4
3 = 9
4 = 16
5 = 25
6 = 36
7 = 49
8 = 64
9 = 81
10 = 100
Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.
Hence, the square root of 92 lies between 9 and 10.
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Amadou and his children went into a grocery store and he bought $9 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought 4 times as many apples as bananas. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Amadou bought.
Determine THREE ways to have 4 times as many apples as bananas.
There are 3 other ways so please try to answer them!
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of apples is 8.
The number of bananas is 2.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total cost = $9
Cost of one apple = $1
Cost of one banana = $0.50
The number of bananas = x
The number of apples:
y = 4x
Now,
1y + 0.50x = 9
4x + 0.50x = 9
4.50x = 9
x = 9/4.50
x = 2
Now,
y = 4 x 2 = 8
Thus,
The number of apples 8.
The number of bananas is 2.
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A retailer needs to purchase 12 printers. The first printer costs $54, and each additional printer costs 5% less than the price of the previous printer, up to 15 printers. What is the total cost of 12 printers?.
The total cost of 12 printers is; $493.41
Cost of first printer; C1 = $54
Cost of second printer is; 95% × 54 = $51.3
Cost of third printer is; 0.95 × 51.3 = $48.735
Cost of fourth printer = 0.95 × 48.735 = $46.298
Now, let us apply same pattern using a calculator for the remaining costs and we will have them as follows;
Cost of 5th printer = $43.983
Cost of 6th printer = $41.784
Cost of 7th printer = $39.695
Cost of 8th printer = $37.710
Cost of 9th printer = $35.825
Cost of 10th printer = $34.033
Cost of 11th printer = $32.332
Cost of 12th printer = $30.715
Total cos is; 54 + 51.3 + 48.735 + 46.298 + 43.983 + 41.784 + 36.695 + 37.710 + 35.825 + 34.033 + 32.332 + 30.715 = $493.41
Therefore, the total cost of 12 printers is $493.41
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Really need help!
Graph the equation y =x²
+ 4x - 5 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots
of the equation x² + 4x − 5 = 0.
Answer:
See picture below
Step-by-step explanation:
Use Desmos the free calcualtor.
a wheat farmer is investigating the effectiveness of a treatment for controlling a pest. a random sample of 500 plants shows that 47 of them are infected by the pest. what does this sample indicate about the claim that 20% of the plants are infected?
The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
This given test is a test for single sample proportion
The test hypothesis are:
[tex]H_{o} :p=0.20[/tex], null hypothesis
[tex]H_{1} :p\neq 0.20[/tex], alternative hypothesis
The test statistic fallows a standard normal distribution and is given by:
[tex]Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }[/tex]
p=0.20
X=47 plants
Sample size, n=500
x, is the sample mean:
x=X/n=47/500
x=0.094
So, test statistic is calculated as:
[tex]Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }[/tex]
Z=-5.93
From the z-table, the p-value associated with Z=-5.93 is approximately 0
The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level
In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim
So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
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write a linear function f with the given values. f(-10) = 4, f (8) = -5 Can someone please help me with this question
Answer: y=-0.5x-1
Step-by-step explanation:
y=mx+b
Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4) (8,-5)
Hence we use the formula for finding the slope m:
[tex]\displaystyle\\\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=\frac{-5-4}{8-(-10)}\\\\m=\frac{-9}{8+10} \\\\m=\frac{-9}{18} \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\[/tex]
We substitute the value of (-10,4) into equation (1):
[tex]4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1[/tex]
Hence, y=-0.5x-1
The diagram shows a circular disc with radius 6cm in the centre of the disk there is a circular hole with radius 0.5cm
The area of the shaded portion of the circular disc is 112.255 cm².
What is the area of the shaded portion?A circle is a bounded object in which points from its center to its circumference is equidistant.
The area of the shaded portion is the difference between the area of the circular disc and the area of the circular hole.
Area of a circle = πr²
Where :
π = pi = 3.14
R = radius
Area of the circular disc = 3.14 x 6²
Area of the circular disc = 3.14 x 36
Area of the circular disc = 113.04 cm²
Area of the circular hole = 3.14 x 0.5²
Area of the circular hole = 3.14 x 0.25
Area of the circular hole = 0.785 cm²
Area of the shaded portion = area of the circular disc - area of the circular hole
Area of the shaded portion = 113.04 cm² - 0.785 cm²
Area of the shaded portion = 112.255 cm²
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Valentina measured a kitchen and made a scale drawing. She used the scale 1 inch : 2 feet. A countertop in the kitchen is 2 inches wide in the drawing. How wide is the actual counter?
The actual width of the countertop is 4 feet
Given,
Valentina measured a kitchen and made a scale drawing;
The scale she used for the drawing = 1 inch ; 2 feet
The width of countertop of kitchen in drawing = 2 inches.
We have to find the actual width of the countertop;
Here,
The scale factor used in the drawing = 1 inch = 2 feet
1 inch = 2 feet
2 inch = 2 x 2 = 4 feet
Now,
The actual width of the countertop = Width in drawing x 2
= 2 x 2 = 4 feet
That is,
The actual width of the countertop is 4 feet
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4. Find x.
xº
78°
65°
This is problem number 4
I will mark brainless if I get this question right when I turn it in
The answer would be 78 degrees, or 70 degrees
which choice does not determine the sampling distribution? the population size the population variance the population mean the sample size
The population size does not determine the sampling distribution.
In the give question we have to find which choice does not determine the sampling distribution.
We firstly learn more about sampling distribution
A sampling distribution is a probability distribution of a statistic that is derived from a bigger sample size of individuals chosen at random from a given population. The sampling distribution of a particular population is the distribution of frequencies of a variety of potential outcomes for a population statistic.
So, the population size does not determine the sampling distribution.
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Change the following problem to an addition problem.
-5-4
Answer:-9
Step-by-step explanation:
-(5+4)
-(9)
what is 6,000 lb/day = ____ t/wk?
Answer: 21 tons/wk
Step-by-step explanation:
6000 lb/day = 3 tons/day
3 t/day * 7 = 21 t/wk
What does 25 DIVIDE by 3 equal?
Step-by-step explanation:
25/3 = 8.33
hope it's helpful
Please help
What equation is represented by the values in this table
Answer:
y=2x-2
Step-by-step explanation:
use y2-y1/x2-x1 to find slope
4-2/3-2
2/1
2 is the slope
A and B are the only possible answers so far
Now to find y intercept
We know it can’t be +2 because at 2 x is equal to 2 so -2 is the only option
Hopes this helps please mark brainliest
find the growth or decay rate: y=2.5(0.72)^x
Answer: decay
Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers
the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]