The expressions (4×2⁵) / (2³ × 1/16) written as the power of 2 is 2⁸
How to write the expressions as the power of 2?
Given: (4×2⁵) / (2³ × 1/16)
In order to write this expression as the power of 2, we need to use some in indices law:
Product law: To multiply two variables or numbers with the same base, we need to add their powers and raise them to that base": 5⁴ x 5³ = 5⁴⁺³ = 5⁷ and P⁴ x P⁶ = P¹⁰
Division law: To divide two variables or numbers with the same base, we need to subtract their powers and raise them to that base": 5¹⁰ ÷ 5³ = 5¹⁰⁻³ = 5⁷ and P⁸ ÷ P² = P⁸⁻² = P⁶
Reciprocal Law: If the index is a negative value, then it can be shown as the reciprocal of the positive index raised to the same variable:
8⁻² = 1/8² and b⁻⁶ = 1/b⁶
Let's use the laws to create the given expressions as the power of 2:
(4×2⁵) / (2³ × 1/16) = (2²×2⁵) / (2³× 1/2⁴) Note: 4 = 2² and 16 = 2⁴
= (2²⁺⁵) /(2³⁺⁽⁻⁴⁾) Note: 1/2⁴ = 2⁻⁴ (reciprocal law)
= 2⁷ / 2⁻¹
= 2⁷⁻⁽⁻¹⁾ Division law
= 2⁸
Therefore, the expressions as the power of 2 is 2⁸
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a point lies on the line y=3x-2, its y coordinate is 25. what is the coordinates of this point?
Answer:
x=9 (9,25)
Step-by-step explanation:
9*7=27
27-2=25
Please show your work:
-5/2(8a - 2b) =
[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)
How can the answer is zero?
The first thing that we should do is simplify questions.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]
After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.
[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]
Next step is find the "a" by enter the "b" into the same question.
[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]
After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.
[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]
So, the answer is zero (0).
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Answer:
[tex] - 20a + 5b[/tex]
Step-by-step explanation:
[tex] - \frac{5}{2} (8a - 2b)[/tex]
[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]
[tex] - 20a + 5b[/tex]
A group of 15 athletes participated in a golf competition. Their scores are below:
Score (points) 1 2 3 4 5
Number of Athletes 1 2 3 4 5
Would a line plot or a histogram best represent the data presented here? Why?
Histogram, because a large number of scores are reported as ranges
Histogram, because a small number of scores are reported individually
Line plot, because a large number of scores are reported as ranges
Line plot, because a small number of scores are reported individually
The solution is Option D.
Line plot , because a small number of scores are reported individually
What is a line plot?
A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.
If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions
Given data ,
Total number of athletes = 15
The score points of athletes = { 1 , 2 , 3 , 4 , 5 }
The number of athletes = { 1 , 2 , 3 , 4 , 5 }
The best option to plot the line plot because of the data set
The line plot , a data visualization chart that more accurately represents the small data set, is chosen.
And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation
Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps
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Answer:D
Step-by-step explanation:
Diego is solving this system of equations:
4x + 3y = 10
-4x + 5y = 6
Here is his work:
4x + 3y = 10
-4x + 5y =6
-4x + 5y = 6 +
0 + 8y = 16
y = 2
4x + 3(2) = 10
4x + 6 = 10
4x = 4
x = 1
The solutions of the equations are x = 1 and y = 2
The system of equations are
4x + 3y = 10
-4x + 5y = 6
Here we have to use the elimination method. Eliminate the x term and find the value of y term
Add both equation
3y + 5y = 10 +6
Add the like terms
8y = 16
y = 16 / 8
Divide the terms
y = 2
Substitute the value of x in the first equation
4x + 3y = 10
4x + 3×2 = 10
Multiply the terms
4x + 6 = 10
4x = 10 - 6
4x = 4
x = 4 / 4
Divide the terms
x = 1
Hence, the solutions of the equations are x = 1 and y = 2
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Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x = −7 and x = 5 and passes through the point (0, −2).
The formula of the parabola is y = 2/35(x + 7)(x - 5)
How to determine the formula of the parabola?The parameters in the question are given as
Horizontal intercepts (roots) at x = −7 and x = 5 Passes through the point (0, −2).These parameters can be represented as
x₁ = -7 and x₂ = 5
(x, y) = (0, -2)
The quadratic function can be represented as
y = a(x - x₁)(x - x₂)
Substitute the known values in the above equation So, we have the following equation
y = a(x + 7)(x - 5)
At (x, y) = (0, -2), we have
-2 = a(0 + 7)(0 - 5)
Evaluate
a = -2/-35
Divide
a = 2/35
So, we have
y = 2/35(x + 7)(x - 5)
Hence, the equation is y = 2/35(x + 7)(x - 5)
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Which inequality is represented by the graph?
Answer:
x<1
Step-by-step explanation:
since the circle is not filled it will not be equal to one but either grater or equal to it
Since the arrow is pointing left than x is less than 1
x<1
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The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high
school preparation class, and no preparation class. Use the information from the table to answer the remaining questions.
Treatment
Private prep class
High school prep class
No prep class
Number of Observations
Source
Between treatments
Within treatments
60
60
60
Using the data provided, complete the partial ANOVA summary table that follows. (Hint: T, the treatment total, can be calculated as the sample mean
times the number of observations. G, the grand total, can be calculated from the values of T once you have calculated them.)
Sum of Squares (SS)
21,000.00
442,500.00
df
2 ▼
Sample Mean
650
645
625
177
Sum of Squares (SS)
132,750.00
147,500.00
162,250.00
Mean Square (MS)
The F Test statistic is 1.58.
Given data is
Source SS df MS
between 21,000.00 2 6,000.00
within 442,500.00 117 3,782.00
The SStotal is sometimes easier to calculate than SSbetween Since ......
SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween.
= 442,500+21,000 = 463,500
In ANOVA, the F test statistic is the ratio of the between - treatments variance and the within-treatments variance. The value of the F test statistic is 1.58 when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely large in general, you should reject null hypothesis for larger values of the F test statistic.
Hence the answer is the F Test statistic is 1.58.
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Solve for x
-21 = -7x
Simplify your answer as much as possible.
Answer:
Step-by-step explanation:
-21 = -7x
-21 divided by -7 = -7 divided by -7
3=x
For a pole-vaulter in training, the height the athelete will be able to pole-vault after t months of training is given by
H(t) = 17-11e^-0.02t
After how many months will she be able to vault 11 ft?
The number of months after which she will be able to vault 11 feet is 30 months.
For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by a mathematical formula. The formula is given below.
H(t) = 17 - 11e^(-0.02t)
We need to find the number of months after which she will be able to vault a height equal to 11 feet. We will substitute the value of height in the given equation.
11 = 17 - 11e^(-0.02t)
11e^(-0.02t) = 17 - 11
11e^(-0.02t) = 6
e^(-0.02t) = 6/11
Now, we will take the natural logarithm on both sides of the equation.
-0.02t = -0.606
t = 0.606/0.02
t = 30.3
Thus, she will be able to vault 11 feet in approximately 30 months.
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onsider the following equation:
3|x+3|−12=0
Step 1 of 4: Rewrite the equation above in standard form and determine if there is a solution.
The value of x in the following equation: 3|x+3|−12=0 is -7 and 1
The equation is 3|x+3|−12=0
We need to rewite the equation above in standard form
The modulus function can be positive and negative
Considering it to be negative,
the equation is
3((-1)(x + 3) - 12
3(-x - 3) - 12
-3x - 9 - 12 = 0
3x + 21 = 0
3x = -21
x = -7
3(x + 3) - 12
3x + 9 - 12
3x - 3 = 0
3x = 3
x = 1
Therefore, the value of x in the following equation: 3|x+3|−12=0 is -7 and 1
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Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart, how far has the eastbound airplane traveled?
The eastbound airplane traveled 44 miles far.
Given:
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart.
Let x be the eastbound airplane traveled.
we know that,
north and east direction are perpendicular and with hypotenuse 55 miles it forms a right angle triangle with side = 33 miles.
According to pythagorean theorem:
[tex]33^2+x^2=55^2[/tex]
[tex]x^{2} =55^2-33^2[/tex]
= 3025 - 1089
x = [tex]\sqrt{1936}[/tex]
= 44 miles.
Therefore The eastbound airplane traveled 44 miles far.
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The measures of the angles of a triangle are shown in the figure below. Find the measure of the largest angle.
The measure of the Largest angle using the angle sum property of a triangle is: 80°
What is the Angle sum property of a triangle?
According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.
One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.
In the given figure, we have:
Measure of 1st angle = 64°
Measure of 2nd angle = (2x + 14)°
Measure of 3rd angle = (6x + 14)°
and we know the angle of the property,
using the angle of property,
64° + (2x + 14)° + (6x + 14)° = 180°
⇒64° + 8x + 14° + 14° = 180°
⇒92° + 8x = 180°
⇒ 8x = 180° - 92°
⇒8x = 88°
⇒ x = 11°
So,
Measure of 2nd angle = (2x11 + 14)°
Measure of 2nd angle = (36)°
Measure of 3rdangle = (6x11 + 14)°
Measure of 2nd angle = (80)°
Hence,
The measure of the Largest angle using the angle sum property of a triangle is: 80°
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A five-gallon tank full of water starts draining at t = 0 at a rate of 1/(1 + t) gallons per hour. How long until the tank is empty?
1. It will take 5 hours for the five-gallon tank full of water to become empty at the drainage rate of 1/(1 + t) gallons per hour.
2. A correct setup of the equation problem above in terms of function is D. None of these will give the correct solution.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions share equality or are equivalent.
Functions, which are mathematical expressions involving one or more variables known as domain (or the independent variable) and range (or the dependent variable), using the equation symbol to show that two expressions are equal.
Drainage rate per hour = 1/(1 + t) gallons
t = 0
The capacity of the tank = 5 gallons
1/(1 + t) gallons
= 1/(1 + 0) gallons
= 1/1 gallons
= 1 gallon per hour
Since the tank is 5 gallons, it will take = 5 hours (5/1)
Thus, based on the drainage equation rate, the five-gallon tank will empty in 5 hours.
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Solve the linear programming problem
After solving the linear programming problem, we get the answer as 250.
What is linear programming?
When a linear function is exposed to multiple restrictions, linear programming maximizes or minimizes the function. This method determines the best way to use the resources that are currently available and aids managers in using the process to make decisions about the most efficient use of scarce resources, such as money, time, materials, and machinery. Linear programming has been useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.
Solution explained:
[tex]\left \{ {{2x + y = 12} \atop {x + y = 7}} \right.[/tex] x=3, y=4 P(3,4) Coordinates of the solution point
[tex]\left \{ {{x + y = 7} \atop {x + 2y = 10}} \right.[/tex] x=4, y=3 Q(4,3)
Coordinates of the simultaneous eqs.
[tex]\left \{ {{2x + y = 12} \atop {x + 2y = 10}} \right.[/tex] x=14/3, y=8/3
Putting the values of x and y in the equation P = 30x + 40y and calculating we get
P(P) = 250, P(Q) = 240, P(R) = 246.67
So, the answer is 250
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A survey of 780 was conducted while visiting Sonoma county on vacation. Each person was asked if they drank wine on their trip. 532 people responded "Yes".
What proportion of people did NOT drink wine in the survey? Round your answer to two decimal places.
Answer:
0.32
Step-by-step explanation:
[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.
The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.
The lengths of the base of the triangle are 31cm while the height of the triangle is 39cm
A triangle is a polygon that has 3 sides, three angles and three vertices whose sum of angles equal to 180 degrees.
How to find the lengths and height of a triangle?
from the statement,
h=b+8Area = 256.5 square centimetersA=1/2bh
A=1/2 xbx(8+b)
cross multiplying,
713 = 8b+b²
rearrange the function
b²+8b-713=0
Simplyfying the equation,
(b²+23b)-(31b-713)=0
b(b+23)-31(b+23)=0
b-31=0 or b+23 =0
b=31 or b=-23
length cannot be negative. therefore base = 31cm
Recall the h= b+8
this implies that h=8+31
h=39cm
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Find the distance between 7 and 18 on a number line.
Answer:
11
Step-by-step explanation:
Find the difference using subtraction:
18 - 7 = 11
So, the numbers are 11 units apart.
given f(x)=2x-2, find f (-3)
Answer:
-8
Step-by-step explanation:
f(-3) = 2(-3)-2
f(-3) = -6 -2
f(-3) = -8
Answer:
[tex] \huge{f( - 3) = - 8}[/tex]
Step-by-step explanation:
[tex]f(x) = 2x - 2[/tex]
In order to find f(-3) we substitute the value of x that's -3 into f(x) that's wherever we find x in f(x) we substitute it with -3 and solve for f(-3).
We have
[tex]f( - 3) = 2( - 3) - 2 \\ = - 6 - 2 \\ = - 8[/tex]
We have the final answer as
[tex] \bold{f( - 3) = - 8}[/tex]
Hope this helps you
Use the calculator below to approximate √59 as a decimal to the tenths place.
Note that you must do the approximation without using a square root button.
Your answer must be within a tenth of the actual value.
The approximate of √59 is 7.7 when rounded off to the nearest tenth place.
Given, √59
we are asked to determine the approximation without using a square root button.
√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.
the square root of the number 59 is:
7.6811
You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.
= 7.7
When the digit to the right is 5 or greater we round away from 0.
7.6811 was rounded up and away from zero to 7.7
Hence we get the required approximation.
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a polytunnel for growing plants has a semi circular opening. the diameter of the opening is 14 feet and the length is 10 feet. the air inside the polytunnel needs to be heated to grow the plants. what is the volume of air inside the polytunnel in cubic feet.
anyone know the answer please it's for a level 2 booklet
Answer:140
Step-by-step explanation:
14 x 10=
Let f(x) = -4x + 3 and g(x) = 6+ 7x Find the function. f/g (f/g)(x) =
The solution of the composite function (f/g)(x) is [tex]\frac{-4x+3}{6+7x}[/tex]
How to solve composite function?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Composite function involves the composition of functions is combining two or more functions as a single function.
Therefore, let's solve the function below:
f(x) = -4x + 3
g(x) = 6 + 7x
Hence,
(f/g)(x) = f(x) / g(x)
Therefore,
f(x) / g(x) = [tex]\frac{-4x+3}{6+7x}[/tex]
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P(H)=
P(T)=
let me know if you know how to do this
Answer:
Step-by-step explanation:
they are asking for probability
so they want to know, what's the probability of getting a "heads" on a coin toss. What do you think it is? You probably know this intuitively.
P(H) = ?
P(T) = ?
They are asking for fractions, so just say what you already know to be how often you'll get a "heads" in words, then just make that a fraction. :)
solve the equation for y
5x+7y=35
Answer:
[tex]y=-\frac{5}{7}+5[/tex]
Step-by-step explanation:
the goal is to isolate y on one side
5x+7y=35
-5x. -5x
7y=35-5x
/7. /7. /7
y=-5/7x+5
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3 years is to 4 , , ,
Stefanie bought a package of pencils for \$ 1.75$1.75 and some erasers that cost \$ 0.25\$0.25 each. She paid a total of \$ 4.25$4.25 for these items, before tax
Exactly how many erasers did Stefanie buy?
The number of eraser Stefanie bought is 10.
How to find the number of eraser she bought?Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax.
Therefore, the number of eraser Stefanie bought can be calculated as follows;
let
x = number of eraser bought
Therefore,
4.25 = 1.75 + 0.25x
subtract 1,75 from both sides of the equation
4.25 - 1.75 = 1.75 - 1.75 + 0.25x
2.5 = 0.25x
divide both sides by 0.25
x = 2.5 / 0.25
x = 10
Therefore,
number of eraser = 10
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water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches express the volume v of the water in the cone as a function of the height h of the water
The volume V of the water in the cone as a function of the height h of the water is,
V = (1/48)πh³
Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.
We have to express the volume V of the water in the cone as a function of the height h of the water.
Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,
So, using the concept of similarity in triangles
we get, r/4 = h/16
r = h/4
Now, the volume of the water in the cone be,
V = (1/3)πr²h
V = (1/3)π(h/4)²h
V = (1/48)πh³
So, the function expressing the volume of the water in the cone be,
V = (1/48)πh³
Hence, the volume V of the water in the cone as a function of the height h of the water is,
V = (1/48)πh³
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Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four
Answer: 2(x+4) >3(x+7)-4
Step-by-step explanation:
Hope this helps
Answer:
2(n+4)≤3(n+7)-4
Step-by-step explanation:
The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4
What is a solution set to an inequality or an equation?
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.
We need to find the inequality of the statement given;
"Two times the sum of a number and four is no more; than three times the sum of the number and seven decreased by four"
Let n be the unknown number
Then it would be;
2(n+4) ≤ 3(n+ 7) - 4
Hence, The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4
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c. Write two different expressions you could use to represent the
combined area of the Description and Small Diagram sections.
What information about the combined area does each
expression show
500
Step-by-step explanation:
research
1. A circle is divided into 9 uneven pie shaped pieces. Each section is labeled 1, 2, ... 9. The circle is then spun and the number pointing north recorded. Estimate the probability that the next number pointing north will be between 2 and 7 inclusive.
4 3 2 1 9 8 5 6 7 4 3 2 1 5 8 6 5 4
13/18
5/18
5/8
8/5
2. How many shoppers made a purchase at a big-box store, or online, or at a locally- owned store?
250
359
380
400
3. How many shoppers made a purchase online and at a locally owned store, but not at a big box store?
38
56
109
179
The probability that the next number pointing north is between 2 and 7 is 13/18 .
1) The circle is divided into 9 parts.
Now the parts are uneven.
So the data about the spins is required to calculate the probability .
The total number of items in the box = 18
favorable outcomes (between 2 and 7) = 13 possible outcome.
Required probability
= favorable outcome / total outcome
= 13 / 18
2) Using the Venn diagram we can calculate the various parts of the problem:
Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers
3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.
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Triangles ABD and BCD are right-angled triangles.
A
5 cm
B
x cm
Work out the value of x.
Give your answer correct to 2 decimal places.
10 cm
D
4 cm
C