Answers
The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.
How to determine the equivalent expressionWe shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:
squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)
a² is common and can be cancel out
square root of (36a⁸/255a²) = square root of (36a⁶/255)
square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}
square root of (36a⁸/255a²) = 6a³/15
square root of (36a⁸/255a²) = 2a³ × 3/5 × 3
we divide through by the common factor 3
square root of (36a⁸/255a²) = 2a³/5
Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.
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Related Questions
Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years: Number of years 1 2 3 House 1 (value in dollars) 294,580 303,417.40 312,519.92 House 2 (value in dollars) 295,000 304,000 313,000 Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer. (2 points) Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)
Answers
a) The type of function that can be used to describe the value of each house is:
House 1: Exponential function.House 2: Linear function.b) The functions that define the value of each house are given as follows:
House 1: H1(x) = 294580(1.03)^x.House 2: H2(x) = 295,000 + 9,000x.What are the functions?For House 1, the change each year is a percentage, as follows:
312519.92/303417.30 = 303417.30/294580 = 1.03.
Hence, considering the initial value of $294,580, the exponential function is defined as follows:
H1(x) = 294580(1.03)^x.
For House 2, the change each year is a fixed amount, as follows:
313,000 - 304,000 = 304,000 - 295,000 = 9,000.
Hence, considering the initial value of 295,000, the linear function is defined as follows:
H2(x) = 295,000 + 9,000x.
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y = x^4 , y = 2 − |x|
Answers
Answer:
no solution
y=x^3
y= 2-1 x 1
Step-by-step explanation:
Work out m and c for the line: y = 3-4x
Answers
Answer:
m = -4 ; c = 3
Step-by-step explanation:
m is the number that multiplies x
c is the number without letters
Which function has the same graph as f(x) = 0.3|x|?
Answers
Answer:
D
Step-by-step explanation:
b/c
A B and C are not true
Answer:
D
Step-by-step explanation:
We can visualize this by ignoring the constant of 0.3 and remembering the |x| graph.
It has a -x slope when x < 0, and a +x slope when x > 0
The only answer that has a negative slope when x is less than 0 and a positive slope when x is greater than 0 is D.
Fill in the blank using the function y=4x+2 use the photo to help
Answers
Answer:
just substitute each value of x into the function
Step-by-step explanation:
1. (x=-2) y= 4(-2)+2
2. (x=0) y= 4(0)+2
3. (x=2) y= 4(2)+2
4. (x=4) y= 4(4)+2
use the same steps but change the value of x. go ahead a use your calculator
Substitute the x values into the function:
Row 1:
y=4(-2)+2
y=-8+2
y=-6
Row 2:
y=4(0)+2
y=2
Row 3:
y=4(2)+2
y=8+2
y=10
Row 4:
y=4(4)+2
y=16+2
y=18
Write the equation of the line, in slope-intercept form, with the following information: slope:-1/12 point: (36, 2)
Answers
Answer:
y = - 1/12x + 5------------------------------------
Use point-slope form first and convert to slope-intercept.
Point-slope form:
y - y₁ = m(x - x₁), where (x₁, y₁) is a point and m- slopeSlope-intercept form:
y = mx + b, where m- slope, b- y-interceptPlug in the values:
y - 2 = - 1/12(x - 36)y - 2 = - 1/12x + 3y = - 1/12x + 3 + 2y = - 1/12x + 5Answer:
y = - 1/12x + 5
Step-by-step explanation:
researchers hoped to determine whether time spent watching television is associated with cardiovascular fitness. subjects were asked how many hours per day they watch television and were classified as physically fit if they scored in the excellent or very good category on a step test. the data obtained is as follows:
Answers
A hypothesis Test will be used to check the association the researchers were interested in exist or not. Chi-square test statistic will be used for testing the relationship between gender and participation in the last election.
The hypothesis test we shall use here is -
Chi-square test for independence
Reason - this type of hypothesis test is used to test whether there is a significant association between two categorical variables.
The two variables in this question are hours spent watching TV and cardiovascular fitness.
2.) Test statistic here is
Chi-square test statistic
Reason - here also to test the association we should use the chi-square test for
and thus the test statistic would be Chi-square.
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Find an equation of the line passing through the given points. Express your answer in slope-intercept form.
(3.8) and (3.-5)
Answers
There is only one way to represent a vertical line as an equation:
[tex]x=d[/tex]
d = x-interceptSolving the Question
We're given:
Line passes through (3, 8) and (3, -5)Both of the x-coordinates in these points are equal.
This indicates that this is a vertical line.
The x-intercept of a vertical line will always look like [tex](x,0)[/tex], where x is the same x-value as the given points.
[tex]x=3[/tex]
Answer[tex]x=3[/tex]
a random sample of adults was surveyed about their exercise habits. of the 100 surveyed, 56 stated they exercise regularly. which of the following is the 95% confidence interval for p, the proportion of all adults who exercise regularly? find the z-table here. (0.50, 0.62) (0.48, 0.64) (0.46, 0.66) (0.43, 0.69)
Answers
The 95% confidence interval for p, the proportion of all adults who exercise regularly is (0.46, 0.66).
What is a confidence interval?
An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.
Here, we have
Given
Sample size(n) = 100
x = 56
Sample proportion (p) = x/n = 56/100 = 0.56
Here, c = 95%, a = 0.95
1-a = 0.05, a/2 = 0.025
Z(a/2) = 1.96
95% confidence interval for p is:
= p-Z(a/2)√{p(1-p)}/n, p+Z(a/2)√{p(1-p)}/n
= 0.56- 1.96√{0.56(1-0.56)}/100, 0.56+1.96√{0.56(1-0.56)}/100
= 0.56 - 0.0972, 0.56+0.0972
= 0.4628, 0.6572
= (0.46, 0.66)
Hence, the 95% confidence interval for p, the proportion of all adults who exercise regularly is (0.46, 0.66).
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A property is available for sale that could normally be financed with a fully amortizing $82,800 loan at a 10 percent rate with monthly payments over a 25-year term. Payments would be $752.40 per month. The builder is offering buyers a mortgage that reduces the payments by 50 percent for the first year and 25 percent for the second year. After the second year, regular monthly payments of $752.40 would be made for the remainder of the loan term.
Required:
a. How much would you expect the builder to have to give the bank to buy down the payments as indicated?
b. Would you recommend the property be purchased if it was selling for $5,000 more than similar properties that do not have the buydown available?
Answers
The builder must pay the bank $6005.66. for further details read below.
what is the mortgage?A mortgage is a type of loan used to purchase or maintain a home, land, or other types of real estate.
For the given problem We must determine the present value of all the relaxations granted to us over the first two years in order to determine how much the builder must pay the bank for this buydown payment. The output and Excel formulae are listed below.
Monthly payment 726.96
Monthly interest rate 10.%/12
Relaxation value in 1st year:
Amount reduced C2*50%
No. of months 12
present value PV(C3,C7, -C6)
Relaxation value in 2nd year:
The amount reduced C2*25%
No. of months 12
present value PV(C3,C12, -c11)
Present value today C13/(1+ C 3)^12
Present value of buy option C14 + C8
Therefore, the buydown option's current value is $6005.66. In order to provide this option to the customers, the builder must pay the bank $6005.66.
b. It is advised to take advantage of this option since the benefit the house buyer would get, or its current value exceeds the additional cost. Benefits to the purchaser of this option include. The benefit to the buyer equals the Present Value of the BuyDown Option - Additional Payment
Buyer benefit is equal to 6005.66 - 5000, or 1005.66$.
So, if a buyer received this option, he would profit $1005.66. It is thus advised to purchase real estate using this buydown option.
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help me pls to find the slope
Answers
greed. bad luck. failing to treat each throw of the dice as independent of previous throws. treating each throw of the dice as independent of previous throws. regression toward the mean.
Answers
The Gambler's Fallacy is due to treating each throw of the dice as independent of previous throws
The gambler's fallacy, also known as the Monte Carlo fallacy, is when someone mistakenly thinks that the outcome of a prior event or series of events will make a given random occurrence more or less likely to occur.
This kind of thinking is flawed since past occurrences do not alter the likelihood that specific events will occur in the future.
In circumstances where the probability of various events is not independent, the gambler's fallacy is not applicable.
The outcome of previous events, such as the statistical permutation of events, might alter the probability of future happenings in such circumstances.
In response to the query,
The Gambler's Fallacy results from treating each roll of the dice as if it were unrelated to prior rolls. Option(4) is correct
The question is incomplete , the complete question is
The Gambler's Fallacy is due to
(1) greed.
(2) bad luck.
(3) failing to treat each throw of the dice as independent of previous throws.
(4) treating each throw of the dice as independent of previous throws.
(5) regression toward the mean.
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An infant drinks about 28 ounces of milk per day. About how many quarts of milk does the baby drink in 4 weeks?
options 49 qt 7 qt 32 qt 24.5 qt
Answers
An infant drinks about 28 ounces of milk per day. There are 32 ounces in a quart, so the baby drinks 28 ÷ 32 = 0.875 quarts of milk per day.
Four weeks is 4 × 7 = 28 days.
In 4 weeks, the baby drinks 28 × 0.875 = 24.5 quarts of milk.
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 25.75 mpg and a standard deviation of σ = 2.75 mpg. (a) What is the standard error of X⎯⎯⎯ , the mean from a random sample of 36 fill-ups by one driver?
Answers
The standard error of X⁻, the mean from a random sample of 36 fill-ups by one driver is; 0.4167
How to find the standard error?
We are given;
Mean; μ = 26 mpg
Standard deviation; σ = 2.50 mpg
Sample size; n = 36 fill ups
The formula for standard error is;
SE = Standard deviation/√Number of samples
Thus, plugging in the relevant values into the standard error formula gives;
SE = 2.5/√36
SE = 2.5/6
SE = 0.4167
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What is the last blank?
Answers
A square-based pyramid has a total of five faces. Four of the faces are triangles and one of the faces is a square. The surface area of a square-based pyramid is the total area of all its sides.
hope this helps!! :D
Please help!
Use the table to write a function rule.
X Y
7 -21
6 -19
-3 -1
8 -23
Answers
The function rule of the given table is f(x) = -19x + 107.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the table we have,
f(7) = - 21
f(6) = -19
f(-3) = -1
f(8) = -23
The function rule.
f(x) = mx + c
m = (-19 + 21) / (6 - 7)
m = 21/-1
m = -21
f(6) = -19
x = 6 and f(x) = -19
-19 = -21 x 6 + c
-19 + 126 = c
c = 107
Now,
The function rule is f(x) = -19x + 107.
Thus,
f(x) = -19x + 107 is the function rule.
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Hi, I need help with this. I need this solved using the Pythagorean Theorem. Jake needs to construct a ramp to roll a cart from your garage into the back of your truck
The truck is 15 feet from the garage. The back of the truck is 4 feet above the ground. How long does the ramp have to be (in feet)? Also, can you tell me whether you are finding the leg or hypotenuse?
Answers
Answer:
Step-by-step explanation:
i know this isnt the answer but see if this problem can be a guide to find the answer;/
is their a simplified way of understanding the proof limit?
Answers
Yes, there are several ways to understand the concept of a limit in calculus without going into the details of a formal proof. One way to understand the concept of a limit is to think of it as a way to measure how close a function gets to a particular value as the input to the function gets closer and closer to a certain number. For example, if we have a function f(x) and we want to find the limit of the function as x approaches 2, we can think of this as asking "how close does f(x) get to a certain number as x gets closer and closer to 2?"
Another way to understand the concept of a limit is to think of it as a way to describe the behavior of a function as the input gets very large or very small. For example, if we have a function f(x) and we want to find the limit of the function as x approaches infinity, we can think of this as asking "how does f(x) behave as x gets very large?"
Overall, the concept of a limit is a fundamental concept in calculus that allows us to describe and analyze the behavior of functions as the input to the function changes. While a formal proof of the limit can be quite complex, there are several intuitive ways to understand the concept without going into the details of the proof.
How do I start on this equation?
what is the value of the expression 2/5 m - 1/3 when
m = 3?
Answers
Answer:
when m=3,
then,2/5×3-1/3
=6/5-1/3
=(6×3-1×5)/15
=13/15 Ans...
Proceed to answer question as following:
Step one:
Substitute
2/5(3) - 1/3
Step two:
Multiple 2/5 by 3
Giving:
Exact form: 6/5
Decimal form: 1.2
Mixed number form: 1 1/5
Step three:
Choose which from to use
*note*
No matter which form you use, answer will always be the same.
I’ll use decimal form:
1.2 - 1/3 *this can be converted to decimal form as well*
E.g. 1.2 - 0.3
Answer:
0.9
Fraction form: 9/10
Hopes this helps <3
17. Identify any congruent figures in the coordinate plane at the right . Explain .
Answers
The rectangle PQMN to rectangle RSTU and triangle XYZ to triangle ABC are congruent figures.
What are congruent figures?
Two figures are said to be 'congruent' if they can be placed exactly over each other. When you place one slice of bread on top of the other, you'll notice that they're both the same shape and size. The term "congruent" refers to having exactly the same shape and size.
To identify the congruent figures in the given figures:
Two polygons are congruent if they have the same size and same shape.
(1) Rectangle PQMN and rectangle RSTU are the same shapes.
MN ≅ RS
NP ≅ ST
QP ≅ UT
MQ ≅ UR
Therefore rectangle PQMN and rectangle RSTU are congruent figures.
(2) Triangle XYZ and triangle ABC:
XY ≅ AB
YZ ≅ BC
XZ ≅ AC
Therefore triangle XYZ and triangle ABC are congruent figures.
Hence, the rectangle PQMN to rectangle RSTU and triangle XYZ to triangle ABC are congruent figures.
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Which of the following represents the characteristics of the graph of x > 3?
Open circle on 3, shaded to the left.
Closed circle on 3, shaded to the left.
Open circle on 3, shaded to the right.
Closed circle on 3, shaded to the right.
asap 50 points!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Open circle shaded to the right
Step-by-step explanation:
Since its a more than inequality, its is shaded to the right.
Since the inequality applies to numbers GREATER than 3 you have a open circle because you are not including 3.
Use the diagram to estimate the perimeter, rounding each number to the nearest thousand.
18,167 cm/
43,812 cm
39,412 cm
O 102, 000 centimeters
O 103, 000 centimeters
O 100, 000 centimeters
O 101, 000 centimeters
Answers
Answer:
101000 centimeters
Step-by-step explanation:
The perimeter is the sum of the lengths of the sides. Thus, the perimeter is [tex]18167+39412+43812 \approx 101000[/tex]
Surwatullah is starting university in 3 years and would like to have $4000 when he starts. He has $3000 to invest now, and his bank pays 5% compounded quarterly. Will he have enough?
Answers
Answer:
Answer found by the following formula/e: CI = A – P
A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary statistics are as follows.
Do Not Exercise - Do Exercise
x1 = 73.4 beats/min - x2 = 69.7 beats/min
s1 = 10.3 beats/min - s2 = 8.6 beats/min
n1 = 16 - n2 = 12
test the claim that he difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly.
Answers
The claim "The difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly" is true.
What is meant by mean of data?
In math, mean refers an average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers
Here we have given that a researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded.
And we need to find the the claim that he difference between the mean pulse rate of people who do not exercise regularly is higher than the mean pulse rate of people who exercise regularly is true or not.
Here we have the hypothesis is H0:μ1−μ2=0H1:μ1−μ2>0
Here the Level of significance is 0.05
And the value of test statistics is calculated as,
=> t = [(X1−X2)−(μ1−μ2)]/[√S1²n1+S2²n2]
=> t = (73.5−69.3)/ [√10.2216+8.7212]
=> t = 1.1734
Hence, the value of test statistics is 1.1734.
And the critical value at 26 degree of freedom from t-table is 1.706, thus it provides insufficient evidence to reject null hypothesis.
Here, there is a direct relationship between the width of san interval or the sample standard deviation.
Therefore, if variance increases the width of an interval also increase and vice versa. Therefore, above statement is true
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Solve the given problem related to population growth. During the first decade of this century, the population of a certain city grew exponentially. The population of the city was 145,210 in 2000 and 219,185 in 2010. Find the exponential growth function that models the population growth of the city. Use t = 0 to represent 2000, t - 10 to represent 2010, and so on. (Round k to five decimal places.) N(C) = Use your exponential growth function to predict the population of the city in 2016. Round to the nearest thousand.
Answers
The exponential growth function that models the population growth of the given city is P(t) = P(0) x e^rt and the population of the city in 2016 is 328,029.39.
The population of the city in 2000 (t=0) = 145,210
The population of the city in 2010 (t=10) = 219,185
Rate of growth for 10 years = ((219185 - 145210)/145210) x 100
Rate of growth for 10 years = 50.943%
Rate of growth per year = Rate of growth for 10 years/10
Rate of growth per year = (50.943/10)%
Rate of growth per year = 5.094%
According to the exponential growth function,
P(t) = P(0) x e^rt
Population in 2016 (t=16) is:
P(16) = 145210 x e^((5.094/100) x 16)
P(16) = 145210 x 2.259
P(16) = 328029.39
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Find the coordinates of the circumcenter of the triangle with the given vertices.
A(2, 2), B(2, 4), C(8, 4)
The circumcenter is (_ ,_)
Answers
The circumference of the triangle is 14.3 Units
How to find the circumference?We know that a triangle is a polygon that has three sides, three angles and three vertices whose sum of interior angles is 180 degrees.
The coordinates of the given vertices are:
A(2,2)
B(2,4)
C(8,4)
To find the sides of the triangle, we use the formula for distance between two points
/AB/=[tex]\sqrt{(X_{2}-X_{1}) ^{2} +(Y_{2} -Y_{1})^{2} }[/tex]
= applying the figures in the formula we have
[tex]\sqrt{(2-2)^{2}+(2-4)^{2} }[/tex]
AB=√0+4
AB=2 Units
Applying the formula for /AC/
/AC/=[tex]\sqrt{(2-8)^{2}+(2-4)^{2} }[/tex]
simplifying to have
√40
/AC/=6.6 Units
Applying the formula for /BC/
/BC/=[tex]\sqrt{(8-2)^{2} +(4-4)^{2}[/tex]
/BC/=√36
/BC/=6
Therefore, the circumference of the triangle is 2+6+6.3
= 14.3 units
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Based on the definition of similar solids, the value of x would be: D. 31.
How to Find the Side Lengths of Similar Solids?Similar solids are defined as two solids that have proportional corresponding linear measures, which means the ratio of their linear measures are equal.
Examples of linear measures include height, length, width, circumference or radii. This means that, if two cylinders for example are similar, then the ratios of their radii or heights will be equal or proportional to each other.
The two solids are similar as stated in the image above, which means their corresponding linear measures will have ratios that are equal or they are proportional.
The linear measures here are the sides of the base of the solids. Therefore, the ratios would be:
29/14.5 = x/15.5
(14.5)(x) = (29)(15.5)
x = (29 × 15.5) / 14.5
x = 31
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Two pieces of metal measure one and one third yards and five sixths yards each. Three times the amount of metal is needed for a project. How many total yards of metal is needed? one and one half yards, 2 yards, four and one third yards, six and one half yards.
Pls help
Answers
Answer: 6 1/2 yards
Step-by-step explanation: you have to add 1 1/3 + 5/6, which is 2 1/6. 2 1/6x3=6 1/2
What is the expected sum of the numbers that appear on two dice, each biased so that a 3 comes up twice as often as each other number? A. 48/7 B. 3 C. 10/3 D. 44/7 E. 52/7
Answers
When we have a biased dice where 3 comes up twice as often as each other number, the expected sum of the numbers that appears on two such dice is 48/7.
Therefore, the answer is (A) 48/7.
From given condition of bias, probability of getting 3 is
P(3) = 2 × p
where P(1) = P(2) = P(4) = P(5) = P(6) = p
We also know P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
That is 2p + 5p = 1
p = 1/ 7
P(3) = 2/7
Expected sum of the numbers that appear on a dice can be obtained by
EV = 1×1/7 + 2×1/7 + 3×2/7 + 4×1/7 + 5×1/7 + 6×1/7
EV = 24/7
Expected sum of the numbers that appear on two dice can be obtained by twice of one dice that is
EV = 2×24/7
EV = 48/7
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DEATH RACE FOR LOVE 999
In 1941, the ________ was signed by Great Britain and the United States, stating that neither country wanted to acquire territory nor would attempt to govern other nations.
Marshall Plan
United Nations Charter
Truman Doctrine
Atlantic Charter
Answers
Answer:
Step-by-step explanation:
D. Atlantic Charter
The Atlantic Charter established the creation of the United Nations.