The expression that represents the surface area of the square based pyramid is 36 + 15 + 15 + 15 + 15
How to find the surface area of a square based pyramid?The surface area of the pyramid is the sum of the area of the whole faces of the pyramid.
Therefore, the pyramid has 4 triangular faces and 1 square faces.
Therefore,
surface area of the pyramid = area of the square + 4(area of the triangle)
area of the square = 6² = 36
area of each triangular faces = 1 / 2 bh
where
b = base areah = heightTherefore,
area of each triangular faces = 1 / 2 × 6 × 5 = 30 / 2 = 15
Hence, the expression is as follows:
surface area of the pyramid = 36 + 15 + 15 + 15 + 15
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Please help me fast!!!. Joe and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and shop on Michigan Avenue before their dinner reservations at 5:10 P.M. They plan to spend 1 hour and 10 minutes at the Willis Tower, 3 hours and 10 minutes at Navy Pier, and 1 hour and 15 minutes shopping. What is the latest time Joe's family can start their tour of Chicago and still make it to dinner on time?
Include A.M. or P.M. in your answer.
Answer:
11:10 am.
Step-by-step explanation:
The first thing I'm going to do is to add all the given time together
Total time = time spent at Willis tower + time spent at Navy Pier + time spent shopping
Total time = 1 HR and 10 minutes + 3 HR and 10 minutes + 1 hour and 15 minutes
Total time = (1 + 3 + 1) hr + (10 + 10 + 15) minutes
Total time = 5 hours + 35 minutes
The question doesn't make mention of how long they spent making the journey so, I'm assuming they spent 35 minutes driving around from Willis to the Pier and finally while shopping
Time = total time + time spent driving
Time = 5 hours 35 minutes + 35 minutes
Time = 6 hours and 10 minutes
Now, this time we've calculated, is what we're going to subtract from the dinner time to get our final answer
Needed time = dinner time - time
Needed time = 5:10 pm - 6:10
Needed time = 17:10 - 6:10
Needed time = 11:10
This means that they ought to start their tour by 11:10 am, so that they can meet their dinner
what is the most effluence first step to isolate the variable term on one side of this equation -9x=-4x+5
A cyclist rides his bike at a rate of 30 kilometers per hour. What is this rate in miles per hour? How many miles will the cyclist travel in 3 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answer:4.8
Step-by-step explanation:
30/3 x 1.6
In two or more complete sentences, explain how to use ordered pairs of points in f(x) = 2x + 5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other. PLEASE EXPLAIN WITH WORDS IN TWO SENTENCES I NEED HELP ASAP
Answer:
See below.
Step-by-step explanation:
The given functions f(x) and g(x) are linear functions. Therefore, their inverses are a reflection about the line y = x.
The mapping rule for reflecting a point about the line y = x is:
(x, y) → (y, x)To determine if f(x) and g(x) are inverses of each other:
Input the x-value of the ordered pair into one function.Input the y-value of the ordered pair as the x-value of the other function.If the y-value of one function equals the x-value of the other function (and the x-value of one function equals the y-value of the other function), the functions are inverses of each other.
Given functions:
\(\begin{cases}f(x) = 2x+5\\\\g(x)=\dfrac{x-5}{2} \end{cases}\)
Ordered pair: (2, 9)
Substitute x = 2 into f(x):
\(\implies f(2)=2(2)+5=9\)
Substitute x = 9 into g(x):
\(\implies g(9)=\dfrac{9-5}{2}=2\)
Therefore, the functions are inverses of each other since the x-value of function f equals the y-value of function g, and the y-value of function f equals the x-value of function g.
mDE
Q D E
8.73 in
10 in
The measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.
How to evaluate for the measure of the the arc angle DEThe arc measure DE and the angle it subtends at the center of the circle are directly proportional.
so arc DE = m∠DQE {central angle}
Arc length of the sector = (central angle / 360) x (2 x π x radius)
8.73 in = (m∠DQE / 360) x (2 x 22/7 x 10 in)
m∠DQE = (8.13 in × 360 × 7)/(2 × 22 × 10) {cross multiplication}
m∠DQE = 46.5055° = arc DE
Therefore, the measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.
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a money market fund advertises a simple interest rate of 9% find the total amount received on an investment of 5000 for 17 months
Answer:
Step-by-step explanation:
Formula: Simple interest = PRT
P= 5000
R= 9%
T= 17
So, 5000 x 9/100 x 17 = 7650
1. GIVE ANOTHER NAME FOR CM?
Answer:
decimetre is the answer
A 2015 Gallup poll of 1,627 adults found that only 22% felt fully engaged with their mortgage provider.
What is the sample size? Give only the number:
The margin of error for this data set is 2.5%. What is the 95% confidence interval for those who say they felt fully engaged with their mortgage provider (rounded to 1 decimal place)?
The sample size for the Gallup poll is 1,627 adults. The 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
To calculate the 95% confidence interval, we need to consider the margin of error. The margin of error is given as 2.5%, which means that we need to account for plus or minus 2.5% around the observed proportion of 22%.
First, let's calculate the margin of error:
Margin of Error = 2.5% of 22% = 0.025 * 22% = 0.0055
Next, we can calculate the lower and upper bounds of the confidence interval:
Lower Bound = 22% - Margin of Error = 22% - 0.0055 = 21.995% ≈ 22.0%
Upper Bound = 22% + Margin of Error = 22% + 0.0055 = 22.005% ≈ 22.0%
Therefore, the 95% confidence interval for those who say they felt fully engaged with their mortgage provider is approximately 22.0% (rounded to 1 decimal place).
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Help due soon plss!!!!
Answer:
Cube=150cm^2
Triangular Prism=228ft^2
Step-by-step explanation:
Cube
\(A=6a^2=6*5^2=150cm^2\)
Triangular prism
Using these formulas
\(A=2A_{B}+(a+b+c)h\\A_{B} =\sqrt{s(s*a)(s*b)(s*c)} \\s=\frac{a+b+c}{2}\)
Solving for A
\(A=ah+bh+ch+\frac{1}{2} \sqrt{-a^4+2(ab)^2+2(ac)^2-b^4+2(bc)^2-c^4} \\=6.5*11+5*11+6.5*11+\frac{1}{2} *\sqrt{-6.5^4+2*(6.5*5)^2+2*(6.5*6.5)^2-5^4+2*(5*6.5)^2-6.5^4} \\=228ft^2\)
The mean of a set of credit scores is Mu = 690 and Sigma = 14. Which statement must be true?
Answer:
B
Step-by-step explanation:
Answer: It’s C
Step-by-step explanation:
i would appreciate it if you could help me! :) reward: 15 pts, 5 stars (if its right), and a thanks!
Answer:
9.92 x 10⁷
Also, if you could label this brainliest that would be a great help!
Thanks xx
-Dante
Answer:
Step-by-step explanation:
\((3.2*10^{5}})*(3.1*10^{2})=3.2*3.1* 10^{5+2}\\\\= 9.92*10^{7}\)
help me asap. my exam is tomorrow.
The total surface area of the doghouse is 1452 ft²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.
area of the roof part = 2( 13×11) + 2( 12× 10)×1/2
= 286 + 720
= 1006 ft²
surface area of the building
= 2( lb + lh + bh) -bh
= 2( 10× 11 + 10×8 + 11×8) - 10×11
= 2( 110+80+88)-110
= 2( 278) -110
= 556 -110
= 446ft²
The total surface area = 1006 + 446
= 1452 ft²
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What is the value of x3 . Y1 when x= 5 and y = 10
Answer:
x³ = 125
y¹ = 10
Step-by-step explanation:
x³
5³ = 125
y¹
10¹ = 10
Answer:
150
Step-by-step explanation:
(5*3) . (10*1) = 150
Hope this helps, good luck!
Write a function rule for
Answer:
x^2
Step-by-step explanation:
1^2=1
2^2=4
3^2=9
A scientist is studying wildlife. She estimates the population of bats in her state to be 345,000. She predicts the population to grow at an average annual rate of 1.2%. Using the scientist’s prediction, create an equation that models the population of bats, y, after x years.
y=345,000(0.012)^x
y=345,000(0.988)^x
y=345,000(1.012)^x
y=345,000(1.2)^x
Answer:
Step-by-step explanation:
The equation that models the population of bats, y, after x years can be found using the formula:
y = P(1 + r)^x
where P is the initial population, r is the annual growth rate as a decimal, and x is the number of years.
In this case, the initial population P is 345,000, the annual growth rate r is 1.2% or 0.012 as a decimal, and x is the number of years. Substituting these values into the formula, we get:
y = 345,000(1 + 0.012)^x
Simplifying the expression in the parentheses, we get:
y = 345,000(1.012)^x
Therefore, the equation that models the population of bats, y, after x years is:
y = 345,000(1.012)^x
Step-by-step explanation:
the other answer is correct.
I just want to point out some mechanism used here :
the increase by 1.2%
an increase by x% means adding x% to the original 100%.
so, we end up with (100 + x)%.
"%" just stands for 1/100.
so, if y = 100%, an increase by x% is
y×(100 + x)/100 = y×(1 + x/100)
in our case here that is
345,000 × (1 + 0.012) = 345,000 × 1.012
and since the increase rate of 1.2% applies per year, we multiply the end population of every year by 1.012 for the following year.
so, each year a new factor of 1.012 is being integrated into the calculation.
it goes then
345,000×1.012×1.012×1.012×...×1.012 x times after x years.
and we get
y = 345,000 × (1.012)^x
Brett and Andy applied for the same credit card from the same bank. Brett was given a card with an APR of 12.6%. What was his monthly percentage rate? Andy was given a card with an APR of 16.2% what was his monthly percentage rate? if each of them had an average daily balance of $7,980, and had to pay a finance charge, how much more would. Andy pay than Brett?
Andy would pay $23.94 more in finance charges compared to Brett, given their respective APRs, average daily balances, and monthly percentage rates.
To calculate the monthly percentage rate (MPR) from the given annual percentage rate (APR), we divide the APR by 12.
For Brett:
APR = 12.6%
MPR = 12.6% / 12 = 1.05%
For Andy:
APR = 16.2%
MPR = 16.2% / 12 = 1.35%
Next, we can calculate the finance charge for each individual using the formula: finance charge = average daily balance * MPR.
For Brett:
Finance charge = $7,980 * 1.05% = $83.79
For Andy:
Finance charge = $7,980 * 1.35% = $107.73
To find the difference in the finance charges between Andy and Brett, we subtract Brett's finance charge from Andy's finance charge:
Difference = $107.73 - $83.79 = $23.94
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Find the slope of each line passing through the given points using the slope formula.
(-3, -10) and (-1, -1) URGENT Please answer
Slope (m)= y\x= 9/2 = 4.5
your equation for the line is
y=4.5x+3.5
638 divided by 34 long division
Answer:
18 R26
Step-by-step explanation:
\(\ \ \ \ \ \ \,\,\, 18 \textrm{ R}26\\{34\ \overline{\smash{)}\ 638}}\\\textrm{ } \ \ \ \underline{-34}\\\textrm{ } \ \ \ \ \ \, 298\\\textrm{ } \: \, \ \ \underline{-272}\\\textrm{ } \ \ \ \ \ \ \: \, 26\)
How do I figure out x and y
Answer:
x = 7, y = 45
Step-by-step explanation:
\(7x+13=6x+20\)
\(x=20-13\\x=7\)
Angle
\(7(7)+13=49+13=62^{0}\)
supplementary angle
180 - 62 = 118°
\(3y-17=118\)
\(y=\frac{118+17}{3} =135/3=45\)
Hope this helps
saleswoman sells a dried-fruit mixture for $ 5.90 per pound and nuts for $ 14. 75per pound. She wants to blend the two to get a -15lb mixture that she will sell for $ 9.44per pound. How much of each should she use? Solve using matrices.
To get a 15-lb mixture, she should use enter your response here( = -lb )of dried-fruit mixture and enter your response here( = lb )of nuts.
A 15-lb mixture, she should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts.
Based on the given information, we can set up the following system of equations:
Equation 1: x + y = 15 (since the total weight of the mixture is 15 pounds)
Equation 2: (5.90 * x) + (14.75 * y) = 9.44 * 15 (since the total cost of the mixture is the cost per pound multiplied by the weight of each component)
Now, let's convert this system of equations into matrix form:
| 1 1 | | x | | 15 |
| 5.90 14.75 | | y | = | 9.44 * 15 |
To solve for x and y, we can use matrix algebra. We can multiply the inverse of the coefficient matrix by the right-hand side matrix to get the solution matrix:
| x | | 1 1 |^-1 | 15 |
| y | = | 5.90 14.75 | | 9.44 * 15 |
Using matrix calculations, we find that the inverse of the coefficient matrix is:
| 0.0877 -0.0576 |
| -0.0059 0.0678 |
Now, multiplying the inverse matrix by the right-hand side matrix gives us:
| x | | 0.0877 -0.0576 | | 15 |
| y | = | -0.0059 0.0678 | * | 9.44 * 15 |
Simplifying the multiplication gives us:
x = 1.256
y = 13.744
Therefore, the saleswoman should use 1.256 pounds of dried-fruit mixture and 13.744 pounds of nuts to get a 15-pound mixture.
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1. Refer to g(t) = t² - 8t + 15. (a) Graph the function g on the domain -6 ≤ t ≤ 6. Be sure to label the vertex and any intercept(s).
The vertex of the function is a = 1 , b = -8 and c = 15
The intercept of the function is 15
The equation is given as
g(t) = t² - 8t + 15
The graph can be plotted with the given function,which gives us the parabolic graph and lets us keep the domain as
-6 ≤ t ≤ 6
The graph of this equation is attached.
Vertex and InterceptsThe vertex of the function can be found by comparing it with the parabolic equation.
at² + bt + c = 0
t² - 8t + 15 = g(t)
Therefore, the vertex of the function is
a = 1 , b = -8 and c = 15
The intercept can be found by taking t=0 , we get
g(0) = 0² - 8(0) + 15
Therefore, the intercept of the function is 15
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Simplify the product
-n(6n+3)
Please do Step-by-Step
Answer:
\(\boxed{\sf{-6n^2-3n}}\)Step-by-step explanation:
This product can be solved by multiplying these parentheses left to right using a distributive property.
Distributive property:
\(\Longrightarrow:\sf{A(B+C)=AB+AC}\)
\(\Longrightarrow: \sf{-n(6n+3)=-n*6n-n*3}\)
Rewrite the problem down.
-n*6n-n*3
Solve.
-n*6n-n*3=-6n²-3n
\(\Longrightarrow:\boxed{\sf{-6n^2-3n}}\)
Therefore, the correct answer is -6n²-3n.I hope this helps you! Let me know if my answer is wrong or not.
Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. Choose the correct answer below. A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column. B. The system is consistent because all the columns in the augmented matrix will have a pivot position. C. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix. D. The system is consistent because the augmented matrix will cont
Answer: A.
The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
Explanation: a system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column. Since every column of the coefficient matrix is a pivot column, none of the leading coefficients are in the rightmost column of the augmented matrix. Therefore the rightmost column of the augmented matrix cannot be a pivot column and the system must be consistent.
Need help with this question
Answer:
y = -2x - 2
Step-by-step explanation:
Please explain how to solve this
The solution to the variables are x = 7 and y = 4
How to determine the solution to the variables?From the question, we have the following parameters that can be used in our computation:
Shape = Triangle
The marks on the triangles imply that
The visibly smaller triangle is an equilateral triangleThe other triangle is an isosceles triangleSo, we have the following representation
3x - 5 = 5y - 4
3x - 5 = y + 12
Substitute 3x - 5 = y + 12 in 3x - 5 = 5y - 4
y + 12 = 5y - 4
Evaluate the like terms
4y = 16
So, we have
y = 4
Substitute y = 4 in 3x - 5 = y + 12
3x - 5 = 4 + 12
So, we have
3x = 21
This gives
x = 7
Hence, the values are x = 7 and y = 4
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A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Answer:
Step-by-step explanation:
a) The formula for the regression function is:
Maintenance Cost = 54.7757 + 120.689 x Age of Car
b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.
c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:
Y = a + bX ± tα/2 * SE
where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.
Plugging in the values, we get:
Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442
Y = 923.167 ± 26.010
Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.
d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.
To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of
your response as Part A, Part B, and Part C.
Part A: Suppose event A and event B are mutually exclusive. Is the statement P(A and B)-0 true?
Part 9: Explain why or why not to support your answer to Part A.
Part C: Provide an example to support your explanation.
Part A :
Yes, the statement is true that P( A and B ) = 0 .
Given,
Event A and Event B are mutually exclusive.
Thus P ( A and B ) = 0
Part B:
A and B are mutually exclusive events if they do not occur at the same time.
This means that A and B do not share any common outcomes and
P(A and B) = 0.
Part C:
Let,
The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.
A and B do not have any numbers in common so P(A and B) = 0.
Hence, A and B are mutually exclusive.
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Are 3x + 9 = 6 and x + 3 = 2 equivalent to each other
Answer: yes!
Step-by-step explanation:
A company that sells paper has a tiered pricing model based on how much paper you buy. If you buy less than 10 reams, they charge you $7 per ream and a shipping cost of $8. If you buy 10 or more reams but less than 20 reams, they charge you $6 per ream and a shipping cost of $16. If you buy 20 or more reams, they charge you $6 per ream and shipping is free.
a. Write a function that models the price in terms of the number of reams bought.
b. What is the domain of the function?
c. What is the range of the function?
d. How much will it cost to buy 25 reams of paper?
f. How much paper can you buy for $60?
The function can be defined as price = 6x
It will cost $150 to buy 25 reams of paper.
How to explain the functionThe domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.
The range of the function is all non-negative real numbers, since the price cannot be negative.
Fir 25 items, price = 6(25) = $150
It will cost $150 to buy 25 reams of paper.
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There are 3 types of PercentProblems.
a) Number compared to the Base is unknown: x/100 = ?/b
b) Base Number is unknown: a/?= x/100
c) Percent is unknown: a/b = ?/100
Solve the following percent problems using the appropriate percent equation. Describe
the steps used to calculate each answer.
1) What distance is 24% of 710 miles?
2) 62 hours is what percent of 3 days?
3) 16% of what number is 8?
Answer:A. x= .100
Step-by-step explanation:because of the distance in miles