This pentagonal right pyramid has a base area of 30\text{ m}^230 m
2
30, start text, space, m, end text, squared.

What is the volume of the figure?

Answer:

32 possible outcomes

Step-by-step explanation:

There are two options for each question (true or false).

Hence, according to the counting principle :

Question 1 = true or false = 2

Question 2 = true or false = 2

Question 3 = true or false = 2

Question 4 = true or false = 2

Question 5 = true or false = 2

2 * 2 * 2 * 2 * 2 = 2^5 = 32

The 90% confidence interval for the average time for drive-thru service is (4.551, 5.449) minutes. This means that we can be 90% confident that the true population mean of the waiting time for drive-thru service is between 4.551 and 5.449 minutes.

The 90% confidence interval for the average time for drive-thru service can be calculated using the formula:
CI = X ± (z×σ/√n)
Where:
CI = Confidence Interval
X = Sample mean
z = Z-score for the desired confidence level
σ = Population standard deviation
n = Sample size
Given that X = 5 minutes, σ = 1.5 minutes, and n = 30, we can plug these values into the formula to calculate the 90% confidence interval.
First, we need to find the z-score for the 90% confidence level. Using a z-table, we can find that the z-score for a 90% confidence level is 1.645.
Now, we can plug the values into the formula:
CI = 5 ± (1.645×1.5/√30)
CI = 5 ± (1.645×1.5/5.477)
CI = 5 ± (0.449)

Hence, the true population mean of the waiting time for drive-thru service is between 4.551 and 5.449 minutes.

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Answer:

Step-by-step explanation:

To solve the equation (3.4)(6.7) using the standard algorithm, first multiply 3.4 and 6.7. Then, the result is 22.78.

The standard algorithm for multiplication is a step-by-step process that involves breaking down the numbers being multiplied into simpler parts, and then multiplying those parts together.

First, you would need to multiply the ones place of the first number (4) by the ones place of the second number (7), which would give you 28.

Next, you would need to multiply the ones place of the first number (4) by the tens place of the second number (6), which would give you 24.

Then, you would add the two products from steps 1 and 2 to get the result: 28 + 24 = 52.

Alternatively, you can use the distributive property of multiplication to simplify the problem.

(3.4)(6.7) = 3.46 + 3.40.7 = 22.8

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Answer:

C 0<h<1400

Step-by-step explanation:

You have to calculate the first 40 hours of pay at a 20$ rate which is $800. Then you have to calculate the overtime which is the remaining 20 out of 69 hours he can work times 30$ which is $600

$600+$800=$1400, which is the maximum amount he could make

Answer:

Elga is 32 years old.

Step-by-step explanation:

Let Alvin's age = A

Let Elga's age = E

Alvin is 10 years younger than Elga, so A = E - 10

The sum of their ages is 54, so A + E = 54

Replace the A in the second equation with E - 10, then solve for E.

A + E = 54 becomes (E - 10) + E = 54

Combine like terms

2E - 10 = 54

Add 10 to both sides

2E = 64

Divide both sides by 2

E = 32

1) Estimate value of the product of 2/3 and 0.55 is, 2/3.

2) The fraction part is, 55 / 100

3) The product of the two numbers is, 11/30

We have to given that,

Estimate the product of 2/3 and 0.55.

And, Convert the decimal 0.55 to a fraction.

And, The product of the two numbers.

Now,

Estimate the product of 2/3 and 0.55,

So, we can round 0.55 to the nearest whole number, which is 1.

Then, multiply 2/3 by 1 to get an estimate of the product.

so, The correct answer is 2/3.

Now, we can convert the decimal 0.55 to a fraction,

= 0.55

= 55/100

= 11/20

Thus,  The correct answer is, 55/100.

And,  the product of 2/3 and 0.55,

= 2/3 x 55/100

= 110/300

= 11/30.

Hence, The correct answer is, 110/300 or 11/30

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Given:

\(x=-\dfrac{8}{9},\ y=-\dfrac{3}{5}\)

To verify:

\(x+y=y+x\)

Solution:

We need to verify,

\(x+y=y+x\)

Taking left hand side, we get

\(LHS=x+y\)

After substituting the values, we get

\(LHS=-\dfrac{8}{9}+\left(-\dfrac{3}{5}\right)\)

\(LHS=-\dfrac{8}{9}-\dfrac{3}{5}\)

\(LHS=\dfrac{-40-27}{45}\)

\(LHS=\dfrac{-67}{45}\)

Now,

Taking right hand side, we get

\(RHS=y+x\)

After substituting the values, we get

\(RHS=-\dfrac{3}{5}+\left(-\dfrac{8}{9}\right)\)

\(RHS=-\dfrac{3}{5}-\dfrac{8}{9}\)

\(RHS=\dfrac{-27-40}{45}\)

\(RHS=\dfrac{-67}{45}\)

Clearly,

\(LHS=RHS\)

Hence verified.

Answer:

x cannot = -2

Step-by-step explanation:

if x = -2 then the denominator is 0 and a fraction with 0 as a denominator is undefined.

Answer:

A

Step-by-step explanation:

f(x) = \(\frac{x-3}{x+2}\)

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be.

x + 2 = 0 ⇒ x = - 2 ← excluded value in the domain

The domain of f(x) is all real values of x such that x ≠ - 2

You can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

Determine the range of the data: 0.6 to 4.7.

Divide the range by the number of classes (5) to find the class width: (4.7 - 0.6) / 5 = 0.76.

Determine the lower limits of each class by starting at the minimum value (0.6) and adding the class width repeatedly: 0.6, 1.36, 2.12, 2.88, 3.64, 4.4.

Count the number of data values that fall into each class and record it in a table.

Draw a bar for each class using the lower limit of the class as the x-axis value and the height of the bar equal to the number of data values in the class.

After creating the histogram, you can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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The number of bacteria will double after 15.93 hours, or approximately 15 hours and 56 minutes.

The given exponential growth equation for N(t) is N(t) = 10000011.

To solve the problems related to it, we need to follow these steps:a) What is the number of bacteria at t = 0 hours?

We need to plug in t = 0 in the given equation of N(t) to find out the number of bacteria at t

= 0 hours.

N(0) = 10000011

= 1

Therefore, the number of bacteria at t = 0 hours is 1.b) When will the number of bacteria double?

Give the exact solution in the simplest form. Do not evaluate.

We know that the formula for the exponential growth function is given by the equation y = abx.

Here, x is the number of units of time passed, a is the initial value of y, b is the growth factor, and y is the final value of the function. We can use this formula to find out the time when the number of bacteria doubles.To find out the time when the number of bacteria doubles,

we can set y = 2 and s

olve for x.2 = abx

Since we are given that

N(t) = 10000011, we can write the above equation as:

2 = 10000011 * bxTaking the natural logarithm of both sides,

ln 2 = ln 10000011 + ln bx

Simplifying,

ln 2 - ln 10000011 = ln b + x ln b

Using a calculator, we get,

ln b = ln 2 - ln 10000011ln b

≈ -20.723

Using the properties of logarithms, we get,

x = [ln 2 - ln 10000011] / ln bSubstituting the value of ln b,

we get,x ≈ 15.93

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The simplified form is 67/10x + 9. Option B

From the information given, we have that;

We have the algebraic expression written as;

3(7/5x + 4) - 2(3/2 - 5/4x)

expand the bracket, we have;

21/5x + 12 - 6/2 + 10/4x

Now, collect like terms, we get;

21/5x + 10/4x + 12 - 6/2

Find the lowest common multiple, we have;

(84x+50x)/20 + (24-6)/2

subtract and add the value, we have;

134/20x + 18/2

Divide the common terms, we get;

67/10x + 9

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What is the simplified form of 3(7/5x + 4) - 2(3/2 - 5/4x)?

A. 75/4 x +8

B. 67/10x + 9

C. 66/10x + 2

D. 67/10x - 9

what is the question???

Step-by-step explanation:

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The probability that more heads are tossed using coin A than using coin B is \($\frac{7}{8}$\).

This is because there are 8 possible outcomes when both coins are tossed: (H, H), (H, T), (T, H), (T, T) for both coins A and B.

Out of these 8 possible outcomes, 7 of them have more heads from coin A than from coin B, so the probability is \(\frac{7}{8}\).

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen. Probability is used to measure the likelihood of uncertain events, such as the outcome of a coin flip or the result of a dice roll.

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Using the Empirical Rule, the percent of pails with volumes between 0.90 gallons and 1.10 gallons is 95%.

From the given data,

Mean  = 0.05

By the empirical rule,

68% of data falls within 1 standard deviation from the mean,

between μ - σ and μ + σ.

95% of data falls within 2 standard deviations from the mean,

between μ – 2σ and μ + 2σ.

99.7% of data falls within 3 standard deviations from the mean,

between μ - 3σ and μ + 3σ.

Now ,

μ – 2σ = 1-(2*0.05) = 0.90

μ + 2σ = 1 +(2*0.05) = 1.10

That is 0.90 and 1.10 lies with in 2 standard deviation.

Therefore, The percent of pails with volumes between 0.90 gallons and 1.10 gallons is 95% .

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When the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set.

A number line is a  vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval

From the number line in the question, we can see that:

As a general rule, open circles implies that the number at that endpoint is not included part of the solution set.

Hence, the complete statement is "when the endpoint is a(n) open dot or circle, the number represented by the endpoint is not a part of the solution set."

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The sub duplicate ratio of 16:9 is

4: 3

The sub-duplicate ratio is found by finding the square root of both the numerator and denominator

The given ratio is 16:9

Find the square root of 16

\( \sqrt{16} = 4\)

Find the square root of 9

\( \sqrt{9} = 3\)

Combining the two square roots that were found, the sub duplicate is:

\( \frac{4}{3} \)

Therefore, the sub duplicate ratio of 16:9 is

4: 3

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Step-by-step explanation:

So, we can find the points to graph by looking at the table. The left column is where we find our x-values and the right column is where we find the y-values. We get the points (1, 3), (3, 9), (5, 15), and (6, 18). I added a picture showing where to plot these and hope it helps!!

A) The new box with dimensions 10cm by 10cm by 3cm holds more cereal.

B) The new box with dimensions 10cm by 10cm by 3cm requires more material to make.

To determine which box holds more cereal, we need to calculate the volume of each box.

The volume of a rectangular box is given by the formula:

Volume = Length × Width × Height

Let's calculate the volumes for both boxes:

Original Box:

Length = 8 cm

Width = 3 cm

Height = 11 cm

Volume = 8 cm × 3 cm × 11 cm = 264 cm³

New Box:

Length = 10 cm

Width = 10 cm

Height = 3 cm

Volume = 10 cm × 10 cm × 3 cm = 300 cm³

A) The new box with dimensions 10cm by 10cm by 3cm holds more cereal because it has a larger volume of 300 cm³ compared to the original box with a volume of 264 cm³.

To determine which box requires more material to make, we need to calculate the surface area of each box.

The surface area of a rectangular box is given by the formula:

Surface Area = 2 × (Length × Width + Length × Height + Width × Height)

Let's calculate the surface areas for both boxes:

Original Box:

Length = 8 cm

Width = 3 cm

Height = 11 cm

Surface Area = 2 × (8 cm × 3 cm + 8 cm × 11 cm + 3 cm × 11 cm) = 374 cm²

New Box:

Length = 10 cm

Width = 10 cm

Height = 3 cm

Surface Area = 2 × (10 cm × 10 cm + 10 cm × 3 cm + 10 cm × 3 cm) = 380 cm²

B) The new box with dimensions 10cm by 10cm by 3cm requires more material to make because it has a larger surface area of 380 cm² compared to the original box with a surface area of 374 cm².

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Answer: UT

Step-by-step explanation:

Not sure but side BC is more elevated and looks similar to side UT in the other shape.

Answer: Step 4

Step-by-step explanation:

There is no equation to substitute into, the reason should be 'Pythagorean theorem'.

Answer:

2n+22

Step-by-step explanation:

22 more than twice a number

n represents the number.

twice a number --> 2n

22 more than --> +22

2n+22

Hey there!

Guide:

• Difference means subtract/subtraction
• Product means multiply/multiplication
• Quotient means divide/division
• Sum means add/addition
• “more than”, “greater than” or “increased by” either means add/addition or >
• “less than, “smaller than”, or “decreased by” either means subtract/subtraction or <

• “unknown number” is a number we’re NOT so sure yet so we label them as variables. A variable is any letter from A to Z.

ANYWAYS, LETS ANSWER the QUESTION

“22 more than 2 twice a number”

• Since, your instructions say that “n” will be the unknown number, we should label the unknown number as that!

“22 MORE THAN twice a NUMBER”

This could be simply written as:

“22 > 2n” or even “2n + 22”

But we will just say that’s [2n + 22] would mostly fit this scenario

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

Function: A(t) = (t+1)/(t-1)For the given function A(t), the following values are to be calculated: A(8), A(-5), A(3/1), and A(-71/1)A(8):We need to substitute t=8 in the function. A(8) = (8+1)/(8-1) = 9/7Therefore, A(8) = 9/7A(-5):We need to substitute t=-5 in the function. A(-5) = (-5+1)/(-5-1) = -1/3Therefore, A(-5) = -1/3A(3/1):We need to substitute t=3/1 in the function. A(3/1) = (3/1+1)/(3/1-1) = (4)/(2/1) = 4*1/2 = 2Therefore, A(3/1) = 2A(-71/1):We need to substitute t=-71/1 in the function. A(-71/1) = (-71/1+1)/(-71/1-1) = (-70/1)/(-72/1) = (-5/36)Therefore, A(-71/1) = -5/36Therefore, the respective answers for the given values of the function A(t) are as follows: A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

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The solution of the double inequality is -11 <= a <= 1 and the  three solutions in the solutions are -11, -10 and -9

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

1 <= (4 - a)/3 <= 5

Multiply through the inequality expression by 3

So, we have the following inequality expression

3 * 1 <= 3 * (4 - a)/3 <= 5 * 3

Evaluate the products in the above inequality expressions

So, we have

3 <= 4 - a <= 15

Subtract 4 from all sides of the inequality expression

So, we have

-1 <= - a <= 11

Multiply all sides of the inequality expression by 1

So, we have

1 >= a >= -11

Rewrite as

-11 <= a <= 1

The numbers in the above solution are -11, -10 and -9

Hence, the solution of the double inequality is -11 <= a <= 1 and the  three solutions in the solutions are -11, -10 and -9

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3 consecutive even integers adds up to 12

So, Let the numbers are :

so, the sum of the numbers = 12

so, the numbers are : 2 , 4 and 6

So, the greatest number = 6

The mean for the number of people with the genetic mutation in a group of 800 is approximately 116.

For the mean for the number of people with the genetic mutation in groups of 800, we can multiply the proportion of the population with the mutation by the total number of people in each group.

We know that about 14.5% of the population has the genetic mutation, we can express this as a proportion by dividing 14.5 by 100: 0.145.

Next, we multiply this proportion by the total number of people in each group (800) to find the expected number of people with the genetic mutation in a group of 800:

Mean = Proportion × Total number of people

     = 0.145 × 800

     ≈ 116

Therefore, the mean for the number of people with the genetic mutation in a group of 800 is approximately 116.

This means that, on average, we would expect about 116 out of the 800 people randomly selected to have the genetic mutation where each eye has a different color.

However, it's important to note that this is an expected value and the actual number may vary in each group due to randomness.

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