please help me with this problem i have been struggling!

To obtain the volume of the solid figure, the following steps are necessary:

Step 1: Since the figure is made up of a square base pyramid and a rectangular solid, we recall the formulas for the volumes of a square base pyramid and that of a rectangular solid, as below:

And:

Step 2: Apply the dimensions given in the question to obtain the volumes, as follows:

Consider the rectangular solid sketched out below:

Thus, for the rectangular solid, we have that:

Length = 9in

width = 9in

height = 16in

Therefore, the volume of the rectngular solid is:

Now, consider the square base pyramid sketched out below:

Thus, for the square base pyramid, we have that:

Also:

Therefore, the volume of the square base pyramid is:

Step 3: Now, we find the total volume of the solid figure as follows:

Since:

And:

Therefore:

Thus, the volume of the solid figure is 1566 cubic inches

If the original number can be written as ab, where a is the digits in the tens place and b is in the ones place, then it can be expanded as

10a + b

where a and b are chosen from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. The sum of the digits is 9, so

a + b = 9

Reversing the digits gives the number ba, or

10b + a

which is larger than ab by 45, so

10b + a = (10a + b) + 45

-9a + 9b = 45

a - b = -5

Solve for a and b :

(a + b) + (a - b) = 9 + (-5)

2a = 4

a = 2

Then

a + b = 9

2 + b = 9

b = 7

So the original number if (C) 27.

False. The expression \((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

The expression\((3ab - 6a)^2\) is not the same as 2(3ab - 6a).

To simplify \((3ab - 6a)^2\), we need to apply the exponent of 2 to the entire expression. This means we have to multiply the expression by itself.

\((3ab - 6a)^2 = (3ab - 6a)(3ab - 6a)\)

Using the distributive property, we can expand this expression:

\((3ab - 6a)(3ab - 6a) = 9a^2b^2 - 18ab^2a + 18a^2b - 36a^2\)

Simplifying further, we can combine like terms:

\(9a^2b^2 - 18ab^2a + 18a^2b - 36a^2 = 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\)

The correct simplified form of \((3ab - 6a)^2 is 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\).

The statement that\((3ab - 6a)^2\) is the same as 2(3ab - 6a) is false.

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Answer: 1/5

Step-by-step explanation: It might be first easier to put it in decimal form so 8/10 is 0.8 and 0.8 divided by 4 is 0.2. 0.2 as a fraction is 1/5.

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

convert element to fraction: 4 = \(\frac{4}{1}\)

= \(\frac{8}{12}\) ÷\(\frac{4}{1}\)

The fraction rule: a/b ÷ c/d = a/b x d/c

= \(\frac{8}{12}\) × \(\frac{1}{4}\)

Cross - cancel common  factor: 4

= \(\frac{2}{12}\)

Cancel the common factor: 2

= \(\frac{1}{6}\)

We can perform a scatter plot of this data as:

It seems that there is an inverse relation between the cost per unit and the number of copies.

The cost per unit approaches an asymptote, so it may correspond to a total cost that is equal to a fixed cost plus a variable cost depending on the number of copies.

We can then calculate the total cost for each option by multiplying the unit cost by the number of copies and we will get:

Then, if we transform the data, we can see a positive correlation between the total cost and the number of copies.

This correlation can not be seen just by looking at the unit cost per copy.

Answer:

- If we consider the transformed data (total cost vs. number of copies), we can see a positive correlation.

- If we ony consider the original table (unit cost vs. number of copies), we can not see any correlation.

Answer:

12

Step-by-step explanation:

substitute x = 2 and y = 1 into the expression

(x + y + 3) × (y + 1)

= (2 + 1 + 3) × (1 + 1)

6 × 2

= 12

Answer:

x = 61

Step-by-step explanation:

The angle above the line n adjacent to 2x - 6 is (x + 3) alternate angle.

Adjacent angles are supplementary, thus

2x - 6 + x + 3 = 180, that is

3x - 3 = 180 ( add 3 to both sides )

3x = 183 ( divide both sides by 3 )

x = 61

The mathematical average of the number of feet in a yard, seconds in a minutes and months in a year is 25.

In Mathematics and Geometry, the arithmetic average for any data set can be calculated by using the following formula:

Arithmetic average = [∑(x)]/n

Generally speaking, we have the following standard parameters;

∑(x) = 3 + 60 + 12

∑(x) = 75

Now, we can determine the arithmetic average as follows;

Arithmetic average = 75/3

Arithmetic average = 25.

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Answer:

-1 and 4

Step-by-step explanation:

first you bring the terms on the right side to the left and you get:

-x^2 + 3x + 4 = 0

then you divide both sides of the quadratic by -1:

x^2 - 3x - 4 = 0

then you factor the equation:

(x + 1)(x - 4) = 0

for any product to be zero, one of the factors must be zero. hence, either x + 1 or x - 4 can be zero. so x can be -1 and//or 4.

have a great day <3

Use the distance formula to solve for the direct distance from (4,-4) up to (-14,8)

Since 1 grid is equal to 0.125 miles. Multiply the distance in units and we get

Rounding to 2 decimal places, the direct distance is 2.70 miles.

Step-by-step explanation:

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Answer:

what is this? ahdhdjxkdjjshsysusiiaiajsjjdyxc

The statement is true. The mean of all possible differences between the two sample means does equal the difference between the two population means, regardless of the distributions of the variable on the two populations.

This concept is known as the Central Limit Theorem (CLT) and holds under certain assumptions.

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. This means that even if the populations have different distributions, as long as the sample sizes are large enough, the distribution of the sample means will be normally distributed.

When comparing two independent samples from two populations, the difference between the sample means represents an estimate of the difference between the population means. The mean of all possible differences between the sample means represents the average difference that would be obtained if we were to repeatedly take samples from the populations and calculate the differences each time.

Due to the Central Limit Theorem, the sampling distribution of the sample mean differences will be approximately normally distributed, regardless of the distributions of the variables in the populations. Therefore, the mean of all possible differences will converge to the difference between the population means.

It's important to note that the Central Limit Theorem assumes random sampling, independence between the samples, and sufficiently large sample sizes. If these assumptions are violated, the Central Limit Theorem may not hold, and the statement may not be true. However, under the given conditions, the statement holds true.

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Answer:

Estimate: 22,400

Actual Product: 21,828

Step-by-step explanation:

To estimate the product of 68 and 321 by rounding to the nearest ten, you can round 68 to 70 and round 321 to 320. Then you can find the product of 70 and 320:

70 × 320 = 22,400

This is an estimate of the actual product.

To find the actual product, you can multiply 68 and 321:

68 × 321 = 21,828

Therefore, the estimate is 22,400 and the actual product is 21,828.

Answer:

I believe that he answer would be the third one , 3240 cm2 .

Wish u good luck . ^^

Answer :i think its -13

Step-by-step explanation:

Answer:

Step-by-step explanation:

If we divide W(x) by (x-a) then the remainder is W(a)

W(x) = 2x³ - 5x - 7

x - a = x + 2    ⇒  a = -2

W(-2) = 2(-2)^3 - 5(-2) - 7 = 2(-8) + 10 - 7 = -16 + 3 = -13

Based on the information given, it is possible to analyze the effectiveness of the new anxiety medicine. The medicine was formulated to lower anxiety and was prescribed to participants.

The participants were divided into three groups, where 20 received a 10 mg dosage, another 20 received a 20 mg dosage, and the last 20 participants received a placebo.
After three weeks, a questionnaire was administered that measured anxiety on a scale of 1-30. To compare the groups, the mean score of anxiety for each group can be calculated. If the mean score for the group receiving the medicine is significantly lower than the mean score for the placebo group, it can be concluded that the medicine is effective.

Therefore, statistical analysis of the results would be necessary to determine if the new anxiety medicine is effective in lowering anxiety levels.
 Based on the provided information, the study has been formulated to evaluate the effectiveness of the anxiety medicine by comparing three groups of participants: one group receiving a 10 mg dosage, another receiving a 20 mg dosage, and the last group receiving a placebo. To determine if the new anxiety medicine is effective, it's essential to compare the average anxiety scores of each group after the 3-week period. If the scores in the groups receiving the medicine are significantly lower than the placebo group, it could suggest that the anxiety medicine is effective.

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Answer:

The measure of U is  106 degrees

Step-by-step explanation:

Ok, so first let's solve for x (noting that the interior angles add up to 360)

W=90 (right angle)               V = 11x+1               X=75              U=12x+10

now let's put them into equation format:

90 + 11x + 1 + 12x + 10 + 75 = 360

combine like terms:

90 + 1 + 10 + 75=176    11x + 12x=23x

we get:           23x + 176=360

solve:                       -176   -176

                                 23x = 184

                                /23x  /23x

                                x  =    8

Now we have to solve for U:

12(8) + 10 = ?

96 + 10 = 106

Thus, it is 106 degrees

Answer:

9 ≤ x ≤ 7

Step-by-step explanation:

2x – 3 ≤ 11 or –8x – 10 ≤ – 82

We shall determine the value of x in both case.

2x – 3 ≤ 11

Collect like terms

2x ≤ 11 + 3

2x ≤ 14

Divide both side by 2

x ≤ 14/2

x ≤ 7

–8x – 10 ≤ – 82

Collect like terms

–8x ≤ – 82 + 10

–8x ≤ – 72

Divide both side by –8

x ≤ – 72 / –8

x ≥ 9 (since we divided by a negative sign)

9 ≤ x

Combining both answers

x ≤ 7

9 ≤ x

Thus,

9 ≤ x ≤ 7

The basis for W is {x - 1, x^2 - 1}, and since there are two linearly independent polynomials, the dimension of W is 2, which confirms our conjecture.

a) To show that the set W of polynomials in P2 such that p(1) = 0 is a subspace of P2, we need to verify the three conditions for a subset to be a subspace:

The zero polynomial, denoted as 0, must be in W:

Let p(x) = ax^2 + bx + c be the zero polynomial. For p(1) = 0 to hold, we have:

p(1) = a(1)^2 + b(1) + c = a + b + c = 0.

Since a, b, and c are arbitrary coefficients, we can choose them such that a + b + c = 0. Thus, the zero polynomial is in W.

W must be closed under addition:

Let p(x) and q(x) be polynomials in W. We need to show that their sum, p(x) + q(x), is also in W.

Since p(1) = q(1) = 0, we have:

(p + q)(1) = p(1) + q(1) = 0 + 0 = 0.

Therefore, p(x) + q(x) satisfies the condition p(1) = 0 and is in W.

W must be closed under scalar multiplication:

Let p(x) be a polynomial in W and c be a scalar. We need to show that the scalar multiple, cp(x), is also in W.

Since p(1) = 0, we have:

(cp)(1) = c * p(1) = c * 0 = 0.

Thus, cp(x) satisfies the condition p(1) = 0 and is in W.

Since W satisfies all three conditions, it is indeed a subspace of P2.

b) Conjecture about the dimension of W:

The dimension of W can be conjectured by considering the degree of freedom available in constructing polynomials that satisfy p(1) = 0. Since p(1) = 0 implies that the constant term of the polynomial is zero, we have one degree of freedom for choosing the coefficients of x and x^2. Therefore, we can conjecture that the dimension of W is 2.

c) Confirming the conjecture by finding the basis for W:

To find the basis for W, we need to determine two linearly independent polynomials in W. We can construct polynomials as follows:

Let p1(x) = x - 1.

Let p2(x) = x^2 - 1.

To confirm that they are in W, we evaluate them at x = 1:

p1(1) = (1) - 1 = 0.

p2(1) = (1)^2 - 1 = 0.

Both p1(x) and p2(x) satisfy the condition p(1) = 0, and they are linearly independent because they have different powers of x.

Therefore, the basis for W is {x - 1, x^2 - 1}, and since there are two linearly independent polynomials, the dimension of W is 2, which confirms our conjecture.

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

Answer:

number of pennies = 19

number of dimes = 19

number of quarters = 45 - 2 × 19 = 45 - 38 = 7

Step-by-step explanation:

The total number of coins in the box is 45 . The coins consist of pennies, dimes and quarters.

The number of pennies is equal to the number of dimes. The remaining number is the quarters. Therefore,

number of pennies = a

number of dimes = a

number of dimes = 45 - 2a

1 dime = 0.1 dollars

1 penny = 0.01 dollars

1 quarters = 0.25 dollars

Thee total cost can be expressed as follows

3.84 = a(0.01) + a(0.1) + 0.25(45 - 2a)

3.84 = 0.01a  + 0.1a + 11.25  - 0.5 a

3.84 = -0.39 a + 11.25

3.84 - 11.25 = -0.39 a

-7.41  = -0.39 a

divide both sides by -0.39

a = -7.41/-0.39

a = 19

number of pennies = 19

number of dimes = 19

number of quarters = 45 - 2 × 19 = 45 - 38 = 7

Answer:

  (b)  y = -7x -27

Step-by-step explanation:

When x and y in the equation y = f(x) are replaced by (x-h) and (y-k), the function graph is translated h units right and k units up. The translated function can be written as ...

  y -k = f(x -h)

  y = f(x -h) +k . . . . . . add k

__

Your function is ...

  y = -7x

and you want to translate it by (h, k) = (-5, 8). That makes it ...

  y' = -7(x -(-5)) +8 = -7x -35 +8

  y' = -7x -27

In the study conducted by John Darley and Bibb Latané, the number of people present in the room with the participant served as an independent variable, as it was manipulated by the researchers to observe its effects on helping behavior.

Specifically, the researchers examined how the presence of other people in the room would affect whether or not the participant would choose to help in a given situation. By changing the number of people present in the room, the researchers were able to measure the effects of diffusion of responsibility on helping behavior.

Diffusion of responsibility is a phenomenon in which individuals are less likely to help a victim when they are in the presence of other people, as they assume that someone else will take responsibility. Therefore, the number of people present in the room was an important variable in the study, as it allowed the researchers to measure how the presence of others affected helping behavior.

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9 block rhombuses would create 3 hexagons.

In order to increase the total number by three, a hexagon can be divided into a minimum of three rhombuses, each of which can be further divided into four rhombuses. With n being a positive integer, the result is 3n. The top two hexagons in this image are each divided into 8 and 10 rhombuses. The total number of rhombuses that can fit in a hexagon is not limited to multiples of three, given that the total number of rhombuses dividing a hexagon can be raised by three by quartering a single component rhombus. The amount might actually be any integer larger than 7.

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Answer:

5 ft

Step-by-step explanation:

not sure what the wuestion is but using the formula. A^2 + B^2 = C^2 we find that 100 / 4 = 25 and the square root of 25 is 5

It will take Thomas 40 months to empty the account if he continues to take out $400 each month of $16,000.

To find out how many months it will take for Thomas to empty the account, we need to set M to 0 and solve for t. This will give us the number of months it will take for Thomas to spend all of the $16,000 he won on the game show. The equation we need to solve is:
0 = 16000 - 400t

First, we'll isolate the variable t on one side of the equation by adding 400t to both sides:
400t = 1600

Next, we'll divide both sides of the equation by 400 to get the value of t:
t = 16000/400

Simplifying the right side of the equation gives us:
t = 40

So, it will take Thomas 40 months to empty the account if he continues to take out $400 each month for spending money.

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