One cubic foot of a chemical weighs 50 pounds. How many pounds of the chemical can a container with the dimensions shown hold?

Answer: If there are 60 questions and the student has to answer 75% of questions then the number of questions the student must answer is 45

Step-by-step explanation:

No of questions= 60,

Answers to be given= 75%

then no of questions to pass the exam= No of questions*Answers to be given in percentage

=60*75/100\

=45

We can see here that the amplitude of the function is: A. 3.

The amplitude of a function is the measure of its maximum deviation from its central value. In simpler terms, it is the height of a wave or the distance from the center line to the peak or trough of a function.

For example, in a sine wave, the amplitude is the distance from the center line (or zero) to the highest point of the wave. In mathematical terms, if f(x) is a periodic function with period T, then the amplitude A of f(x) is given by:

A = (f(x)_max - f(x)_min)/2

where f(x)_max and f(x)_min are the maximum and minimum values of f(x) over one period.

Max = 4

Min = -2

A = [4 - (-2)]/2 = 6/2 = 3

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Based on the given information, the correct statement is: The area of the rectangle is twice the area of the shaded triangle.

The shaded triangle is a part of the rectangle, as indicated by the given dimensions of 10 in. and 4 in. The shaded triangle is formed by one of the shorter sides of the rectangle and a diagonal line connecting the opposite corner of the rectangle to the midpoint of that shorter side.

Since the area of the rectangle is given by the formula length × width, the area of the rectangle is 10 in. × 4 in. = 40 square inches.

On the other hand, the area of the shaded triangle is given by the formula 1/2 × base × height, where the base is the length of the shorter side of the rectangle (4 in.) and the height is the length of the longer side of the rectangle (10 in.) divided by 2, since the triangle only occupies half of the height of the rectangle.

So, the area of the shaded triangle is 1/2 × 4 in. × (10 in./2) = 1/2 × 4 in. × 5 in. = 10 square inches.

Comparing the area of the rectangle (40 square inches) to the area of the shaded triangle (10 square inches), we can see that the area of the rectangle is indeed twice the area of the shaded triangle. Therefore, the correct statement is "The area of the rectangle is twice the area of the shaded triangle."

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Answer:

2(5)(5) + 4(5)(10) = 50 + 200 =

250 square centimeters

Answer: y = 3.75x + 2.50

Step-by-step explanation:

The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:

y = 3.75x + 2.50

Explanation:

Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:

The correct answer is (a) a = 0, b = two-thirds, c = 3.

This can be seen by comparing the given equation, y = two-thirds x squared + 3, to the general form of a quadratic equation, y = ax^2 + bx + c.

In the given equation, the coefficient of x^2 is two-thirds, so a = two-thirds. The coefficient of x is 0, so b = 0. And the constant term is 3, so c = 3.

Therefore, the correct answer is (a) a = 0, b = two-thirds, c = 3.

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The solution to the given problem of the triangle comes out to be AC are 20 units long.

If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything identical to a standard triangle form can only be distinguished from it by edges across A and B. Euclidean geometry does not completely describe the cube, despite the fact that its edges are all collinear. A triangle is formed by a circle with five sides and three angles.

Here,

If DE is the midpoint of triangle ABC, DE is parallel to AC and has a length of 50% of AC.

Let's use "x" units to represent the length of AC.

Given the information, DE equals 10 units, or 50 percent of AC's length. So that we may create the equation:

=>  DE = AC/2

When we enter DE's value as 10 units, we get:

=> 10 = x/2

To separate x, we multiply both sides of the equation by 2 and obtain:

=> 2 * 10 = x

=> x = 20

Therefore, AC is 20 units long.

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There are 144 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order

To solve this problem, we can break it down into two parts:

Part 1: Arranging the consonants in alphabetical order
The consonants in UNIVERSALLY are N, R, S, V, and Y. Since we want them to appear in alphabetical order, there is only one way to arrange them: NRSVY.

Part 2: Arranging the vowels so that no two occur consecutively
There are four vowels in UNIVERSALLY: E, I, U, and A. To arrange them so that no two occur consecutively, we can use the following strategy:

1. Start with the two consonants N and R. There are three spaces between them where we can place the vowels: _N_R_. We can place the vowels in these spaces in 4! = 24 ways.

2. Next, we add the consonant S to the left of N. There are now four spaces between S and R: S _ N _ R _. We can place the vowels in these spaces in 3! = 6 ways.

3. We continue adding consonants in alphabetical order and placing the remaining vowels in the available spaces. After adding V and Y, we end up with the following arrangement:

S U N I V E R S A L L Y R

There are 24 ways to arrange the vowels between the consonants at step 1, 6 ways to arrange them at step 2, and only 1 way to arrange them after all the consonants have been added. Therefore, the total number of arrangements that satisfy both conditions is:
24 x 6 x 1 = 144

So there are 144 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

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a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.

To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64

Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.

b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L

Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75

Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.

In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.

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The supplementary angle means the sum of angles will be 180°. Hence the supplementary angle (or supplement) to a 55º angle is 125°.

When adding two or more angles, the result is 180°, and such pairs of angles are called linear pairs. The word 'linear' means 'straight', and 180° is also referred to as a straight angle. That is why a linear pair is always 180°.

Given angle is 55°.

To find the supplementary angle or supplement of 55º we must subtract 55º from 180°.

That is Supplement = 180 - 55 = 125°.

This is because supplementary angle means sum of two angles results in 180°.

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The volume of the solid figure bis 1465. 33 in³

The formula for the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters are;

From the information given, we have;

Volume = 3.14 × 4² × 18

Multiply the values

Volume = 904. 32 in²

Volume of the smaller cylinder

Volume = 3.1 4 × 4 × 18

Volume = 226. 08 in³

Volume of a cone = πr²h/3 = 3.14 × 8² × 5/3

Multiply the values

Volume = 334. 93 in³

Then, the volume of the solid = 904. 32 + 226. 08 + 334. 93 = 1465. 33 in³

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The standard deviation of the sample mean weight will decrease by a factor of √2, so the answer is C) It will decrease by a factor of 2. The mean of the sample mean weight will remain unchanged, so the answer is E) It will remain unchanged. It is a correct statement, and it is a result of the Central Limit Theorem, so the answer is C) It is a correct statement, and it is a result of the Central Limit Theorem.

When the sample size is doubled, the standard deviation of the sample mean weight decreases by a factor of √2 according to the formula σ/√n, where σ is the standard deviation of the population and n is the sample size. So, The correct answer is C).

The mean of the sample mean weight is an unbiased estimator of the population mean and is not affected by the sample size. Therefore, doubling the sample size will not change the mean of the sample mean weight.  So, The correct answer is E).

The Central Limit Theorem states that the distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the underlying distribution of the population. Therefore, the statement is correct and a result of the Central Limit Theorem.  So, The correct answer is C).

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To find the proportion of observations on the Standard Normal Curve between z = -1.8 and z = 0.67, we need to find the area under the curve between these two values.

Using the Standard Normal Table, we can find the area to the left of z = -1.8 and z = 0.67, and then subtract the former from the latter to get the area between them.

The area to the left of z = -1.8 is 0.0359, and the area to the left of z = 0.67 is 0.7486.

Therefore, the area between z = -1.8 and z = 0.67 is:

0.7486 - 0.0359 = 0.7127

So the proportion of observations on the Standard Normal Curve between z = -1.8 and z = 0.67 is approximately 0.7127, or 71.27%.

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Answer:

x = - [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

14 = [tex]\frac{8}{3}[/tex] (x + 6) ← multiply both sides by 3 to clear the fraction

42 = 8(x + 6) ← distribute parenthesis

42 = 8x + 48 ( subtract 48 from both sides )

- 6 = 8x ( divide both sides by 8 )

[tex]\frac{-6}{8}[/tex] = x , that is

x = - [tex]\frac{3}{4}[/tex]

The equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.

Explain the term centre

A centre is a point or location that is at the middle or heart of something. It can refer to the physical centre of an object or the conceptual centre of an idea or system. Centres can be used as reference points for measurements, calculations, or decision-making processes.

According to the given information

Here we can use the distance formula:

√((x - 2)² + (y + 3)²) = r

We also know that the circle passes through the point (6, 1). Substituting these coordinates into the equation above, we get:

√((6 - 2)² + (1 + 3)²) = r

√(16 + 16) = r

r = 4√(2)

Now we can use the centre and radius to write the equation of the circle in standard form:

(x - 2)² + (y + 3)² = (4√(2))²

(x - 2)² + (y + 3)² = 32

Therefore, the equation of the circle passing through (6,1) and having a centre at (2,-3) is (x - 2)² + (y + 3)² = 32.

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The remainder when p(x) = x^4 - 4x³ - 11x² + 66x - 72 is divided by x - 4 is given as follows:

16.

The Remainder Theorem is a theorem in algebra that provides a quick way to find the remainder of a polynomial division problem. The theorem states that when a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).

Hence for this problem, the remainder is given by the numeric value at x = 4, which is calculated as follows:

p(4) = 4^4 - 4(4)³ - 11(4)² + 66(4) - 72

p(4) = 16.

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The annual interest rate of the account is 3.5%

The formula for simple interest is:

I = Prt

where I is the interest earned, P is the principal (initial amount deposited), r is the annual interest rate (as a decimal), and t is the time in years.

We know that P = £13,000, t = 15 years, and I = £19,825 - £13,000 = £6,825.

Plugging in these values, we get:

£6,825 = £13,000 * r * 15

Simplifying this equation, we get:

r = £6,825 / (£13,000 * 15) = 0.035 = 3.5%

Therefore, the annual interest rate of the account is 3.5% to 1 decimal place.

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Angles in standard position with their terminal side in quadrant II have measures between 90 and 180 degrees.

Therefore, the angles that have their terminal side in quadrant II are

120 degrees

135 degrees

150 degrees

165 degrees

So, all of the above angles apply.

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Answer:

[tex]percentage = \frac{56}{145} \times 100[/tex]

56/145×100

0.386...×100

38.6%

Answer:

The new perimeter will be 2 times the old perimeter.

Step-by-step explanation:

Both dimensions are doubled doubled: times 2 or x2 or *2

4*2=8

2*2=4

if both measures are doubled, then the result will be doubled too.

If Y is directly proportional to the cube root of x, the percentage increase in y when x is increased by 700% is 100%.

If y is directly proportional to the cube root of x, we can write this relationship as y = [tex]kx^{(1/3)[/tex], where k is the constant of proportionality.

To find the percentage increase in y when x is increased by 700%, we first need to determine the new value of x. An increase of 700% means that x is multiplied by (1 + 700%) = 8. Therefore, the new value of x is 8 times the original value.

Substituting the new value of x into the equation for y, we get:

y = [tex]k(8x)^{(1/3)[/tex]

Simplifying this expression, we can write:

y = [tex]k(2^{3x)^{(1/3)[/tex]

y = k2x

So, we can see that when x is increased by 700%, y is increased by a factor of 2. This corresponds to a percentage increase of 100%.

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The steps for each expression here is

a.

Step 1: (x)-2

Step 2: 9-2

Step 3: 7

b.

Step 1: 3(y)+2

Step 2: 3*7+2

Step 3: 23

c.

Step 1: 8+((r)/6)

Step 2: 8+(24/6)

Step 3: 12

What is meant by expression?

An expression is a representation of a mathematical equation, logical statement, or string of characters using symbols, numbers, and operators. It can be evaluated to produce a value or result. In programming, expressions can be used to assign values to variables, perform mathematical operations, or compare values. They are an essential part of most programming languages and play a crucial role in the execution of computer programs.

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The perimeter of the figure is 38.52.

We have,

The perimeter of the figure:

Side + 18 + 18

From the figure,

82 + 90 + x = 180

172 + x = 180

x = 180 - 172

x = 8

Now,

Using trigonometric identities Sin.

Sin 8 = Side/18

0.14 = side/18

side = 0.14 x 18

side = 2.52

Now,

The perimeter of the figure.

= Side + 18 + 18

= 2.52 + 18 + 18

= 38.52

Thus,

The perimeter of the figure is 38.52.

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Approximately 304,657,600 Americans were there in July 2009 based on the estimated 2008 growth rate of 0.88%.

To find the approximate US population in July 2009, we need to apply the growth rate of 0.88% to the initial population in July 2008.

Convert the growth rate from percentage to decimal:

0.88% = 0.0088
Calculate the number of people added to the population in 2008: 302,000,000 * 0.0088 = 2,657,600
Add this number to the initial population to find the population in July 2009:

302,000,000 + 2,657,600 = 304,657,600.

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Answer:

P=9600000000

Step-by-step explanation:

1 point is =0.150119

40x10=400x20=8000x50x400000x10=400000x20=800000x30=240000000x40=9600000000

Answer:

50/100 or 1/2 or 50%

Step-by-step explanation:

total =  30 + 20 + 50 = 100

the probability of choosing a marble that is not blue is equal to the total minus all marbles that are blue therefore 100-30-20=50 therefore the probability is 50/100 or 1/2 or 50%

It can be concluded that we are 95 percent confident that the mean increase in the weight of a black bear for each one year increase in the age of the bear is between 7.0 and 18.4 pounds.

What is mean?

In statistics, the mean is one of the measures of central tendency which is nothing but simple average, apart from the mode and median. Mean is  the average of the given set of values. Mean denotes the equal distribution of values for a given set of data.  

A zoologist selected 12 black bears in a Canadian habitat at random to examine the relationship between the age in years, x, and the weight in tens of pounds, y. The 95 percent confidence interval for estimating the population slope of the linear regression line predicting weight in tens of pounds based on the age in years given by 1.272 ±0.570.

From the given data it is clear that the 95 confidence interval given by 1.272±0.570, or (0.702,1.842)

[ 1.272-0.570 = 0.702 and 1.272+0.570= 1.842]

It estimates the relationship between weight in tens of pounds and age in years. So the given data makes us 95 percent confident that the mean increase in the weight of a black bear must be in between 7.02 and 18.42 pounds and it is  for each one-year increase in the age of the bear.

Hence, it can be concluded that we are 95 percent confident that the mean increase in the weight of a black bear for each one year increase in the age of the bear is between 7.0 and 18.4 pounds.

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The exact amount of copper foil covering the steeple is 720√3 square meters.

The lateral area of the prism is given as 2400 m². We know that the lateral area of a prism is given by the formula:

Lateral area = perimeter of base x height of the prism

Let's denote the side length of the hexagonal base by s. The perimeter of the base is then 6s, and the height of the prism is 100 m. Using the given lateral area, we can solve for s:

2400 = 6s x 100

s = 4 x √15

The base area of the steeple is the same as the base area of the prism, which is given by:

Base area = (3 x √3 x s²) / 2

The steeple is composed of equilateral triangles, so each face of the steeple is an equilateral triangle with side lengths. The area of an equilateral triangle is given by the formula:

Area = (√3 * s²) / 4

The total surface area of the steeple is the sum of the areas of its faces. There are six faces, so the total surface area is:

Total surface area = 6 x Area

Total surface area = 6 x (√3 x s²) / 4

Total surface area = (3 x √3 x s²) / 2

Substituting the value of s we found earlier, we get:

Total surface area = (3 x √3 x (4 x √15)²) / 2

Total surface area = 720 x √3

Therefore, the exact amount of copper foil covering the steeple is 720√3 square meters.

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