Select the decimal that is equivalent to (27)/(32). Choose 1 answer: (A) 0.76418 (B) 0.764bar (18) (C) 0.84375 (D) 0.84bar (375) (E) None of the above

The true statements are

Total number of people that went to a theme park = 15 people
From the data in the histogram,

The x axis of the histogram represents the time spend in the line and y axis represents the number of people.

From the histogram we have to check each given statement

1 person was in the line for at least 150 minutes, this is a true statement

3 people were in the line for less than 50 minutes, this is a true statement

Most people spent over 100 minutes in the line, this is wrong statement

1 person spent 0 minutes in the line, this is true statement

No one spent exactly 125 minutes in the line, this is true statement.

Hence, the true statements are

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Answer:

400.3 m³ (nearest tenth)

Step-by-step explanation:

The composite solid comprises:

\(\boxed{\begin{minipage}{3.4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)

Therefore, the volume of the cylinder is:

\(\begin{aligned}\implies V_{\sf cyclinder}&=\pi \cdot 2^2 \cdot 4\\&=\pi \cdot 4 \cdot 4\\&=16 \pi \; \sf m^3\end{aligned}\)

\(\boxed{\begin{minipage}{5 cm}\underline{Volume of a rectangular prism}\\\\$V=w\:l\:h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}\)

Therefore, the volume of the rectangular prism is:

\(\begin{aligned}\implies V_{\sf rectangular\;prism}&=7 \cdot 10 \cdot 5\\&=70 \cdot 5\\&=350 \; \sf m^3\end{aligned}\)

Therefore the volume of the composite solid is:

\(\begin{aligned}\implies V_{\sf composite\;solid}&=V_{\sf cycinder}+V_{\sf rectangular\;prism}\\&=16 \pi +350\\&=400.2654825\\&=400.3\; \sf m^3\;\;(nearest\;tenth)\end{aligned}\)

a. An exponential growth rate equation to represent the cost C₁ of this home is \(C_1 = 250000e^{0.038t}\).

b. An exponential growth rate equation to represent the cost C₂ of this home is \(C_2 = 275000e^{0.022t}\).

c. The time in which each home would reach a price of $320,000 is 6.5 and 6.8 years respectively.

d. The price of the home in the first area is lower.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

\(A(t) = P_{0}e^{rt}\)

Where:

Part a.

Based on an exponential growth rate of 3.8% in the first area, the cost of this home in t years can be written as follows;

\(A(t) = P_{0}e^{rt}\\\\C_1 = 250000e^{0.038t}\)

Part b.

Based on an exponential growth rate of 2.2% in the second area, the cost of this home in t years can be written as follows;

\(A(t) = P_{0}e^{rt}\\\\C_1 = 275000e^{0.022t}\)

Part c.

At a price of $320,000 for the home, the number of years to reach this price is given by:

\(C_1 = 250000e^{0.038t}\\\\320000 = 250000e^{0.038t}\\\\1.28= e^{0.038t}\)

ln(1.28) = 0.038t

Time, t = 0.24686007793/0.038

Time, t = 6.49 ≈ 6.5 years.

\(C_2 = 275000e^{0.038t}\\\\320000 = 275000e^{0.022t}\\\\1.16= e^{0.022t}\)

ln(1.16) = 0.022t

Time, t = 0.14842000511/0.022

Time, t = 6.75 ≈ 6.8 years.

Part d.

The house with the lower price can be determined as follows;

\(C_1 = 250000e^{0.038 t}\\\\C_1 = 250000e^{0.038\times 3}\)

C₁ = 250,000 × 1.12075212488

C₁ = $280188.03122

\(C_2 = 275000e^{0.038t}\\\\C_2 = 275000e^{0.022 \times 3}\)

C₂ = $293762.347221.

In conclusion, the home in the first area is cheaper.

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The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

We have,

The total number of people who watch drama.

= 12 + 20 + 19

= 51

The total number of people who is older than 20 years who watch drama.

= 20 + 19

= 39

Now,

The probability that the person selected is older than 20 years old and watching the drama movie.

= 39/51

= 0.765

Thus,

The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

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Answer:

E

Step-by-step explanation:

You dont have enough data to solve for x

Answer:

D

Step-by-step explanation:

Math.

Hope this helps

Answer:

Step-by-step explanation:

n17 = ?

n  = 17

d = 6

a1 =12

a17 = a1 +(n - 1)d

a17 = 12 + (17 - 1)*6

a17 = 12 + 16*6

a17 = 12 + 96

a17 = 108

Let x be the dilation factor, then we can write

If we move 28 to the right hand side, we get

therefore, the answer is option D

Odd integers are:

1, 3, 5, ...

They are spaced "2" units apart.

So,

if the first odd number is "x",

the next is "x + 2"

the third one is "x + 2 + 2"

the fourth one is " x + 2 + 2 + 2"

Thus, the four consecutive odd numbers are:

We sum the expressions and equal to -8. Then solve for x:

So,

This is the least integer out of the 4:

There are 27 elements in set B but not in set A.

Given:

Total number of elements in the universal set S = 69

Number of elements in set A = 10

Number of elements in set B = 36

Total number of elements in either A or B = 37

To find the number of elements in B but not in A, we can use the principle of inclusion-exclusion. The formula is:

|A ∪ B| = |A| + |B| - |A ∩ B|

In this case, |A ∪ B| represents the total number of elements in either A or B, which is given as 37.

|A| represents the number of elements in A, which is 10.

|B| represents the number of elements in B, which is 36.

Plugging these values into the formula, we get:

37 = 10 + 36 - |A ∩ B|

To find |A ∩ B|, we rearrange the equation:

|A ∩ B| = 10 + 36 - 37

|A ∩ B| = 9

Since |A ∩ B| represents the number of elements that are common to both A and B, and we need to find the number of elements in B but not in A, we subtract |A ∩ B| from the number of elements in B:

Number of elements in B but not in A = |B| - |A ∩ B|

Number of elements in B but not in A = 36 - 9

Number of elements in B but not in A = 27

There are 27 elements in set B but not in set A.

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From the calculations, the best loan option is

A. 3-year loan with a 7% annual simple interest rate

To determine which loan option would allow the customer to pay the least amount of interest, we need to compare the amount of interest charged by each loan option.

For the 3-year loan with a 7% annual simple interest rate,

the interest charged would be $15,000 x 7% x 3 = $2,550.

For the 4-year loan with a 5% annual simple interest rate,

the interest charged would be $15,000 x 5% x 4 = $3,000.

For the 5-year loan with a 4.5% annual simple interest rate,

the interest charged would be $15,000 x 4.5% x 5 = $3,375.

For the 6-year loan with a 3.7% annual simple interest rate,

the interest charged would be $15,000 x 3.7% x 6 = $3,870.

From the calculations, it is clear that the 3-year loan with a 7% annual simple interest rate would result in the least amount of interest charged, with $2,550.

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The partial fraction decomposition of the function is given by x^4 / ((x^3-x)(x^2-x-4)) is A/x + B/(x-1) + C/(x+1) + D/(x^2+2x+2) + E/(x^2-x-4) and 2x^6 - 64x^3 is F/x + G/x^2 + H/x^3 + I(x-4) + J(x^2+4x+16) + K(x+4), respectively.

Partial fraction decomposition is a method used to simplify complex rational expressions by expressing them as a sum of simpler fractions. In first part, the given function is factored as x^4/(x^3-x)(x^2-x-4).

To perform the partial fraction decomposition, we need to find the coefficients A, B, C, D, and E, such that

x^4 / ((x^3-x)(x^2-x-4)) = A/x + B/(x-1) + C/(x+1) + D/(x^2+2x+2) + E/(x^2-x-4)

Similarly, in next part, the given function is factored as 2x^3(x^3-32), and the partial fraction decomposition would involve finding coefficients F, G, H, I, J, and K, such that

2x^6 / (x^3-32) = F/x + G/x^2 + H/x^3 + I(x-4) + J(x^2+4x+16) + K(x+4)

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Answer: Therefore, we need to choose the smaller positive value of x:

x ≈ 1.8/8 = 0.225 inches

So, each side should be shortened by approximately 0.225 inches.

Step-by-step explanation:

Let's call the amount by which each side is shortened "x". After the board is shortened on all sides by "x", its new dimensions will be (12-2x) inches by (8-2x) inches. The area of the new board will be:

(12-2x)(8-2x)

We want this area to be 45 square inches, so we can set up the equation:

(12-2x)(8-2x) = 45

Expanding the left side of the equation, we get:

96 - 40x + 4x^2 = 45

Rearranging and simplifying, we get a quadratic equation:

4x^2 - 40x + 51 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 4, b = -40, and c = 51. Plugging in these values, we get:

x = [40 ± sqrt((-40)^2 - 4(4)(51))] / (2(4))

x = [40 ± sqrt(136)] / 8

x ≈ 3.3/8 or x ≈ 1.8/8

However, we can see that if we choose x = 3.3/8 (approximately 0.4125 inches), then the new dimensions of the board would be negative, which does not make sense. Therefore, we need to choose the smaller positive value of x:

x ≈ 1.8/8 = 0.225 inches

So, each side should be shortened by approximately 0.225 inches.

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Answer:

Step-by-step explanation:

Slope= y2-y1/x2-x1

5-2/1-(-4) = 3/5

Slope: 0.6

Answer:

b ruh its c

Step-by-step explanation:

Answer:

c.

Step-by-step explanation:

The weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5. The correct option is A.

We know that the formula to calculate the weighted average is: weighted\ average=\frac{w_1x_1+w_2x_2+...+w_nx_n}{w_1+w_2+...+w_n} Where, $x_1,x_2,..x_n$ are the values, and $w_1,w_2,...,w_n$ are the weights. To find the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number, we substitute the values in the above formula as follows.

Weighted\ average=\frac{\frac{2}{3}\times 1+\frac{1}{3}\times 6}{\frac{2}{3}+\frac{1}{3}}\implies weighted\ average=\frac{\frac{2}{3}+2}{1}\implies weighted\ average=\frac{8}{3}\implies weighted\ average=2.67 approx 3.5 Therefore, the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5.

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The probability of drawing a spade or diamond card from a standard deck of shuffled cards is 0.5.

We know that:

The total number of cards in a deck of cards is:

T = 52 cards

We also know that:

Number of spade cards in the deck = 13 cards

Number of diamond cards in the deck = 13 cards

Number of possible outcomes = 13 + 13 = 26 cards

Probability of drawing a spade or diamond card from a standard deck of shuffled cards will be:

P = 26 / 52 = 1 / 2

P = 0.5

Therefore, we get that, the probability of drawing a spade or diamond card from a standard deck of shuffled cards is 0.5.

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The lengths of the legs of the right triangle are given as follows:

2.39 feet and 4.39 feet.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

c is the length of the hypotenuse.

a and b are the lengths of the other two sides (the legs) of the right-angled triangle.

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

x² + (x + 2)² = 5²

x² + x² + 4x + 4 = 25

2x² + 4x - 21 = 0.

Using a calculator, the positive solution for x is given as follows:

2.39.

Hence the legs are:

2.39 feet and 4.39 feet.

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Answer:

10.6

Step-by-step explanation:

Answer:

10.67

Step-by-step explanation:

75% of 10.67 is 8. 100% of 10.67 is 10.67, therefore 75 percent of 10.67 equals 8.

Hope this helps sir/ma'am!!!!!;)

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of expo functions.

f(x) = -8(2)^x - 12 ,

for f(0) ,here substitute x = 0

so we get as ,

==> f(0) = -8(2)^0 -12

==> f(0) = -8-12

==> f(0) = -20

hence, f(0) = -20

Answer:

Step-by-step explanation:

If it went from f(x) ⟹ f(0), that means that x=0.

So, you would plug in 0 for x in f(x)=-8(2)^x-12.

After plugging in the value of x, x=0, into the equation, you should have

f(0)=8(2)^0-12

Now, we are solving for f(0) (or f(x)).

You would use PEMDAS to solve this:

P-PARENTHESIS

E-EXPONENT

M-MULTIPLICATION

D-DIVISION

A-ADDITION

S-SUBTRACTION

There are no parenthesis

there are exponents,

(2)^0 and that =1

so we have f(0)=8(1)-12

there is multiplication, 8(1) which =8

so now we have f(0)=8-12

there is no division

there is subtraction

8-12, which equals -4

f(0)=-4

Answer:

there are two incorrect 2 and 3

Step-by-step explanation:

The solution is:

A) Deceleration of the car is -6.6667 m/s² while it came to stop.

B) The total distance the car travels is 200 meter during the 10 s period.

Here, we have,

Explanation:

Given Data

Initial velocity of the car () =   20.0 m/s

Final velocity of the car () = 0 m/s

Time (in motion) =7.00 s

Time (in rest) =3 s

To find - A) car's deceleration while it came to a stop

             B) the total distance the car travels in 10 s

A) The formula to find the deceleration is

Deceleration = (( final velocity - initial velocity ) ÷ Time)        (m/s²)

Deceleration = (() - ()) ÷ time     (m/s²)

Deceleration =  ( 0.0 - 20 ) ÷ 3      (m/s²)

Deceleration =   (- 20) ÷ 3  (m/s²)

Deceleration   =  - 6.6667 m/s²

(NOTE : Deceleration is the opposite of acceleration so the final result must have the negative sign)

The car's deceleration is  - 6.6667 m/s² while it came to a stop

B) The formula to find the distance traveled by the car is  

Distance traveled by the car is equals to the product of the speed and time

Distance = Speed × Time  (meter)

Distance = 20.0 × 10

Distance = 200 meters

The total distance the car travels during the period of 10 s is 200 meters.

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complete question:

A car is traveling at a 20.0 m/s for 7.00 s and then suddenly comes to a stop over a 3 s period.

a. What was the car’s deceleration while it came to a stop?

b. What is the total distance the car travels during the 10 s period?

Answer: so if Zhi earns $16.54 / h. H = Hour

and he works 34 hours per week we can do the math

16.54x34h = 562.36

Rounded to the nearest 5 cents is = 562.35

there's your answer!

A pony walks approximately 78.4 feet to complete one trip around the circular pony ride.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The circumference of a circle or the distance around the circle is expressed mathematically as;

C = 2πr or C = πd

Where r is radius, d is diameter and π is constant pi ( π = 3.14 ).

The distance traveled by a pony to complete one trip around the circle is equal to the circumference of the circle.

Given that the diameter of the circle is 25 feet, we can calculate the circumference using the above formula as follows:

C = πd

C = 3.14 × 25 feet

C = 78.5 feet.

Therefore, the measure of the circumference is approximately 78.5 feet.

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Answer:

1. f(2) = 5

2. h(0) = 15

3. f(0) = 2

4. f(3) = 4

5. f(x) = 5; x = 2

6. h(x) = 4; x = 1

7. f(4) + h(4) = 3 + 10 = 13

Step-by-step explanation:

f(x) means find the y-value at x.

for example:

f(3) means find the y-value at x=3 on the graph. the answer would be 4. you can also look at it like (3,?).

h(x)= 4 means that the y-value is 4, so you need to look at the table and find the x-coordinate that corresponds with h(x)=4

To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

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The total number of fishes present in the lake on my 1 is 840.

The given data for the question-

September is equivalent to a percentage of tagged fish in May.

3/42 = 60/x

x = 60 *42 / 3

x = 840

Thus, the total number of fishes present in the lake on my 1 is 840.

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The empirical rule state that, for normally distributed data, almost all of the data fall within three standard deviations either side of the mean. Specifically,

-68% of data within 1 standard deviation.

-95% of data within 2 standard deviation

-99.7 of data within 3 standard deviation.

In our case the mean is

and the standard deviation is

then, the empirical formula imply that

and

then, the answer is 14 minutes to 34 minutes

Answer:

D

Step-by-step explanation:

Answer:

$4.80

Step-by-step explanation:

First, apply the coupon to the original price

20% of 14.99 = 2.998

or

0.20 x 14.99 = 2.998

Then, find the sales tax of the new price

%6 of 2.998 = 1.7988

or

0.60 x 2.998 = 1.7988

Finally, add the sales tax to the new price

2.998 + 1.7988 = 4.7968

Round 4.7968 to the nearest tenth to get 4.80

Hope this helped!

Total cost

\(\\ \sf\longmapsto 14.99-0.14(14.99)\)

\(\\ \sf\longmapsto 14.99-2.09\)

\(\\ \sf\longmapsto 12.9\$\)

Done

The amount of  energy must be removed from the drink for it to reach this temperature is 35.5kJ

Here we have given that a 12oz can of soft drink at 25c is placed in a freezer where the temperature is -12c.

As we all know that the equation of the given measurement is written as,

=> Q1=m.c.AT

From the given, now we have to know that the mass "m" = 340gm

And the value of C= 4.18 J/g°C

Then at 25°C it will at the temperature of

=> Q1340g x 4.18 x 25

=> Q1 = 35, 5300J or 35.5kJ

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The value of price per pint is $3.88.

What is the total cost?

Total cost is an economic metric that includes both the initial cash outlay and the opportunity cost of the decision-makers options when calculating the costs incurred to produce a good, buy an investment, or acquire a piece of equipment.

Here, we have

Given: A 4-cup bottle of mouthwash costs $7.44.

We have to find the price per pint.

4 cups = 1 quart

2 pints = 1 quart

So you have 1 pint of mouthwash.

But there are two in the bottle.

Therefore you divide the price by 2

7.76 / 2 = 3.88 dollars.

Hence, the value of the price per pint is $3.88.

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