I need help with this

The volume of the prism is equal to 40x m³.

The volume of the cylinder is equal to 72π m³.

The value of x to the nearest tenth is equal to 5.7 meters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula for the volume of a rectangular prism, we have;

Volume of a rectangular prism, V = 5 × x × 8

Volume of a rectangular prism, V = 40x m³.

For the volume of the cylinder, we have:

Volume of a cylinder, V = πr²h

Volume of a cylinder, V = π × 3² × 8

Volume of a cylinder, V = 72π m³.

Next, we would solve for x;

40x = 72π

40x = 226.1947

x = 226.1947/40

x = 5.7 meters.

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Complete Question:

Rectangular prism and a cylinder both have a height of 8 m, and their cross-sectional areas are equal at every level parallel to their respective bases.

A rectangular prism and a cylinder both have a height of 8 meters. The rectangle has base dimensions of 5 meters by x. The cylinder has a radius of 3 meters.

Complete the steps to find the width of the prism.

Find the volume of the prism.

V = m3

Find the volume of the cylinder.

V = m3

Set the volumes equal to each other and solve for x. Round to the nearest tenth.

x = m

Point (-24,7) on terminal side on angle theta having trigonometric ratio equals to,

sin(θ) = 7/25                       csc(θ) = 25/7

cos(θ) = -24/25                   sec(θ) = -25/24

tan(θ) = -7/24                      cot(θ) = -24/7

Values of the trigonometric functions for an angle θ.

In standard position with the given point (-24, 7) on its terminal side.

Hypotenuse of the right triangle formed by the angle and its terminal side using the Pythagorean theorem,

Hypotenuse = √((-24)^2 + 7^2)

⇒Hypotenuse = √(576 + 49)

⇒Hypotenuse = √(625)

⇒Hypotenuse = 25

Signs of the sine, cosine, tangent, cosecant, secant, and cotangent based on the quadrant in which the angle lies.

x-coordinate is negative and the y-coordinate is positive, the angle is in the second quadrant.

This implies,

sin(θ) = 7/25

cos(θ) = -24/25

tan(θ) = -7/24

csc(θ) = 25/7

sec(θ) = -25/24

cot(θ) = -24/7

cosecant, secant, and cotangent are the reciprocals of the corresponding sine, cosine, and tangent values.

Therefore, the exact values of trigonometric ratios for the given point are,

sin(θ) = 7/25                       csc(θ) = 25/7

cos(θ) = -24/25                   sec(θ) = -25/24

tan(θ) = -7/24                      cot(θ) = -24/7

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Answer: 6 pounds

Step-by-step explanation:

If 1 pound of raw spaghetti makes 5 cups of cooked spaghetti, then we can set up a proportion:

1 pound raw spaghetti : 5 cups cooked spaghetti = x pounds raw spaghetti : 30 cups cooked spaghetti

To solve for x, we can cross-multiply and simplify:

1 * 30 = 5 * x

30 = 5x

x = 6

Therefore, 6 pounds of raw spaghetti noodles would be needed to make 30 cups of cooked noodles.

Answer:

54°

Step-by-step explanation:

AB = BC = CD = AD (Because all sides of a rhombus are equal)

Let's consider the triangle DBC:

BC = DC => ∠DBC = 36°

The angle DCB is equal to:

180° - 36*2 = 180° - 72° = 108°

In a parallelogram, opposite angles are equal.

Then the angle DAB = DCB = 108°

Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.

So, the angle DAE = EAB = 108° / 2 = 54°

Answer:

Step-by-step explanation:

Because we want to know how many three-fourths there are, we have to make groups of 3 fourths, or divide the number of fourths we have by 3. So there are (2\times 4)\div 3 = 8\div 3 = 2 \fraction three-fourths in 2.

The sum of the interior angles of a quadrilateral is 360°. We can use this fact to find the measures of the other two angles.

Let x be the measure of one of the two angles in the 2:3 ratio. Then, the measure of the other angle is 3x (since the two angles are in a ratio of 2:3).

We know that:

252° + 63° + 2x + 3x = 360°

Simplifying this equation, we get:

5x + 315° = 360°

5x = 45°

X= 9°

Therefore, one of the angles has a measure of 2x = 18°, and the other angle has a measure of 3x = 27°.

Answer:

The 4 angles of the quadrilateral are : 252, 63, 18 and 27

Step-by-step explanation:

252 + 63 + 2x + 3x = 360

315 + 5x = 360

5x = 45 ( 360-315 )

x = 9

Therefore, 1st angle = 2x = 18

2nd angle = 3x = 27

The approximate probability that more than 10% of the sample would report that they experienced extreme levels of stress during the past month, obtained using the z-score for the proportion of the sample, and the standard error, is about 96.327%

The z-score of a sample proportion, z can be obtained using the formula;

z = (p - π)/√(π·(1 - π)/n)

Where;

p = The sample proportion

π = The proportion of the population

n = The sample size

The percentage of the students out of the 1750 students that experienced extreme levels of stress in the school, p = 15%

The number of students in the sample used by the newspaper, n = 160 students

The number of students in the sample that replied "yes" = 10%

The true proportion of the students that experience stress = 15%

The probability that ,more than 10% of the sample would report that they experienced extreme levels of stress during the past month can be found as follows;

The standard error is; SE = √(p × (1 - p)/n)

Therefore;

SE = √(0.15 × (1 - 0.15)/160) ≈ 0.028

The z-score is therefore;

z = (0.1 - 0.15)/0.028 ≈ -1.79

z = -1.79

The z-score indicates the number of standard deviations the proportion of the sample is from the true proportion

The proportion on the of the sample which is larger than 10% is obtained from the area under the normal curve, to the right of the z-score of -1.79, which is obtained as follows;

The z-value at z = -1.79 is 0.03673, which indicates that the area to the left of the z-value is 0.03673, and the area to the right is; (1 - 0.03673) = 0.96327

The probability observing a sample proportion more than 10% if the actual proportion is 15% is therefore; 0.96327 = 96.327%

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Answer:

Volume = length x width x height

3 in x 8 in x 8 in = 192 cubic inches

Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:

The mean of x is 3.5 and the mean of y is 150.

The variance of x is 2.5 and the variance of y is 2203.5.

The covariance of x and y is 607.5.

Using these values, we can calculate the slope of the regression line:

m = covariance of x and y / variance of x = 607.5 / 2.5 = 243

We can also calculate the y-intercept of the regression line:

b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5

Therefore, the equation for the linear function that best fits the given data is:

y = 243x - 16.5

Rounding both numbers to two decimal places, we get:

y = 243x - 16.50

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Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50

What is linear regression?

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:

The mean of x is 3.5 and the mean of y is 150.

The variance of x is 2.5 and the variance of y is 2203.5.

The covariance of x and y is 607.5.

Using these values, we can calculate the slope of the regression line:

m = covariance of x and y / variance of x = 607.5 / 2.5 = 243

We can also calculate the y-intercept of the regression line:

b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5

Therefore, the equation for the linear function that best fits the given data is:

y = 243x - 16.5

Rounding both numbers to two decimal places, we get:

y = 243x - 16.50

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Answer:

Step-by-step explanation:

its 60

Answer:

$4.50

Step-by-step explanation:

There are 12 inches in a foot. 18 inches is 1.5 feet.

1 foot of wire is $3.00 and a half of foot should be $1.50.

1.5 feet of wire should cost $4.50

1.5 ft × $3/ft

= $4.50

f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.

If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.

If it also has a simple zero at 3, then the factorization must include (x-3).

Therefore, the polynomial function with these zeros is :-

f(x) = (x+4)^2(x-3)

This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.

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Answer:

6

Step-by-step explanation:

We know that a dozen is the value of 12 so to find half a dozen we simply need to half it!

This means that there are 6 eggs in a half dozen.

FUN FACT:

A baker's dozen is 13, one more than a regular dozen!

Hope this helps, have a lovely day!

The direction of the current in the current-carrying wire that produces the field indicated in the figure is given below.

Conventionally, a positive charge would go in the same direction as an electric current. As a result, the battery's positive terminal receives less current in the external circuit than its negative counterpart. Indeed, electrons would go in the reverse direction across the cables.

According to Fleming's right-hand rule gives which direction the current flows. The right hand is held with thumb, index finger & middle finger mutually perpendicular to each other. The thumb is pointed in direction of motion to magnetic field of conductor relative to magnetic field.

(A) from right hand rule direction of current is towards left.

(B) Out of the Screen.

(C) Lower left to upper right.

According to Fleming's Right Hand Rule, if the thumb, forefinger, and middle finger are arranged in a straight line on the right hand, the thumb will point in the direction of the conductor's motion in relation to the magnetic field, the forefinger will point in the direction of the magnetic field, and the middle finger will point in the direction of the induced current.

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The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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The initial squirrel population was 75. The squirrel population t years in an equation can be determined as P(t) = 75 * 2^(t/6). The expected squirrel population 10 years from now is 261.80.

A. Let  initial squirrel population = x

It is given that the population doubles every six years.

so after 18 years, the population has doubled three times. So, the equation will be:

x * 2^3 = 60

x * 8 = 600

x = 75

The initial squirrel population was 75.

B.  Let squirrel population t years = P(t)  

It is given that the population doubles every six years, then the equation will be written as:

P(t) = 75 * 2^(t/6)

C. To calculate the estimation of squirrel population 10 years from now,

t = 10 can be substituted in the above equation.

P(10) = 75 * 2^(10/6)

P(10) =  261.80

Therefore,  we can conclude that the expected squirrel population 10 years from now is 261.80.

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Answer:

1 : 3.5

Step-by-step explanation:

Rewrite the ratio 6:21 as 1 : n .

Divide each side by 6.

6/6 : 21/6

1 : 3.5

To rewrite a number with a radical in the denominator without the radical, we can use the conjugate of the denominator. The conjugate of a binomial expression a + b is a - b, and the conjugate of a - b is a + b.

Suppose we have a number with a radical in the denominator, such as 1/√2. To rewrite this without the radical, we multiply the numerator and denominator by the conjugate of the denominator, which is

√2: 1/√2 = (1/√2) * (√2/√2) = √2/2

Note that the product of the denominator and its conjugate is always a difference of squares, which can be simplified to an integer without a radical.

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Because the resultant is the closing side of the triangle according to the triangle law of vector addition, the resultant vector's magnitude would be 13.93 metres.

A vector quantity is what?

The vector quantities are those that include both the direction and the magnitude of the quantities.

The vector quantities include things like force, acceleration, and displacement.

Scalar quantities only have the magnitude of the quantity measured; they do not have information about the direction.

The triangle law of vector addition can be used to calculate the resultant vector.

Using the right-angled triangle's Pythagoras theorem

[tex]Base^{2} + Height^{2} = Resultant^{2}[/tex]

[tex]132 + 52 = Resultant^{2}[/tex]

Outcome 2 = 194

The outcome is 194

=13.93 m

According to the triangle law of vector addition, the resultant vector would have a magnitude of 13.93 metres since it is the triangle's closing side.

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Answer:

4.3

Step-by-step explanation:

Answer:

x²  + 4x - 6

Step-by-step explanation:

x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left

= x(x + 1 + x + 2x)  - 3(x² - x + 2)

= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis

= 4x² + x - 3x² + 3x- 6 ← collect like terms

= x² + 4x - 6

Therefore , the solution of the given problem of function comes out to be  the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).

All of the subjects, including actual and fictitious locales and arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Every postbox has a specific location that could serve as a refuge.

Here,

We can draw points for different values of x and y to graph the function => y = x² + x- 2:

|x| |y=x²+x-2|

|---|-----------|

|-3 | 4 |

|-2 | 0 |

|-1 | -2 |

|0 | -2 |

|1 | 0 |

|2 | 6 |

|3 | 12 |

We can use the elements in the table above to plot them on a graph and link them to create a parabolic shape.

We can search for the values of x where the function y = 0 to determine the function's zeros.

Using the zeros we discovered, we can recast the function as the polynomial in factored form is:

=> y = (x + 2)(x - 1)

Therefore, the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).

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Answer:

To multiply a whole number and a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator the same.

So, 3 x 3/5 = (3 x 3)/5 = 9/5

Therefore, 3 x 3/5 = 9/5.

Answer:

Step-by-step explanation:

9x/5

Answer:

8

Step-by-step explanation:

2x² + 3x - 6

plug in x with 2

2(2)^2+3(2)-6

2(4)+6-6

8+6-6

14-6

8

The probability that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

According to our question-

z= x-a/u

98-100/15

Hence, A chance of a random individual on the street having an IQ below 98 is 0.4470, or 44.70%.

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The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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Answer:

90 cubes in the box.

Step-by-step explanation:

To find how many cubes would fit into the box, first we must find the volume of each cube. 2cm x 2cm x 2cm= 8 cubic centimeters. The entire volume of the box is 720 cubic centimeters, so we can divide 720 by 8.

720/8=90

90 cubes can fit into the box.

Answer: 90

Step-by-step explanation:

First, we need to calculate the volume of one cube of sugar:

V = s³, where s is the side length of the cube

V = 2³ = 8 cm³

To find the number of cubes that can fit in a box of 720 cm³, we need to divide the volume of the box by the volume of one cube:

720 cm³ ÷ 8 cm³/cube = 90 cubes

Therefore, 90 cubes of sugar can fit in a box with a volume of 720 cm³.

The value of n for the ascending powers of x is found to be 20.

A series expansion is just a representation of a specific function as the sum of powers in a single of its variables or by the sum of powers of this other function, typically an elementary one.

For several popular functions, we give series expansions (most Maclaurin, most Laurent, and some Puiseux). The above-mentioned equation for Taylor's series can be thought of to be the expansion of f(x+h) around the origin x. A function f(x) is frequently expanded around the point x = 0.

Using the expansion of the function-

ⁿC₁= (n!)/(n – 1)!1! = (n(n – 1)!)/(n – 1)!1!= n/1!= n.

(1 + 2x)ⁿ= ⁿC₀(1)ⁿ ⁻ ⁰(2x)⁰ + ⁿC₁(1)ⁿ ⁻ ¹(2x)¹ + ...

            = 1 + n(1)(2x) + ...

(1 + 2x)ⁿ  = 1 + 2nx + ...

Now,

The second term is 2nx.

2n= 40

n = 40/2= 20.

Thus, the value of n for the ascending powers of x is found to be 20.

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Answer:

6)-56+567)-/(05(-)9

Step-by-step explanation:

Question

Katherine bought 312

pounds of oranges for $1.45

per pound, as well as 434

pounds of potatoes that cost $1.69

for 2

pounds. She gives the cashier a $10.00

bill.

Which equation represents the situation if x

is the amount of change in dollars Katherine should receive?

A 312(1.45)+434(1.69)+x=10

3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times 1 point 6 9 plus x is equal to 10

B 312(1.45)+434(1.692)+x=10

3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren plus x is equal to 10

C 312(1.45)+434(1.692)−x=10

3 and 1 half times 1 point 4 5 plus 4 and 3 fourths times open paren 1 point 6 9 over 2 close paren minus x is equal to 10

D (312+434)⋅(1.45+1.69)+x=10

HELP ME I WILL GIVE BRAINLIEST

The inequalities that the given number line represents are:

(A) x > 8

(B) x -4

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics.

On the number line, size comparisons between two numbers are typically conducted.

The outcome is (x/a) > (y/a) when x > Y and a > 0, and (x/a) (y/a) when x Y and a > 0.

The division of both sides of an inequality by a negative integer, on the other hand, produces an analogous inequality if the inequality sign is inverted.

So, the inequality that the given number line represents:

(A) x > 8 is the inequality in the first equation.

(B) Given that the second graph is a dot, the inequality for it is x -4.

Therefore, the inequalities that the given number line represents are:

(A) x > 8

(B) x -4

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