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GEOMETRY A container company wants to make a
cylindrical cardboard container with a volume of 4752 cubic inches. The formula V = roh represents the volume of a cylinder. In this formula, V represents the volume, represents the radius of the cylinder's base, and h represents the height of the cylinder. Solve for h. What height should the company make the container if the radius of the base must be 9 inches?

Explanation:

The initial expression is:

To know the value of m, we need to solve the equation for m, so adding 7 to both sides of the equation, we get:

Then, we can multiply both sides by 4, so:

Answer:

The answer is D.

Step-by-step explanation:

First, you have to find the area of circle using the formula :

A = π × r²

A = π × 3²

A = 9π

Given that PHU is an equilateral triangle so all sides have a degree of 60°. Next, you have to find the area of minor sector of P and U by using the formula :

A = (θ/360) × π × r²

A = (60/360) × π × 3²

A = 1.5π

Lastly, you have to subtract the area of sector from the area of circle in order to find the area of shaded region :

A = (9π × 2) - (1.5π × 2)

A = 18π - 3π

A = 15π

7 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat for two events based on laws of probability multiplication.

The probability multiplication method can be used to determine the number of persons who own both a dog and a cat if we assume that owning either one is an independent occurrence.

We are aware that 15 out of the 30 people—or 50%—have cats. Also, 12 out of the 30 people, or 40%, are dog owners. The likelihood of owning both a cat and a dog is just the sum of the probabilities of owning both a cat and a dog if we believe that these events are unrelated:

P(having a dog and a cat) = P(having a cat) * (owning a dog)

P (having a dog and a cat) equals (15/30) * (12/30).

P(having a dog and a cat) = 0.25

7.5 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat. We cannot allow a fraction of a person to possess both a cat and a dog though, as we are dealing with a discrete number of people. As a result, we can round to the next whole number or down. As there cannot be a half of a person in this situation, we would round down to 7 people having both a dog and a cat.

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Linear models are mathematical representations used to describe the relationship between two variables. They can be expressed in the form of a linear equation, y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope, and b represents the y-intercept.

In mathematics, a linear model is a way to represent the relationship between two variables using a straight line. The equation of a linear model is typically written as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis).

The slope, m, determines the steepness of the line. It represents how much the dependent variable (y) changes for each unit increase in the independent variable (x). A positive slope indicates a positive relationship, where y increases as x increases. A negative slope indicates a negative relationship, where y decreases as x increases. A slope of zero represents a horizontal line, indicating no relationship between the variables.

The y-intercept, b, is the value of y when x is zero. It represents the starting point of the line on the y-axis. It gives an initial value for the dependent variable before considering the effect of the independent variable.

Overall, linear models are useful for analyzing and predicting the relationship between two variables in a simple and straightforward manner. They provide insights into how changes in the independent variable affect the dependent variable and help make predictions based on the observed data.

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Answer:

x=-7  x=4

Step-by-step explanation:

(X-2)(x+5)=18

FOIL

x^2 +5x -2x-10 =18

Combine like terms

x^2 +3x -10 = 18

Subtract 18 from each side

x^2 +3x -10 -18 = 0

Combine like terms

x^2 +3x -28 =0

Factor

What two numbers multiply to -28 and add to 3

7*-4 = -28

7+-4 = 3

( x+7) ( x-4) =0

Using the zero product property

x+7 =0  x-4=0

x=-7  x=4

Answer:

It has reflectional symmetry with four lines of symmetry.

Step-by-step explanation:

======================================================

Explanation:

Choice A is false since it does have rotational symmetry. See choice B.

Choice B is close, but the "90 degrees" needs to be "45 degrees". Each 45 degree rotation of the figure has the "before" and "after" be the same.

Choice C is one of the answers. There's a vertical line of symmetry, and a horizontal one as well.  Then there are two diagonal lines of symmetry. Each goes through the center. A line of symmetry is a mirror line to allow us to reflect one half over this line to get the other half.

Choice D is another answer. It has point symmetry since we can pick any point on the figure and reflect it over the center point, to land on a corresponding image point on the opposite side of the figure. For example, the northern most point reflects over the center to land on the southern most point.

The expression "5 less than the conscious number and 2" can be written mathematically as: n - 5 = 2

A math expression is a combination of mathematical symbols, numbers, and variables that represents a mathematical statement or calculation. It can be as simple as a single number, such as 5, or as complex as a multi-term equation, such as 3x + 4y = 12.

Expressions can include arithmetic operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions such as exponents, logarithms, and trigonometric functions.

Where "n" represents the number in question. To find the value of "n", you can add 5 to both sides of the equation:

n - 5 + 5 = 2 + 5

This is the result:

n = 7

Therefore, the number in question is 7.

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The question in English is:

(What is) 5 less than the conscious of a number and 2

Answer:

x = 44/7

Step-by-step explanation:

7x+3 = 47

Subtract 3 from each side

7x+3-3 = 47-3

7x = 44

Divide by 7

7x/7 = 44/7

x = 44/7

The interval of increase for the function f(x) = ex x8 is (0, ∞).

To determine the intervals of increase or decrease for the given function, we need to analyze the sign of the derivative.

Let's find the derivative of f(x) with respect to x:

f'(x) = (ex x8)' = ex x8 (8x7 + ex)

To determine the intervals of increase, we need to find where the derivative is positive (greater than zero).

Setting f'(x) > 0, we have:

ex x8 (8x7 + ex) > 0

The exponential term ex is always positive, so we can ignore it for determining the sign. Therefore, we have:

8x7 + ex > 0

Now, we solve for x:

8x7 > 0

Since 8 is positive, we can divide both sides by 8 without changing the inequality:

x7 > 0

The inequality x7 > 0 holds true for all positive values of x. Therefore, the interval of increase for the function is (0, ∞), which means the function increases for all positive values of x.

The function f(x) = ex x8 increases in the interval (0, ∞).

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Answer:

Step-by-step explanation:

5ˣ⁺² = 5⁹

log₅(5ˣ⁺²) = log₅(5⁹)

x+2 = 9

x = 7

Answer: The answer is A (40 m)

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\frac{9C}{5}+32=F\\ \\ \frac{9C}{5}=F-32\\ \\ 9C=5F-160\\ \\ C=\frac{5F-160}{9}\)

Answer:

a = 4

b = 10

Step-by-step explanation:

Price of an apple $1.25

Price of a banana $0.5 0

The two equations:

10 = 1.25a + 0.5b

a + b = 14

solve for one variable

b = 14 - a

10 = 1.25a + 0.5(14-a)

10 = 1.25a+ 7 - 0.5a

10 = 0.75a + 7

0.75a = 3

a = 4

Then solve for the second

b = 14 - 4

b = 10

The volume for the boxes that are held by Chris will be 80ft³.

Volume refers to the amount of space that a three-dimensional object occupies. It is typically measured in cubic units, such as cubic meters or cubic feet. The volume of an object can be calculated using various formulas depending on the shape of the object.

Volume is an important concept in many fields, including physics, engineering, and architecture. It is also used in everyday life, such as when measuring the amount of liquid in a container or determining the capacity of a storage space.

Volume = area of the base × height

V= L× w × h =B × h

The volume for one box = 1 1/3 × 10

                                     = 40/3 = 13 1/3

The volume for 6 boxes=  6 × 13 1/3 = 80 ft³

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Total Volume in cubic feet and express answer in mixed fraction

chris has 6 identical boxes. The rectangular base of each box has an area 1 1/3 ft 3. The height of each box is 10 inches. What is the total volume of all the boxes in cubic feet?

The future value of the investment is approximately $129,674 when $100,000 is invested for 5 years at a 5.4% interest rate compounded continuously.

To find the future value, we use the formula P = P0 * e^(kt). Plugging in the given values, we have P = $100,000 * e^(0.054 * 5). Using a calculator, we calculate e^(0.054 * 5) ≈ 1.29674.

Therefore, P ≈ $100,000 * 1.29674 ≈ $129,674. The future value of the investment after 5 years at a 5.4% interest rate compounded continuously is approximately $129,674.

It's worth noting that continuous compounding is an idealized concept used for mathematical purposes. In practice, compounding may be done at regular intervals, such as annually, quarterly, or monthly. Continuous compounding assumes an infinite number of compounding periods, which leads to slightly higher future values compared to other compounding frequencies.

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Answer:

The value of x is 4.

Step-by-step explanation:

The perimeter of the triangle is the sum of the lengths of all its sides.

The perimeter of the rectangle is twice the sum of the length and the width.

base of triangle = x

two equal sides = x + 5

length of rectangle = x - 1

width of rectangle = x + 4

According to the question,

Perimeter of triangle = perimeter of rectangle

x + x + 5 + x + 5 = 2 ( x - 1 + x + 4)

3 x + 10 = 2 (2 x + 3 )

3 x + 10 = 4 x + 6

4 x - 3 x = 10 - 6

x = 4

Reason:

Multiply both sides by 5 to undo the division.

w/5 = 3

5*(w/5) = 5*3

w = 15

As a way to check, plug in w = 15

w/5 = 3

15/5 = 3

3 = 3

We get a true statement at the end to confirm w = 15 is indeed the answer.

Answer:

x=33

Step-by-step explanation:

Use trig functions SOH, CAH, TOA.

In this situation, the function is sine (opposite/hypotenuse)

So, on your calculator, plug in (inverse function because you're solving for an angle) sin-1(22/40)

and you should get the answer as

33.367

=33

Answer:

relationship between perpendicular and hypotenuse is given by si n angle

sin angle =perpendicular/hypotenuse

sin ?=22/40

?=sin-1(22/40)=33.36=33

The genre which had the same number of votes in each study is: B. horror.

See the attached charts.

From the bar chart, the number of votes for horror movie is equal to 40 votes. Next, we would calculate the number of votes for horror movie in the pie chart as follows;

Number of votes = 16/100 × 250

Number of votes = 0.16 × 250

Number of votes = 40 votes.

Finally, we may infer rationally that horror is a film genre that receives the same amount of votes in each independent research.

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Answer: 1 mph

Step-by-step explanation:

Given

Speed of Mariah is  \(v_m=6\ mph\)

Bobby walks 4400 yards in 0.5 hr

speed of bobby is  

\(v_b=\dfrac{4400}{0.5\times 1760}=5\ mph\quad [\text{converting yards into miles by dividing by 1760}]\)

The difference in the speed of Mariah and bobby is

\(\Rightarrow v_m-v_b=6-5=1\ mph\)

Answer:

i dont know

Step-by-step explanation:

i is spelt with i, and so on.  

Answer:

97.5% of the students passed this test.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 78, standard deviation of 9.

What percentage of the  students passed this test?

Above 60.

60 = 78 - 2*9

So 60 is two standard deviations below the mean.

The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

Of the 50% above, all passed.

Of the 50% below, 95%(within 2 standard deviations of the mean) passed.

So

\(p = 0.5 + 0.5*0.95 = 0.975\)

97.5% of the students passed this test.

The quotient is  \(x-1+\frac{9}{x+6}\)

The formula to calculate the division of two numbers is: Dividend ÷ Divisor = Quotient + Remainder. Here, The dividend is the number, which is being divided. The divisor is the number, which divides the number (dividend) into equal parts.

Division in maths is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.

In the above question we simply have to divide the dividend that is \(x^2+5x+3\) with x + 6

and then we will get the quotient as x - 1 and remainder 9 .

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Answer: 450

Step-by-step explanation: 450 x 10 = 4500

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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Answer:

al menos 2-3

lo siento si te equivocas