The volume of a prism with side lengths measured in millimeters is 20. How could this measurement be written? Check all that apply.

Data collected about a population is not a characteristic of both observational studies and experiments.

Through experiments, two variables' cause and effect relationships are examined. This is where they differ from observations and interviews, which can only assume the existence of contexts and cannot provide evidence for them. The environment of the test subjects is managed in an experiment depending on the issue.

Three things characterize statistical experiments in general:

There are various outcomes that the experiment could produce.

In an experiment, the cause, the independent variable, is changed while the effect, the dependent variable, is measured and any unrelated factors are controlled.

It is possible to anticipate every outcome.

Chance determines how the experiment turns out.

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A piece-wise function that has domain of all real numbers and range of [tex][-3, \infty)[/tex] is f(x) = |x| - 3, as:

[tex]|x| - 3 = x - 3, x \geq 0[/tex]

[tex]|x| - 3 = -x - 3, x < 0[/tex]

A piece-wise function is a function that has different definitions, depending on the input.

One example is the absolute value function, defined as follows:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

The function is defined for all real values, with a range of [tex][0, \infty)[/tex]. Shifting it down 3 units, it will have the desired range, as follows:

[tex]|x| - 3 = x - 3, x \geq 0[/tex]

[tex]|x| - 3 = -x - 3, x < 0[/tex]

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Answer:

hello :

f(x)=x/4-3 and g(x)= 4x²+2x-4,

(f+g)(x).=f(x)+g(x)=x/4-3  + 4x²+2x-4,

(f+g)(x).= 4x²+(2x+x/4)-7

(f+g)(x).= 4x²+x(3+1/4) - 7......continu

The integers are therefore -2, -2, 0, 1 and 2

Let the five consecutive integers be x-3, x-2, x-1, x and x+1

If the  sum of five consecutive integers equals 5.5 times the middle integer, then;

x-3+x-2+x-1+x+x+1 = 5.5(x-1)

5x - 5 = 5.5x - 5.5

Collect the like terms

5x-5.5x = -5.5 + 5

-0.5x = -0.5

x = 1

The integers are therefore -2, -2, 0, 1 and 2

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The number of female contestants who signed up to compete is; 43.

Let number of females = x

Let number of males = y.

Hence, it follows from the task content that;

x+y = 50

x-y = 36.

Hence, by adding both equations together in a bid to determine the number of females; we have;

2x = 86

x = 43.

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Answer:

a = 4 first term, r = ?, T10 = 100.Tn = ar^n - 1 formula for g.pT10 = 4r^ 10 - 1100 = 4r^9Divide both side by 4100/4 = 4/4r^925 = r^9 take the 9th root of both side 9√25 = 9√r^9r = 9√25To find the nth term Since Tn = ar^n - 1

The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵

An equation is an expression that shows the relationship between two or more variables and numbers.

The greatest common factor is the highest number that all the numbers share.

The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵

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The 99% Confidence interval for the mean sale time for all homes in the neighborhood is:87.857, 112.143.

a. The assumption is: Assume that the population has a normal distribution.

The CI  is exact for the normal populations and for small samples the z-interval method should be used in a situation where the variable is normally distributed.

b. Confidence interval:

CI=Sample mean±z-score×Standard deviation/√Size of the sample

CI=100-2.576×20/√18, 100+2.576×20/√18

CI=100-12.143, 100+12.143

CI=87.857, 112.143

Therefore the 99% Confidence interval is 87.857, 112.143.

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Answer:

13

Step-by-step explanation:

7+2x=3x-6

knowing this then you solve it

Step-by-step explanation:

7 more = + 7

twice a number = 2*x = 2x

6 less = -6

3 times the same number = 3 * x = 3x

Putting this together we get:

2x + 7 = 3x - 6

subtract two from both sides to isolate x

(-2x) + 2x + 7 = 3x - 6 (-2x)

7 = x - 6

add 6 to both sides to get your answer

7 (+6) = x - 6 (+6)

13 = x

or

x = 13

The time needed for the investment to become $10,413 is 54.7 years

Number of years = (In FV / PV) / r  

r = 4.252/12 = 0.354%

(In 10, 413 / 1,018.40) / 0.00354 = 656.73 months = 54.7 years

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115.2 pounds of type A coffee were used.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of pounds of type A coffee be x and the number of pounds of Type B coffee be y.

According to the question, the equations are,

5.50x + 4.40y = 762.30

x = 4y

So, the solution of the equation is obtained as follows:

5.50(4y) + 4.40y = 762.30

26.40y = 762.30

y = 762.30/26.40

y = 28.8 pounds

x = 4*28.8 = 115.2 pounds

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Answer: 8

Step-by-step explanation:

Since x=3, we can plug in 3 for x in the equation:

[tex]5(3-1)-2\\5(2)-2\\10-2\\8[/tex]

⊱________________________________________________________⊰

Answer:

8

Step-by-step explanation:

Plug in 3 for x

[tex]\sf{5(2)-2} \ \ \ \ \ \large\textbf{[Multiply 5 by 2 next]}[/tex]

[tex]\sf{10-2} \ \ \ \ \large\textbf{[Subtract]}[/tex]

[tex]\sf{8}[/tex]

Done !! Hope this made sense to you !!

⊱________________________________________________________⊰

[tex]\small\pmb{\tt{CALLIGRAPHY}}[/tex]

Answer:

2.4536 years

Step-by-step explanation:

compound formula:

A=P*(1+r/n)^nt

A = 6000

P = 5000

r = rate

n = 4 times per year compounded

t = time in years

6000 = 5000(1 + .075/4)^4t

divide both sides by 5000

1.2 = (1.01875)^4t

log both sides

log(1.2) = 4t * log(1.01875)

solve for t

t = 2.4537 years

Subtracting 4 from both sides of the equation ¹/₂x = -¹/₂ gives us; ¹/₂x - 4 = -¹/₂ - 4

We want to simply the expression which is;

¹/₂x = -¹/₂

Now, when we subtract 4 from both sides, it means we are using subtraction property of equality which states that subtracting the same value from both sides of an equation makes the equation still to be equal. Thus, we have;

¹/₂x - 4 = -¹/₂ - 4

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Answer:

y = - 7x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

7x + y = 7 ( subtract 7x from both sides )

y = - 7x + 7 ← in slope- intercept form

Answer:

0.2135

Step-by-step explanation:

When something asks to find the product, it indicates multiplication.

We are given two decimals which are: 3.05 and 0.07.

We are asked to multiply and find the product of these decimals.

Let's use the algorithm method.

                   3  .    0   5

x                 0   .    0   7

_____________________

                  2        3

          0 .    2      1    3    5

Therefore, 3.05 × 0.07 = 0.2135.

Please see the graph below

The blue curve of the image attached below represents the graph of the function f(x) = 3 · x².

In this question we have a power function formed by the product of a primitive function g(x) = x² and vertical dilation h(x) = 3, then:

f(x) = h(x) · g(x)

f(x) = 3 · x²

Now we proceed to graph both the primitive function and the transformed function with a graphing tool. Please notice that the primitive function is the red curve.

The statement presents typing mistakes. Correct form is shown below:

Show a graph for the following: f(x) = 3 · x².

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Answer:

For an exact answer the width would be the square root of 1011 and the length would be 1.5x the square root of 1011.

Step-by-step explanation:

A = lw

1516.5 = w(1.5)w

1516.5 = 1.5w^2  Divide both sides by 1.5

1011 = w^2  Take the square root of each side

Square root of 1011 = w.

Answer:

[tex](f \cdot g)(x)[/tex] = [tex]2x^2 -1[/tex]

Step-by-step explanation:

[tex](f \cdot g)(x)[/tex], read as "f of g of x", means we have to use the function [tex]\bf g(x)[/tex] as input for the function [tex]\bf f(x)[/tex]. This means, we have to replace the [tex]x[/tex] in the definition of  [tex]f(x)[/tex] with [tex]g(x)[/tex].

[tex]f(x)=x+3[/tex]

[tex]g(x) = 2x^2 - 4[/tex]

∴ [tex](f \cdot g)(x) = f(g(x))[/tex]

                 ⇒ [tex]g(x) + 3[/tex]

                 ⇒ [tex](2x^2 - 4) + 3[/tex]

                 ⇒ [tex]2x^2 -1[/tex]

Answer:

Step-by-step explanation:

Okay, so first of all, when a slope is negative, the line goes down from left to right, not up from left to right. Then, plot the Y intercept as -2. Finally, either go up 2 and left 3 or down 2 and right 3.

Answer:

Graph attached.

Step-by-step explanation:

As we have been given the slope and the y-intercept, we can create a linear equation using the slope-intercept form.

Slope-intercept form of a linear equation:

[tex]y=mx+b[/tex]

where:

Substitute the given values into the formula to create an equation for the line:

[tex]\implies y=-\dfrac{2}{3}x-2[/tex]

Now we have an equation for the line, find at least two points on the line by inputting values of x into the found equation:

[tex]x=0 \implies y=-\dfrac{2}{3}(0)-2=-2 \implies (0,-2)[/tex]

[tex]x=3 \implies y=-\dfrac{2}{3}(3)-2=-4 \implies (3,-4)[/tex]

[tex]x=-6 \implies y=-\dfrac{2}{3}(-6)-2=2 \implies (-6,2)[/tex]

Plot the found points and draw a straight line through them (see attachment).

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Answer:

Vertex (2 , -25)

Axis of symmetry: x = 2

Step-by-step explanation:

 The vertex is the highest point if the parabola open downwards and the lowest point if the parabola opens upward.

 f(x) = (x - 2)² - 25

The given quadratic function  is in vertex form.

 f(x)  = a(x - h)² + k

Here,  (h , k) is the vertex of the parabola.

 h = 2  ; k = -25

[tex]\sf \boxed{\bf Vertex (2 , -25)}[/tex]

 The axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

Axis of symmetry: x = h

  [tex]\sf \boxed{\bf x = 2}[/tex]

The point-slope equation of the line is: y - 2 = 8(x - 2).

The point-slope equation is: y - b = m(x - a), where:

Using the coordinates of the point shown in the graph, substitute (a, b) = (2, 2) and m = 8 into y - b = m(x - a):

y - 2 = 8(x - 2)

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Considering the function for the net worth of the function, it is found that it will not be in debt for the first time after 6 months in month 14, at point (14,0), which is plotted on the graph.

A company is said to be in debt if it's net worth is negative. On a graph, it is represented by the curve being below the x-axis.

From month 2 until the end of month 13, the company is in debt, hence it will not be in debt for the first time after 6 months in month 14, at point (14,0), which is plotted on the graph.

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Using the Poisson distribution, there is a 0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

A bank gets an average of 12 customers per hour, hence the mean is [tex]\mu = 12[/tex].

The probability that there will be 4 or more customers at this bank in one hour is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} \approx 0[/tex]

[tex]P(X = 1) = \frac{e^{-12}12^{1}}{(1)!} \approx 0[/tex]

[tex]P(X = 2) = \frac{e^{-12}12^{2}}{(2)!} = 0.0004[/tex]

[tex]P(X = 3) = \frac{e^{-12}12^{3}}{(3)!} = 0.0018[/tex]

Then:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0.0004 + 0.0018 = 0.0022.

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0022 = 0.9978[/tex]

0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.

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The equation of the asymptote is y = 3x - 5. The correct answer is option C

The distance from a point and the distance to a line in hyperbola is known as asymptote. The general equation is [tex]x^{2}/ a^{2} - y^{2}/b^{2} = 1[/tex]

From the given equation of hyperbola, which is

[tex]\frac{(x - 2)^{2}}{4}[/tex]  - [tex]\frac{(y - 1)^{2} }{36}[/tex] = 1

The center (h , k) of the hyperbola = C(2, 1)

a = 2

b = 6

Where C = [tex]\sqrt{a^{2} + b^{2} }[/tex]

C = [tex]\sqrt{4 + 36}[/tex]

C = [tex]\sqrt{40}[/tex]

C = [tex]2\sqrt{10}[/tex]

The equation of the asymptote will be y - K = +/-(b/a)(x - h)

That is,

y - 1 = +/-(6/2)(x - 2)

y - 1 = +/-3(x - 2)

y - 1 = +/-3x - 6

y = +/-3x - 6 + 1

y = +/- 3x - 5

Therefore, the equation of the asymptote is y = 3x - 5.

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From the calculation, we can see that /BC/ is 8 sin 35. Option D

We can see the image of the triangular piece of cloth as shown in the image. This shows that we have to approach the problem by the use of the trigonometric ratios.

Hence;

/AC/ = 8 in

/BC/ = x

<A = 35 degrees

Sin 35 = /BC//8

/BC/ = 8 sin 35

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Answer:

a

Step-by-step explanation:

the median is the middle value of the data arranged in ascending order

5 , 6 , 6 , 7 , 8 , 10 , 12 , 13 , 14 ← ascending order

                    ↑ middle value

median = 8

Answer:

8

Step-by-step explanation:

To find the median, we must put all of the data in order and select the middle number. Since there are 9 terms, the median will be the 5th term.

5, 6, 6, 7, 8, 10, 12, 13, 14

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