A wooden box in the shape of a rectangle prism has a diagonal with a length of 25 centimeters, as shown.

What is the length of DH ?

___ centimeters

Answer:

x = 2

Step-by-step explanation:

6 : 4 = 3 : x

x = 4 * 3 / 6

x = 4/2

x = 2

The value of x in the given figure is 2

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

Given that, Triangle ABC is dilated into A'B'C'

We know that dilated triangles are similar

Hence, their corresponding sides are in equal ratio,

BC : B'C' = AC : A'C'

6 : 4 = 3 : x

x = 4 × 3 / 6

x = 4/2

x = 2

Hence, The value of x in the given figure is 2

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The happening in the graph is that the speed of the roller skater increases and decreases with time

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following axes

x-axis = Time

y-axis = Speed

The x-axis is continually increasing while the y-axis decreases and increases (as in a sine function)

This means that the speed increases and decreases with time

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The rate of change in the profit for the five months earned by the given small business is $2750.

The rate of change explains the relationship between two quantities.

Consider two quantities such profit and time in a small business.

Then, the rate of change in the profit is calculated by the ratio of change in the profit for the particular period to the time. I.e.,

rate of change in the profit = (change in the profit)/time

or

r = (p2 - p1)/(t2 - t1)

Where p1 is the profit gained at time t1 and p2 is the profit gained at time t2.

Given that, a small business earns a profit of $6500 in January (the first month of the year) and $17,500 in May (the fifth month of the year).

So, here p1 = $6500; p2 = $17,500; t1 = 1; and t2 = 5

Then, the rate of change in the profit for this period is

r = (17,500 - 6500)/(5 - 1)

 = 11000/4

 = 2750

Therefore, the rate of change in the profit for the five months is $2750.

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Answer:

180

Step-by-step explanation:

xdcjuggggggggggggggggggggg

The rewritten summation is [tex]\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)[/tex].

A recursive function is a function that calculates subsequent terms by repeating or using its own prior terms, creating a succession of terms. By definition, the recursive function can be used to write the summation by separating the final term of the summation and adding a final term to the summation.

Given, the function is [tex]\sum_{m=1}^{n+1}m(m+1)[/tex].

First, we have to separate the final term from the given summation. The final term is m = n+1 which is present above the summation. For this replace the n+1 with n.

Then, add the term m(m+1) with m in the given summation replaced by n+1.

The new summation is rewritten as,

[tex]\begin{aligned}\sum_{m=1}^{n+1}&=\sum_{m=1}^{n}m(m+1)+(n+1)((n+1)+1)\\&=\sum_{m=1}^{n}m(m+1)+(n+1)(n+2)\end{aligned}[/tex]

The new summation is rewritten.

The complete question is -

Rewrite by separating off the final term [tex]\sum_{m=1}^{n+1}m(m+1)[/tex]

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Answer:

LOL

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

2 multiplied by 24 = 48

48 - 18 = 30

The solution to the inequality - 5.3 + x > 21 is x > 26.3

In mathematics, inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions. In other words, it is a relationship between two expressions or values that are not equal to each other. It is used generally used to compare two numbers on the number line by their size.

In order to solve the given inequality - 5.3 + x > 21, add 5.3 both sides.

- 5.3 + x + 5.3 > 21 + 5.3

x > 26.3

The solution means that the value of x is greater than 26.3. The solution is graphed on a number line.

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The inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{x}{4}-3[/tex] .

Option (A) is correct.

What is the inverse of a function?

The inverse of a function is a new function that "undoes" the original function. If f(x) is a function that takes in an input x and produces an output y, then the inverse function denoted as [tex]f^{-1}(x)[/tex], takes in an input y and produces an output x.

The inverse function of f(x) = 4x + 12 is denoted as [tex]f^{-1}(x)[/tex]. To find the inverse function, we can follow these steps:

Replace f(x) with y.

Interchange x and y.

Solve for y.

Following these steps, we get:

y = 4x + 12

x = 4y + 12

x - 12 = 4y

y = (x - 12)/4

Hence, the inverse function of f(x) = 4x + 12 is [tex]f^{-1}(x) = \frac{(x - 12)}{4}[/tex] = (x/4) - 3

Option (A) is correct.

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The probability that a child chosen at random from the class has both a cat and a dog is 1/10.

Suppose b is the total number of kids that have both:

• children having a cat Only must be 14 - b

• children having a dog Only must be 19 - b

We also get:

We also know there are 30 kids, therefore

⇒ (14 - b) + b + (19 - b) = 30

⇒ 33 - b = 30

⇒ b = 3

Consequently, we now understand:

3/30 = 1/10

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Answer:

75.

Step-by-step explanation:

We need to divide 375 by 5 since we are looking for 5 times a number. This will give us the answer, 75.

Answer:

75.

Step-by-step explanation:

We need to divide 375 by 5 since we are looking for 5 times a number. so the answer is 75

The system of equations plotted on the graph are -

y = (-3/5)x + 9

y = - (1/2)x - 12

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought

Given are two graphs as shown in the image.

The equation of line [1] can be written as -

y = {(9 - 0)/(0 - 15)}x + 9

y = (-9/15)x + 9

y = (-3/5)x + 9

The equation of line [2] can be written as -

y = {(12 - 0)/(0 + 24)}x - 12

y = - (1/2)x - 12

Therefore, the given system of equations is -

y = (-3/5)x + 9

y = - (1/2)x - 12

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Answer:

Step-by-step explanation:

57,555

Answer:5755

Step-by-step explanation: 40 X 3453 = 138,120

138,120 / 24 = 5755

Answer: 3a2b2+3a2b−6ab2+3ab

Step-by-step explanation:By simplifying,

6ab+2a2b+5a2b2−3ab−6ab2+a2b−2a2b2

= 3a2b2+3a2b−6ab2+3ab

Hope this help's You

On solving the provided question we can say that - as the probability the result will be either a red- or green-colorblind individual.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.

In the US, there are more males than women who are colorblind to red and green  = 0.07adults

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The solution to the equation |2 +1| = 10x is x = 3/10

From the question, we have the following parameters that can be used in our computation:

|2 +1| = 10x

Evaluate the sum in the above equation

So, we have the following representation

|3| = 10x

Remove the absolute bracket in the above equation

So, we have the following representation

3 = 10x

Divide both sides by 10

This gives

3/10 = x

Rewrite as

x = 3/10

Hence, the solution is 3/10

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Answer:

7/2 second

Step-by-step explanation:

The equation is: h= -2t²-9t+56

h = the height

We ask how many seconds the object will strike the ground. That means the h will be 0, and we have the equation!

0 = -2t^2 -9t + 56

First, we factor the equation and get

-(2t - 7) (t + 8) = 0

If any individual factor on the left side of the equation equals 0, the entire expression will be similar to 0. So we have the equations

2t - 7 = 0                    

t + 8 = 0

t = 7/2 and -8

Because a time can't be negative, so the answer is 7/2 second

So, the answer is in 7/2 seconds, the object will strike the ground.

.

The amount of calories you consume for the rest of the day is 1800

From the question, we have the following parameters that can be used in our computation:

Total amount of calories for a day = 2200 calories

Total amount of calories for one session = 400 calories

The above parameters can be represented as

Total amount of calories for one session + Total amount of calories for the end of the day = Total amount of calories for a day

Substitute the known values in the above equation, so, we have the following representation

400 + Total amount of calories for the end of the day = 2200

Evaluate the like terms

Total amount of calories for the end of the day = 2200 - 400

So, we have

Total amount of calories for the end of the day = 1800

Hence, the amount of calories is 1800

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The required mean as calculated from the given data is 13.

To calculate the mean x + y

mean of x + mean of y

= 5 + 8

=13

In addition to the mode and median, the mean is one of the measurements of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the

Standard Deviation

The indicator of dispersion is the standard deviation. It denotes how widely apart the data values are from the mean value.

Formula: σ=∑i=1nxi-μ2n

NOTE :

Complete question:

A random variable X has a mean of 5 and a st. dev of 0.40. A random variable Y has a mean of 8 and a st. dev of 0.60. If both are independent, what is the mean of X + Y?

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Answer:

  see the attachment

Step-by-step explanation:

You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).

The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.

The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.

The red and blue graphs are attached. The asymptotes are dashed lines.

Answer:

5.5 hours

Step-by-step explanation:

6, 12, 18

20, 18, 16, 14, 12, 10, 8, 6, 4, 2

The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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The height of the pyramid can be represented ,as per the given details as 3x.

The volume is 3/2 times 3 x 3, and the hexagon base's area is six times greater than the equilateral triangle's.

A pyramid's base edge's length is equal to x units.

In other words, the pyramid's height is three times as long as its base edge.

The pyramid's height is equal to 3x

A three-dimensional structure with a polygon at its base is referred to as a pyramid. You must be familiar with The Great Pyramid of Giza, which was built using a similar framework. This structure has a distinct shape because each corner is connected to a single apex.

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The final coordinates of the vertices of quadrilateral A'B'C'D';

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

The coordinates of the quadrilateral ABCD are;

A(-3, 4)

B(-7, -3)

C(-3, -7)

D(-4, -3)

Now, the first sequence of transformation is reflection across the y-axis. Now, the transformation rule for reflection across the y-axis is;

(x, y) → (−x, y) .

Thus, we now have;

A'(3, 4)

B'(7, -3)

C'(3, -7)

D'(4, -3)

It is now translated 9 units left and as such the transformation rule is;

((x + 9), y)

We now have;

A'(12, 4)

B'(16, -3)

C'(12, -7)

D'(13, -3)

It is now translated 5 units up and as such, the final coordinates are;

A''(12, 9)

B''(16, 2)

C''(12, -2)

D''(13, 2)

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Answer:

since a || b

<A = <ABb = 60°

in a triangle the sum of all angles is 180°

so,

30 + 60 + x = 180

x= 180-90

x= 90

The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.

It is given that, an investor invested $2300 in two mutual funds.

Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.

So, we can write the equation for the total investment is

x + y = 2300 ...(1)

The percentage of profit earned from the fund1 = 6% = 0.06

The percentage of profit earned from the fund2 = 4% = 0.04

The total profit for the investor = $102

Then, the equation from this statement is

0.06x + 0.04y = 102 ...(2)

Then the system of equations is

x + y = 2300 ...(1)

0.06x + 0.04y = 102 ...(2)

Applying the substitution method to solve the obtained system of equations.

So, from (1), we can write x = 2300 - y

Then, equation (2) becomes

0.06(2300 - y) + 0.04y = 102

⇒ 6(2300 - y) + 4y = 10200

⇒ 13800 - 6y + 4y = 10200

⇒ 13800 - 2y = 10200

⇒ 2y = 13800 - 10200 = 3600

∴ y = 3600/2 = $1800

So, the value of x is x = 2300 - 1800 = $500

Thus, the amount of investment in two mutual funds is $500 and $1800.

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Option D. parallelogram is the correct option of the given statement.

The parallelogram is a quadrilateral with two sets of opposing sides that are equally and parallel. The opposing angles are also equal in magnitude.

Four sides, four vertices, and four angles make up a quadrilateral, which is a two-dimensional shape. Concave and convex are the two most common forms. Additionally, there are numerous subgroups of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombus, and squares.

The significance of quadrilaterals Creating floor plans for new buildings, as well as engineering and designing buildings and spaces, all rely on the properties and mathematical rules regulating the geometric shape known as a quadrilateral.

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Answer:

[tex]\left[\begin{array}{cc}x&y\\1&5\\2&7\\3&9\end{array}\right][/tex]

Step-by-step explanation:

Note that f(x) is typically used in replacement of y. So in reality, to make the question simple to understand, we will replace f(x) with y.

y = 2x + 3

Remember to follow PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

You are finding a table of value, which results in something similar to:

[tex]\left[\begin{array}{cc}x&y\\1&5\\2&7\\3&9\end{array}\right][/tex]

Proof 1:

Plug in 1 for x in the given equation:

y = 2x + 3

y = 2(1) + 3

y = 2 + 3

y = 5

Proof 2:

Plug in 2 for x in the given equation:

y = 2x + 3

y = 2(2) + 3

y = 4 + 3

y = 7

Proof 3:

Plug in 3 for x in the given equation:

y = 2(3) + 3

y = 6 + 3

y = 9

~

Do this for as much values as you need.

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When testing individual cofficients of a Multiple regression model, i.e y = β + β₁x₁ + β₂x₂ + ---+βₖxₖ + ε where β , β₁ , --- , βₖ are regression cofficients

the sampling distribution is tested by hypothesis testing.

Testing the Regression Coefficients:

An individual regression coefficient, if we want to test if there is a relationship between the dependent variable and the independent variable.

for the test and identify the significance level α.

The p-value is the sum of the area in the tails of the t -distribution. The t-score and degrees of freedom are t , df = n−k−1

Compare the p-value to the significance level and state the outcome of the test:

The results of the sample data are significant. There is sufficient evidence to conclude that the null hypothesis H₀ is an incorrect belief and that the alternative hypothesis. Hₐ is most likely correct.

The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis Hₐ may be correct.

Write down a concluding sentence specific to the context of the question.

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