solve for r.
4(r+15)+4r=300

Answer:

Step-by-step explanation:

the magnitude of ∠DGF= ∠BAD (alternate angles)

∴the magnitude of ∠DGF=40°

∠ FDG=∠ADB(VERTICALLY OPP. ANGLES)

∠FDG= 180-(90+40)

          = 50°

by using the Pythagoras' theorem

FD²+2²= 4²

FD²= 12

FD= 2√3

Answer:

(7x + 5) (7x+5)

Step-by-step explanation:

Hope this helps

Answer:

complementary angles, x=19

Step-by-step explanation:

since the two parts of the angle add up to 90, they are complementary angles.

you can find x by adding them and setting it equal to 90:

3x-2+2x-3 = 90

5x-5 = 90

5x = 95

x = 19

The sοlutiοns tο the inequality are x values greater than 5.

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.

-6x - 5 < 10 - x and -6x + 15 < 10 - 5x are cοrrect representatiοns οf the inequality –3(2x – 5) < 5(2 – x).

Tο sοlve the inequality -3(2x - 5) < 5(2 - x), we can start by distributing the negative 3 and the pοsitive 5 οn the right side:

-6x + 15 < 10 - 5x

Then, we can simplify by mοving all the x terms tο οne side and all the cοnstant terms tο the οther side:

-x < -5

Finally, we can divide bοth sides by -1, remembering tο reverse the inequality sign:

x > 5

Therefοre, the sοlutiοns tο the inequality are x values greater than 5. The representatiοns οf this sοlutiοn οn a number line are:

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at 5 and a bοld line starts at 5 and is pοinting tο the right.

A number line frοm negative 3 tο 3 in increments οf 1. An οpen circle is at negative 5 and a bοld line starts at negative 5 and is pοinting tο the left.

Hοwever, οnly the first representatiοn is cοrrect, since the secοnd representatiοn shοws the sοlutiοns tο x < -5, which is the οppοsite inequality tο the οne we fοund.

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Answer:

there both similar by using inverse operations to isolate the variable term by using addition or subtraction and multiplying or dividing to solve for the variable .

the difference is for an inequality if u multiply or divide by a negative number then u have to reverse the inequality symbol, for regular equations u don't have to do that , and for regular equations there is a equal sign and not a inequality symbol

Step-by-step explanation:

just explained it above

hope I helped ! pls mark me brainlest if I got it right thanks :)

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

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

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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Answer:

y=x+1

Step-by-step explanation:

Answer:

C= 54.O4

.................

Answer:

a_n = 47 - 8n

Step-by-step explanation:

a_1 = 39

a_2 = 31

a_3 = 23

31 - 39 = -8

23 - 31 = -8

This is an arithmetic sequence with constant difference -8.

a_1 = 39

a_2 = 39 - 8

a_3 = 39 - 8 - 8 = 39 - 2(8)

a_4 = 39 - 8 - 8 - 8 = 39 - 3(8)

...

a_n = 39 - (n - 1)(8)

a_n = 39 - 8(n - 1)

a_n = 39 - 8n + 8

a_n = 47 - 8n

Answer:

\(a_n=47-8n\)

Step-by-step explanation:

Given sequence:

Calculate the differences between the terms:

\(39 \underset{-8}{\longrightarrow} 31 \underset{-8}{\longrightarrow} 23\)

As the differences are constant (the same), this is an arithmetic sequence with:

\(\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\end{minipage}}\)

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

\(\implies a_n=39+(n-1)(-8)\)

\(\implies a_n=39-8n+8\)

\(\implies a_n=47-8n\)

Answer:

? what i never learned this is school

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

1 x 7/6 x 6/7 = 1

A scale factor of 6/7 would shrink the dilated figure back to its original size.

To return the dilated figure back to its original size, you would need to use a scale factor that is the reciprocal of the original dilation scale factor. The reciprocal of a fraction is obtained by flipping the numerator and denominator.

Given the original dilation scale factor of 7/6, the scale factor that would shrink the dilated figure back to the original size is:

Reciprocal of 7/6 = (6/7)

So, using a scale factor of 6/7 would shrink the dilated figure back to its original size.

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A scatter plot visually represents the relationship between two variables. It shows a positive correlation between the number of books read per month and SAT Verbal Test scores, with the equation y = 6.4828x + 520.6962.

A scatter plot is a graphical representation of a set of data that allows the observer to observe the relationship between two variables. It is used to graphically display how one variable is affected by the other. It is a chart of data points plotted on a two-dimensional graph with one variable represented on the X-axis and the other variable on the Y-axis.

Scatter Plot of the Data: From the data provided by the Language Arts department, we can create the scatter plot as shown below:
Equation of the line of best fit: The line of best fit is a straight line that is used to model the relationship between the two variables. It is determined by minimizing the sum of the squares of the differences between the observed values and the predicted values.

From the scatter plot, we can see that there is a positive correlation between the number of books read per month and the score on the SAT Verbal Test. This suggests that the more books a student reads per month, the higher their score on the SAT Verbal Test.

The equation of the line of best fit for the given data set is y = 6.4828x + 520.6962. Here, y represents the score on the SAT Verbal Test and x represents the number of books read per month.

To find the equation of the line of best fit, we can use a regression analysis tool such as Excel. The regression analysis will give us the values of the slope and intercept of the line of best fit, which we can use to write the equation of the line.

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Answer:

49.5

Step-by-step explanation:

area of triangle = (b x h) / 2

9 x 11 = 99

99 / 2 = 49.5

Hope this helps!

- profparis

Answer: A translation 1 unit to the left

Step-by-step explanation:

See attached image.

To find y, you can follow the steps:

Step 1: Substitute x by -1/6 in the equation.

Step 2: Solve the equation.

Answer : y = -6.

Answer:

1.78f

Step-by-step explanation:

7/4=1.78 and then you add f

hello

the answer to the question is:

therefore there will be 1024 cells after 10 divisions

Answer:

0.23

Step-by-step explanation:

A formula I like to use to find the answer to these types of questions is

\(\frac{828}{3600} =\frac{x}{100}\)

first, multiply 828×100=82,800

now divide 82800÷3600=23

so your answer is 23%=\(\frac{23}{100}\)=0.23

\((7 \times {10}^{5} ) + (2 \times {10}^{2} )\)

\((7 \times 100000) \div (2 \div 100)\)

\( \frac{700000}{200} = \frac{3500 \times 200}{200} = 3500\)

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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The number 'n' is equal to 14

In the question, we have been given that the number n is equal to 7 more than half of the number 'n'.

So in these linear equation-solving types of problems, first of all, we convert the written sentence into an equation.

So the equation for the following problem statement is -

n = 7 + n/2  

{since we have been given the number equals 7 more than half of the number }

Solving the equation we have,

n = 14.

We can easily see that 14 is the number which is 7 more than half of itself.

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On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

a) 0.8088 = 80.88% probability that there are at most 2 typos on a page.

b) 0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.

c) 0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.

d) 0.717 = 71.7% probability that there is at least one page with no typos in a 5-page paper.

e) 0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.

Step-by-step explanation:

Poisson distribution:

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

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The number of typos made by a student follows Poisson distribution with the rate of 1.5 typos per page.

This means that \(\mu = 1.5n\), in which n is the number of pages.

(a) Find the probability that there are at most 2 typos on a page.

One page, which means that \(\mu = 1.5\)

This is

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.5}*(1.5)^{0}}{(0)!} = 0.2231\)

\(P(X = 1) = \frac{e^{-1.5}*(1.5)^{1}}{(1)!} = 0.3347\)

\(P(X = 2) = \frac{e^{-1.5}*(1.5)^{2}}{(2)!} = 0.2510\)

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2231 + 0.3347 + 0.2510 = 0.8088\)

0.8088 = 80.88% probability that there are at most 2 typos on a page.

(b) Find the probability that there are exactly 10 typos in a 5-page paper.

5 pages, which means that \(n = 5, \mu = 5(1.5) = 7.5\).

This is P(X = 10). So

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 10) = \frac{e^{-7.5}*(7.5)^{10}}{(10)!} = 0.0858\)

0.0858 = 8.58% probability that there are exactly 10 typos in a 5-page paper.

(c) Find the probability that there are exactly 2 typos on each page in a 5-page paper.

Two typos on a page: 0.2510 probability.

Two typos on each of the 5 pages: (0.251)^5 = 0.001

0.001 = 0.1% probability that there are exactly 2 typos on each page in a 5-page paper.

(d) Find the probability that there is at least one page with no typos in a 5-page paper.

0.2231 probability that a page has no typo, so 1 - 0.2231 = 0.7769 probability that there is at least one typo in a page.

(0.7769)^5 = 0.283 probability that every page has at least one typo.

1 - 0.283 = 0.717 probability that there is at least one page with no typos in a 5-page paper.

(e) Find the probability that there are exactly two pages with no typos in a 5-page paper.

Here, we use the binomial distribution.

0.2231 probability that a page has no typo, so \(p = 0.02231\)

5 pages, so \(n = 5\)

We want P(X = 2). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 2) = C_{5,2}.(0.2231)^{2}.(0.7769)^{3} = 0.2334\)

0.2334 = 23.34% probability that there are exactly two pages with no typos in a 5-page paper.

Answer: A. The number is a sample statistic because it is a numerical description of all of the passengers that survived.

Step-by-step explanation:

A population is simply similar items or events that a researcher or an experimenter is interested and wants to carry out an experiment on.

A statistic is simply referred to as the piece of information gotten from the population while a sample statistic is the piece of statistical information which a researcher will be able to get from the statistic.

In this scenario, the number is a sample statistic because it is a numerical description of all of the passengers that survived.

I do not understand what do you mean

Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)