Given: △EIJ, k(O, r)
EI = EJ = r=10 cm
EP ⊥ IJ
Find: JP

Answer:

E

Step-by-step explanation:

The given expression is

5(2x-7)

In order to check the options we will have to simplify the expression so that we can match with the answers.

To simplify the expression , first we have to multiply the 5 written outside the bracket with the terms inside the bracket i.e. 2x -7

So,

=> 5(2x-7)

Multiplying 5 inside

=> (5)(2)x - (5)(7)

=> 10x - 35

So, comparing with the given options, we observe that option E is the correct answer..

Step 1: Order the numbers from least to greatest

112, 130, 142, 150, 178, 206

The two middle numbers are 142 and 150.

The number between 142 and 150 is 146.

The median weight is 146 pounds.

The median weight of the wrestlers is 146 pounds.

To find the median weight, we need to arrange the weights in ascending order and identify the middle value(s).

Arrange the weights in ascending order:

112, 130, 142, 150, 178, 206

Since there is an even number of weights (6), the median is the average of the 3rd and 4th weights.

The 3rd weight is 142, and the 4th weight is 150.

Calculate the median:

(142 + 150) / 2 = 292 / 2 = 146

Answer:

The numbers are 578 and 264

Step-by-step explanation:

Let

x-----> the greater number

y----> the smaller number

we know that

x+y=842 -----> equation A

x-y=314 -----> equation B

Adds equation A and equation B

x+y=842

x-y=314

------------

x+x=842+314

2x=1,156

x=578

Find the value of y

578+y=842

y=842-578=264

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&30\\ \theta =&35 \end{cases}\implies s=\cfrac{\pi (35)(30)}{180} \\\\\\ s=\cfrac{35\pi }{6}\implies s\approx 18.32596[/tex]

Answer: 18.33 inches

Step-by-step explanation:

A P E X

Data suitable for dot plots are quantitative and involve individual values. Options A), D), E), and F) can be graphed using dot plots because they involve numerical data where each dot represents an individual value. Options B) and C) involve categorical data, which are not typically displayed using dot plots.

A dot plot is a type of graphical display that uses dots to represent the frequency or distribution of data points along a number line. It is suitable for displaying quantitative data that consists of individual values. Let's analyze each option:

A) Time taken to complete a test:

Yes, this data could be graphed using a dot plot. Each dot would represent a student's time taken to complete the test, and the position of the dot along the number line would correspond to the time taken.

D) Number of cars in a household:

Yes, this data could also be graphed using a dot plot. Each dot would represent a household, and the position of the dot along the number line would correspond to the number of cars in that household.

E) Number of siblings:

Yes, the number of siblings could be graphed using a dot plot. Each dot would represent an individual, and the position of the dot along the number line would correspond to the number of siblings that individual has.

F) Distance driven to school:

Yes, this data could also be graphed using a dot plot. Each dot would represent a student, and the position of the dot along the number line would correspond to the distance driven to school by that student.

Options B) Favorite pet and C) Zip Code do not lend themselves well to dot plots. Favorite pet is a categorical variable, and dot plots are typically used for displaying quantitative data. Similarly, zip codes are categorical and do not have a natural numerical order suitable for a dot plot.

So, the data that could be graphed using a dot plot are A), D), E), and F). Each dot plot would display the distribution of values for the respective variables, providing a visual representation of the data's spread and concentration.

Complete question :- Which of the following data could be graphed using a dot plot? Select all that apply.

A) Time taken to complete a test

B) Favorite pet

C) Zip Code

D) Number of cars in a household

E) Number of siblings

F) Distance driven to school

Answer:A dot plot.

Step-by-step explanation: it shows the 5 number summary.

The correct answer is dot plot!

Answer:

The expected revenue of an airline ticket sold by this travel website is $408

Step-by-step explanation:

For the revenues per ticket we have;

airline A; 600

airline B; 360

For the probability of choosing the airlines we have;

airline A; 20% = 0.2

airline B; 80% = 0.8

Therefore, the expected revenue of an airline ticket sold by this travel website is;

600(0.2) + 360(0.8) = 408

Therefore, the expected revenue of an airline ticket sold by this travel website is $408

Answer:

$962.82 will be in John's account after 8 years if compounded semiannually.

Step-by-step explanation:

The formula used to find the amount after 8 years is:

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

Where A = future value

P= principal value

r = interest rate ( in decimals)

n = no of times interest is compounded

t = time

Putting the values:

P = $600

r = 6% = 0.06

n = 2

t = 8

A= 600 *(1+0.06/2) ^2(8)

A= 600 *(1.03) ^16

A =600*1.605

A = 962.82

So, $962.82 will be in John's account after 8 years if compounded semiannually.

Answer:

(x^5 - y)(x^5 + y)

Step-by-step explanation:

Answer:

Final answer is x=23.

Step-by-step explanation:

Given that m∠A = 60°, m∠B = (3x − 2)°, m∠C = (2x + 7)°

We know that sum of all three angles of a triangle equals 180 degree.

So we can write equation:

m∠A + m∠B + m∠C = 180°

60° +(3x − 2)° + (2x + 7)°  = 180°

60 +3x − 2 + 2x + 7  = 180

67 +5x − 2  = 180

65 +5x  = 180

5x  = 180 - 65

5x  = 115

[tex]x=\frac{115}{5}[/tex]

x=23

Hence final answer is x=23.

A. 34 square rooted

[tex]lm = \sqrt{34} [/tex]

Answer:

The vector will change in direction and decrease in magnitude

Step-by-step explanation:

Given:

vector multiplication by -π/4

-π/4= -0.785

Due to the negative sign "-", the, vector will change/reverse its direction.

And as of the magnitude, 0.785<1 hence the magnitude of vector will be decreased by this factor !

The period of the wave is this explanation: A group will 'modulate' the wave amplitude; it's like another long wave on top. So the first wave in a group is tiny, the next one is bigger and so on until you get the biggest one in the middle of the group. Then they get smaller again. The last one is tiny, so the biggest wave in the group is in the middle, and if there are 14 waves in a group, the seventh wave is the biggest.

Answer:

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

Step-by-step explanation:

Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230.

Step 1: P = 200, r = 5, t = 3

Step 2: I = 200*0.05* 3

Step 3: I = 30

Step 4: 30 + 200 = 230

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

Above it is given, that annual compound interest rate of 5%

So, she should have calculated using the compound interest formula.

[tex]A=p(1+r/n)^{nt}[/tex]

So, amount becomes :

[tex]A=200(1+0.05)^{3}[/tex]

[tex]A=200(1.05)^{3}[/tex] = $231.53.

Answer:

Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.

Step-by-step explanation:

Just did it

Answer:

The domain by the interval notation is (-∞ , 3)∪(3 , 4)∪(4 , ∞) ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the domain of the function

- The domain is all values of  x  that make the expression defined

- To find where the expression is undefined put the denominator

  equal 0, to get the values of x which make denominator equal to 0

- The domain will be all the real number except those values

* Now lets solve the problem

∵ f(x) = (x² - 9)/(x² - 7x + 12)

- Let the denominator x² − 7x + 12  equal to  0

∵ x² − 7x + 12 = 0 ⇒ factorize it

- Consider the form  x² + bx + c

- Find a pair of integers whose product is c and whose sum is b

- In this case, whose product is 12 and whose sum is −7

- They are -3 and -4

- Write the factored form using these integers.

∴ (x -3)(x - 4) = 0 ⇒ put each bracket = 0

∴ x - 3 = 0 or x - 4 = 0

∵ x - 3 = 0 ⇒ add 3 to both sides

∴ x = 3

∵ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

∴ The domain of f(x) is all real number except 3 and 4

* The domain by the interval notation is

 (-∞ , 3)∪(3 , 4)∪(4 , ∞)

Answer:

V≈1231.5in³

Step-by-step explanation:

ANSWER

[tex]Volume = 1231.5 {in}^{3} [/tex]

EXPLANATION

The volume of the cylinder is

EXPLANATION

The volume of a right cylinder is given by the formula:

[tex]Volume = \pi \: {r}^{2} h[/tex]

From the given information, the height of the cylinder is 2 inches and the base radius is 14 inches.

This implies that, r=14 inches and r=2 inches.

We plug in the values into the formula to get;

[tex]Volume = \pi \times {14}^{2} \times 2[/tex]

[tex]Volume = \pi \times 196 \times 2[/tex]

[tex]Volume =392 \pi [/tex]

[tex]Volume = 1231.5 {in}^{3} [/tex] to the nearest tenth.

Answer:

5 between Martin's place and the school

Step-by-step explanation:

I don't know if you can draw a diagram from by directions, but you can try. It will help you to see the problem.

Draw

Draw a line that looks like this on your paper.

<===============:

school         X        Martin's place

Now draw a line going upwards from the arrow head.

∧                 Haley's place.

|

|

|

|

|

|

<=============:

school       x      Martin's place

Label the distance from the school to Haley's place as 12

I can't draw a line between martin's place and Haley's but you can. Label it as 13

So the givens are

c = distance between Haley's place and Martin's = 13

b= distance from the school to Haley's is 12

a = ? Distance from Martin't and the school = x

Formula

c^2 = a^2 + b^2

Solution

13^2 = 12^2 + a^2

169 = 144 + a^2          Subtract 144 from both sides.

169 - 144 = 144 - 144 + a^2

25 = a^2

sqrt(25) = sqrt(a^2)

a = 5              

The distance from Martin's place to the school (a) is 5 units, determined using the Pythagorean theorem with given values of 12 units from the school to Haley's place (b) and 13 units between Haley's and Martin's places (c).

Distance from the school to Haley's place (b): 12

Distance between Haley's place and Martin's place (c): 13

Using the Pythagorean theorem:

c^2 = a^2 + b^2

Substitute the given values:

13^2 = a^2 + 12^2

Simplify the equation:

169 = a^2 + 144

Subtract 144 from both sides:

25 = a^2

Take the square root of both sides:

a = √25

Simplify:

a = 5

Therefore, the distance from Martin's place to the school (a) is 5 units.

Answer:

the first option is correct

Step-by-step explanation:

Two triangles: b ≈ 2.62 or 22.94

Answer:

sides are     a = 16                   c = 14             b =22.96

angles are   A = 43.39°           B = 99.61°        C = 37°

Step-by-step explanation:

using sine law of triangle,

[tex]\frac{sin A}{a} = \frac{Sin B}{b}= \frac{sinC}{c}[/tex]

using,

[tex]\frac{sin A}{a} = \frac{sinC}{c}[/tex]

given that,

C= 37°                 a = 16                   c = 14

now,

[tex]\frac{sin A}{16} = \frac{sin37^o}{14}[/tex]

sin A = 0.687

A = 43.39°

hence B = 180° - (43.39° + 37°)

           B = 99.61°

[tex]\frac{sin 43.39^o}{16} = \frac{sin99.61^o}{b}[/tex]

b = 22.96

Hence, there will be only one triangle which will form and there

sides are     a = 16                   c = 14             b =22.96

angles are   A = 43.39°           B = 99.61°        C = 37°

Answer: $54

Step-by-step explanation:

18% of $54 is $9.72

Answer:

Bill amount is $54

Step-by-step explanation:

Tip is a gratuity and amount of money which a customer gives for some specific services workers on the the work they performed. It is the additional amount to the original value of the service  

As per given data

Percentage of Tip = 18% = 0.18

Formula for Tip

Tip = Bill amount x Tip rate

$9.72 = Bill amount x 0.18

Bill amount = $9.72 / 0.18

Bill amount = $54

Answer:

2√2 / 3 (first answer choice)

Step-by-step explanation:

If tan Ф < 0, then Ф must be in either Quadrant II or Quadrant IV.

If sin Ф = +1/3, then Ф (for this problem) is in Quadrant II.

Remembering that sin Ф = opp / hyp = 1 / 3, we use the Pythagorean Theorem to find the adj side:

adj² + 1² = 3²,  or

adj² + 1 = 9, or    adj² = 8.  Since Ф is in Quadrant II, adj is negative.

The value of cos Ф = adj / hyp = √8 / 3 = 2√2 / 3

Answer:

Step-by-step explanation:

A. you: Number of sandwiches = .5 * time

friend: # of sandwiched = .5 * t + 5

B. Your friend makes 10 and you make 5

The equations y1=x/2 and y2=(x+10)/2 model the sandwich-making process, where y1 and y2 are the number of sandwiches you and your friend make respectively. In 20 minutes, you can make 10 sandwiches and your friend can make 15 sandwiches. The graphs of these equations are lines with the same slope, indicating the same rate of sandwich-making but different start times.

Let's define the variables first. Let's say x stands for time in minutes, and y1 and y2 stand for the number of sandwiches you and your friend make, respectively.

a) The equations modeling the number of sandwiches made as a function of time would be y1 = x/2 for you (since you make one sandwich in 2 minutes) and y2 = (x+10)/2 for your friend (since your friend starts 10 minutes earlier than you).

b) If x is 20 minutes: for you, replacing x in the equation y1 = x/2, we get the number of sandwiches you make (y1) is 20/2 = 10 sandwiches. For your friend, replacing x in the equation y2 = (x+10)/2, we get the number of sandwiches your friend makes (y2) is (20+10)/2 = 15 sandwiches.

c) In comparison, the graphs of the two equations are lines with the same slope (0.5), indicating the same sandwich-making rate. However, they have different y-intercepts, signifying that your friend started earlier and therefore made more sandwiches.

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Answer:

2

Step-by-step explanation:

The average rate of change of a function over the interval a to b is:

(f(b) − f(a)) / (b − a)

In this case:

(f(4) − f(0)) / (4 − 0)

(7 − -1) / 4

2

Answer:

The answer is 8

Step-by-step explanation:

count them

There are 8 data points plotted in the given scatterplot. The given scatterplot gives the relationship between the given variables.

The given graph is a scatterplot between two variables

The given plot shows the graph is increasing as the time increases. And in the graph, there are 8 data points.

Learn more about scatterplots here:

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To find the original amount of sugar in each cake recipe, we can set up a proportion and solve for x. The original amount of sugar in each cake recipe was 7/6 cups.

To solve this problem, we can use a proportion to find the original amount of sugar in each cake recipe. Let x represent the original amount of sugar in each cake recipe. We know that reducing the amount of sugar by 1/2 cup from 1 cake results in 4 cups of sugar for 6 cakes. So we can set up the proportion:

(x - 1/2) / 1 = 4 / 6

Cross-multiplying, we get (x - 1/2) * 6 = 4 * 1. Simplifying further, we have 6x - 3 = 4. Adding 3 to both sides, we get 6x = 7. Finally, dividing both sides by 6, we find that x = 7/6 cups of sugar.

Therefore, the original amount of sugar in each cake recipe was 7/6 cups.

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Answer:

x ≤ -4

Step-by-step explanation:

Less than or equal to ≤

x ≤ -4

Answer: Positively Skewed

Step-by-step explanation: I believe it looks to me like it's positively skewed. If you Google how negatively skewed and positively skewed distributions look like, I think it would help you. But hope this helped! :)

Answer: Symmetric

Step-by-step explanation:

For a box plot , a symmetric data set displays the median in the middle of the box.

Also, We know that a distribution is said to be skewed if it has longer whisker at one side than the other.

But in the given box plot , the median looks at the middle of the box.

Therefore, the given box-plot describes a symmetric distribution.

64 is the correct answer

Answer: [tex]A = 201.06\ in^2[/tex] or [tex]A = 64\pi\ in^2[/tex]

Step-by-step explanation:

The surface area of a sphere is calculated by the following formula

[tex]A = 4\pi r^2[/tex]

Where r is the radius of the sphere

In this case we know that the diameter d of the sphere is

[tex]d=8\ inches[/tex]

So the radius r is:

[tex]r=\frac{d}{2}\\\\r=\frac{8}{2}\\\\r=4\ inches[/tex]

So the surface area of the sphere is:

[tex]A = 4\pi (4)^2[/tex]

[tex]A = 64\pi[/tex]

[tex]A = 201.06\ in^2[/tex]

Answer:

51.34

Step-by-step explanation:

First, things first, identify the opposite, adjacent, and hypotenuse.

Since you are trying to find the value of x, the length measuring 4 is the adjacent because it is one of the lengths that creates that angle measure you are trying to find. 5 is the opposite because the angle is on the opposite side of the length. The [tex]\sqrt{41}[/tex] is the hypotenuse.

Now, which trig equation do you want to use?

sin(x) = opposite / hypotenuse

cos(x) = adjacent / hypotenuse

tan(x) = opposite / adjacent

Let's first try solving with sine.

sin(x) = 5/[tex]\sqrt{41}[/tex]

Since you want to find the angle, you have to use the [tex]sin^{-1} (\frac{5}{\sqrt{41}} )=x[/tex]

Plug it into your calculator, then you should get something like this: 51.34019175.

That is the angle measurement of x.

Let's use cosine.

cos(x) = 4/[tex]\sqrt{41}[/tex]

Again, since you want to find the angle, you have to use the [tex]cos^{-1} (\frac{4}{\sqrt{41}} )=x[/tex]

Plug it into your calculator, then you should get something like this: 51.34019175.

You realize that it gave the same answer, right? Yep, let's also do tangent.

tan(x) = 5/4

Again, since you want to find the angle, you have to use the [tex]tan^{-1}(\frac{5}{4}} )=x[/tex]

Type it into the calculator and you should get 51.34019175 again!

Area is defined as a product of sides when we talk about squares.

[tex]A=a\cdot a=20\cdot20=\boxed{400}[/tex]

The area of the front cover of notebook is 400 centimetres squared.

Hope this helps.

r3t40

Answer:

400 cm

Step-by-step explanation: