Hi, can you help me to evaluate (if possible) thesix trigonometric functions of the real number.Please.

Answers

Answer 1

Okay, here we have this:

Considering the provided angle, we are going to evaluate the trigonometric functions, so we obtain the following:

Sine:

[tex]\begin{gathered} \sin (-\frac{2\pi}{3}) \\ =-\sin (\frac{2\pi}{3}) \\ =-\cos \mleft(\frac{\pi}{2}-\frac{2\pi}{3}\mright) \\ =-\cos \mleft(-\frac{\pi}{6}\mright) \\ =-\cos \mleft(\frac{\pi}{6}\mright) \\ =-\frac{\sqrt{3}}{2} \end{gathered}[/tex]

Cos:

[tex]\begin{gathered} cos\mleft(-\frac{2\pi}{3}\mright) \\ =\cos \mleft(\frac{2\pi}{3}\mright) \\ =\sin \mleft(\frac{\pi}{2}-\frac{2\pi}{3}\mright) \\ =\sin \mleft(-\frac{\pi}{6}\mright) \\ =-\sin \mleft(\frac{\pi}{6}\mright) \\ =-\frac{1}{2} \end{gathered}[/tex]

Tan:

[tex]\begin{gathered} tan\mleft(-\frac{2\pi\:}{3}\mright) \\ =\frac{\sin (-\frac{2\pi\: }{3})}{\cos (-\frac{2\pi\: }{3})} \\ =\frac{-\frac{\sqrt[]{3}}{2}}{-\frac{1}{2}} \\ =\sqrt[]{3} \end{gathered}[/tex]

Csc:

[tex]\begin{gathered} \csc \mleft(-\frac{2\pi}{3}\mright) \\ =\frac{1}{\sin\left(-\frac{2\pi}{3}\right)} \\ =-\frac{1}{\frac{\sqrt{3}}{2}} \\ =-\frac{2\sqrt{3}}{3} \end{gathered}[/tex]

Sec:

[tex]\begin{gathered} \sec \mleft(-\frac{2\pi}{3}\mright) \\ =\frac{1}{\cos\left(-\frac{2\pi}{3}\right)} \\ =\frac{1}{-\frac{1}{2}} \\ =-2 \end{gathered}[/tex]

Cot:

[tex]\begin{gathered} \cot \mleft(-\frac{2\pi}{3}\mright) \\ =\frac{1}{\tan (-\frac{2\pi}{3})} \\ =\frac{1}{\sqrt[]{3}} \\ =\frac{\sqrt{3}}{3} \end{gathered}[/tex]

Related Questions

The slant height and the base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?

Answers

The most appropriate choice for cone and total surface area of cone will be given by-

Total surface area of the cone is [tex]198235.71 cm^2[/tex]

What is cone and total surface area of cone?

Cone is a 3 dimensional figure whose base is a circle and upper surface finally converge to a point.

Cone is obtained by revolving a right angled triangle about one of its legs.

Total surface area of the cone is the sum of curved surface area of the cone and the area of the base of the cone.

If r is the radius of the base of the cone and l is the slant height of the cone, then total surface area of the cone will be given by

[tex]\pi r(r+l)[/tex]

Here

Ratio of the slant height and radius of base of the cone = 2:1

Radius = 145cm

Slant height = [tex]145 \times 2[/tex]

= 290 cm

Total surface area of cone = [tex]\pi r(r+l)\\[/tex]

= [tex]\frac{22}{7} \times 145\times (145+290)\\[/tex]

= [tex]\frac{22}{7} \times 145 \times 435[/tex]

= [tex]198235.71 cm^2[/tex]

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Complete Question

The slant height and the radius of base of the cone are in the ratio 2:1. If the radius of the cone is 145cm. What is the total surface area of the cone?

A person invests $6,750 in an account that earns 5.25% annual interest compounded continuously. Findwhen the value of the investment reaches $15,000. If necessary round to the nearest tenth.The investment will be reach $15,000 in approximatelyyears.

Answers

[tex]\begin{gathered} \text{Given} \\ A=15000 \\ P=6750 \\ r=5.25\%\rightarrow0.0525 \end{gathered}[/tex]

Recall the formula for the Future value of a principal amount, compounded continuously.

[tex]\begin{gathered} A=Pe^{rt} \\ \text{where} \\ A\text{ is the Future Value} \\ P\text{ is the Principal amount} \\ r\text{ is the rate in decimals} \\ t\text{ is time in years} \end{gathered}[/tex]

Rearrange the equation so that we can solve for time t.

[tex]\begin{gathered} A=Pe^{rt}^{} \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=e^{rt} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt\ln e^{}=\ln \mleft(\frac{A}{P}\mright) \\ rt^{}=\ln \mleft(\frac{A}{P}\mright) \\ \frac{rt}{r}=\frac{\ln (\frac{A}{P})}{r} \\ t=\frac{\ln(\frac{A}{P})}{r} \end{gathered}[/tex]

Now substitute the following given and we have

[tex]\begin{gathered} t=\frac{\ln(\frac{A}{P})}{r} \\ t=\frac{\ln (\frac{15000}{6750})}{0.0525} \\ t=\frac{\ln (\frac{20}{9})}{0.0525} \\ t=15.2096704\text{ years} \end{gathered}[/tex]

Rounding the answer to the nearest tenth, the investment will reach $15000, in approximately 15.2 years.

Fill in the blank to correctly complete the sentence.
Consider the following function.
f(x)
=
2x4+6x3−4x2+2x+12
=
x−2)2x3+10x2+16x+34+80
By inspection, we can state that f(2)=

Answers

The value of f(2) would be 80 which is determined by substituting the value of x = 2in the given function f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80.

What is a function?

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The given function below is:

f(x) = 2x⁴ + 6x³ −4x² +2x + 12

f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80

We have to determine the value of f(2).

⇒ f(x) = (x −2)(2x³ + 10x² + 16x + 34) + 80

Substitute the value of x = 2 in the given function,

⇒ f(x) = (2 −2)(2(2)³ + 10(2)² + 16(2) + 34) + 80

⇒ f(x) = (0)(2(2)³ + 10(2)² + 16(2) + 34) + 80

⇒ f(x) = 0 + 80

⇒ f(x) = 80

Therefore, the value of f(2) would be 80.

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A cyclist rides her bike at a rate of 8 miles per hour. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 2 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers. Rate:km/hDistance traveled in 2 hours:km

Answers

Given:

1 mile = 1.6 km

So, 8 miles per hour in kilometers per hour is given by:

[tex]\frac{1}{8}=\frac{1.6}{x}[/tex]

Where x = # of kilometers

So, solve for x:

[tex]\begin{gathered} x\cdot1=1.6\cdot8 \\ x=12.8 \end{gathered}[/tex]

This is 12.8 km per hour

Next, the distance traveled in 2 hours is:

[tex]rate=\frac{distance}{time}\rightarrow distance=rate\times time[/tex]

Substitute the values:

[tex]distance=12.8\times2=25.6[/tex]

Answer:

Rate: 12.8 km/h

Distance traveled in 2 hours: 25.6 km

a student measures which method of taking notes improves grades more, using a computer or a pencil and paper. what type of study is described?Sample StudyExperiment Observational Study Cluster Study

Answers

Since the student is meausuring something we conclude that this is an experiment.

9m^2 - 49factor each expression. Be sure to check for the greatest common factor first.

Answers

We need to factor the following polynomial:

[tex]9m^2-49[/tex]

We can see that:

[tex]9m^2=3^2m^2=(3m)^2[/tex]

And

[tex]49=7^2[/tex]

Then, we can use the following factor rule:

[tex]x^2-y^2=(x-y)(x+y)[/tex]

We have that:

[tex]x=3m,y=7[/tex]

Then, we can factor the polynomial as follows:

[tex]9m^2-49=(3m)^2-(7)^2=(3m-7)(3m+7)[/tex]

In summary, we have:

[tex]9m^2-49=(3m-7)(3m+7)[/tex]

PLS HELP ME WITH THIS QUESTION ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

The value of (x) will be equal to → x = 16 - K.

What is the perimeter?

Perimeter is the measure of the length of the boundary of any two dimensional shape.

Given is a quadrilateral with its sides given.

The perimeter of this quadrilateral will be the sum of the length of its sides. Since, in the question, the final value of perimeter is not given, therefore we will assume it as K. The perimeter will be equal to -

(7x - 1) + (- 8x - 5x) + (6x + 13) + (4 - x) = K

7x - 1 - 8x - 5x + 6x + 13 + 4 - x = K

16 - x = K

x = 16 - K

Therefore, the value of (x) will be equal to → x = 16 - K.

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HELP ASAP Determine the values of x in the equation x2 = 81.

x = −9
x = ±9
x = ±40.5
x = 40.5

Answers

The value of x in the given quadratic equation are; +9 and -9.

What is a quadratic equation?

A quadratic equation is the second-order degree algebraic expression in a variable. An equation of degree 2 containing a single variable is known as the quadratic equation. Its general form is ax² + bx + c = 0 , where variables are x and constants are a, b, and c.

As equation is x²= 81

Taking square root on both sides;

⇒ √x² = √81

⇒ X = ± 9

Thus the value of X is ± 9

Hence, The roots of the given quadratic equation are; +9 and -9.

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I'll give brainliest!

Answers

Answer:

=1/1024

Step-by-step explanation:

4^-5

=1/4^5

=1/1024

Rate as brainliest

Answer. =1/1024.

Here is it step-by-step:
4^-5
=1/4^5
and 1/1=1024

Determine the continuity at x = 2. Be sure to clearly state your reasoning. fastest answer get ranked brainliest

Answers

The answer is in my screenshot pic.

2 PointsMULTIPLE CHOICEQuestion 42: PracticeWhich statements are true for the decimals 0.04 and 0.004?Choose two correct answers.in Base TenA0.04 is 10 times as much as 0.004.B.0.04 is 100 times as much as 0.004.Etice Solvingс0.004 is 10 the amount of 0.04.uizD0.004 is 100 the amount of 0.04

Answers

From the question;

we are given the decimal numbers

[tex]0.04\text{ and 0.004}[/tex]

If we consider dividing 0.04 by 0.004 we will have

[tex]\frac{0.04}{0.004}=10[/tex]

Therefore, 0.04 is 10 times as much as 0.004

Also, if we consider dividing 0.004 by 0.04 we will get

[tex]\frac{0.004}{0.04}=0.1=\frac{1}{10}[/tex]

Therefore, 0.004 is 1/10 the amount of 0.04

Hence

Given the decimals 0.04 and 0.004 we have

1. 0.04 is 10 times as much as 0.004

2. 0.004 is 1/10 the amount of 0.04

The tree diagram represents an experiment consisting of two trials
What is P(A)

Answers

The value of probability P(A) is 0.60

How to determine the probability?

The clear tree diagram is added as an attachment

The given parameters from the tree diagram are:

Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7

The probability is calculated using the following probability formula

P(A) = P(A and D) + P(A and C)

Substitute the known values in the above equation

P(A) = 0.6 * 0.7 + 0.6 * 0.3

Evaluate the products

P(A) = 0.42 + 0.18

Evaluate the sum

P(A) = 0.60

Hence, the value is 0.60

Answers

We are told that 11 mg of Achromycin per patient pound must be administered, we are also given the weight of the patient as 34 kg, in order to properly use this weight we must convert it from kg to pounds by multiplying the weight in kg by 2.2, like this:

34×2.2 = 74.8

Then, the patient weight is 74.8 lbs, by multiplying this by the 11 mg per pound of Achromycin that have to be administered we can determine the mg of Achromycin, like this:

74.8×11 = 822.8

Then, 822.8 mg of Achromycin has to be administered, by dividing this amount by 4, we can determine the amount for each dose:

822.8/4 = 205.7

Then 205.7 mg are given per dose, since 5 mL contains 125 mg, we can take the ratio of mL to mg to get:

5/125 = 1/25

By multiplying the above ratio by 205.7 we can determine the milliliters that should be given per dose, like this:

205.7×1/25 = 8.2

Then, 8.2 mL must be given per dose

Can someone pls help me find the equation for the arithmetic sequence and help me fill out the graph

Answers

Solution

- The question gives us the following arithmetic sequence:

[tex]t(n+1)=t(n)-4[/tex]

- We are asked to write out the explicit function for the sequence.

- To do this, we simply write out the terms of the sequence. After this, we would determine the common difference of the sequence.

- We will use the common difference to find the first term of the sequence and then use the formula below to find the explicit form of the arithmetic sequence:

[tex]\begin{gathered} t(m)=a+(m-1)d \\ \text{where,} \\ a=\text{first term of the sequence} \\ d=\text{common difference} \\ m=\text{ number of terms} \\ \\ (\text{Note that: }m=n+1\text{, since the formula starts assumes that the sequence starts from the 1st term not zeroth term} \end{gathered}[/tex]

- We have been given that the second term of the sequence is 10. We would also use this term to form our sequence.

[tex]\begin{gathered} \text{Let n=2} \\ \text{The formula becomes} \\ t(2+1)=t(2)-4 \\ t(3)=t(2)-4 \\ \\ \text{But we know that }t(2)=10 \\ \therefore t(3)=10-4 \\ t(3)=6 \\ \\ \text{Let n=3} \\ t(3+1)=t(3)-4 \\ t(4)=6-4 \\ t(4)=2 \\ \\ \text{Let n=4} \\ t(4+1)=t(4)-4 \\ t(5)=2-4 \\ t(5)=-2 \\ \\ \text{Thus, we can write out the terms of the sequence as follows:} \\ \ldots,t(2),t(3),t(4),t(5),\ldots=\ldots10,6,2,-2\ldots \\ \\ \text{ We can observe that the common difference is -4 since,} \\ 6-10=-4 \\ 2-6=-4 \\ -2-2=-4 \\ \text{And so on}\ldots \\ \\ \text{Thus, we can trace our sequence back to its first term as follows:} \\ t(2)-t(1)=-4 \\ 10-t(1)=-4 \\ \text{Subtract 10 from both sides} \\ -t(1)=-4-10 \\ \therefore t(1)=14 \\ \\ t(1)-t(0)=-4 \\ 14-t(0)=-4 \\ \text{Subtract 14 from both sides} \\ -t(0)=-4-14=-18 \\ \therefore t(0)=18. \\ \\ \text{Thus, the first term }t(0)=18 \end{gathered}[/tex]

- Let us now apply the formula for the nth term of a sequence to find the explicit formula:

[tex]\begin{gathered} first\text{ term =}t(0)=a=18 \\ \text{common difference}=d=-4 \\ t(m)=a+(m-1)d \\ \\ t(m)=18+(m-1)(-4) \\ \text{Expand the bracket} \\ t(m)=18+m(-4)-1(-4) \\ t(m)=18-4m+4 \\ \\ \therefore t(m)=22-4m \\ \\ \text{Let us write the sequence in terms of n} \\ m=n+1 \\ t(n)=22-4(n+1) \\ t(n)=22-4n-4 \\ t(n)=18-4n \\ \\ \text{Thus, the explicit function is:} \\ t(n)=18-4n \end{gathered}[/tex]

- With the above formula, we can proceed to populate the table. Let us use the formula to calculate all the terms for each value of n.

[tex]\begin{gathered} t(n)=18-4n \\ \\ \text{when n = 0} \\ t(0)=18-4(0) \\ t(0)=18 \\ \\ \text{when n= 1} \\ t(1)=18-4(1) \\ t(1)=14 \\ \\ \text{when n=2} \\ t(2)=18-4(2) \\ t(2)=10 \\ \\ \text{when n = 3} \\ t(3)=18-4(3) \\ t(3)=18-12=6 \\ \\ \text{when n = 4} \\ t(4)=18-4(4) \\ t(4)=2 \\ \\ \text{when n = 5} \\ t(5)=18-4(5) \\ t(5)=-2 \end{gathered}[/tex]

- On the table, we have the values filled in below:

Final Answer

The explicit form of the sequence is:

[tex]t(n)=18-4n[/tex]

it’s 6%86 gainsborough she

Luna brought all her savings with her to Rome, in euros. For the first week, she spent the same amount of money each day. The table shows how much Luna had left at the end of each day. What was the initial value of Luna's savings? Day Euros ? 315 1 2 280 3 245 4 210 5 175 6 140 7 105 35 euros 315 euros 80 euros 350 euros

Answers

every day she spent $35, if after 1 day she still have $315, the day before that she had $315+$35=$350

Therefore, the initial value was $350

a crew can clear 1/2 ton of dirt in 30 minutes. how many tons can they clear in 4 hours

Answers

Answer: 4 tons

Step-by-step explanation:

Since the crew can clear 1/2 ton in 30 minutes, 4 hours has eight 30 minutes, which means that 8x1/2 = 4

Answer: 4 tons

Step-by-step explanation:

30 minutes multiplied by 2 is 1 hour and 1 half times 2 is 1 ton, so the crew can clear one ton every hour. 4 hours times 1 ton is 4 tons an hour.

which number is a rational number?A. √3B. √36C. √7D. π

Answers

We have to identify the rational number.

Any number that can be expressed as a fraction is a rational number.

In this case the options are:

A. The square root of 3. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.

B. The square root of 36, unlike the square root of 3, does have a rational solution: 6. So the square root of 36 is a rational number.

C. The square root of 7. This does not have a solution with finite number of decimals, so it can not be expressed as a fraction. Then, it is not rational.

D. The number π has an infinite number of decimals, so it can not be represented as a fraction. Thn, it is not a rational number.

nswer: O√36 [ption B]

determine the answer to the nearest tenth of a percent.12 out of 52 cards in a deck are face cards.What percentage of cards in a deck are face cards?

Answers

Total number of cards: 52

Number of face cards: 12

To calculate the percentage that the face cards represent we need to divide the number of face cards by the total number of cars, and then multiply by 100%:

[tex]\frac{12}{52}\times100[/tex]

The first division 12/52 will give us the proportion that the face cards represent, and by multiplying that by 100 we find the percentage.

Solving the operations:

-solving the division

[tex]0.2308\times100[/tex]

-solving the multiplication:

[tex]23.08[/tex]

The face cards represent 23.08%.

Rounding to the nearest tenth of a percent (one decimal place):

[tex]\approx23.1[/tex]

Answer: 23.1%

6.Landscaping Calculate the area (in square feet) of a flower garden shaped like a circularsector with radius 60 ft and central angle 40 degrees.

Answers

The area of the circular sector is given as:

[tex]\begin{gathered} \text{Area}=\frac{\theta}{360}\times\pi r^2 \\ \end{gathered}[/tex]

Given that, radius= 60ft and angle =40 degrees

[tex]\begin{gathered} \text{Area}=\frac{40}{360}\times3.14\times60\times60 \\ \text{Area}=\frac{452160}{360} \\ \text{Area}=1256\text{square f}eet \end{gathered}[/tex]

What percent of 90 is 200?

Answers

45.00% because the total answers count 200- its 100% so we get to divide 1% value divide 200 by 100 to get 2.00 next calculate the percentage of 90: divide 90 by 1% value(2.00) and you get 45.00%

The entire graph of the function g is shown in the figure below.
Write the domain and range of g using interval notation.
(a) domain=
(b) range =

Answers

Domain = -5 (< or =) X (< or =) 3
Range = -3 (< or =) Y (< or =) 5

Use the inverse trigonometric keyson a calculator to find the measureof angle A

Answers

ANSWER

A = 51°

EXPLANATION

ABC is a right triangle. We know the length of the hypotenuse, AB = 44 m, and the length of the adjacent leg to angle A, AC = 28 m. To find the measure of angle A we have to use the cosine of that angle,

[tex]\cos A=\frac{AC}{AB}[/tex]

Solving for A,

[tex]A=\cos^{-1}\left(\frac{AC}{AB}\right)[/tex]

Replace with the known values and solve,

[tex]A=\cos^{-1}\left(\frac{28}{44}\right)=\cos^{-1}\left(\frac{7}{11}\right)\approx50.4788\degree\approx51\degree[/tex]

Hence, the measure of angle A is 51°, rounded to the nearest whole number.

Real world compositionsShoe sizes are marked differently in many countries. In Japan, a shoe size is 16 more than the size in the United States. In Korea, a shoe size is 224 more than the size in Japan. Determine the function of the U.S. size of a shoe in terms of the shoe size in Korea. What is the U.S. shoe size of a shoe that is 250 in Korea? Solve using composite functions

Answers

To solve this exercise, we define the following variables:

• j = Japan size of shoes,

• u = United Sates size of shoes,

• k = Korea size of shoes.

From the statement of the problem, we know that:

0. In Japan, shoe size is 16 more than the size in the United States →, j = 16 + u,,

1. In Korea, shoe size is 224 more than the size in Japan →, k = 224 + j.

We must find a function for the U.S. size of a shoe (u) in terms of the shoe size in Korea (k).

1) From point 1, we have:

[tex]\begin{gathered} j=16+u, \\ u=j-16. \end{gathered}[/tex]

2) From point 2, we have:

[tex]\begin{gathered} k=224+j, \\ j=k-224. \end{gathered}[/tex]

Replacing the expression of j in terms of k in the expression of u, we get:

[tex]u=j-16=(k-224)-16=k-240.[/tex]

Replacing the value k = 250 in the last equation, we get:

[tex]u=250-240=10.[/tex]

Answer

The U.S. shoe size of a shoe that is 250 in Korea is equal to 10.

Under his cell phone plan, Deion pays a flat cost of $39 per month and $4 per gigabyte. He wants to keep his bill at $49.40 per month. How many gigabytes of data can he use while staying within his budget?

Answers

Answer:

(49.4 - 39) / 4

= 10.4 / 4

= 2.6GB

Step-by-step explanation:

What is the equation of the
line that goes through
(-1, 3) and is perpendicular
to y = 4x - 7?

Answers

Answer:

Step-by-step explanation:Perpendicular lines have a slope that is the negative reciprocal of the given line.

For example, if a given line has the slope 3/2, the the perpendicular line would have the slope -2/3.

For the given line: y = 4x - 7, the perpendicular line would have a slope of -1/4

There isn't enough info in the question to determine the y-intercept. Literally, any y-intercept could work and the line would still be perpendicular. Is the line supposed to pass through a certain point?

Your answer would be something like: y = -1/4 x + b

b is the y-intercept...if your question paper is multiple choice, choose the answer with the slope of -1/4. If it's supposed to pass through a certain point (x,y) replace x and y with the values in that point and solve for b to get the y-intercept.

I need this answered From my prep guid, pre calc

Answers

Given:

The equation of the ellipse is,

[tex]\frac{(x-2)^2}{36}+\frac{(y+3)^2}{12}=1[/tex]

Explanation:

The general equation of ellipse with center (h,k) is,

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

The center of te given ellipse is (2,-3).

Determine the value of a and b.

[tex]\begin{gathered} a=\sqrt[]{36} \\ =6 \end{gathered}[/tex][tex]\begin{gathered} b=\sqrt[]{12} \\ =2\sqrt[]{3} \end{gathered}[/tex]

The value of a is more than b. so major axis is horiontal and minor axis is vertical.

The coordinates of endpoints of major axis are,

[tex](2+6,3)=(8,-3)[/tex]

and

[tex](2-6,3)=(-4,-3)[/tex]

The coordinates of endpoints of minor axis,

[tex](2,-3+2\sqrt[]{3})[/tex]

and

[tex](2,-3-2\sqrt[]{3})[/tex]

or we can expressed coordinates of endpoints of minor axis as,

[tex](2,-3\pm2\sqrt[]{3})[/tex]

Look Ahead To find the new temperature, you found the sum of a positive anda negative integer. You can use a number line to help you think about addinga. During the day, the temperature at another weather station is 4°C. Overnight,it changes by-9°C Enrico models the situation on the number line below.Hasina says she can model it with one arrow. How can she model the situationLook Back whalHow do you know?positive and negative numbers.with just one arrow?434520 1-3 -2 -1

Answers

Let's begin by listing out the information given to us:

How do scatter plots and histograms differ from line graphs?
None of the above
All three are used synonymously
Scatter plots and histograms show trends, or how data changes over time while line
graphs show how data is distributed.
Scatter plots and histograms show how data is distributed while line graphs show
trends, or how data changes over time.

Answers

Answer: Scatter plots, to show relationships among numerical variables. Line graphs, to show change over time. Histograms, to show data distributions.

Step-by-step explanation: I looked it up

The sales tax in Arizona is 7.5%. The price tag on a T-shirt in Arizona says $11.50. What is the sales tax, in dollars, for this item?

Answers

Answer:

$0.8625

Explanation:

The sales tax for the t-shirt will be 7.5% of the price. So, 7.5% of $11.50 can be calculated as:

[tex]\text{ \$11.50 }\times\text{ 7.5\% = 11.50}\times\frac{7.5}{100}=\text{ \$0.8625}[/tex]

So, the sales tax for this item is $0.8625

The tape diagram represents the ratio of your monthly allowance to your friend's monthly allowance. The monthly allowances total $72.How much is each allowance?
you [][][][][]
friend[][][][]

Answers

The allowance of each person is

You: $40Friend: $32

How to determine the amount of each person's allowance?

From the question, the tape diagram that can be used in our computation is given as

you [][][][][]

friend[][][][]

Counting the number of boxes, we have

You = 5

Friend = 4

Next, we represent the boxes as a ratio

So, we have

You : Friend = 5 : 4

This means that

You = 5/9 * Total allowance

Friend = 4/9 * Total allowance

From the question, we have

Total allowance = $72

Substitute the known values in the above equation

So, we have the following equation

You = 5/9 * 72

Friend = 4/9 * 72

Evaluate the products

You = 40

Friend = 32

Hence, the amount of each person's allowance is $40 and $32, respectively