The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter. The cost of every mirror is proportional to the cube of the mirror's radius. What is the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors? Express your answer as a common fraction

Answers

Answer 1

Answer: 1:5

Step-by-step explanation:

Given: The cost of every mirror is proportional to the cube of the mirror's radius.

i.e. [tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}[/tex]

Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.

Then,

[tex]\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}[/tex]

The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:

[tex]\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}[/tex]

Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .


Related Questions

Provide an appropriate response. At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a random sample of 12 of the freshmen, a random sample of 9 of the sophomores, a random sample of 11 of the juniors, and a random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example.

Answers

Answer: Stratified Sampling

Step-by-step explanation: Stratified Sampling involves creating subdivisions of the population such that each subdivisions is seen as a subgroup or smaller chunk of the population which is split based on certain criteria or attribute. The stratified random sampling may be employed in delineating certain characteristics or to investigate further how a feature or characteristics vary between one subdivision to the other.

In the scenario above, the researcher made use of the stratified sampling by performing a random sampling selection of its subjects based on the different subdivisions of students available in the college

Convert the following to Slope-Intercept Form: 4x – 3y = 24.

Answers

The answer is 2x it should be

The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4x – 3y = 24

Convert the equation from standard form to slope-intercept form. Then we have

4x – 3y = 24

3y = 4x - 24

y = (4/3)x - 24 / 3

y = (4/3)x - 8

The equation 4x – 3y = 24 can be represented in the slope-intercept form will be y = (4/3)x - 8.

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A square has side length x and a triangle has a base (3x - 2) and height (2x + 4). At what value of x will the two figures have the same area?
Show work and explain all steps.

Answers

Answer:

0.73

Step-by-step explanation:

Data obtained from the question include the following:

Length (L) of square = x

Base (b) of triangle = (3x – 2)

Height (h) of triangle = (2x + 4)

Area of square = L²

Area of square = x²

Area of triangle = ½bh

Area of triangle = ½(3x – 2) (2x + 4)

Expand

½ [3x(2x + 4) –2(2x + 4)]

½[6x² + 12x – 4x – 8]

½[6x² + 8x – 8]

3x² + 4x – 4

Area of triangle = 3x² + 4x – 4

Now, to find the value of x which makes the area of the two figures the same, we simply equate both areas as shown below:

Area of triangle = area of square

Area of triangle = 3x² + 4x – 4

Area of square = x²

Area of triangle = area of square

3x² + 4x – 4 = x²

Rearrange

3x² – x² + 4x – 4 = 0

2x² + 4x – 4 = 0

Solving by formula method

a = 2, b = 4, c = –4

x = – b ± √(b² – 4ac) / 2a

x = – 4 ± √(4² – 4×2×–4) / 2×2

x = – 4 ± √(16 + 32) / 4

x = – 4 ± √(48) / 4

x = (– 4 ± 6.93)4

x = (– 4 + 6.93)4 or (– 4 – 6.93)4

x = 0.73 or –2.73

Since the measurement can not be negative, the value of x is 0.73.

Could someone give a quick response to the second question? i'd appreciate it.
Given that €1 = £0.75
a. How much is €530 in £?
b. What is the £ to € exchange rate?
Hint: It can be helpful to think of it like this: if €1 = £0.75, then €100 = £75 Now work out what £1 is worth.

Answers

Answer:

Hey I know!

1.10 euro

Answer:

397.5 :)

Step-by-step explanation:

Dora bought a bottle of nail polish that was marked down by 20 percent from its original price of $4.50. Including a 9 percent sales tax, what is the final cost of the bottle of nail polish?

Answers

Answer:3.82

Step-by-step explanation: Find 80% of 4.50 (4.50 x 0.8=3.60) then find 6% of 3.6 (0.06 x 3.6= 0.216) add 0.216 + 3.6= 3.816 but in money you have to round so the answer is 3.82

Answer:

1.8

Step-by-step explanation:

$4.50-%20=3.6

3.6- %9=1.8

Pleas answer this question now

Answers

Answer:

[tex]x = 17[/tex]

Step-by-step explanation:

According to the two tangent theory, tangent MN and tangent NP, which are both from point N, are congruent.

That is, [tex]x + 4 = 21[/tex]

Solve for x

[tex]x + 4 = 21[/tex]

Subtract 4 from both sides

[tex]x + 4 - 4 = 21 - 4[/tex]

[tex]x = 17[/tex]

Which statement(s) is(are) true about cones? Statement 1: A cone has a triangular base. Statement 2: A cone is 3 times larger than a cylinder with the same height and radius. Statement 3: A cone is one-third the size of a cylinder with the same height and radius. Statement 4: A cone has a circular base.

Answers

Answer:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

Step-by-step explanation:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

The true statement is:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

What is Cone?

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top . A cone has one face . There are no edges for a cone.

Properties of Cone

A cone is a shape that has a curved surface and a circular base. The following properties of a cone help us identify it easily. They are as follows.A base of a cone is circular.There is one face, one vertices, and no edges for a cone.The slant height of a cone is the length of the line segment joining the of the cone to any point on the circumference of the base of the cone.A cone have circular base at a perpendicular distance is called a right circular cone.A cone have  circular base is an oblique cone.

As, from the properties of cone we can say that.

A cone is one-third the size of a cylinder with the same height and radius. and, : A cone has a circular base..

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MATH HELP ME ASAP!!!!

Answers

Answer:

You get 12$ per B and 15$ per A.  Thus, the answer is A) $282

Step-by-step explanation:

4A+4B=108

Divide by 4

A+B=27

Subtract B

A = 27 - B

3A+5B=105

Substitution

3(27-B)+5B = 105

Distribute

81-3B+5B=105

Combine like terms

81+2B=105

Subtract 81

2B=24

Divide by 2

B = 12

A = 15

14(15)+6(12)=x

210+72=x

282=x

Hope it helps <3

Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages

Answers

Answer:

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Step-by-step explanation:

Let the present age of Devi be x years.

Therefore, mother's present age = 3x

Five years ago:

Devi's age = (x - 5) years

Mother's age =( 3x - 5) years

According to the given condition:

Five years ago:

Devi's mother's age = 4 times Devi's age

3x - 5 = 4( x - 5)

3x - 5 = 4x - 20

20 - 5 = 4x - 3x

15 = x

x = 15 years

3x = 3* 15 = 45 years

Hence,

Devi's present age = 15 years

Devi's Mother's present age = 45 years

Determine whether the study is an observational study or an experiment.
Research is conducted to determine if there is a relation between hearing loss and exposure to mumps. Does the description correspond to an observational study or an​ experiment?

Answers

Answer: Observational study

Researchers are observing those with mumps to see how it affects hearing loss at all. There may be strong correlation, weak correlation, or no correlation at all.

With an experiment, researchers would break the participants into two groups: control group and treatment group. Those in the control group get the placebo (fake treatment) while the treatment group gets the treatment applied to them. If we were dealing with an experiment for this context, then the treatment group would get exposed to mumps on purpose. Of course, this is unethical and dangerous so an experiment for this type of project is not a good idea. It's better to go with an observational study.

Find the value.
X3-4 when x=3
PLEASE HELP!!! ASAP!!!

Answers

Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

[tex]x^3 - 4[/tex]

[tex](3)^3 - 4[/tex]

step 2 - solve the exponent

[tex](3)^3 - 4[/tex]

[tex]27 - 4[/tex]

step 3 - subtract

[tex]27 - 4[/tex]

[tex]23[/tex]

therefore, the value of the expression is 23.

The governor of state A earns $53,745 more than the governor of state B. If the total of their salaries is $289,405, find the salaries of each.

Answers

Answer:

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Step-by-step explanation:

If the governor of state A's salary is "x" and the governor of state B's salary is "y", then:

[tex]x = y + 53,745[/tex]

If the total of their salaries is $289,405, then the sum of x and y should be equal to that number.

[tex]x + y = 289,405\\[/tex]

Applying the first expression on the second allows us to solve for y as shown below.

[tex]y + 53745 + y = 289405\\2y = 289405 - 53745\\2y = 235660\\y = 117830[/tex]

Using this data on the first expression allows us to solve for the first governo's salary.

[tex]x = 117830 + 53745 = 171575[/tex]

The salary of the governor of state A is $171,575 and the salary of the governor of state B is $117,830.

Select the correct answer.
What is the justification for step 2 in the solution process?

10x − 25 − 3x = 4x − 1
Step 1: 7x − 25 = 4x − 1
Step 2: 7x = 4x + 24
A.
the multiplication property of equality
B.
the division property of equality
C.
the addition property of equality
D.
the subtraction property of equality

Answers

Answer:

The answer is C addition property of equality.

Step-by-step explanation:

In step 1, 7x − 25 = 4x − 1 there are the numbers -25 and -1

In step 2, 7x = 4x + 24 The -25 is removed and -1 is replaced with 24

Meaning that in step 2 25 was added to those numbers meaning the answer C addition property of equality.

Answer:

C

Step-by-step explanation:

If alpha and beta are the angles in the first quadrant tan alpha = 1/7 and sin beta =1/ root 10 then usind the formula sin (A +B) = sin A. CosB + sina. CosB find the value of alpha + 2beta​

Answers

Answer:

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Step-by-step explanation:

[tex]\alpha \text{ and } \beta \text{ in Quadrant I}[/tex]

[tex]$\tan(\alpha)=\frac{1}{7} \text{ and } \sin(\beta)=\frac{1}{\sqrt{10}}=\frac{\sqrt{10} }{10} $[/tex]

Using Pythagorean Identities:

[tex]\boxed{\sin^2(\theta)+\cos^2(\theta)=1} \text{ and } \boxed{1+\tan^2(\theta)=\sec^2(\theta)}[/tex]

[tex]$\left(\frac{\sqrt{10} }{10} \right)^2+\cos^2(\beta)=1 \Longrightarrow \cos(\beta)=\sqrt{1-\frac{10}{100}} =\sqrt{\frac{90}{100}}=\frac{3\sqrt{10}}{10}$[/tex]

[tex]\text{Note: } \cos(\beta) \text{ is positive because the angle is in the first qudrant}[/tex]

[tex]$1+\left(\frac{1 }{7} \right)^2=\frac{1}{\cos^2(\alpha)} \Longrightarrow 1+\frac{1}{49}=\frac{1}{\cos^2(\alpha)} \Longrightarrow \frac{50}{49} =\frac{1}{\cos^2(\alpha)} $[/tex]

[tex]$\Longrightarrow \frac{49}{50}=\cos^2(\alpha) \Longrightarrow \cos(\alpha)=\sqrt{\frac{49}{50} } =\frac{7\sqrt{2}}{10}$[/tex]

[tex]\text{Now let's find }\sin(\alpha)[/tex]

[tex]$\sin^2(\alpha)+\left(\frac{7\sqrt{2} }{10}\right)^2=1 \Longrightarrow \sin^2(\alpha) +\frac{49}{50}=1 \Longrightarrow \sin(\alpha)=\sqrt{1-\frac{49}{50}} = \frac{\sqrt{2}}{10}$[/tex]

The sum Identity is:

[tex]\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)[/tex]

I will just follow what the question asks.

[tex]\text{Find the value of }\alpha+2\beta[/tex]

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]\text{I will first calculate }\cos(2\beta)[/tex]

[tex]$\cos(2\beta)=\frac{1-\tan^2(\beta)}{1+\tan^2(\beta)} =\frac{1-(\frac{1}{7})^2 }{1+(\frac{1}{7})^2}=\frac{24}{25}$[/tex]

[tex]\text{Now }\sin(2\beta)[/tex]

[tex]$\sin(2\beta)=2\sin(\beta)\cos(\beta)=2 \cdot \frac{\sqrt{10} }{10}\cdot \frac{3\sqrt{10} }{10} = \frac{3}{5} $[/tex]

Now we can perform the sum identity:

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]$\sin(\alpha + 2\beta)=\frac{\sqrt{2}}{10}\cdot \frac{24}{25} +\frac{3}{5} \cdot \frac{7\sqrt{2} }{10} = \frac{129\sqrt{2}}{250}$[/tex]

But we are not done yet! You want

[tex]\alpha + 2\beta[/tex] and not [tex]\sin(\alpha + 2\beta)[/tex]

You actually want the

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Answer:

ok bye guy................

Solve the system of equations algebraically.

{Y=(x-2)^2+2
{Y+4=3x

Answers

Answer:

(5, 11) and (2, 2)

Step-by-step explanation:

y = (x-2)² + 2

y + 4 = 3x

(x-2)² + 2 + 4 = 3x

x² - 4x + 4 + 6 = 3x

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

x - 5 = 0, x = 5

x - 2 = 0, x = 2

y = (5-2)² + 2 = 11

(5, 11)

y = (2-2)² + 2 = 2

(2, 2)

Answer:

[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We want to solve this system of equations.

[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]

This is equivalent to (subtract 4 from the second equation).

[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]

Then, we can write y = y, meaning:

[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]

[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]

For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)

So the solutions are (2,2) and (5,11)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Please help I’m being timed!!! When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population. What is the significance of 160,000 in the function? A) the maximum population of the city B) the expected population in 5 years C) the initial population at the time of the estimation D) the amount of increase in the population in 5 years

Answers

The correct answer is C) The initial population at the time of the estimation

Explanation:

A mathematical function represents the relationship between two variables by showing how one increases or decreases as the other changes. In the case presented, the variables are the time in years represented by x and the population represented by f (x). In this context, the value 160.000 in column f(x) represents the population on the year 0, this means the current population or initial population when the function or estimation is created. On the other hand, other values represent the population in the future, for example, the value 173189 represents the population in 4 years.

Answer:

yes the 3ed answer in correct on ENG 2022

PLEASE ASWER FASTThe x-intercept of the equation 2y – x = -6 is: 3. -3. 6. None of these choices are correct.

Answers

Answer:

6

Step-by-step explanation:

Well first we need to tfraph the following equation,

2y - x = -6

Look at the image below

Thus,

by looking at the graph we can tell that the x-intercept is 6.

Hope this helps :)

Answer:

x -intercept = 6

Step-by-step explanation:

Method 1

[tex]2y -x = -6\\Let ; y =0\\2(0) -x =-6\\-x =-6\\x = 6\\\\ (6 , 0 )[/tex]

Method 2

[tex]x - interept = -c/a\\a = -1\\b =2\\c = 6\\\\x - intercept =\frac{ -(6)}{-1} \\\\x - intercept = 6[/tex]

to solve the equation 3 x + 1 = 4 x + (negative 4)

Answers

Answer:

x=5

Step-by-step explanation:

3x+1 = 4x -4

Subtract 3x from each side

3x+1-3x = 4x-3x-4

1 = x-4

add 4 to each side

1+4 = x-4+4

5 =x

Answer: x=5

Step-by-step explanation:

3x+1=4x+(-4)

3x+1=4x-4

3x+5=4x

5=x

which set of steps will translate f(x)=6x to g(x)=6x-5-7

Answers

THIS IS THE COMPLETE QUESTION BELOW;

Which set of steps will translate f(x) = 6x to g(x) = 6x – 5 – 7?

Shift f(x) = 6x five units to the left and seven units up.

Shift f(x) = 6x five units to the right and seven units down.

Shift f(x) = 6x seven units to the right and five units up.

Shift f(x) = 6x seven units to the left and five units down.

Answer:

Shift f(x)=6x five units to the left and seven units down.

Step-by-step explanation:

We are told to translate the function below

f(x) = 6x to g(x) = 6x – 5 – 7

Which means the process to translate f(x) into g(x) is required.

According to the translation rule

f(x)-------->f(x)+a

If a<0 it shift to downward

If a>0 it shift to upward

Then we have

(X,y) ----->((x - 5, y)

There is a shift by x coordinates towards left by 5 units

then we would have the function as

f'(x) = 6(x-5)

Following the translation rule there is a shift by the function by 7 units downward direction then we have

(x,y) ----->(x,y -7)

Then we have g(x) = 6x – 5 – 7 as our translation product.

Therefore, shift f(x)=6x five units to the left and seven units down.

PLZZZZZZ HELP I NEED IT I AM GOING TO FAIL PLZZZZ I AM COUNTING ON YOU For which situations is it appropriate to use a sample? Select three options. A. What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck? B. What is the average number of rainbows each year in Honolulu? C. How many pedestrians would use a walkway built over a busy road? D. How many police cars are equipped with computers? E. What is the most popular car color in the teachers’ parking lot?

Answers

Answer:

b-What is the average number of rainbows each year in Honolulu?

c-How many pedestrians would use a walkway built over a busy road?

d-How many police cars are equipped with computers?

this is the answer

Step-by-step explanation:

E D G E N U I T Y

The situations it is appropriate to use a sample:

B. What is the average number of rainbows each year in Honolulu?

C. How many pedestrians would use a walkway built over a busy road?

D. How many police cars are equipped with computers?

What is a simple sample technique?

Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method.  The sample is chosen by a random method as every subject in the sample is assigned a number.

Why do we use sampling techniques?

Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searchinh people and collecting data from them.

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HALLLLPPP Let g(x) = 2x and h(x) = x^2 + 4. Evaluate each expression: g(-2) - h(4)

Answers

Answer:

-24

Step-by-step explanation:

g(-2) = 2(-2)

g(-2) = -4

h(4) = 4² + 4

h(4) = 16 + 4

h(4) = 20

g(-2) - h(4)

-4 - 20

= -24

Answer:

g(-2) - h(4) = - 24

Step-by-step explanation:

g(x) = 2x

To find g( -2) substitute - 2 into g(x)

That's

g( -2) = 2(-2) = - 4

h(x) = x² + 4

To find h(4) substitute 4 into h(x)

That's

h(4) = (4)² + 4 = 16 + 4 = 20

So

g(-2) - h(4) is

- 4 - 20

= - 24

Hope this helps you

g(x)= √x+3 help plsss

Answers

Answer:

All real values of x such that x ≥-3

Step-by-step explanation:

g(x) = sqrt(x+3)

A sqrt must be greater than or equal to zero

sqrt (x+3) ≥ 0

Square each side

x+3≥ 0

Subtract 3 from each side

x ≥-3

The restrictions on x are x ≥-3

That means the domain is x ≥-3

All real values of x such that x ≥-3

Answer:

[tex]\boxed{\mathrm{B}}[/tex]

Step-by-step explanation:

[tex]g(x)=\sqrt{x+3}[/tex]

A square root must have a value of greater than or equal to 0.

[tex]\sqrt{x+3}\geq 0[/tex]

Square both sides.

[tex]x+3\geq 0[/tex]

Subtract 3 from both sides.

[tex]x\geq -3[/tex]

How much will Bob need to save each month if he wants to buy a $30,000 car with cash in 5 years? He can earn a nominal interest rate of 10% compounded monthly.

a) $2.50
b) $250.00
c) $25.00
d) $1,862.76​

Answers

Answer:

B

Step-by-step explanation:

C is too little and D is too much

Help..... please math

Answers

Answer:

Ones: 91

Hundredths: 91.20

Step-by-step explanation:

All numbers that comprises the digits, 91.20, have place value.

The 9 in the digit has a place value of tens, i.e. 9*10 = 90.

The 1 has a place value of one's, i.e. 1*1 = 1

The 2, after the decimal point to the right, has a place value of tenth, i.e. 1*10-¹ = ⅒ = 0.1

While the zero has a place value of hundredth.

Therefore, the digits, in the ones place = 91

In the hundredths place = 91.20

Instructions: Find the measure of the indicated angle to the
nearest degree

Answers

Answer:

? = 33

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan ? = opp / adj

tan ? = 13/20

Take the inverse tan of each side

tan ^-1 tan ? = tan ^-1 ( 13/20)

? = 33.02386756

To the nearest degree

? = 33

Answer:

33.

Step-by-step explanation:

inverse tan (13/20) = 33.023867579302

evaluate sine squared theta for theta equals 45 degrees ​

Answers

sin(45), or sin(pi/4) = sqrt(2)/2. So sin^2(45)= (sqrt(2)/2)^2, which is 1/2.

please help me. I will love u forever if u do <333

Answers

Answer:

61% is a reasonable choice

Step-by-step explanation:

The probability of a strike is 79% or 0.79

=> Independently, the probability of 2 consecutive strikes:

P = 0.79 x 0.79 = 0.6241 ~ 61%

HELP

A twelve-sided die with sides labeled 1 through 12 will be rolled once. Each number is equally likely to be rolled.
What is the probability of rolling a number less than 9?
Write your answer as a fraction in simplest form.

Answers

Answer:

3/4

Step-by-step explanation:

Answer:  2/3

Explanation:

List out the total number of outcomes = {1,2,3,4,5,6,7,8,9,10,11,12}

We have 12 items in this list.

From this list, highlight the outcomes that are less than 9. So we will have this smaller list of {1,2,3,4,5,6,7,8} which has 8 items in it.

There are 8 ways to get what we want (a number less than 9) out of 12 outcomes total

The probability is therefore 8/12 = 2/3

PLZ HELP ME NEED THIS FAST WILL GIVE BRAINLIEST

Answers

Answer: l = 60 ft and w = 30 ft

P = 2(l + w)

180 = 2(l + w)

Let x = width of his yard

Let 2x = length of his yard

[tex]180=2(2x+x)[/tex]

[tex]\frac{180}{2}=\frac{2(2x+x)}{2}[/tex]

[tex]90=3x[/tex]

[tex]\frac{90}{3} =\frac{3x}{3}[/tex]

[tex]x=30ft[/tex]

l = 2x = 30(2) = 60 ft

Check:

180 = 2(l + w)

180 = 2(60 + 30)

180 = 2(90)

180 = 180

LS = RS

solve the systems by the addition method x - 2y = - 4 2x + y = 7

Answers

x - 2y = -42x + y = 7

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, if we add these two equations together right away, nothing

will cancel so we need to set things up so a variable will cancel.

Notice that we have an 2x in our second equation.

If we had a -2x in our first equation, then the x's would cancel out.

In order to create a -2x in the first equation, we simply

multiply both sides of the first equation by -2.

So we have (-2)(x - 2y) = (-4)(-2) which can be rewritten as -2x + 4y = 8.

Now rewrite both equations, as shown below.

-2x + 4y = 82x + y = 7

Now when we add the equations together, the x terms

will cancel out and we're left with 5y = 15.

Dividing both sides by 5, y = 3.

To solve for x, plug a 3 in for y in either one of our 2 original equations.

So let's go with our second equation.

Plugging a 3 in for y, we get 2x + (3) = 7.

Now subtract 4 from both sides to get 2x = 4.

Dividing both sides by 2, we fid that x = 2.

Since x = 2 and y = 3, our answer is the ordered pair (2, 3).

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