Marlena must answer three out of eight essay questions on her writing test. How many ways can she choose 3

Answer:

1. f(x)=x+7

2. f(x)=1.2x

Step-by-step explanation:

1. If f(x+5)=x+12, then substitute

[tex]t=x+5\Rightarrow x=t-5[/tex]

Hence,

[tex]f(t)=(t-5)+12\\ \\f(t)=t+7[/tex]

Now change t into x:

[tex]f(x)=x+7[/tex]

2. If f(x-5)=1.2x-6, then substitute

[tex]t=x-5\Rightarrow x=t+5[/tex]

Hence,

[tex]f(t)=1.2(t+5)-6\\ \\f(t)=1.2t+6-6\\ \\f(t)=1.2t[/tex]

Now change t into x:

[tex]f(x)=1.2x[/tex]

Answer:

3n

Step-by-step explanation:

Answer:

x = 13.7

Step-by-step explanation:

Sin = Opp./Hypo.

so

Sin (17) = x / 47

x = sin (17) * 47

x = 0.2924 * 47

x = 13.7

Answer:

A) −3x + y = 3

B) 2x − y = −1  Adding both equations:

-x = 2

x = -2  y = -3

Step-by-step explanation:

Answer:

D). (-2, -3)

x = -2  y = -3

Step-by-step explanation:

Answer:

  160 in³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base and h is the height. Filling in the given numbers, you have ...

  V = (20 in²)(8 in) = 160 in³

The volume of the prism is 160 cubic inches.

Final answer:

The volume of a right pentagonal prism can be found by multiplying the base area by the height of the prism. In this case, the volume is 160 cubic inches.

Explanation:

To find the volume of a right pentagonal prism, we need to multiply the area of the base by the height of the prism. In this case, the area of the base is 20 square inches and the altitude (height) is 8 inches. So, the volume can be found by multiplying 20 by 8.

Volume = Base Area x Height

Volume = 20 square inches x 8 inches = 160 cubic inches

Therefore, the volume of prism is 160 cubic inchinches

Answer:

Answer (a):

distance traveled per revolution = 1.5 feet

Answer (b):

slope = 1.5 feet per revolution

Step-by-step explanation:

We have been given a graph which shows number of revolutions v/s distance traveled in feet.

Answer (a):

Now we need to find about how far does Miguel travel per revolution. That means find distance traveled in 1 revolution.

From graph we see that 10 revolution corresponds to 15 feet.

then 1 revolution = 15/10 = 1.5 feet

hence final answer is 1.5 feet.

Answer (b):

slope means [change in y-value] / [change in x-value]

From graph we see that 10 revolution corresponds to 15 feet.

then slope = 15/10 = 1.5 feet per revolution

Answer a is 1.5 and so is b

There are 3 times as many females as males in a maths course, giving a ratio of 3:1. The fraction of the course that is female is therefore 3/(3+1), simplifying to 3/4.

If there are three times as many females as males in the course, this implies a ratio of females to males of 3:1, which means for every 3 females, there's one male. However, we're interested in the fraction of the course that is female, so we're looking at the fraction of total participants (females + males) that are female.

To get this, we add females and males together to get the total number of participants. There are 3 'parts' females and 1 'part' males, for a total of 4 parts. Each 'part' represents a group of students, so the total number of students is divided into 4 equal parts.

The fraction of the maths course that are females is therefore the number of parts that are female (3) over the total number of parts (4). So the fraction is 3/4.

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Answer:

  Eighty percent of the recipes in a cookbook require salt.

Step-by-step explanation:

The above statistic describes the entire population of recipes in the cookbook. It is not projecting anything about the population based on a sample.

The total number of buckets of fish walruses were fed each day is

A = 35/3 buckets or 11 2/3 buckets

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of buckets of fish walruses were fed each day be = A

Now , the equation will be

The number of buckets of fish dolphins were fed each day = 2 1/3 buckets

The value 2 1/3 = 7/3 buckets

And ,

The number of buckets of fish walruses were fed each day = 5 x number of buckets of fish dolphins were fed each day

Substituting the values in the equation , we get

The number of buckets of fish walruses were fed each day = 5 x 7/3

The number of buckets of fish walruses were fed each day = 35/3 buckets

Number of buckets of fish walruses were fed each day = 11 2/3 buckets

Therefore , the value of A is 11 2/3 buckets

Hence , The total number of buckets of fish walruses were fed each day is

A = 35/3 buckets or 11 2/3 buckets

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Final answer:

To determine how much fish the walruses are fed, multiply the 2 1/3 buckets of fish fed to dolphins by 5. The calculation gives us an answer of 11 2/3 buckets of fish fed to walruses each day.

Explanation:

The dolphins at the sea aquarium are fed 2 1/3 buckets of fish each day. To find out how much the walruses are fed, we have to multiply the quantity of fish fed to dolphins by 5, since walruses are fed 5 times as much.

First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3.
Now, multiply 7/3 by 5 to get the walruses' daily fish intake in buckets.
7/3 × 5 = 35/3.

35/3 is an improper fraction, and when converted to a mixed number, it equals 11 2/3 buckets of fish per day.

Hence, the walruses at the sea aquarium are fed 11 2/3 buckets of fish each day.

Answer:

square root of 25 and square root of 16

Step-by-step explanation:

Answer:

30 + 20 = 50

Step-by-step explanation:

I think the answer would be 50? Wouldn’t it

Answer:

  • 72 ft²

Step-by-step explanation:

The bottom side length of the triangle is the difference between the top base length and the bottom base length:

  13 ft - 5 ft = 8 ft

The vertical side length of the triangle is the same, because the triangle is an isosceles right triangle.

Since we know the base lengths and height of the trapezoid, we can use the usual formula for the area:

  A = (1/2)(b1 +b2)h

  = (1/2)(5 ft + 13 ft)(8 ft) = 72 ft²

Answer:

5.2 m

Step-by-step explanation:

5.2 m

To find the minimum depth of the water, we look at the minimum of the function h, given by the equation h = 2.5 sin 2π (t−4) /12.4 + 6.2. The minimum depth is -2.5 + 6.2 = 3.7m, but this option is not provided.

In this mathematics problem, we are given a sinusoidal function representing the depth of water, h, at a seaport over time, t. The equation is h = 2.5 sin 2π (t−4) /12.4 + 6.2.

To find the minimum depth of the water, we need to focus on the properties of the sine function, which varies from -1 to 1. Therefore, the minimum value of 2.5 * sin(2π(t−4)/12.4) is -2.5 when sin(x) = -1.

By adding 6.2 to the minimum value of the function (-2.5), we obtain -2.5 + 6.2 = 3.7, which is the minimum value of h. However, this option is not provided in the choices. There seems to be a mistake in the given problem or its options.

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Answer:

We apply the chain rule, along with the quotient rule, to find d ... 3. (4 pts) A particle moves on a line so that its coordinate at time t is y ... (10 pts) A cylindrical tank with radius 5 m is being filled with water at a rate of ... h/(t) = V /(t)/25π m2. ... cup has the shape of a cone with height 10 cm and radius 3 cm (at.

Step-by-step explanation:

Answer:

V = 392.7 m3

Step-by-step explanation:

To find the volume of the cone, first calculate the hieght and the radius.

To find the length of the radius, equate the given area to the formula for the area of a circle and solve for r.

πr2=25π

Divide both sides by π.

r2=25

Take the positive square root of both sides.

r=5 m

It is given that the height of the cone equal to three times the radius. So, use the radius to find the height.

h=3r

Substitute 5 for r.

h=3⋅5

Simplify.

h=15 m

To find the volume of the cone, use the formula for the volume of a cone.

V=13πr2h

Substitute 5 for r and 15 for h.

V=13⋅π⋅52⋅15

Simplify.

V=125π

Use a calculator to approximate.

V≈392.7 m3

Therefore, the volume of the cone is about 392.7 m3.

The half life is 138 days, meaning exactly half of the material will decay after this time. Use this information to find the decay factor [tex]k[/tex]:

[tex]\dfrac12=e^{138k}\implies k=-\dfrac{\ln2}{138}[/tex]

Then after 250 days, there will be

[tex]265e^{250k}\approx75.492[/tex]

grams left.

Answer:

[tex]\boxed{\text{75.5 g}}[/tex]

Step-by-step explanation:

The amount of substance decreases by 50 % every half-life.

Thus, 50 % of the substance remains at the end of each half-life.

The exponential function is

[tex]a = a_{0}\left( \dfrac{1}{2}\right)^{x}[/tex]

where x = the number of half-lives.

Data:

a₀ = 265 g

[tex]t_{\frac{1}{2}} = \text{138 da}[/tex]

t = 250 da

Calculations:

(a) Calculate x

[tex]x = \dfrac{250}{138} \approx 1.812[/tex]

(b) Calculate a

[tex]a = 265\left( \dfrac{1}{2}\right)^{1.812}\\\\a = 265 \times 0.2849 = \boxed{\textbf{75.5 g}}[/tex]

Answer:

Step-by-step explanation:

Divide 5.8/8

The cross section is A. Hexagon, a 6-sided figure.

Answer:

Hexagon

Step-by-step explanation:

A polygon are plane figure with more than 3sides e.g Pentagon , hexagon, heptagon etc.

Based on the diagram the cross section of the solid contains a six sided plane figure known as a hexagon.

An hexagon is a polygon with six equal sides and angles.

Answer:

a= -2

b= 3

Step-by-step explanation:

solving for a:

-6 times what equals 12?

-2

solving for b:

when multiplying two variables that have exponents you simply add the two exponents together. so to find b you want to subtract 2 from 5

The first step is to combine like terms, 35 and 11 are both integers without variables, so we can combine.

24+3x= 23

Now we subtract 24 from 23 to isolate 3x, and we get -1.

3x=-1

To solve we just need to divide -1 by 3.

Answer: -1/3

The value of x after solving the equation will be equal to -1/3

The expression is defined as the relationship between the numbers and variables and are arranged in the form of an equation.

The first step is to combine like terms, 35 and 11 are both integers without variables, so we can combine.

24+3x= 23

Now we subtract 24 from 23 to isolate 3x, and we get -1.

3x=-1

To solve we just need to divide -1 by 3.

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Answer:

After 12 years the investment will be worth $5145.

Step-by-step explanation:

The formula used for compounded interest is:

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

where,

A = future value

P = Principal Amount

r = interest rate

n = no of times interest is compounded

t = time

In the question given:

A=?

P = $2100

r = 7.75% or 0.0775

n = 1

t= 12

A= 2100*(1+0.0775/1)^1*12

A= 2100 *(1+0.0775)^12

A= 2100 *(1.0775)^12

A= 2100 * 2.45

A= 5145

So, after 12 years the investment will be worth $5145.

For this case we have that the volume of the cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

h: It is the height of the cylinder

A: It is the radius of the cylinder

We have to, according to the given data:

[tex]h = 7\\r = 6[/tex]

Substituting:

[tex]V = \pi * (6) ^ 2 * 7\\V = \pi * 36 * 7\\V = 252 \pi[/tex]

ANswer:

Option A

[tex]252 \pi \ units ^ 3[/tex]

the answer is 252π option A

Answer:

pretty sure the answer is 35%

Step-by-step explanation:

because thats what i got on my quiz and it was right

Answer:

[tex]36\ liters\ of\ soil[/tex]

Step-by-step explanation:

we know that

The ratio of soil, manure and leaf mould is [tex]3:1:2[/tex]

That means

For every 6 liters of the compost, he use 3 liters of soil

so by proportion

Find how many liters of soil does he use for 72 liters of compost

[tex]\frac{3}{6}=\frac{x}{72}\\ \\x=3*72/6\\ \\x=36\ liters\ of\ soil[/tex]

Answer:

a=72 and b=36

Step-by-step explanation:

A=2B

A-10-13=B+13

Answer:

Number of cars in Parking lot A = 72 and in Parking Lot B = 36

Step-by-step explanation:

Let the number of cars in parking A is = A and in parking B is = B

Now we will make the equations

" Parking lot A has twice as many cars as Parking lot B"

A = 2B  ------(1)

"After 10 cars draw away form parking lot A, and 13 cars moved from parking lot A to parking lot B then both the lots have same amount of cars."

A - 10 - 13 = B + 13

A - 23 = B +13

A = B + 13 + 23

A = B + 36 ------(2)

Now we equate the values of A in both the equations

2B = B + 36

2B - B = 36

B = 36

From equation 1

A = 2B

A = 2×(36) = 72 cars

Therefore, number of cars in Parking lot A = 72 and in Parking Lot B = 36

Answer:

33.33

Step-by-step explanation:

Answer:

Sample Response: The probability gets smaller and approaches 0 because 9 or 10 successes in 10 trials is unlikely.

The pattern observed is that the probability of getting a higher number of correct answers decreases exponentially as the number of correct answers increases.

We have given probabilities for getting exactly 7, 8, 9, and 10 correct answers in a sequence of trials.

To describe the pattern, we can observe how the probabilities change as the number of correct answers increases.

Let's calculate the Ratios Between Successive Probabilities:

1. [tex]\frac{P(\text{8 correct})}{P(\text{7 correct})} = \frac{0.000386}{0.0031} = 0.1245[/tex]

2. [tex]\frac{P(\text{9 correct})}{P(\text{8 correct})} = \frac{2.86 \times 10^{-5}}{0.000386} = 0.0741[/tex]

3.  [tex]\frac{P(\text{10 correct})}{P(\text{9 correct})} = \frac{9.54 \times 10^{-7}}{2.86 \times 10^{-5}}= 0.0334[/tex]

Analysis of the Pattern:

The probabilities decrease rapidly as the number of correct answers increases. The ratios themselves are decreasing, which indicates that the reduction in probability is not linear but rather exponential or follows a more pronounced pattern of decay.

This kind of pattern is typical in scenarios where the events are rare or become increasingly unlikely as the number of successes increases, such as in the binomial or geometric distributions.

Complete question:

P(getting exactly 7 correct) = 0.0031

P(getting exactly 8 correct) = 0.000386

P(getting exactly 9 correct) = 2.86 × 10⁻⁵

P(getting exactly 10 correct) = 9.54 × 10⁻⁷

Describe the pattern in the probability of getting greater numbers of successes.

Answer:

D

Step-by-step explanation:

The best answer is D.

A number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10.

Final answer:

The correct statement is that a number divisible by 10 is also divisible by 5 because 5 is a factor of 10. Any number ending in 0 can be divided by both 10 and 5 to yield whole numbers, confirming this relationship. So, option D is correct.

Explanation:

The statement that BEST explains the relationship between numbers divisible by 5 and 10 is 'a number that is divisible by 10 is also divisible by 5 because 5 is a factor of 10'. This is because any number that ends with a 0 is divisible by 10, and since 10 is made up of 2 and 5, that same number must also be divisible by 5. For example, take the number 30; it ends in a 0, so it is divisible by 10. When you divide 30 by 10, you get 3, which shows that 10 is a factor of 30. Now, if you take 30 and divide it by 5, you also get a whole number, which is 6 in this case. This further confirms that any number divisible by 10 will also be divisible by 5.

Answer:

The answer is 5

Step-by-step explanation:

Got it right on edg :)

The value of 3 - (-2) is 5. In math, value can mean different things that are closely related. Generally, a mathematical value can be any specific mathematical thing.

To calculate the value of 3 - (-2), we need to understand that subtracting a negative number is equivalent to adding its positive counterpart.

So one can say that

3 - (-2)

Then Rewrite the double negative as addition:

3 + 2

So add the numbers:

3 + 2 = 5

Therefore, the value of 3 - (-2) is 5.

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Answer:

The radius of the cylinder is [tex]11.5\ in[/tex]

Step-by-step explanation:

we know that

The volume of a cylinder is equal to

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

we have

[tex]V=2,908.33\ in^{3}[/tex]

[tex]h=7\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values and solve for r

[tex]2,908.33=(3.14)r^{2}(7)[/tex]

[tex]r^{2}=2,908.33/[(3.14)(7)][/tex]

[tex]r=11.5\ in[/tex]

I believe it’s the second option 2^2x+6=2^6

Answer:

[tex]\large\boxed{2^{2x+6}=2^6}[/tex]

Step-by-step explanation:

[tex]4^{x+3}=64\\\\4^{x+3}=4^3\\\\(2^2)^{x+3}=(2^2)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{2(x+3)}=2^{(2)(3)}\\\\2^{2x+6}=2^6[/tex]