help me please find the equation of line.​

We are given a spinner with equal sections numbered from 1 to 20. The question is about the probability of spinning a multiple of 5. We need to determine which statements are true regarding this probability.

P(A) = 20%: This statement is false. The probability of spinning a multiple of 5 is not 20% because there are four multiples of 5 (5, 10, 15, and 20) out of 20 possible outcomes.

P(A') = 0.8: This statement is false. P(A') represents the probability of not spinning a multiple of 5. The correct probability would be P(A') = 1 - P(A) since it includes all outcomes not in A.

n(A') = 16: This statement is true. n(A') represents the number of outcomes not in A, which is 16 (20 - 4 = 16).

A = {5, 10, 15, 20}: This statement is true. A is the set of outcomes representing the multiples of 5 on the spinner.

P(A) = 4/20: This statement is true. There are four favorable outcomes (multiples of 5) out of a total of 20 possible outcomes, giving a probability of 4/20.

n(S) = 20: This statement is true. n(S) represents the total number of outcomes in the sample space, which is 20 in this case.

P(A) = 1/5: This statement is false. The probability of spinning a multiple of 5 is 4/20, not 1/5.

P(A') = 4/5: This statement is true. P(A') represents the probability of not spinning a multiple of 5, which is 16/20 or 4/5.

In conclusion, the true statements regarding the probability of spinning a multiple of 5 on the spinner are: n(A') = 16, A = {5, 10, 15, 20}, P(A) = 4/20, n(S) = 20, and P(A') = 4/5.

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The area of a circle is the measure of the surface enclosed by the circle. It is given by the formula A = πr², where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

To calculate the area of a circle, you need to know the value of its radius. The radius is the distance from the center of the circle to any point on its edge. Once you have the radius, simply plug it into the formula and solve for A.
For example, if the radius of a circle is 5 units, the area can be calculated as follows:
A = πr²
A = π(5)²
A = π(25)
A = 78.5 (rounded to one decimal place)
Therefore, the area of the circle with a radius of 5 units is approximately 78.5 square units.

It is worth noting that the area of a circle is proportional to the square of its radius. This means that if you double the radius, the area will increase by a factor of four. Similarly, if you halve the radius, the area will decrease by a factor of four. In summary, the area of a circle is given by the formula A = πr², where A is the area and r is the radius. To calculate the area, simply plug in the value of the radius and solve for A.

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In the production possibilities framework, economic growth is depicted by the PPF (Production Possibilities Frontier) shifting rightward (away from the origin). This indicates an increase in the economy's capacity to produce goods and services.

The production possibilities framework represents the different combinations of goods and services that an economy can produce given its resources and technology.

The PPF is typically depicted as a curve, showing the trade-off between producing different goods or allocating resources between different sectors of the economy.

When the PPF shifts rightward, it means that the economy's production capacity has increased.

This can happen due to various factors such as technological advancements, increased capital investment, improved infrastructure, or an expansion of the labor force.

As a result, the economy can produce more goods and services at each point along the PPF.

The shift of the PPF rightward indicates economic growth because it signifies an expansion of the production possibilities.

With a larger production capacity, the economy has the potential to achieve higher levels of output, leading to increased living standards, higher incomes, and greater overall economic prosperity.

On the other hand, if the PPF became a straight line or shifted leftward (toward the origin), it would indicate a decrease in the economy's production capacity or a decline in resources or technology.

In such cases, the economy would experience a contraction in its production possibilities and potentially face challenges in meeting the needs and wants of its population.

Therefore, the correct answer is that economic growth in the production possibilities framework is depicted by the PPF shifting rightward (away from the origin).

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Explanation

Given the function

We can find the value of p when f(-2 )=10 below;

Therefore, we will have;

Answer: p = -3

Answer: 18 cups

Step-by-step explanation:

Answer:

the answer is 18 cups :))

number a should given any of the clues. It does not make any sense.

The largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

An initial-value problem is a type of boundary-value problem in mathematics, particularly in the field of differential equations.

The given initial-value problem is a separable differential equation, which can be written as:

dy/dt = -2(t + 1)y²

Integrating both sides, we get:

(1/y) = t² + 2t  + C

where C is the constant of integration.

Since we have an initial condition, we can use it to find the value of C:

y(0) = -1/15
C = -1/15

Solving for C, we get:

C = -1/15

So, the solution to the differential equation is:

(1/y) = t² + 2t -1/15

y = 1 / (t² + 2t -1/15)

The solution is defined for all t ≠ -1, since y = 0 is not defined. So, the largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

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It shows that the values of the mileages are close to 24 mpg. Hence statistics refes 24 as the mean.

Mean is one of the measure of dispersion and is the avearage of a set of data.

According to the question, the magazine reports that the most common gas mileage was 24 mpg. This shows that reports have published several gas mileages for cars and truck and the average of this mileage is 24mpg

It shows that the values of the mileages are close to 24 mpg. Hence statistics refes 24 as the mean.

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Answer:

Step-by-step explanation:

For example, we have a coordinate grid below as shown.

If you count the units you will get a number around 7.

a) The distance traveled by the car is 240 km, b) the average speed of the car is 30 km/s, c) the speed of the car changes from increasing to constant to decreasing, d) and the total area under the curve 240 km/s.

a. To find the distance traveled by the car between 1 and 9 seconds, we need to find the area under the curve of the velocity-time graph between 1 and 9 seconds. By counting the number of squares, we can estimate the area to be approximately 24 square units. Since each square represents a velocity of 10 km/h and the time interval is 8 seconds, the distance traveled by the car is approximately 240 km.

b. The average speed of the car between 1 and 9 seconds is equal to the total distance traveled divided by the time taken, which is 240 km / 8 s = 30 km/s.

c. The speed of the car increases from 0 km/h to 60 km/h in the first 2 seconds, then remains constant at 60 km/h for the next 6 seconds, and finally decreases to 0 km/h in the last 2 seconds. Therefore, the speed of the car changes from increasing to constant to decreasing throughout its test run.

d. If we had a graph of velocity versus time for this test, the total area under the curve would represent the total displacement of the car, which is equal to the distance traveled in this case. Since the area under the curve is a trapezoid, we can calculate it as the average of the two parallel sides multiplied by the height, which is (0 + 60) / 2 x 8 = 240 km/s.

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Answer:

15,10

Step-by-step explanation:

let the numbers be 3x and 2x

3x-2x=5

x=5

∴ numbers are 3×5,2×5

or 15,10

Answer:

BTW C= containers and AC = area of all the containers all together.

Step-by-step explanation:

So first off you calculate the area of the container that had a crack so its

Width X Length X height    |   6 x 8 x 5 = 240

So then you look at the possible answers and then calculate the area of those   plastic containers. So then you start with the first one and it would be like this

First possible answer: 3 and 1/3  x 6 x 5 = 100 x 3c = 300ac

Second possible answer: 2 and 1/4 x 4 and 3/4 x 6 = 64.125 x 4c = 256.5ac

Third possible answer: 3.5 x 6.5 x 6 = 136.5 x 2c = 273ac

Fourth possible answer: 3 and 1/2 x 3 and 1/4 x 5 = 56.875 x 5c = 284.375ac

Hopefully this will help you find your answer!! I tried my best!! Please give brainly!!

Diego will have 74 pencils remaining after giving 14 pencils to Marcus and 32 pencils to Anna.

The question is about simple Subtraction. First, we know that the total number of colored pencils in the box is 120. Following is the step-by-step explanation for this question.
Let suppose,
Total Colored pencils = x = 120
Pencils given to Marcus = y = 14
Pencils are given to Anna = z = 34.

And, Total Pencil Remaining = R =?

We can show the given information in the equation as given below:
R = x - y - z

By putting the value in the above equation:
R  = 120 - 14 -34
R  = 74.

So, after giving the 14 and 32 pencils to Marcus and Anna, respectively. Marcus would remain with 74 Pencils.

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Answer:

-1x+3 or -x+3

Step-by-step explanation:

2x-3(x+1)

2x-3x+3

-1x+3 or -x+3

Answer:

The coefficient of the second tern in the expression , 4+ 5c, is 5

Step-by-step explanation:

Second term: 5c

C is a variable,therefore, making 5 the coeffiecient.

Answer:

Mrs. Rodriquez is purchasing trophies for each child that plays little league. She wants to

spend no more than $7.00 per trophy. Which of the following purchases will satisfy her budget?

Select all that apply.

A. 3 trophies for $24.00

B. 5 trophies for $30.00

C. 7 trophies for $49.00

D. 9 trophies for $72.00

E. 12 trophies for $96.00

Step-by-step explanation:

Answer:

the answer is D

Step-by-step explanation:

i explain it here

Answer:

the answer is d

Step-by-step explanation:

Here are the values of f(1), f(2), f(3), f(4), and f(5) for each recursive definition:

a) \(\[f(1) = -6, \quad f(2) = 12, \quad f(3) = -24, \quad f(4) = 48, \quad f(5) = -96\]\)

b) \(\[f(1) = 16, \quad f(2) = 55, \quad f(3) = 172, \quad f(4) = 523, \quad f(5) = 1576\]\)

c) \(\[f(1) = 1, \quad f(2) = -3, \quad f(3) = 11, \quad f(4) = 107, \quad f(5) = 11365\]\)

d) \(\[f(1) = 3, \quad f(2) = 3, \quad f(3) = 3, \quad f(4) = 3, \quad f(5) = 3\]\)

a) Recursive definition: \(\(f(n + 1) = -2f(n)\)\)

To find \(\(f(1)\)\), we use the initial condition \(\(f(0) = 3\)\) and apply the recursive definition:

\(\[f(1) = -2f(0) = -2 \cdot 3 = -6\]\)

To find \(\(f(2)\)\):

\(\[f(2) = -2f(1) = -2 \cdot (-6) = 12\]\)

Similarly, we can continue applying the recursive definition to find \(\(f(3)\), \(f(4)\), and \(f(5)\)\):

\(\[f(3) = -2f(2) = -2 \cdot 12 = -24\]\)

\(\[f(4) = -2f(3) = -2 \cdot (-24) = 48\]\)

\(\[f(5) = -2f(4) = -2 \cdot 48 = -96\]\)

b) Recursive definition: \(\(f(n + 1) = 3f(n) + 7\)\)

Using the initial condition \(\(f(0) = 3\):\)

\(\[f(1) = 3f(0) + 7 = 3 \cdot 3 + 7 = 16\]\)

To find \(\(f(2)\)\):

\(\[f(2) = 3f(1) + 7 = 3 \cdot 16 + 7 = 55\]\)

Continuing in the same manner:

\(\[f(3) = 3f(2) + 7 = 3 \cdot 55 + 7 = 172\]\)

\(\[f(4) = 3f(3) + 7 = 3 \cdot 172 + 7 = 523\]\)

\(\[f(5) = 3f(4) + 7 = 3 \cdot 523 + 7 = 1576\]\)

c) Recursive definition: \(\(f(n + 1) = f(n)^2 - 2f(n) - 2\)\)

Using the initial condition \(\(f(0) = 3\)\)

\(\[f(1) = f(0)^2 - 2f(0) - 2 = 3^2 - 2 \cdot 3 - 2 = 1\]\)

To find \(\(f(2)\):\)

\(\[f(2) = f(1)^2 - 2f(1) - 2 = 1^2 - 2 \cdot 1 - 2 = -3\]\)

Continuing in the same manner:

\(\[f(3) = f(2)^2 - 2f(2) - 2 = (-3)^2 - 2 \cdot (-3) - 2 = 11\]\)

\(\[f(4) = f(3)^2 - 2f(3) - 2 = 11^2 - 2 \cdot 11 - 2 = 107\]\)

\(\[f(5) = f(4)^2 - 2f(4) - 2 = 107^2 - 2 \cdot 107 - 2 = 11365\]\)

d) Recursive definition: \(\(f(n + 1) = \frac{{3f(n)}}{3}\)\)

Using the initial condition \(\(f(0) = 3\):\)

\(\[f(1) = \frac{{3f(0)}}{3} = \frac{{3 \cdot 3}}{3} = 3\]\)

Since the recursive definition is \(\(f(n + 1) = \frac{{3f(n)}}{3}\)\), the value of \(\(f(n)\)\) remains constant as 3 for all values of \(\(n\)\). Hence,  \(\(f(2)\), \(f(3)\), \(f(4)\),\)  \(\(f(5)\),\) the value will be 3.

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Answer:

x = -5 or x= 2

Step-by-step explanation:

|-4x-6| = 14

There are two solutions, one positive and one negative

-4x-6 = 14       -4x-6 = -14

Add 6 to each side

-4x-6+6 = 14+6       -4x-6+6 = -14+6

-4x = 20                      -4x = -8

Divide by -4

-4x/-4 = 20/-4               -4x/-4 = -8/-4

x = -5                                x = 2

Now we have to,

find the required value of x.

Given that,

→ |-4x -6| = 14

Let's find the both positive value and negative value,

===================

→ -4x -6 = 14

→ -4x = 14 + 6

→ -4x = 20

→ x = 20/-4

→ [x = -5]

===================

→ -4x -6 = -14

→ -4x = -14 + 6

→ -4x = -8

→ x = -8/-4

→ x = 8/4

→ [x = 2]

===================

Therefore, x is -5 (or) 2 is the answer.

The resistance of a 20-ft wire with a diameter of 0.1-in is 0.08ω

The variation is given as:

Resistance varies directly as its length and inversely as square of diameter

Mathematically, this is represented as

R =kL/D^2

Where k represents the constant of variation.

When L = 50, D = 0.4 in and R = 0.0125, we have

0.0125 =k * 50/0.4^2

This gives

k = 0.4^2 * 0.0125/50

Evaluate

k = 0.00004

Substitute k = 0.00004 in R =kL/D^2

R = 0.00004L/D^2

When L = 20-ft wire and D = 0.1-in, we have:

R = 0.00004 * 20/(0.1)^2

Evaluate

R = 0.08

Hence. the resistance of a 20-ft wire with a diameter of 0.1-in is 0.08ω

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Ed Moura invests $192000 in certificates of deposit paying 2%.

According to the question,

Ed Moura has $64000 invested in stocks paying 6%.  

He invests additional money in certificates of deposit paying 2% =x  

so the average return on the two investments is 3%.

  64000*6% +2%*x = 3%(64000+x)

Convert percentage to decimal,

⇒64000*0.06 +0.02*x = 0.03(64000+ x)

⇒3840 + 0.02x = 1920 +0 .03x ( using multiply)

⇒3840-1920 = 0.03x - 0.02x

⇒0.03x - 0.02x = 3840 -1920

⇒0.01x = 1920

Both side divide by 0.01,

⇒x = 192000

∴ So, Ed Moura invests $192000 in certificates of deposit paying 2%.

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Answer:SORRY CANT HELP U THERE

Step-by-step explanation:

Answer:

\(98\)

Step-by-step explanation:

Given the following question:

\(7(10+4)\)

In order to find the answer, we use PEMDAS and solve.

\(7(10+4)\)
\(10+4=14\)
\(7\times14\)
\(7\times14=98\)
\(=98\)

Hope this helps.

Answer:

3/4x + 12 =48

3/4x=36

x=48

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.