Given: an=3+an−1 and a1=5

What is the explicit rule for the arithmetic sequence?

Answer:

30% gain

Step-by-step explanation:

$30 for 10 = $3 each

$46.80 for 12 = $3.9 each

percentage change = (final price- initial price)/inital price  *100

3.9-3 = 0.9

0.9/3 = 0.3

0.3 x 100 = 30

so gain of 30%

For the x-bar chart, the upper control limit is 19.15 and the lower control limit is 12.87; for the R-chart, the upper control limit is 10.17 and the lower control limit is 0.43.

To calculate the control limits for the x-bar (sample mean) chart and the R-chart (sample range) chart, we need to use statistical formulas based on the sample size and the average values.

For the x-bar chart:

Calculate the standard deviation (σx-bar) of the sample means using the formula σx-bar = σ / √n,

where σ is the population standard deviation and n is the sample size.

Calculate the control limits for the x-bar chart using the formula:

Upper Control Limit (UCL) = x-bar + A2 \(\times\) σx-bar

Lower Control Limit (LCL) = x-bar - A2 \(\times\) σx-bar

Here, A2 is a constant depending on the sample size and the desired level of control. For a sample size of 5, A2 is typically 0.577.

For the R-chart:

Calculate the control limits for the R-chart using the formula:

Upper Control Limit (UCL) = D4 \(\times\) R

Lower Control Limit (LCL) = D3 \(\times\) R

Here, D3 and D4 are constants depending on the sample size. For a sample size of 5, D3 is 0 and D4 is typically 2.115.

Given the information provided, we can calculate the control limits as follows:

Calculate σx-bar = σ / √n = σ / √5.

Calculate the x-bar chart limits:

UCL (x-bar) = x-bar + 0.577 \(\times\) σx-bar

LCL (x-bar) = x-bar - 0.577 \(\times\) σx-bar

Calculate the R-chart limits:

UCL (R) = 2.115 \(\times\) R

LCL (R) = 0 \(\times\) R (which is 0)

Please note that the population standard deviation (σ) is not provided, so we cannot calculate the exact control limits without that information.

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Answer: Shirt = $7 and Sweater = $18

Step-by-step explanation:

5 Shirts, 3 sweaters = $89   (1)
9 Shirts, 8 sweaters = $207 (2)

1 Shirt = $?

1 Sweater = $?

Shirts = x

sweaters = y

(1) -> 5x + 3y = 89

(2) -> 9x + 8y = 207

(1) * 8 = 40x + 24y = $712

(2) * 3 = 27x + 24y = $621

(1) single out 24y -> 24y = $712 - 40x

put value of 24 y into (2)

(2) -> 27x + $712 - 40x = $621

Now solve

-13x = $-91

remove negative -> 13x = $91

x = $7

So a shirt is $7

And we can put $7 into (1) at the start -> 5(7) + 3(y) = $89

35 + 3y = $89

3y = $54

y = $18

Hence x = $7 and y = $18

So Shirt = $7 and Sweater = $18

The given function f(x) = 25e^(-2x) represent the exponential decay.

According to th egiven question.

We have an exponential function.

f(x) = 25e^(-2x)

As we know that

If \(P = P_{o} e^{-kt}\) be an exponential function, then it will represent

Where,

P is the final amount

\(P_{o}\) is the intial amount

t is the time interval

k is the constant of proportionality

For the given question if we compare the given exponential function with the standard exponentential function we get

\(P_{o}\) = 25

k = 2

and t = x

Now,

e^(-2) = 0.13

Since, e^(-2) < 1.

Hence, the given function f(x) = 25e^(-2x) represent the exponential decay.

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Answer:

25

Step-by-step explanation:

percentage calculator 40 is what percent of 160=25;)

Answer:

40/100×160

Step-by-step explanation:

2/5×160

320/5

64

Hey there! :)

Answer:

(2, 3) and (-2, 11).

Step-by-step explanation:

To solve this system of equations, we can set both equations equal to each other:

x² -2x + 3 = -2x + 7

Combine like terms:

x² -4 = 0

Factor using difference of squares:

(x - 2)(x + 2) = 0

Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:

f(x) = -2(2) + 7

f(x) = -4 + 7

f(x) = 3

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

f(x) = -2(-2) + 7

f(x) = 4 + 7

f(x) = 11

Therefore, the two ordered pairs are (2, 3) and (-2, 11).

Answer:

x = 9

Step-by-step explanation:

\(2x + 3 = 3x - 6\)

\(3 = x - 6\)

\(x = 9\)

Infinitely many solutions exist for a system with fewer equations than unknowns, yet there may be none. An underdetermined system is one that operates in this manner.

What in mathematics is a linear system?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

                          Equations with unknowns or variables that have powers of one are known as linear equations. Because the variables x, y, and z are linear, for instance, 3x - 4y + 5z = 3 is a linear equation, however xy + 3z = 7 is not because the phrase xy is a product of two variables.

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Answer:

x = - 2, x = 7

Step-by-step explanation:

Given

f(x) = 4x² - 20x - 56

To find the zeros let f(x) = 0, that is

4x² - 20x - 56 = 0 ( divide through by 4 )

x² - 5x - 14 = 0 ← in standard form

(x - 7)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 7 = 0 ⇒ x = 7

The diameter of the hemisphere with a volume of 557 m³ is approximately 12.8 m, to the nearest tenth of a meter.

The volume of a hemisphere can be calculated using the formula V = (2/3)πr³, where V is the volume and r is the radius. Given that the volume of the hemisphere is 557 m³, we can find the radius by solving for r:

557 = (2/3)πr³

To find the radius, first, we need to isolate r³ by multiplying both sides by 3/(2π):

r³ = (3 * 557) / (2 * π)

r³ ≈ 265.18

Now, take the cube root of both sides to find the radius:

r ≈ 6.4 m

To find the diameter, simply multiply the radius by 2:

d ≈ 2 * 6.4
d ≈ 12.8 m

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Answer:

30p + 5

You do destibutive property

(6p+1)(5)

6p * 5

1 * 5

=30p+5

Answer:

Hello! The Answer is not proportional. Hope this helps!

Step-by-step explanation:

Typically the letters in each figure correspond to the same letter in the second figure so D = Q, E = R, etc.

You are told E = 143, so since E = R , then R should also be 143 degrees.

Answer:

143

Step-by-step explanation:

The variable associated with the interior and exterior angles in the triangle is equal to 56.

The value of the exterior angle is equal to 116°.

This question presents the case of a geometric system formed by a triangle and a semirray that includes two interior angles and a exterior angle. Please notice that the sum of the measures of interior angles in a triangle equals 180° and the sum of two supplementary angles equals 180°.

First, derive the equation of the missing interior angles in triangle PQR:

m ∠ R = 180° - 60° - x

m ∠ R = 120° - x

Second, obtain the equation for the two supplementary angles:

(120° - x) + (2 · x + 4°) = 180°

124° + x = 180°

x = 56

Third, determine the value of the exterior angle:

θ = 2 · x + 4

θ = 2 · 56 + 4

θ = 116°

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Answer:

\(m=2\)

General Formulas and Concepts:

Pre-Alg

Alg I

Step-by-step explanation:

Step 1: Define

Point (0, 7)

Point (4, 15)

Step 2: Find slope m

Answer:

x < 3

Step-by-step explanation:

Your inequality: 4x - 1 < 11

4x - 1 < 11

Add 1 to both sides

4x < 11 + 1

4x < 12

**Don't switch signs because no negatives nor any specifications**

Divide 12 by 4

x < 3

Blake's recorded result of a probability model in a 12 times die roll:

Part A: 0 %

Part B: 25 %

Part C:  41.67 %

To complete the probability model

Part A:

To find the experimental probability of rolling a 3, count the number of times 3 appears in the table and divide by the total number of rolls:

Number of 3's rolled: 0

Total number of rolls: 12

Experimental probability of rolling a 3: 0/12 = 0/1 = 0

So the probability of rolling a 3 is 0, or 0/1 as a fraction, 0 as a decimal number, and 0% as a percentage.

Part B:

To find the experimental probability of rolling a 6, we need to count the number of times 6 appears in the table and divide by the total number of rolls:

Number of 6's rolled: 3

Total number of rolls: 12

Experimental probability of rolling a 6: 3/12 = 1/4 = 0.25

So the probability of rolling a 6 is 1/4 as a fraction, 0.25 as a decimal number, and 25% as a percentage.

Part C:

To find the experimental probability of rolling a number less than 4, add the experimental probabilities of rolling a 1, 2, or 3:

Experimental probability of rolling a 1: 2/12 = 1/6 = 16.67%

Experimental probability of rolling a 2: 3/12 = 1/4 = 25%

Experimental probability of rolling a 3: 0/12 = 0/1 = 0

Experimental probability of rolling a number less than 4: 16.67% + 25% + 0 = 41.67%

So the probability of rolling a number less than 4 is 5/12 as a fraction, 0.4167 as a decimal number, and 41.67% as a percentage.

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Image transcribed:

16. For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.

Blake rolled a die 12 times. He recorded the results in the table below.

Results

6 | 2 | 1 | 4

4 | 3 | 1 | 5

2 | 2 | 6 | 6

Then, Blake created the probability model shown below from the data in the chart. Blake was only able to complete part of the model.

Probability Model

1 | 2 | 3 | 4 | 5 | 6

P(1) 17% | P(2)-25% | ? | P(4) 17% | P(5) 8% | ?

Part A: Help Blake complete the probability model by finding the experimental probability of rolling a 3. Provide your answer as a fraction, a decimal number, and a percent.

Part B: Help Blake complete the probability model by finding the experimental probability of rolling a 6. Provide your answer as a fraction, a decimal number, and a percent.

Part C: Use your probability model to find the experimental probability of rolling a number less than 4. Provide your answer as a fraction, a decimal number, and a percent.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. is y= 3 x +8

-3 x +  y - 8= 0

y = 3x+ 8

2. is in the pictures

3.

3 X + 5 y - 10 = 0

Real solution:

y = 2 - (3 X)/5

Solution:

y = 2 - (3 X)/5

Integer solution:

X = 5 n, y = 2 - 3 n, n element Z

Solution for the variable y:

y = 1/5 (10 - 3 X)

Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.

Answer:

5.1

Step-by-step explanation:

Before we calculate  the y value for the point Q that is located two thirds the distance from point P to point R, we need to get the distance of point p from point R using the formula for calculatingf the distance between two points

D = √(x2-x1)²+(y2-y1)²

Given P(−2, 7), and R(1, 0)

RP = √(1-(-2))²+(0-7)²

RP = √3²+(-7)²

RP = √9+49

RP =√58

To get the y value for point Q that is located two thirds the distance from point P to point R, this will give

PQ = y = 2/3 of √58

= 5.1

Answer: I Believe its 2.3

Step-by-step explanation:

P is located at (-2,7)

R is located at (1,0)

Look at the y coordinates

P(-2,7)  R(1,0)

7 to 0= distance of 7

multiply 2/3 by 7 = 4.7      (it was originally 4.666666665 but i couldnt find the answer with just 4.6 so i rounded it to 4.7)

Now plug in the info we know:

.y axis = 7 - 4.7 = 2.3

Hope this helped! Im taking the test and ill be back if this is wrong

Answer:

4

Step-by-step explanation:

cause undefined is straight down and its not on the 0 and its up 4

Answer:

0

Step-by-step explanation:

Any line that is horizontal its slope is 0.

If the line is vertical then its slope would be undefined.

Answer:

ok

Step-by-step explanation:

Answer:

Answer choice C

Step-by-step explanation:

It is f(x)= -3(x+3)^2+3. For proof, enter equation into desmos graphing. Also I got it right on edge. Hope this helps.

Answer:

C. \(f\left(x\right)=-3\left(x+3\right)^2+3\)

Step-by-step explanation:

I did it on edge

To solve this problem, we can use the inverse operations to reverse the steps that Albert took.

First, we need to multiply the result by 2 and add 6 to get the result before the division by 2. This gives us:

8 * 2 + 6 = 16 + 6 = 22

Next, we need to divide this result by 2 and subtract 5 to get the original number that Albert thought of. This gives us:

(22 / 2) - 5 = 11 - 5 = 6

Therefore, the number that Albert originally thought of was 6.

A component of a counting and calculation system, or its symbol, which represents a quantity or place in a series: You can write numbers in words, like six, seven, and eight, or using symbols, like six, seven, and eight.

Using terms you are familiar with, a dictionary translates unknown words. Using words you can understand, Dictionary of Numbers translates complex numbers for you. When you browse websites, Dictionary of Numbers searches those pages for numbers it can comprehend.

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Answer:

3 x 4 + 44 x 3 + 139 x 2 − 168 x + 88 /x + 8

Step-by-step explanation:

Step-by-step explanation:

a) 3x + 5y = 8

4x - 3y = 1

• using the elimination method:

3x + 5y = 8 (×4)

4x -3y = 1 (×3)

12x + 20y = 32

12x -9y = 3

subract 12x from both equation:

20y - - 9y= 32 -3

20y +9y = 29

29y= 29

y= 29/29

y= 1

- substituting y= 1 in :

4x - 3y= 1

4x - 3(1) = 1

4x -3 = 1

4x = 1 + 3

x = 4/4

x= 1

b) 6p+ 4q = 20

5p - 2q = 6

• using the elimination method:

6p + 4q = 20

5p - 2q = 6 (×2)

6p + 4q = 20

10p - 4q = 12

add 4q + -4q to eliminate q.

6p+ 10p = 20+12

16p = 32

p = 32/ 16

p = 2

- subtituting p = 2 in :

5p - 2q = 6

5(2) -2q =6

10 -2q = 6

-2q = 6 - 10

q = -4 / -2

q = 2

hope this helps you,

-s.

Answer:

Step-by-step explanation:

3x + 5y = 8 ________( 1 )

4x - 3y = 1________ ( 2 )

( 1 ) × 3 ____ 9x + 15y = 24 _____ ( 3 )

( 2 ) × 5____ 20x - 15y = 5 _____ ( 4 )

( 3 ) + ( 4 )

\(9x + 15y + 20x - 15y = 24 + 5 \\ 9x + 20x + 15y - 15y = 29 \\ 29x = 29 \\ x = \frac{29}{29} \\ x = 1 \\ \)

x = 1 substitute to ( 1 ) ,

\(3x + 5y = 8 \\ 3(1) + 5y = 8 \\ 3 + 5y = 8 \\ 5y = 8 - 3 \\ 5y = 5 \\ y = \frac{5}{5} \\ x = 1 \\ \)

6p + 4q = 20_______ ( 1 )

5p – 2q = 6 _______ ( 2 )

( 2 ) × 2 ____ 10p - 4q = 12 _______ ( 3 )

( 1 ) + ( 3 )

\(6p + 4q + 10p - 4q = 20 + 12 \\ 6p + 10p + 4q - 4q = 32 \\ 16p = 32 \\ p = \frac{32}{16} \\ p = 2 \\ \)

p = 2 substitute to ( 1 ) ,

\(6p + 4q = 20 \\ 6(2) + 4q = 20 \\ 12 + 4q = 20 \\ 4q = 20 - 12 \\ 4q = 8 \\ q = \frac{8}{4} \\ q = 2 \\ \)

Answer:

\( \boxed{c = -17} \)

Step-by-step explanation:

\( = > 3 - 7c - 20c = 7( - 7c - 19) + 14c \\ \\ = > 3 - 27c = ( - 7c \times 7) - (7 \times 19) + 14c \\ \\ = > 3 - 27c = - 49c - 133 + 14c \\ \\ = > 3 - 27c = - 35c - 133 \\ \\ = > 3 - 27c + 35c = - 133 \\ \\ = > 3 + 8c = - 133 \\ \\ = > 8c = - 133 - 3 \\ \\ = > 8c = - 136 \\ \\ = > c = - \frac{136}{8} \\ \\ = > c = - 17\)

Answer:

c = -17

Step-by-step explanation:

→Distribute the 7 to (-7c - 19):

3 - 7c - 20c = -49c - 133 + 14c

→Add like terms (-7c and -20c, -49c and 14c):

3 - 27c = -35c - 133

→Add 35c to both sides:

3 + 8c = -133

→Subtract 3 from both sides:

8c = -136

→Divide both sides by 8:

c = -17