What is the equation of the following line?

Answer:

C = 45d + 15

Step-by-step explanation:

105= (45 x 2) + 15

The equation represents the condition of the function as a linear function. Then the linear equation is C = 45d + 15.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The cost, C, to rent a car for d days is shown in the table.

Days (d) Cost (C)

  2         $105

  4         $195

  5         $240

  6         $285​

Then the linear equation of the given table will be

Let d be the number of days and C be the total cost.

[tex]\rm C - 285 = \dfrac{285-240}{6-5} (d-6)\\\\C - 285 = 45d - 270\\\\45d - C = -15 \\\\C - 45d = 15[/tex]

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer:

54 grams

Step-by-step explanation:

To hard to explain.

Answer: A

Step-by-step explanation: I am a big brain pro

Answer:

96 in.²

Step-by-step explanation:

Surface Area of the prism = 2(area of the 2 equal triangles) + area of rectangle A + rectangle B + rectangle C

✔️Area of the two triangles with the following dimensions:

height = 3 in.

base = 4 in.

Area = 2(½*4*3) = 12 in.²

✔️Area of rectangle A = L*W

L = 7 in

W = 5 in

Area of rectangle A = 7*5 = 35 in.²

✔️Area of rectangle B = L*W

L = 7 in

W = 4 in

Area of rectangle B = 7*4 = 28 in.²

✔️Area of rectangle C = L*W

L = 7 in

W = 3 in

Area of rectangle C = 7*3 = 21 in.²

✔️surface area of the prism = 12 + 35 + 28 + 21 = 96 in.²

Answer:

2p=18

2p=2p the answer is p=9

Step-by-step explanation:

Answer:

7 in.

Step-by-step explanation:

1 in - - > 12 ft

x in - - > 84 ft

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

12*x=84 - - >x=7in

Answer:

they are alternate interior angles to parallel lines.

Step-by-step explanation:

The reason for this is that they are alternate interior angles to parallel lines. The straight dotted lines that represent the line of sight of each individual are parallel to each other while the elevation line in this scenario would be considered the Transversal as it passes through both of them. This ultimately causes the angles between the transversal and the line of sight to be alternate interior angles which are equal to one another, as can be seen in the attached demonstration in the image below.

9514 1404 393

Answer:

Step-by-step explanation:

Angle U = angle N = 180° -142° -24° = 14°

The expression for angle U tells us the value of x.

  2x -50 = 14

  x -25 = 7 . . . . . divide by 2

  x = 32 . . . . . . . .add 25

__

The measure of side SU is the same as that for side PN.

  13 = (2x -y)

  y = 2x -13 = 2(32) -13 . . . . solve for y, substitute for x

  y = 51

Answer:

No

Step-by-step explanation:

Hello, 35.336 is would not be an irrational number because irrational numbers are messy numbers that go on forever like 3.14159..... A rational number is a number with clean numbers like 1.222222....., 35.336, ect. I hope this helped you!

Answer:

192.5 m²

Step-by-step explanation:

The formula for calculating the area if a circle

= πr²

Find the area of the larger circle first, then subtract the area of the smaller circle.

The area of the larger circle

= π×(21÷2)²

= 346.4 m² (rounded to the nearest tenth)

The radius of the smaller circle

= 21÷2 - 3.5

= 7 m

The area of the smaller circle

= π×7²

= 153.9 m² (rounded to the nearest tenth)

The area of the shaded region

= 346.4 - 153.9

= 192.5 m²

Answer:

See step by step explanation

Step-by-step explanation:

From the problem statement, we understand that we need to investigate if 2nd graders RETAIN OR LOSE knowledge comparing information concerning two different months, therefore we are going to find out if the information gives us enough evidence of a difference in the two groups

a) The test should be a two tail-test

Sample sizes are small ( n₁ = n₂  = 9 ) which means we have to use  t-student test

b   and    c) Test Hypothesis:

For Null Hypothesis H₀,  we establish that the two means are equal, which in this case means that the two samples´ means are equal. And as Hypothesis alternative Hₐ that the H₀ is not true,  or that the samples mean are different.

Null Hypothesis     H₀             x₁  -  x₂   = 0   or    x₁  =  x₂

Alternative Hypothesis  Hₐ    x₁  -  x₂   ≠  0   or   x₁  ≠  x₂

d) Significance level α  = 0,05   then   α/2  = 0,025

then t(c)  with  α/2  =  0,025  and degree of freedom  

df =  n₁  +  n₂  - 2      df =  9 + 9 -2     df = 16

From t s-tudent table we find     t(c) =  2,12

e) Calculating:

x₁   and  σ₁

x₂  and  σ₂

σₓ  = [ ( n₁ - 1 )* σ₁² + ( n₂  - 1 )*σ₂² ]/ n₁ + n₂ - 2

Using a calculator:

x₁  =  77,11        σ₁  = 13,86

x₂  = 85,89      σ₂  = 12,74

σₓ  = [ ( 8*(13,86)² + 8*( 12,74 )² ] / 16

σₓ  =  (8* 192,1) + 8* ( 162,31) / 16

σₓ  = (1536,8 + 1298,48 ) / 16

σₓ  =  177,205

t(s) = ( x₁ - x₂ ) /√ σₓ²/ n₁  + σₓ²/ n₂

t(s) = ( 77,11 - 85,89 )/ (177,205)²/n₁ + (177,205)²/n₂

t(s) = - 8,78 / √3489,07 + 3489,07

t(s) = -8,78 / 83,54

t(s) =  - 0,11

Comparing  t(s) and  t(c)

|t(s)| < |t(c)|      

0,11 <  2,12

t(s) is in the acceptance region. We accept H₀

Answer:

a. 135 g

b. 60.6 min

Step-by-step explanation:

a. What mass of Cu(s) is electroplated by running 28.5 A of current through a Cu2+ (aq) solution for 4.00 h? Express your answer to three significant figures and include the appropriate units.

The chemical equation for the reaction is given below

Cu²⁺(aq) + 2e⁻ → Cu(s)

We find the number of moles of Cu that are deposited from

nF = It where n = number of moles of electrons, F = Faraday's constant = 96485 C/mol, I = current = 28.5 A and t = time = 4.00 h = 4.00 × 60 min/h × 60 s/min = ‭14,400‬ s

So, n = It/F = 28.5 A × ‭14,400‬ s/96485 C/mol = ‭410,400‬ C/96485 C/mol = 4.254 mol

Since 2 moles of electrons deposits 1 mol of Cu, then 4.254 mol of electrons deposits 4.254 mol × 1 mol of Cu/2 mol = 2.127 mol of Cu

Now, number of moles of Cu = n' = m/M where m = mass of copper and M = molar mass of Cu = 63.546 g/mol

So, m = n'M

= 2.127 mol × 63.546 g/mol

= 135.15 g

≅ 135 g to 3 significant figures

b. How many minutes will it take to electroplate 37.1 g of gold by running 5.00 A of current through a solution of Au+(aq)?

The chemical equation for the reaction is given below

Au⁺(aq) + e⁻ → Au(s)

We need to find the number of moles of Au in 37.1 g

So, number of moles of Au = n = m/M where m = mass of gold = 37.1 g and M = molar mass of Au = 196.97 g/mol

So, n = m/M = 37.1 g/196.97 g/mol = 0.188 mol

Since 1 mol of Au is deposited  by 1 moles of electrons, then 0.188 mol of Au deposits 0.188 mol of Au × 1 mol of electrons/1 mol of Au = 0.188 mol of electrons

We find the time it takes to deposit 0.188 mol of electrons that are deposited from

nF = It where n = number of moles of electrons, F = Faraday's constant = 96485 C/mol, I = current = 5.00 A and t = time

So, t = nF/It

= 0.188 mol × 96485 C/mol ÷ 5.00 A

= ‭18173.30‬ C/5.00 A

= 3634.66 s

= 3634.66 s × 1min/60 s

= 60.58 min

≅ 60.6 min to 3 significant figures

Answer:

−200y − 2

Step-by-step explanation:

y(2.5 + 7) + y −210.5y − 2

=9.5y + y + −210.5y + −2

=(9.5y+ y + −210.5y) + (−2)

−200y − 2

Mark me brainllest

Answer:

a-The Linear Model is as follows:

[tex]X+Y+Z\leq 100,000\\{0.001X}\geq 20\\{0.001Z}\leq 50\\0.00001X+0.00004Y+0.00008Z\leq5\\X\geq0\\Y\geq0\\Z\geq0[/tex]

b-The values are

X=$33,333.33

Y=$16,666.67

Z=$50,000.00

Leading to a total expected return of $4333.33.

c-The values of constraints are as follows

X+Y+Z=33333.33+16666.67+50000=100,000

X=33%, Y is 16.67% and Z is 50%

Risk component of X is 0.33

Risk component of Y is 0.66

Risk component of Z is 4.00

Step-by-step explanation:

a

From the conditions, the first special constraint is the total amount which is that the sum of investments must not be  more than the total available amount of $100,000 so

[tex]X+Y+Z\leq 100,000[/tex]

The second special constraint is that the percentage of X must be at least 20% So

[tex]\dfrac{X}{100,000}\times100 \geq20\\\dfrac{X}{1000} \geq20\\{0.001X}\geq 20[/tex]

The third special constraint is that the fraction of total investment of Z must not exceed 50% So

[tex]\dfrac{Z}{100,000}\times100 \leq50\\\dfrac{Z}{1000}\leq 50\\0.001Z\leq50[/tex]

The fourth special constraint is that the combined portfolio risk index must not exceed 5 so

[tex]\dfrac{X}{100,000}\times1+\dfrac{Y}{100,000}\times4+\dfrac{Z}{100,000}\times8\leq5\\0.00001X+0.00004X+0.00008Z\leq5[/tex]

As the investments cannot be negative so three basic constraints are

[tex]X\geq0\\Y\geq0\\Z\geq0[/tex]

The maximization function is given as

[tex]f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times1\%+\dfrac{Y}{X+Y+Z}\times3\%+\dfrac{Z}{X+Y+Z}\times7\%\\f(X,Y,Z)=\dfrac{X}{X+Y+Z}\times0.01+\dfrac{Y}{X+Y+Z}\times0.03+\dfrac{Z}{X+Y+Z}\times0.07[/tex]

b

By using an LP solver with BigM method the solution is as follows:

X=$33,333.33

Y=$16,666.67

Z=$50,000.00

Leading to a total expected return of $4333.33.

c

The values of constraints are as follows

X+Y+Z=33333.33+16666.67+50000=100,000

X=33%, Y is 16.67% and Z is 50%

Risk component of X is 0.33

Risk component of Y is 0.66

Risk component of Z is 4.00

Answer:

median = 93.5

median = 65

MAD = 7.125

MAD = 3.75

Step-by-step explanation:

The median is the middle value when the values of the data set are placed in order from smallest to largest.

Data set:  72 82 92 93 94 97 98 102

As the number of values in the data set is even, the median is the mean of the middle two values.

[tex]\implies \sf median=\dfrac{93+94}{2}=93.5[/tex]

Data set: 53 59 64 65 65 66 67 69

As the number of values in the data set is even, the median is the mean of the middle two values.  

[tex]\implies \sf median=\dfrac{65+65}{2}=65[/tex]

To find the Mean Absolute Deviation (MAD):

1. calculate the mean (by summing the data values and dividing by the number of values)

2. Subtract the mean from each value in the data set and take the absolute value of each result.

3. Sum the absolute values from step 2.

4. Divide by the number of values.

Data set: 72, 82, 93, 98, 102, 97, 92, 94

[tex]\sf Mean=\dfrac{72+82+93+98+102+97+92+94}{8}=91.25[/tex]

|72 - 91.25| = 19.25

|82 - 91.25| = 9.25

|93 - 91.25| = 1.75

|98 - 91.25| = 6.75

|102 - 91.25| = 10.75

|97 - 91.25| = 5.75

|92 - 91.25| = 0.75

|94 - 91.25| = 2.75

Sum of absolute values = 57

[tex]\sf MAD=\dfrac{57}{8}=7.125[/tex]

Data set: 53 59 64 65 65 66 67 69

[tex]\sf Mean=\dfrac{53 +59+ 64+ 65+ 65+ 66+ 67+ 69}{8}=63.5[/tex]

|53 - 63.5| = 10.5

|59 - 63.5| = 4.5

|64 - 63.5| = 0.5

|65 - 63.5| = 1.5

|65 - 63.5| = 1.5

|66 - 63.5| = 2.5

|67 - 63.5| = 3.5

|69 - 63.5| = 5.5

Sum of absolute values = 30

[tex]\sf MAD=\dfrac{30}{8}=3.75[/tex]

Answer:

Both are TRUE

Step-by-step explanation:

✔️The statement, "angles 1 and 5 are corresponding angles" is TRUE.

Rationale/reason:

Angles that have corners that match are called corresponding angles. Angles 1 and 5 are angles found in the corners that match each other. Therefore, they are corresponding.

✔️The statement, "Angle 6 is congruent to angle 4" is TRUE.

Rationale/reason:

When two lines that are parallel is crossed by a transversal, the alternate interior angles formed are congruent to each other.

Angles 4 and 6 are interior angles that alternate each other along the transversal. Therefore they are congruent to each other.

Answer:

I think 5?................

Answer:

probability of selecting the square is 63.7% approximately

Step-by-step explanation:

First of all, the probability of the point of choice is within the red square can be obtained with this formula

probability = expected outcome / total number of possible outcomes

In this case, we are not dealing with discrete values which can be counted. instead, we are dealing with areas.

We are to go about this problem by finding the area of the internal square and dividing it by the area of the circle.

Area of the square

Area of the square = [tex]l^2[/tex]

where length = [tex]4\sqrt{2}[/tex]

Area = [tex](4\sqrt{2}) ^2 = 32cm^2[/tex]

Area of the circle

Area of the circle = [tex]\pi r^2[/tex]

area of circle =[tex]\pi \times 4^2 =50.26cm^2[/tex]

Probablity of selecting the square =

32/50.26 = 0.6366

To express this as a percentage, we multiply our answer by 100.

This will give us 0.6366 X 100 = 63.7% approximately

Answer:

Step-by-step explanation:

1.11

The expected value for the number of siblings of a randomly chosen student is 1.11.

The correct answer is C. 1.11.

To calculate the expected value for the number of siblings of a randomly chosen student, we need to multiply each possible number of siblings by its corresponding probability and sum up the results.

Expected Value = (0 x 0.18) + (1 x 0.65) + (2 x 0.09) + (3 x 0.05) + (4 x 0.02) + (5 x 0.01)

Expected Value = 0 + 0.65 + 0.18 + 0.15 + 0.08 + 0.05

Expected Value = 1.11

Therefore, the expected value for the number of siblings of a randomly chosen student is 1.11.

Learn more about Probability here:

https://brainly.com/question/31828911

#SPJ5

Answer:

8x^2 - 26x - 10

Step-by-step explanation:

3(6x2 + 3x - 5 ) = 18x^2 + 9 -15

5(2x2 + 7x - 1) = 10x^2 + 35 - 5

18^2 - 10x^2 = 8x^2

9x - 35x = - 26x

-15 -(-5) = -10

final answer = 8x^2 - 26x - 10

Answer:

B)  (-6,5)

Step-by-step explanation:

Quadrant I:  (+,+)

Quadrant II: (-,+)

Quadrant III: (-,-)

Quadrant IV: (+,-)

Answer:

This is so easy!

ONLY RIGHT TRIANGLES

Did you really ask this question?

Tip: You should learn the basics first.

1 pound = 16 ounces

2 pounds = 32 ounces

4 + 12 + 16 = 32

Use the 4, 12 and 16 ounce weights.

Answer:

Solution given:

1 pound = 16 ounces

2 pounds = 32 ounces

we have 32=4×12×16

so

the 4, 12 and 16 are ounce weights.

Answer:

B) Box-and-Whisker plot

Answer:

1/2^42 because the 45 will be dividing it b half 3 more times

Step-by-step explanation:

Answer:

0.111

Step-by-step explanation:

It is given that a manufacturing company found out that the intrastate contracts having a low bid which are [tex]$\text{uniformly}$[/tex] distributed between [tex]$22$[/tex]  and [tex]$31$[/tex] [tex]$\text{units of thousands}$[/tex] of dollars.

Therefore, the probability that a low bid on the [tex]$\text{next intrastate}$[/tex] shipping contract is in excess of [tex]$\$ 28,000$[/tex] is given by :

P(x ≥ 30) = 1 - P(X ≤ 30)

              [tex]$=1-\frac{30-22}{31-22}$[/tex]

             [tex]$=1-\frac{8}{9}$[/tex]

             [tex]$=\frac{1}{9}$[/tex]

            = 0.111

Answer:

11,15,7

Step-by-step explanation:

11+15+7=33 33/3=11 the mean

then 15-7=8 the range