2x−15y=−10 −4x+5y=−30
Solve the following system for y:

The mean of the test that has a normal distribution is 55.

Let's denote the mean of the test by μ, and the standard deviation by σ. We can use the information given to set up a system of two equations:

49 = μ - 3σ  equation (1)

59 = μ + 2σ  equation (2)

To solve for μ, we can eliminate σ by adding equations (1) and equation (2) to get:

49 + 59 = μ - 3σ + μ + 2σ

Simplifying, we get:

108 = 2μ - σ

We can also solve for σ by subtracting equation (1) from equation (2) to get:

59 - 49 = μ + 2σ - (μ - 3σ)

Simplifying, we get:

10 = 5σ

Therefore, σ = 2.

Substituting this value of σ into the equation we found earlier, we get:

108 = 2μ - σ

108 = 2μ - 2

Solving for μ, we get:

2μ = 108 + 2

2μ = 110

μ = 110/2

μ = 55

Therefore, the mean of the test is 55.

Learn more about normal distribution here: https://brainly.com/question/29509087

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Answer:

between 128 and 144 ounces

Step-by-step explanation:

Recall that 1 pound equals 16 ounces.

8 pounds is 128 oz; 9 pounds is `144 oz.

Therefore, a gallon of milk weighs between 128 and 144 ounces.

Angle B = ADC arc / 2

32 = ADC arc / 2

ADC arc = 2 × 32

ADC arc = 64

_________________________________

ADC arc + ABC arc = 360

64 + ABC arc = 360

ABC arc = 360 - 60 - 4

ABC arc = 300 - 4

ABC arc = 296

_________________________________

Angle D = ABC arc / 2

x = 296 / 2

x = 148

_________________________________

Angle A = x - 40

Angle A = 148 - 40

Angle A = 108 degrees

Answer:

When the coefficient of the variable is negative, as shown below,

Step-by-step explanation:

2-4y>14

-4y>14-2

-4y>12, divde through by - 4

y>-3

Given:

The given sets are:

Set a : 200, 104, 100, 160.

Set b: 270, 400, 483, 300, x.

Mean of set a: mean of set b= 3:8

To find:

The value of x.

Solution:

Formula for mean:

[tex]Mean=\dfrac{\text{Sum of observations}}{\text{Number of observation}}[/tex]

The mean of set of a is:

[tex]Mean=\dfrac{200+104+100+160}{4}[/tex]

[tex]Mean=\dfrac{564}{4}[/tex]

[tex]Mean=141[/tex]

The mean of set of b is:

[tex]Mean=\dfrac{270+400+483+300+x}{5}[/tex]

[tex]Mean=\dfrac{1453+x}{5}[/tex]

[tex]Mean=\dfrac{1453+x}{5}[/tex]

It is given that,

Mean of set a: mean of set b= 3:8

[tex]\dfrac{141}{\dfrac{1453+x}{5}}=\dfrac{3}{8}[/tex]

[tex]\dfrac{705}{1453+x}=\dfrac{3}{8}[/tex]

[tex]8\times 705=3\times (1453+x)[/tex]

[tex]5640=4359 +3x[/tex]

Isolate the variable x.

[tex]5640-4359 =3x[/tex]

[tex]1281 =3x[/tex]

Divide both sides by 3.

[tex]\dfrac{1281}{3} =x[/tex]

[tex]427 =x[/tex]

Therefore, the value of x is 427.

Answer:

C. 0.305

Step-by-step explanation:

100 - 39 = 61

.5 x .61 = .305

30.5%

Answer:

(d) -15

Step-by-step explanation:

Given system of equations are:

[tex] \begin{cases}kx-5y=2\\\\6x+2y=7\end{cases}[/tex]

Since, given system of equations have no solution.

[tex] \therefore \frac{k}{6}=\frac{-5}{2} \neq\frac{2}{7}[/tex]

[tex] \implies \frac{k}{6}=\frac{-5}{2} [/tex]

[tex] \implies k=\frac{6(-5)}{2} [/tex]

[tex] \implies k=\frac{-30}{2} [/tex]

[tex] \implies k=-15[/tex]

good job guys ik math is hard sometimes

Answer:

8.07 inches

Step-by-step explanation:

7.29+0.78=8.07

Answer:

Ratio: Tan B = 12/5

Exact value in degrees: [tex]67.38^{o}[/tex]

Step-by-step explanation:

SOH CAH TOA

Means Tan B  means opposite/adjacent.

Tan B = 12/5

B = [tex]Tan^{-1} (\frac{12}{5})\\[/tex]

B = [tex]67.38^{o}[/tex]

Answer:

y=65+ 30x

Step-by-step explanation:

Given data

Cost of rental= $65

Additional month= $30

The expression for the total cost for x  months is

y=65+ 30x

Answer:

The 95% confidence interval for µ based on these data is (408,692).

Step-by-step explanation:

Sample mean and standard deviation:

The first step to solve this question is finding the sample mean and standard deviaton.

[tex]\overline{x} = \frac{550+620+480}{3} = 550[/tex]

[tex]s = \sqrt{\frac{(550-550)^2+(620-550)^2+(480-550)^2}{3}} = 57.1548[/tex]

Confidence interval:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 3 - 1 = 2

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 2 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 4.3027

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 4.3027\frac{57.1548}{\sqrt{3}} = 142[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 550 - 142 = 408

The upper end of the interval is the sample mean added to M. So it is 550 + 142 = 692

The 95% confidence interval for µ based on these data is (408,692).

Answer:

232

Step-by-step explanation:

Answer:

Blue paint: 1, 2, 2.8, 10

Red paint: 2.5, 5, 7, 25

Step-by-step explanation:

constant of proportionality: 2.5

2.5x = y

(B)

Step-by-step explanation:

Look at the triangle with the 65° angle. Note that the 65° angle is opposite the 24-ft side and p is the length of the triangle's hypotenuse so let's use the definition of sine 65°:

sin 65 = opposite/hypotenuse

= (24 ft)/p

Solving for p,

p = (24 ft)/(sin 65°)

= 26.48 ft

Answer:

A

Step-by-step explanation:

Answer:

0.2%

Step-by-step explanation:

The given parameters are;

The percentage of product within the correct range = 95%

The percentage of the times the sensor reject boxes of incorrect weight = 98%

The percentage of the times the company reject boxes with correct weight = 1%

[tex]\begin{array}{cccc}&P&N&T\\P&TP&0.9&90\\N&FP&9.8&10\end{array}[/tex]

We have, FN = 0.9, TN = 9.8, TP = 90 - 0.9 = 89.1, FP = 10 - 9.8 = 0.2

FNR = FN/(FN + TP) = 0.9/(0.9 + 89.1) = 0.01

FPR = 0.2/(0.2 + 9.8) = 0.02

TPR = 89.1/(89.1 + 0.9) = 0.99

TNR = 9.8/(9.8 + 0.2) = 0.98

P(C/A) = TPR × P(C)/((TPR × P(C) + FPR×(1 - P(C)))

Where;

P(C/A) = The probability that a correct weight package is accepted

∴ P(C/A) = 0.99*0.9/(0.99*0.9 + 0.02*0.1) ≈ 0.99776

The probability that a correctly weighed package is rejected, P(C/R), is given as follows;

P(C/R) = 1 - P(C/A)

∴ P(C/R) ≈ 1 - 0.99776 = 0.00224 ≈ 0.2%

The probability that a correctly weighed package is rejected, P(C/R) ≈ 0.2%

Answer:0.9%

Step-by-step explanation:

good luck!!!

Answer:

a) 2x + 6y + 7x

9x + 6y

b) 3a + 8b + 5a

8a + 8b

c) 6u + 3v - 2u

4u + 3v

d) 9p + 8q - p

8p + 8q

e) 2m + 5n + 4m + 3n

6m + 5n + 3n

6m + 8n

f) 6u + 9v + u + 3v

12v + 6u + u

12v + 7u

g) 8b + 7c + 3b - 2c

8b + 3b + 5c

11b + 5c

h) a + 2b + a - b

2a + 2b - b

2a + b

i) 5a + 2b - 5a + 6b

8b + 5a - 5a

8a

h) 9p + 3q - 2p - 3q

7p + 3q - 3q

7p

5x + 16 = ( 2x + 14 ) + 32

...............................................

This the clue and the right direction

You got this

Answer:

what is question?

Step-by-step explanation:

Answer:

324?

Step-by-step explanation:

Answer:

Step-by-step explanation:

5  5 5 m²

Answer:

8, 8, 14

Step-by-step explanation:

Since 8 is the mode, it will appear the most. As there are 3 numbers, 8 will be two of them, so there are 2 8s.

To find the total of the numbers, do the mean multiplied by the amount of numbers, which is 10 times 3, which equals 30.

To find the last number, minus the two numbers you already have from the total, so 30-8-8=14

So the three numbers are 8,8,14.

Hope this helps! :)

Answer:

a=8/2

a=4

Step-by-step explanation:

Answer:

[tex]a = 4[/tex]

Step-by-step explanation:

[tex](2a) = 8[/tex]

[tex]a = \frac{8}{2} [/tex]

[tex]a = 4[/tex]

Answer:

First you would see the picture and you would count how many people had less than 20 which is 18

brainliest

Step-by-step explanation:

Answer:

The coefficient is 7

Step-by-step explanation:

The coefficient of an algebraic expression is the number that is being multiplied by a variable or multiple variables. In this case, 7 is being multiplied by x and y, so 7 is the coefficient.

Answer:

x = 15

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

BC/DC = EC/AC , substitute values

3x×5/32 - 5x-5/56 ( cross- multiply )

56(3x - 5) = 32(5x - 5) ← distribute and simplify both sides

168x - 280 = 160x - 160 ( subtract 160x from both sides )

8x - 280 = - 160 ( add 280 to both sides )

8x = 120 ( divide both sides by 8 )

x = 15

Answer:

–43p + (–25)  is  Equivalent to  –43p – 25.

Step-by-step explanation:

Needed: 25 – 43p ,  25 – 4 , p 3. –25p –43 ,  –43p + (–25)

Answer:

7

Step-by-step explanation:

Answer:

the answer is 2/3

hope this helps

have a good day :)

Step-by-step explanation: