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Answer:

number increased by ten. ... y = x + 0.25.

Step-by-step explanation:

Answer:

0.028 ; 0.649 ; 4

Step-by-step explanation:

P(correctly activation), p = 0.7

Number of sprinklers, n = 10

q = 1 - p = 1 - 0.7 = 0.3

Using the binomial probability relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Probability that all sprinklers activate correctly;

P(x = 10) = 10C10 * 0.7^10 * 0.3^0

P(x = 10) = 1 * 0.0282475249 * 1

P(x = 10) = 0.028

Probability that atleast 7 will operate correctly :

P(x ≥ 7) = p(x = 7) + p(x = 8) + p(x = 9) + p(x = 10)

P(x ≥ 7) = 0.267 + 0.233 + 0.121 + 0.028

P(x ≥ 7) = 0.649

3.)

Probability of atleast 1 operates :

P(x ≥ 1) = 0.98

1 - probability of 0 operates

1 - p(x =0)

P(x = 0) = nC0 * 0.7^0 * 0.3^n = 0.02

Recall :

nC0 = 1 ;

1 - p(x = 0)

P(x = 0) = 1 * 1 * 0.3^n = 0.02

0.3^n = 0.02 - - - (1)

0.3^3.24 = 0.02 - - - (2)

Comparing (1) and (2)

n = 3.24

Since, n cannot be a fraction ;

Then n is rounded to the next whole number = 4

Answer:

The area is 90 sq. cm

Step-by-step explanation:

Given

The variation can be represented as:

[tex]A\ \alpha\ l * w[/tex]

Area = 60, when l = 4 and w = 3

Required

Find Area, when l = 6 and w = 3

Represent the variation as an equation

[tex]A = k(l * w)[/tex]

Where k is the constant of variation.

Substitute 60 for A, 4 for l and 3 for w

[tex]60 = k * (4 * 3)[/tex]

[tex]60 = k * 12[/tex]

Make k the subject

[tex]\frac{60}{12} = k[/tex]

[tex]5=k[/tex]

[tex]k=5[/tex]

To get the value of Area when l = 6 and w = 3.

Substitute 5 for k, 6 for l and 3 for w in [tex]A = k(l * w)[/tex]

[tex]A = 5 * 6 * 3[/tex]

[tex]A = 90[/tex]

The area is 90 sq. cm

Answer:

A. 7%

Step-by-step explanation:

Given the following data;

Principal, P = $2,000

Time, T = 2 years

Simple Interest, I = $280

To find the simple interest rate, R?

Mathematically, simple interest is calculated using this formula;

[tex] S.I = \frac {PRT}{100} [/tex]

Where;

Substituting into the equation, we have;

[tex] 280 = \frac {2000*R*2}{100} [/tex]

Cross-multiplying, we have;

[tex] 280 * 100 = 4000*R[/tex]

[tex] 28000 = 4000R [/tex]

[tex] R = \frac {28000}{4000} [/tex]

Simple interest rate, R = 7%

Answer:

13 hours at Job B, and 17 hours at Job A.

Step-by-step explanation:

13×7.20= 93.60

17×5.90=100.30

100.30+93.60= 193.90

Answer:

7 weeks

Step-by-step explanation:

Answer:

7 weeks

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

2x+y = -4

put into slope-intercept form: y = -2x - 4

-3y = 2x+12

In slope-intercept form: y = -⅔x - 4

Both equations have a y-intercept of -4. There is only one graph where both lines pass through (0,-4).

The solution of the given system of equation is (0, -4). Therefore, option A is the correct answer.

The given system of equations are 2x+y=-4 and -3y=2x+12.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The system of equations can be solved as follows:

Here, 2x+y=-4 ----------(1)

-3y=2x+12 ----------(2)

From equation(1), y=-4-2x

Now, put y=-4-2x in equation (2) and simplify

That is, -3(-4-2x)=2x+12

⇒ 12+6x=2x+12

⇒ 4x=0

⇒ x=0

Substitute x=0 in equation (2), we get

-3y=12

⇒ y=-4

The solution of the given system of equation is (0, -4). Therefore, option A is the correct answer.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

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Answer:

8mph

Step-by-step explanation:

Distance= 1/3 mile

time= 1/24 hour

Speed= distance/time

speed = 1/3 divided by 1/24

           = 8mph

Answer:

8 im pretty sure

Step-by-step explanation:

Im pretty sure its D

Answer:

The answer is D

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

-14x  - 7 + 5y - x = -14x - x - 7 + 5y

                         = -15x - 7 + 5y

Answer:

Step-by-step explanation:

3

E 10 12

x=18*5)14. x=40/4. x=10. y=(15*4)/5 y=60/5 y=12.

resposta : 10 e 12

Answer:

Then substitute 3.14 for pi and 19 for the diameter.

The image shows the circumference formula.

19/2=9.5

C = 2(9.5)times pi.

C = 19 times 3.14

3.14 times 19 ≈ 59.69

Answer:

-3,1

Step-by-step explanation:

When you are doing Systems Of Equations using a graph, the point where the lines intersect is your answer

Answer:

Test scores will increase because the graph shows a positive association.

Step-by-step explanation:

Since it is going upwards to the right instead of going downwards and for the people who steady more hours they get better scores on there test.

btw i just took it and got it right

From given scatter plot, if the number of hours they study increases then the test scores will increase because the graph shows a positive association.

"A type of data representation that shows the relationship between two numerical variables. "

"When the values of one variable tend to increase as the values of the other variable increase, then two variable have positive association."

"When the values of one variable tend to decrease as the values of the other variable increase, then two variable have negative association."

For given question,

The scatter plot shows the test scores of a group of students who studied for different amounts of time in a week.

A scatter plot shows Hours Spent Studying on x axis and Test Score on y axis .

Also we have been given the ordered pairs

(0, 21), (0.8, 32), (1.2, 35),  (1.5, 39), (2.1, 42), (2.3, 45) and (2.5, 49) and   (2.7, 50) and (3, 67) and (4.6, 56) and (5, 69) and (5.3, 70) and (5.7, 74) and (6.4, 78) and (7.2, 80) and (7.5, 84) and (8.5, 88) and (8.7, 92) and (9.5, 96)

From the given data points of scatter plot,

as x - value increases, y - value also increases.

This means,  if the number of hours they study increases, the test scores will increase.

Here, the values of one variable tend to increase as the values of the other variable increase.

This means, there is positive association in variables Hours Spent Studying and Test Scores.

Therefore, from given scatter plot, if the number of hours they study increases then the test scores will increase because the graph shows a positive association.

Learn more about the positive association here:

https://brainly.com/question/858660

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Answer:

x=1 y=11

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the answer is in the attachment

Answer:  negative A.

Step-by-step explanation:

the slope of the line is going down so its negative. hope it helps!

Answer:

Step-by-step explanation:

You can change radicals to fractional exponents and vice versa. The 1/2 power means square root. The 1/3 power means the cubed root. etc etc

A:) [tex](81)^\frac{1}{2} =\sqrt{81} =9[/tex]

B:) [tex](125)^\frac{1}{3} =\sqrt[3]{125} =5[/tex]

C:) [tex](49)^\frac{3}{2}=\sqrt{(49)^3} =343[/tex]

D:) [tex](8)^\frac{5}{3}=\sqrt[3]{(8)^5}=32[/tex]

Answer:

a) The rate of change of the brightness after t days is [tex]B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}[/tex]

b) The rate of increase after one day is of 0.0915.

Step-by-step explanation:

The brightness after t days is given by:

[tex]B(t) = 4.2 + 0.45\sin{(\frac{2\pi t}{4.4})} = 4.2 + 0.45\sin{(0.4545\pi t)}[/tex]

A) Find the rate of change of the brightness after t days.

This is [tex]B^{\prime}(t)[/tex]

The derivative of a constant is 0, the derivative of [tex]\sin{at}[/tex] is [tex]a\cos{at}[/tex]

So, in this case, we have that:

[tex]B^{\prime}(t) = 0.45*0.4545\pi\cos{(0.4545\pi t)} = 0.204525\pi\cos{(0.4545\pi t)}[/tex]

The rate of change of the brightness after t days is [tex]B^{\prime}(t) = 0.204525\pi\cos{(0.4545\pi t)}[/tex]

B) Find the rate of increase after one day.

This is [tex]B^{\prime}(1)[/tex]. So

[tex]B^{\prime}(1) = 0.204525\pi\cos{(0.4545\pi)} = 0.0915[/tex]

The rate of increase after one day is of 0.0915.

Answer:

it is 4/5 because you have to divide by 6

Answer:

Step-by-step explanation:

Domain - Set of x-values

Range - Set of y-values

3). Since, x values vary from x = -6 to x = 5,

    Domain of the graph = [-6, 5]

    Since, y-values vary from y = -2 to y = 3

    Range of the graph = [-2, 3]

4). Domain of the graph = [-3, 3]

    Range of the graph = [-6, 5]

5). Domain of the graph = (-∞, ∞)

    Range of the graph = (-∞, ∞)

6). Domain of the graph = (-∞, 4]

    Range of the graph = (-∞, ∞)

7). Domain of the graph = (-∞, ∞)

    Range of the graph = [-1, 5]

8) Domain of the graph = [-1, 5)

    Range of the graph = [-3, 3)

Answer:

Step-by-step explanation:

Answer:

910293012

Step-by-step explanation:

it is nine thousand four billion atoms in one partial.