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Dennis_Churaev [7]
3 years ago
8

Complete each ordered pair so that it is a solution of the given linear equation. x minus 5 y equals negative 3​; left parenthes

is comma 1 right parenthesis comma left parenthesis 7 comma right parenthesis
Mathematics
1 answer:
never [62]3 years ago
6 0

Answer: The ordered pairs are (2,1) and (7,2).

Step-by-step explanation:

Since we have given that

x-5y=-3

if y=1

we get that

x-5y=-3\\\\x-5(1)=-3\\\\x-5=-3\\\\x=-3+5\\\\x=2

If x= 7, we get that

x-5y=-3\\\\7-5y=-3\\\\-5y=-3-7\\\\-5y=-10\\\\y=\dfrac{10}{5}\\\\y=2

So, the ordered pairs are (2,1) and (7,2).

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Write a function describing the relationship of the given variables.
Oliga [24]

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

  variables that can be expressed by an equation in which one

  variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

 constant of variation

* Now lets solve the problem

# V is varies directly with the square  of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

 by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

3 0
3 years ago
Body armor provides critical protection for law enforcement personnel, but it does affect balance and mobility. The article "Imp
yKpoI14uk [10]

Answer:

No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that true average task time with armor is less than 2 seconds.

Then, the null and alternative hypothesis are:

H_0: \mu=2\\\\H_a:\mu< 2

The significance level is 0.01.

The sample has a size n=52.

The sample mean is M=1.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.2}{\sqrt{52}}=0.028

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1.95-2}{0.028}=\dfrac{-0.05}{0.028}=-1.803

The degrees of freedom for this sample size are:

df=n-1=52-1=51

This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

3 0
2 years ago
What is the area of this figure? enter your answer as a decimal in the box. 7cm 9cm 11cm
ASHA 777 [7]

Answer:

4ed2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Jan wants to protect the wooden box in question 4a by painting varnish on all of the outside surfaces, including the bottom. Wil
Dafna1 [17]

Answer:

As this question is incomplete, but we will try to solve this question by adding our own data to understand the concept of the problem.

Explanation is given below

Step-by-step explanation:

As this question is incomplete, but we will try to solve this question by adding our own data to understand the concept of the problem.

In order to answer this question we need to have the dimensions of the box.

Let's suppose there are 6 outside surfaces of the box and are equal in dimension including the bottom side which Jan wants to varnish.

So,

Let's suppose,

Surface area of the cube = 6a^{2}

Here, Surface area = 275 square inch

Surface area of the cube = 6a^{2} = 275 square inch

a^{2} = 275/6 = 45.833

a = \sqrt{45.833}

a = 6.77 inches

Now, for the amount of the varnish, we need the spreading rate of the varnish to be used on the box,

Let's suppose it is = 11 square incher per litre.

So,

Required Varnish = Surface area / Spreading rate

Required varnish = 275 / 11

Required varnish = 25 liters

If the 1 container of varnish contains 25 liters then it will be sufficient to protest the outside surfaces of the box.

6 0
3 years ago
What is the value of the expression below?<br> 72 ÷ 4.5x3+8
Fofino [41]

Answer:

56

Step-by-step explanation:

Apply PEMDAS:

72 / 4.5*3+8\\\\16*3+8\\\\48+8\\\\\boxed{56}

4 0
3 years ago
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