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3 years ago

When solving -1/3 (x − 15) = −4, what is the correct sequence of operations?

Mathematics

1 answer:

antoniya [11.8K]3 years ago

8 0

Answer:

The correct sequence of operation is multiply each side by (-3), add 15 to each side.

Therefore, option (B) is the correct answer.

Step-by-step explanation:

$\frac{-1}{3} (x - 15) = -4$

Multiply each side by -3

$(-3) \times \frac{-1}{3} (x - 15) = -4 \times (-3)$

$(x - 15) = 12$

Adding 15 to both sides

$x - 15 + 15 = 12 + 15$

x = 27.

So, the correct sequence of operation is multiply each side by (-3), add 15 to each side.

Therefore, option (B) is the correct answer.

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Assume the general population gets an average of 7 hours of sleep per night. You randomly select 45 college students and survey

tekilochka [14]

Answer:

a) ii. This is a left-tailed test.

b) -1.59

c) -1.301

d) i. reject null hypothesis

e) Option i) The data supports the claim that college students get less sleep than the general population.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 7 hours

Sample mean, $\bar{x}$ = 6.87 hours

Sample size, n = 45

Alpha, α = 0.10

Sample standard deviation, s = 0.55 hours

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 7\text{ hours}\\H_A: \mu < 7\text{ hours}$

a) We use one-tailed(left) t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{6.87 - 7}{\frac{0.55}{\sqrt{45}} } =-1.59$

c) Now,

$t_{critical} \text{ at 0.10 level of significance, 44 degree of freedom } = -1.301$

Since,

$t_{stat} < t_{critical}$

d) We fail to accept the null hypothesis and reject it.

We accept the alternate hypothesis and conclude that mean number of hours of sleep for all college students is less than 7 hours.

e) Option i) The data supports the claim that college students get less sleep than the general population.

8 0

3 years ago

Two cars leave a town at the same time heading in opposite directions. One car is traveling 12 mph faster than the other. After

Katena32 [7]

<span>Find the speed of each car.
Let a be the first car
Let b be the second car
=> a = x miles per hour
=> b = x + 12 miles per hour
=> 2 (x+ x + 12) = 232 miles per hour
=> 2x + 12 = 232
=> 2x + 12 = 116
=> 2x = 116 - 12
=> 2x / 2 = 104 / 2
=> x = 52 (speed of Car A)
=> 52 + 12 = 64 miles per hour (speed of Car B)</span>

4 0

3 years ago

Help please i need it bad

evablogger [386]

Answer:

-13, -3

15, 2.6

Step-by-step explanation:

x, y are the numbers

x = 5y + 2

x×y = 39

(5y + 2)×y = 39

5y² + 2y - 39 = 0

the solution of a quadratic equation :

y = (-b ± sqrt(b² - 4ac))/2a

a = 5

b = 2

c = -39

y = (-2 ± sqrt(2² - 4×5×-39))/2×5 =

= (-2 ± sqrt(4 + 780))/10 =

= (-2 ± sqrt(784))/10 = (-2 ± 28)/10

y1 = (-2 + 28)/10 = 26/10 = 2.6

y2 = (-2 - 28)/10 = -30/10 = -3

x1 = 5×2.6 + 2 = 13 + 2 = 15

x2 = 5×-3 + 2 = -15 + 2 = -13

5 0

2 years ago

what is f(x) = 2x2 28x – 5 written in vertex form? f(x) = 2(x 7)2 – 19 f(x) = 2(x 7)2 – 103 f(x) = 2(x 14)2 – 14 f(x) = 2(x 14)2

polet [3.4K]

Hello,
++++++++++++++++++++++
Answer B
++++++++++++++++++++++

2x²+28x-5=2(x²+2*7x+49)-5-2*48
=2(x+7)²-103

++++++++++++++++++++++++++++++

4 0

3 years ago

Read 2 more answers

Given h(x)=5x-2, find h(5)

Tomtit [17]

Answer:

h(5)=23

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers