Marcus sleeps 60 hours a week this is 5 times as many hours as he plays chess. How many hours a week does Marcus play chess?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Root x= 3 of multiplicity 2, it means we can factor it with : (x-3)²

Root x = 1, of multiplicity 1, it means we can factor this polynomial with : (x-1)

Root x = -3, of multiplicity 2, it means we can factor this polynomial with : (x+3)²

Finally we get this expression : (x-3)²(x+3)²(x-1)

This expression is a polynomial of degree 5 but what is the y intercept of it ?

Basically, we need to replace x by zero and the value of the expression will be the y intercept :

let x = 0

then ,

(0-3)²(0+3)²(0-1) = 9*9*(-1) = -81 #-162

We need an y intercept of value = -162

Thus we simply need to multiply by 2, and finally f(x) = 2(x-3)²(x+3)²(x-1)

satisfies all the required condition

Good Luck

Answer:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

0.00885... < 0.01

The test statistic of 46 is significant

There is sufficient evidence to reject H₀ and accept H₁

Air bags are more effective as protection than safety belts

Step-by-step explanation:

821 crashes

46 hospitalisations where car has air bags

7.8% or 0.078 probability of hospitalisations in cars with automatic safety belts

α = 0.01 or 1% ← level of significance

One-tailed test

We are testing whether hospitalisations in cars with air bags are less likely than in a car with automatic safety belts;

The likelihood of hospitalisation in a car with automatic safety belts, we are told, is 7.8% or 0.078;

So we are testing if hospitalisations in cars with air bags is less than 0.078;

So, firstly:

Let X be the continuous random variable, the number of hospitalisations from a car crash with equipped air bags

X~B(821, 0.078)

Null hypothesis (H₀): p = 0.078

Alternative hypothesis (H₁): p < 0.078

According to the information, we reject H₀ if:

P(X ≤ 46 | X~B(821, 0.078)) < 0.01

To find P(X ≤ 46) or equally P(X < 47), it could be quite long-winded to do manually for this particular scenario;

If you are interested, the manual process involves using the formula for every value of x up to and including 46, i.e. x = 0, x = 1, x = 2, etc. until x = 46, the formula is:

[tex]P(X = r) = nCr * p^{r} * (1 - p)^{n - r}[/tex]

You can find binomial distribution calculators online, where you input n (i.e. the number of trials or 821 in this case), probability (i.e. 0.078) and the test statistic (i.e. 46), it does it all for you, which gives:

P(X ≤ 46 | X~B(821, 0.078)) = 0.00885745584

Now, we need to consider if the condition for rejecting H₀ is met and recognise that:

0.00885... < 0.01

There is sufficient evidence to reject H₀ and accept H₁.

To explain what this means:

The test statistic of 46 is significant according to the 1% significance level, meaning the likelihood that only 46 hospitalisations are seen in car crashes with air bags in the car as compared to the expected number in car crashes with automatic safety belts is very unlikely, less than 1%, to be simply down to chance;

In other words, there is 99%+ probability that the lower number of hospitalisations in car crashes with air bags is due to some reason, such as air bags being more effective as a protective implement than the safety belts in car crashes.

Answer:

20 inches

Step-by-step explanation:

If that's centimeters on the x-axis and inches in the y-axis, then the slope is 2/5 and the y-intercept is 0.

[tex]y=\frac{2}{5}x[/tex]

The slope of 2/5 in this context means 2 inches per 5 centimeters. Then, either by solving the equation or by graphing the line, you can determine that there are about 20 inches in 50 centimeters.

Answer:

X miles ( 35, 125, 265, 310)

m = 35 + 45x

755

Step-by-step explanation:

Hope this helps, btw have an awesome day

Answer:

8.72×10²

Step-by-step explanation:

Answer:

Since the centre of the circle is (−4,−5) and its radius =6

Then, the equation of the circle is

⇒(x−(−4))

2

+(y−(−5))

2

=6

2

⇒(x+4)

2

+(y+5)

2

=36

⇒x

2

+8x+16+y

2

+10y+25−36=0

⇒x

2

+y

2

+8x+10y+5=0

Step-by-step explanation:

Paki brainlilest na lng po salamaf

The Formula:

t = cn + 42

Answer:

y = -9x + 18.

Step-by-step explanation:

The general form is y = mx + c , where m = the slope and c = y-intercept.

[tex]\huge\boxed{Hi \: there! :)}[/tex]

We are given the slope of the line: -9.

We are also given its y-intercept: 18.

Slope-Intercept Form:

[tex]\huge\sf\{y=mx+b[/tex]

Where

m is the slope and b is the y-intercept.

Plug in the values:

y=-9x+18

[tex]\huge\boxed{Therefore, \: our \: equation \: is: y=-9x+18}[/tex]~An Unknown Dreamer

Good luck!

Step-by-step explanation:

a. The null hypothesis is generally an exact value and the alternative hypothesis is the one we are trying to show. We are trying to show that the population mean is different from $24.57, so the hypotheses are as follows:

Null: The population mean hourly wage in the manufacturing industry is the same as the population mean hourly wage in the goods-producing industries

Alternative: The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries

b.

Because we know the population standard deviation, we can use a z test

Plugging in the values:

Expected population mean: 24.57

Sample average: 23.89

Sample size: 30

Population standard deviation: 2.4, we get 0.1207 as our p-value.

c. Using a = 0.05, our p-value is greater than that, so we can not conclude the alternative hypothesis (The population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries)

d. Using a critical value calculator, we can find that for a two-tailed approach, the critical value would be 1.96. This would mean that the z score would have to be greater than 1.96 or less than -1.96 for the results to be significant. The population mean we would plug in here is 24.57, while the raw score would be 23.89 and the standard deviation would be 2.4. The z score we get is -0.283, which is not in the values specified (>1.96 or <-1.95) so we cannot conclude the alternative hypothesis

Answer: No.

Step-by-step explanation:

If you multiply 1001 by 1001 it's not another palindromic number.

Answer:

O

2

4

6

8

10

12

Determine the five-statistical summary of the data. Drag the correct number to each variable in the summary.

14

16

18

20

22 24 26

28

30

Minimum:

Maximum:

Median:

First Quartile:

Third Quartile:

1

2

3

4

11

5

12

6

ما تا ته

13

14

8

21

15

22

16

10

23

17

24

18

25

19

26

20

27

28

29

30

Please answer fast

Answer:

no solution

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

1.23 would be your answer.

Have a great day! :)

Answer:

y=2

y=4

y=6

y=8

Step-by-step explanation:

please mark brainlist

Answer:

Step-by-step explanation:

Look at the picture.

(x, y)

left 1 unit: (5 - 1 = 4)

up 1 unit: (0 + 1 = 1)

Answer:

11/3 = 3 2/3 innings

Step-by-step explanation:

3 pitchers = 11 innings

1 pitcher = x innings

in the first equation, divide both sides by 3 to get 1 pitcher on one side

1 pitcher = 11/3 innings = 3 2/3 innings

if 17x-18=7x

then 17x-7x=18

10x=18

x=1.8

factor of 7a²b, 14abc

7a²b, 14abc= 7ab

Answer:

Step-by-step explanation:

0.2(d - 6) = 0.3d + 5 - 3 + 0.1d

0.2d - 1.2 = 0.4d + 2

     - 0.2d = 3.2

           d = - 16

Answer:

d = -16

Step-by-step explanation:

[tex]0.2(d-6)=0.3d+5-3+0.1d\\\rule{150}{0.5}\\0.2d - 1.2 = 0.3d+5-3+0.1d\\\\0.2d - 1.2 = 0.3d+0.1d+ 5-3\\\\0.2d - 1.2=0.4d + 2\\\\0.2d- 0.2d - 1.2 = 0.4d -0.2d + 2\\\\-1.2 = 0.2d + 2\\\\-1.2 -2 = 0.2d + 2 - 2\\\\-3.2 = 0.2d\\\\\frac{-3.2 = 0.2d}{0.2}\\\\-16 = d\\\\\boxed{d = -16}[/tex]

Answer:

A

D

B

C

Step-by-step explanation:

We can simplify the expressions for easier comprehension:

A. 60.7 x 10^-1 = 6.07

B. 6.07 x 10^3 = 6,070

C. 0.67 x 10^4 = 6,700

D. 6.7 x 10^2 = 670

Now, we can order them in ascending order (least to greatest):

A

D

B

C

Answer:

C

Step-by-step explanation:

log5- klog2= log5-log2^k = log(5/2^k)

Answer:

-9.6

Step-by-step explanation:

92-44/17-21

Answer:

-12

Step-by-step explanation:

Formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Identify the values:

[tex]y_2=44[/tex]

[tex]y_1=92[/tex]

[tex]x_2=21[/tex]

[tex]x_1=17[/tex]

Plugin the values; solve:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{44-92}{21-17}[/tex]

[tex]= \frac{-48}{4}[/tex]

[tex]\bold{m=-12}[/tex]

Therefore, the slope of the line containing the points (17,92) and

(21, 44) is -12.

Answer:

Discriminant is [tex] {b}^{2} - 4 \times a \times c [/tex]

[tex]16 - 4 \times 4 \times 1 = 0[/tex]

[tex]\huge\underline\mathtt\colorbox{cyan}{3-7}[/tex]

Step-by-step explanation:

The correct interpretation of 3+(-7) is 3-7, simply

Answer:

The answer will be

3+(-7)

The sum of positive and negative is negative

So 3+(-7) is 3-7

= -4

Step-by-step explanation:

Hope it helps

Please Mark as brainliest

The slope of the line represents that the remainder of the goal decrease by 8 for each card sold.

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The line passes through the point (1, 8) and (2, 16), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-8=\frac{16-8}{2-1}(x-1)\\\\y=8x[/tex]

The equation of the line is given by y =8x

Find out more about linear equation at: https://brainly.com/question/14323743

Find out more on linear equation at: https://brainly.com/question/14323743