After a discount of 25%, the sale price of a game system is $149.25. what is the original price?

Answer: Directix= -1

Focus (11, 2)

Step-by-step explanation:

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.

factor of 7a²b, 14abc

7a²b, 14abc= 7ab

Answer:

58

Step-by-step explanation:

58 because you divide 200 by 100 then getting that answer (3) then divide 175 by 3 which equals one percent and you get 58.333 you round it to the nearest whole and u get 58

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

Answer:

C

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

If the picking is random, there are 4 chances out of a possible 13 options.

4/13

Answer:

8.72×10²

Step-by-step explanation:

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:

yes less than a min

Step-by-step explanation:

if 17x-18=7x

then 17x-7x=18

10x=18

x=1.8

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

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

[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

Answer:

Step-by-step explanation:

Look at the picture.

(x, y)

left 1 unit: (5 - 1 = 4)

up 1 unit: (0 + 1 = 1)

Answer:

45

Step-by-step explanation:

They are both the same length-

Both step 1 and step 2 were correct with the process of moving the value of x into the place of x and continuing to solve. However, step 3 is incorrect because when it is a negative value being subtracted by another negative value, it remains a negative. So the answer is -14 instead of 14.

Answer:

-32 - 8 = -40

Step-by-step explanation: basicly for 1 instead of putting 3 and 2 together he multiplyed then minus 8

then for 2 he did -6 and -8

then: 14............

The goal amount of the student groups are given in percentages, which are fractions based on one hundred.

Reasons:

The amount the school band is raising for the trip = $9,500

Goal of the flutist = To raise 18% of the total amount

Goal of the trumpeters = 85% of the flutist's goal

Required:

The group that raise more money, given that their goals are met

Solution:

Given that the goal of the trumpeters trumpeters is 85% of the goal of the flutist, the flutist raised more money.

Required:

The difference in the amount raised by the students

Solution:

The amount raised by the flutist = 18% of $9,500 = 0.18 × $9,500 = $1,710

Amount the trumpeters raised = 85% of $1,710 = 0.85 × $1,710 = $1,453.5

The difference in the amount raised = $1,710 - $1,453.5 = $256.5

Learn more about percentages here:

https://brainly.com/question/1367867

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]

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

The Formula:

t = cn + 42

%95.79 because it is

Answer:

21(3a-2b)

Step-by-step explanation:

Answer:

21(3a-2b)

Step-by-step explanation:

63a - 42b​

21(3a-2b)

Answer:

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Class 11

>>Maths

>>Sets

>>Complement of Sets

>>If U = {1,2,3,4,5,6, 7, 8, 9 }, A = {2,

Question

Bookmark

If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}. Verify that

(i) (A∪B)

′

=A

′

∩B

′

(ii) (A∩B)

′

=A

′

∪B

′

Medium

Solution

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Verified by Toppr

U={1,2,3,4,5,6,7,8,9}

A={2,4,6,8}

B={2,3,5,7}

(i) (A∪B)

′

={2,3,4,5,6,7,8}

′

={1,9}

A

′

∩B

′

={1,3,5,7,9}∩{1,4,6,8,9}={1,9}

∴(A∪B)

′

=A

′

∩B

′

(ii) (A∩B)

′

={2}

′

={1,3,4,5,6,7,8,9}

A

′

∪B

′

={1,3,5,7,9}∪{1,4,6,8,9}={1,3,4,5,6,7,8,9}

∴(A∩B)

′

=A

′

∪B

I got the X and Y wrong, its 4. Sorry! mark the other answer instead

Reason:

9 - 8 = 1

7 - 3 = 4

Because that 7 and 3 are Y, 4 goes over. so it makes a whole number

Answer:

A. 4

Step-by-step explanation:

yeah-ya............. right?

Answer:

x = 15

Explanation:

First, add both equations on one side, and set it equal to 180° because it's supplementary:

2x + 8 + 8x + 22 = 180

combine like terms:

10x + 30 = 180

subtract 30 on both sides of the equation and you end up with:

10x = 150

divide both sides by 10 and you get:

x = 15

Answer:

x=5

Step-by-step explanation:

Answer:

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

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