Roger Brown works for the sanitation department. He earns a salary of $721.00 biweekly. His boss gave him
a raise that will go into effect at the first of the year. His new annual salary will be $20.995.00. How much
more money will Roger make next year than this year?​

Answer:

2646/100 or 260  46/100 or 260 23/50

u = 2i - 6j

v = 3i + 9j

Take the dot product:

u • v = (2i - 6j) • (3i + 9j)

u • v = (2i • 3i) + (2i • 9j) + (-6j • 3i) + (-6j • 9j)

u • v = 6 (i • i) + 18 (i • j) - 18 (j • i) - 54 (j • j)

The dot product is defined so that for the orthogonal unit vectors i and j, we have i • i = j • j = 1, and i • j = 0. So the above reduces to

u • v = 6 + 0 - 0 - 54

u • v = -48

The range of g(x) = 3|x-1|-1 is (-∞,∞).

The range is "set of all y-coordinates of the function's graph".

According to the question,

g(x) = 3 |x-1| - 1

To find range of linear polynomial 3|x-1|-1  put any value in right 'x' we can able to get any value 'y' in the set (-∞.∞).

Hence, the range of g(x) = 3|x-1|-1 is (-∞,∞).

Learn more about range here

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Answer:

a) Null hypothesis:[tex]\mu = 140[/tex]  

Alternative hypothesis:[tex]\mu \neq 140[/tex]  

b) [tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]  

c) The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]

Now we can calculate the p value, since we are conducting a two tailed test:

[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]  

Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

Step-by-step explanation:

Information provided

[tex]\bar X=170[/tex] represent the sample mean   in minutes

[tex]s=80[/tex] represent the standard deviation

[tex]n=64[/tex] sample size  

[tex]\mu_o =140[/tex] represent the value to verify

[tex]\alpha[/tex] represent the significance level

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We are interested in determining whether or not the average usage in Soddy-Daisy is significantly different from the U.S. average (140 minutes), the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 140[/tex]  

Alternative hypothesis:[tex]\mu \neq 140[/tex]  

Part b

Since we don't know the population deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]t=\frac{170-140}{\frac{80}{\sqrt{64}}}=3[/tex]  

Part c

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]

Now we can calculate the p value, since we are conducting a two tailed test:

[tex]p_v =2*P(t_{63}>3)=0.0039[/tex]  

Since the p value is lower than the significance level of [tex]\alpha=1-0.95=0.05[/tex] we have enough evidence to conclude that the true mean is significantly different from the US average of 140 minutes

The null hypothesis that the average internet usage in Soddy-Daisy is not significantly different from the U.S. average is rejected based on a computed z-score of 3, which falls outside the critical z-score values for a 95% confidence level. Therefore, the average internet usage in Soddy-Daisy is significantly different from the U.S. average.

This problem pertains to the domain of statistical hypothesis testing. Let's first set up the null and alternative hypotheses:

For the second part, we need to compute the test statistic. The formula for the test statistic (z) in this context is z = (x - μ) / (σ/√n), where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

So, (170-140) / (80/√64) = 30 / (10) = 3. The z score is 3.

For the final part of your question, with 95% confidence, the critical z-score values are -1.96 and +1.96. Since our observed z-score of 3 is outside this range, we reject the null hypothesis. Therefore, we can conclude that the average internet usage in Soddy-Daisy is significantly different from the U.S. average.

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Answer:37.5 %

Step-by-step explanation:

Given

School attendance varies between 200 and 275

Most percentage error arises when attendance of 275 students is expected but only 200 students are present

Percentage error[tex]=\frac{275-200}{200}\times 100=37.5\ \%[/tex]

Answer:

300tan43 - 300tan40

Step-by-step explanation:

Use tangent to find the height of the building:

tan40 = b/300

b = 300tan40

The use tangent to find the height to the top of the antenna:

tan43 = a/300

a = 300tan43

The antenna height = a - b

Answer:

c= -10

Step-by-step explanation:

-3(c-1)= 33

-3(c) -3(-1)= 33 (expand)

-3c +3= 33

-3c= 33-3 (-3 on both sides)

-3c= 30 (simplify)

3c= -30 (divide by -1 throughout)

c= -30 ÷3

c= -10

Answer:

You have to break apart the shape into individual shapes to find the volume of each one. Then you add.

hope this helped :)

Answer:

Reject null hypothesis ([tex]H_0[/tex]) since the​ P-value is less than the significance level.

Step-by-step explanation:

We are given that it has long been stated that the mean temperature of humans is 98.6 degrees F. ​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6 degrees F.

The sample data resulted in a sample mean of 98.2 degrees F and a sample standard deviation of 0.9 degrees F.

Let [tex]\mu[/tex] = mean temperature of humans.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu\geq[/tex] 98.6°F      {means that the mean temperature of humans is more than or equal to 98.6°F}

Alternate Hypothesis, [tex]H_A[/tex] : p < 98.6°F    {means that the mean temperature of humans is less than 98.6°F}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                        T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean temperature = 98.2°F

            [tex]\sigma[/tex] = sample standard deviation = 0.9°F

            n = sample of healthy adults = 56

So, test statistics  =   [tex]\frac{98.2-98.6}{\frac{0.9}{\sqrt{56} } }[/tex]  ~ [tex]t_5_5[/tex]

                               =  -3.326

The value of t test statistics is -3.326.

Now, P-value of the test statistics is given by following formula;

         P-value = P( [tex]t_5_5[/tex] < -3.326) = 0.00077 or 0.08%

Since, P-value of the test statistics is less than the level of significance as 0.08% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean temperature of humans is less than 98.6°F.

To determine if the mean human temperature is less than 98.6°F, we conducted a left-tailed t-test using the provided sample data. We calculated the t-test statistic and then used it to find the p-value. We then used the p-value to make our final decision on whether to reject or fail to reject our null hypothesis.

In this scenario, we are performing a hypothesis test about the average human temperature. Let's formulate our hypothesis first:

We will conduct a left-tailed t-test because we are testing whether the average human temperature is less than a stated value.

Given the data: the sample size n = 250, the sample mean (x_bar) = 98.2 F, and the standard deviation (s) = 0.9 F.

To calculate the t-test statistic, use the formula: t0 = (x_bar - μ) / (s/√n)

For getting the p-value, you would use a statistical table or software with the above t statistic and degree of freedom (which is n-1 in this case).

In the end, if your p-value is less than the significance level (α = 0.01 in this case), we reject the null hypothesis, if not, we fail to reject the null hypothesis.

If the P-value is less than α, we would conclude that the research may be correct, and the average human temperature is indeed lower than 98.6 F (37.0 °C).

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Eric and Joshua are playing ping pong and pool. Joshua believes he has a good chance of beating Eric in at least one of the games. The probability Joshua beats Eric in ping pong is 0.48. The probability Joshua beats Eric in pool is 0.46. Joshua is willing to assume the probability of Eric winning a game of ping pong is independent of him winning a game of pool.

Find the probability:

The probability that Joshua beats Eric in ping pong AND pool?

The probability that Joshua beats Eric in ping pong OR pool?

Answer:

P(pp & pool) = 22%

There is 22% probability that Joshua beats Eric in ping pong AND pool.

P(pp OR pool) = 50%

There is 50% probability that Joshua beats Eric in ping pong OR pool.

Step-by-step explanation:

The probability Joshua beats Eric in ping pong is given by

P(pp) = 0.48

The probability Joshua beats Eric in pool is given by

P(pool) = 0.46

The probability that Joshua beats Eric in ping pong AND pool is given by

P(pp & pool) = P(pp)×P(pool)

P(pp & pool) = 0.48×0.46

P(pp & pool) = 0.22

P(pp & pool) = 22%

Therefore, there is 22% probability that Joshua beats Eric in ping pong AND pool.

The probability that Joshua beats Eric in ping pong OR pool is given by

P(pp OR pool) = P(pp)×0.52 + P(pool)×0.54

Where 0.52 is the probability that Eric beats Joshua in the ping pong match (1 - 0.48 = 0.52)

Where 0.54 is the probability that Eric beats Joshua in the pool match (1 - 0.46 = 0.54)

P(pp OR pool) = 0.48×0.52 + 0.46×0.54

P(pp OR pool) = 0.25 + 0.25

P(pp OR pool) = 0.50

P(pp OR pool) = 50%

Therefore, there is 50% probability that Joshua beats Eric in ping pong OR pool.

To calculate the probability of Joshua beating Eric in at least one game of ping pong or pool, taking into account the probabilities for each game.

Probability plays a key role in analyzing the chances of events happening. In this case, we have two independent events: winning ping pong and winning pool. The probability of Joshua winning at least one game can be calculated using the probabilities given for each game.

Calculate the probability of Joshua winning both games: 0.48 × 0.46 = 0.2208

Subtract this value from 1 to find the probability of Joshua winning at least one game: 1 - 0.2208 = 0.7792

Therefore, Joshua has a 77.92% chance of beating Eric in at least one of the games.

A Markov chain is used to model this situation. The transition matrix based on the given probabilities will be [[0.9, 0.1],[0.4, 0.6]]. Also, to calculate the probability of being in a high-volume state two weeks from now given that it is in a high-volume state now, we square the matrix and look at the upper-left entry.

A Markov process, in particular, a Markov chain, is a stochastic process that undergoes transitions from one state to another on a state space following the Markov property, stating that future states depend only on the current state and not on events that occurred before it. The transition matrix in these cases provides the probabilities between state transitions.

Given the data:

Based on these probabilities the transition matrix will be of the form:

[[0.9, 0.1],[0.4, 0.6]].

To find the probability that the volume will be high two weeks from now, we will need to square the matrix as we are considering two steps ahead. The top left element of the resulting matrix will give the desired probability. In general, the i,j-th entry of the square of a transition matrix gives the 2-step transition probability from state i to state j.

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Answer:False

Step-by-step explanation:

False

Whenever a stock is sold more money than what is paid for it is termed as Gain or profit

For example if an item is bought for [tex]\$100[/tex] and it is sell for [tex]\$120[/tex]

then there is a profit of

[tex]\Rightarrow \frac{120-100}{100}\times 100[/tex]

[tex]\Rightarrow 20\%[/tex]

or a gain of [tex]\$20[/tex]

Answer: The answer is False, i know this because i took this quiz on edge and it was correct as false <3 hope this helps

Step-by-step explanation: brainliest please :3

Answer:

153.9 cm

Step-by-step explanation:

A = pi(r²)

= 3.14(7²)

= 3.14(49)

= 153.86

= 153.9 cm

Answer:

The s-score corresponding to a score  of 54 is 4.67

Step-by-step explanation:

In a certain normal distribution of scores:

Mean = [tex]\mu = 40[/tex]

Standard deviation = [tex]\sigma = 3[/tex]

We are supposed to find  the z-score corresponding to a score  of 54.

Formula : [tex]Z=\frac{x-\mu}{\sigma}[/tex]

x=54

Substitute the values

So,[tex]Z= \frac{54-40}{3}[/tex]

Z=4.67

So, Option A is true

Hence the s-score corresponding to a score  of 54 is 4.67

The t-statistic is calculated as: -6.70

What is the test statistic?

The appropriate test to conduct at the alpha equals 0.01 level of significance is a one-tailed t-test.

The null hypothesis is that the mean hippocampal volume of adolescents with alcohol use disorders is equal to 9.02 cm cubed, while the alternative hypothesis is that the mean hippocampal volume is less than 9.02 cm cubed.

Thus:

H₀: μ = 9.02 cm³

Hₐ: μ < 9.02 cm³

The t-statistic is calculated from the formula:

t = (x - μ)/(σ/√n)

t =  (8.02 - 9.02) / (0.7/√(22))

= -6.70.

Therefore, the t-statistic is -6.70

Answer:

95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Step-by-step explanation:

We are given that the engineers take a random sample of 45 cables and apply weights to each of them until they break. The mean breaking weight for the 45 cables is 768.2 lb. The standard deviation of the breaking weight for the sample is 15.1 lb.

Since, in the question it is not specified that how much confidence interval has be constructed; so we assume to be constructing of 95% confidence interval.

Firstly, the Pivotal quantity for 95% confidence interval for the population mean is given by;

                            P.Q. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean breaking weight = 768.2 lb

            s = sample standard deviation = 15.1 lb

            n = sample of cables = 45

            [tex]\mu[/tex] = population mean breaking strength

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.02 < [tex]t_4_4[/tex] < 2.02) = 0.95  {As the critical value of t at 44 degree

                                           of freedom are -2.02 & 2.02 with P = 2.5%}  

P(-2.02 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.02) = 0.95

P( [tex]-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.02 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.02 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                     = [ [tex]768.2-2.02 \times {\frac{15.1}{\sqrt{45} } }[/tex] , [tex]768.2+2.02 \times {\frac{15.1}{\sqrt{45} } }[/tex] ]

                                     = [763.65 lb , 772.75 lb]

Therefore, 95% confidence interval for the mean breaking strength of the new steel cable is [763.65 lb , 772.75 lb].

Answer:

1.22 km/min

Step-by-step explanation:

Let Q be baloon height at a time t. Our goal is to determine the speed of the baloon at the moment.

The dy / dt velocity of the baloon when = π/5?  

So we can restate the question as follows:

Owing to the fact d / dt = 0.2 rad / min at some stage = π/5

from fig:

tanθ = y/4

Differentiating w.r.t "t"

sec2 θ * dθ/dt = 1/4(dy/dt)

=> dy/dt = (4/cos2 θ)dθ/dt

At the given moment θ =  and dθ/dt = 0.2 rad/min.

dy/dt = (4/cos2)* (0.2)

= 1.22 km/min

And the velocity of the baloon currently is 1.22 km / min.

Answer:

  C. 1175

Step-by-step explanation:

At 3 liters per minute, the amount leaked in 27 minutes is ...

  (3 L/min)(27 min) = 81 L

Then the amount remaining is ...

  1256 L - 81 L = 1175 L

There will be 1175 liters in the barrel after 27 minutes.

Answer:

150

Step-by-step explanation:

Answer: You would pay $150

Step-by-step explanation: Take 25 times 4, then add on the additional fee.

Answer:

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

Step-by-step explanation:

Explanation:-

Given data random sample of 46 bins, the sample mean amount was 49.9 pounds and the sample standard deviation was 3.641

The sample size 'n' =46

mean of the sample x⁻ = 49.9

Standard deviation of the sample S = 3.641

Confidence intervals:-

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]

Degrees of freedom = n-1  = 46-1 =45

The tabulated value   t₀.₉₆ =   1.794 ( from t-table)

[tex](49.9 - 1.794 \frac{3.641}{\sqrt{46} } ,49.9+ 1.794 \frac{3.641}{\sqrt{46} })[/tex]

(49.9 -0.9630 , 49.9+0.9630)

(48.937 , 50.863)

Conclusion:-

The   95.7% confidence interval for the expected amount of garbage per bin for all bins in the city

(48.937 , 50.863)

There is 18.75% probability that it takes 9 or more boxes to get all 3 prizes.

No. of Boxes  |  frequency

        3           |         12

        4           |         4

        5           |         5

        6           |         5

        7           |         0

        8           |         0

        9           |         2

        10          |        2

        11           |        0

        12           |       2

Here 9 or more boxes represent that it is equal to 9 boxes or more than 9 boxes.

P(x ≥ 9) = No. of boxes equal or more than 9 / total no. of boxes

And, The total no. of boxes is 32

From the above data, we have to count the number of boxes equal to or more than 9. (6 times) i.e.

[tex]P(x $\geq$ 9) = 6\div 32\\\\P(x $\leq$ 9) = 3\div 16[/tex]

P(x ≥ 9) = 0.1875

P(x ≥ 9) = 18.75%

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Answer:

A Reflection on Edg

Step-by-step explanation:

Answer:B reflection

Step-by-step explanation:

edg 2022

Answer:

He lost $5.

Step-by-step explanation:

When the customer gives him the $20, the salesman does not gain any money because it is fake.

Then, he gets real money summing up to $20. So he gains that, but then gives $5 away. Now he has $15.

Then, the lady tells him the $20 bill is fake, so he must give the lady $20. So, 15 - 20 = -5. He lost $5.

Answer: He lost $35. $15 for the pair of shoes and $20 for having to repay the joined store for the counterfit money.

Step-by-step explanation:

Data for complete question is attached.

Answers

Therefore .

A. The regression equation is

y = beta0 + beta1+ ∈

B. From the given output regression line

y= 2.478+7.717x

The question addresses using a simple linear regression model to determine the relationship between two variables, and how to interpret the parameters of that model, as well as the significance of the correlation coefficient in the context of a hypothetical student protest situation.

The subject of this question is about linear regression analysis in mathematics, particularly in the context of statistical analysis. The question demonstrates the application of a simple linear regression to decipher the relationship between the duration of student sit-ins (independent variable) and the number of arrests (dependent variable).

Answer:

-1/4

Step-by-step explanation:

The slope is found by

m = (y2-y1)/(x2-x1)

    = (-1-2)/(7- -5)

    = (-1-2)/(7+5)

     = -3/12

     = -1/4

Answer:

A. [tex]\frac{64}{25}[/tex] ​, because probability values cannot be greater than 1.

C. -1.5, because probability values cannot be less than 0.

Step-by-step explanation:

Probability is the extent to which an event is likely to happen. It ranges from 0(impossible) to 1(certain). Probability values can be written in decimal form or in fractional form.

The following numbers could not be used to represent the probability of an event.

A. [tex]\frac{64}{25}[/tex] ​, because probability values cannot be greater than 1.

C. -1.5, because probability values cannot be less than 0.

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the step by step solution of the given problem.

Answer:

A. 5

Step-by-step explanation:

5 ÷ 1 = 5

10 ÷ 2 = 5

15 ÷ 3 = 5

Answer:

the slope should be 1/5.

Step-by-step explanation:

slope = change in y / change in x

2-1 = 1 = change in Y

10-5 = 5 = change in X

the slope should be 1/5.

apologies in advance if my answer is wrong or I explain badly.

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hope this helps! <3

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Edit! someone else answered the question. their answer is probably correct, so please ignore my incorrect answer :'D

Answer:

74.1 or 74

Step-by-step explanation: