A hot air balloon rising vertically is tracked by an observer located 4 km from the lift‑off point. At a certain moment, the angle between the observer's line of sight and the horizontal is π/5, and it is changing at a rate of 0.4 rad/min. How fast is the balloon rising at this moment? Let y be the height of the balloon (in km), t be time (in minutes), and θ the angle between the line‑of‑sight and the horizontal (in radians).

Answer:

Step-by-step explanation:

The graph is attached.

Notice that [tex]\angle a=\angle AXY[/tex], [tex]\angle b = \angle YXB[/tex] and [tex]\angle BXC = 90\°[/tex], by given.

[tex]\angle AXB = \angle AXY + \angle YXB[/tex], by sum of angles.

[tex]\angle AXB + \angle BXC = 180\°[/tex], by supplementary angles definition.

[tex]\angle AXB + 90\° = 180\°\\\angle AXB = 180\° - 90\°\\\angle AXB = 90\°[/tex]

Which means,

[tex]\angle AXB = \angle AXY + \angle YXB = 90\°[/tex]

Therefore, [tex]\angle a + \angle b = 90\°[/tex], in other words, angles a and b are complementary by defintion.

So, the right answer is the second choice.

Answer:

supplementary angles

Step-by-step explanation:

Answer:

Null hypothesis: [tex]\mu \leq 300[/tex]

Alternative hypothesis: [tex]\mu >300[/tex]

When we talk about a type I of error we are refering to a“false positive” and is associated when we reject a null  hypothesis when it is actually true.

And for this special case would be reject the null hypothesis that the true mean is lower or equal than 300 [/tex]\mu\leq 300[/tex] but that in fact is true.

This type of error is associated to the significance level [tex]\alpha[/tex] assumed for the statistical test

Step-by-step explanation:

For this case we define the random variable X as the number of automobiles pass at a location per hour and we are tryng to proof this:

Null hypothesis: [tex]\mu \leq 300[/tex]

Alternative hypothesis: [tex]\mu >300[/tex]

When we talk about a type I of error we are refering to a“false positive” and is associated when we reject a null  hypothesis when it is actually true.

And for this special case would be reject the null hypothesis that the true mean is lower or equal than 300 [/tex]\mu\leq 300[/tex] but that in fact is true.

This type of error is associated to the significance level [tex]\alpha[/tex] assumed for the statistical test

Answer:

18.04% probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given time interval.

Suppose the mean number of deviations and incursions per year at the Los Angeles International Airport (LAX) is 2.

This means that [tex]\mu = 2[/tex]

Find the probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year

This is P(X = 3).

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804[/tex]

18.04% probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year

Answer:

1 . Total time = 1 hr 55 minutes

2 Distance = 121 km

Step-by-step explanation:

Mattew journey

stage a

Distance = 20km

Speed = 30km/h

Time = distance/speed

Time = 20/30

Time = 2/3 h

Time = 40 minutes

Stage b

Distance = 50 I'm

Speed = 100 km/h

Time = distance/speed

Time = 50/100

Time = 0.5 h

Time = 30 minutes

Stage c

Distance = 30 km

Speed = 40 km/h

Time = distance/speed

Time = 30/40

Time = 3/4 h

Time = 45 minutes.

Total time taken =( 40 + 30 + 45 ) minutes

Total time = 115 minutes

Total time = 1 hr 55 minutes

2.

Speed =60 km/h

Time= 6 minutes + x

And x = 1 hr 55 minutes

Time = 1 hr 55 minutes + 6 minutes

Time = 2 hr 1 minute

Time = 2.01666667 hr

Distance covered = speed * time

Distance = 60*2.016667

Distance = 121 km

In this exercise we have to use the knowledge of time and distance, so we have to:  

1) Total time = 1 hr 55 minutes

2) Distance = 121 km

To calculate Matthew's journey we have to use the formula of :

[tex]Time= \frac{Distance}{Speed}[/tex]

Are doing the calculations for each Stage, like this:

Stage A, we know that:

[tex]Time = 20/30\\T = 2/3 h\\Time = 40 \ minutes[/tex]

Stage B, we know that:  

[tex]Time = 50/100\\T = 0.5 h\\Time = 30\ min[/tex]

Stage C, we know that:  

[tex]Time = 30/40\\T= 3/4 h\\Time = 45\ min[/tex]

1) So using all the values ​​calculated above, let's calculate the total value of the trip that will take place by:

[tex]Total =( 40 + 30 + 45 ) minutes\\Total = 115 \ minutes\\Total = 1 \ hr \ 55 \ minutes[/tex]

2) For the second part of this question we want to calculate the total distance of travel hours so:  

[tex]x = 1 \ hr \ 55 minutes\\Time = 1 \ hr\ 55 \ minutes + 6 \ minutes = 2 \ hr \ 1 minute\\Time = 2.01666667\\Distance = speed * time\\Distance = 60*2.016667\\Distance = 121 km[/tex]

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Answer:

[tex]C(10,4)=10C_4=210[/tex]

Step-by-step explanation:

A combination is an arrangement where the order is not important. Mathematically, a combination is the number of different groups of "[tex]n[/tex]" elements that can be formed from an initial group of "[tex]k[/tex]" elements. It's calculated with the following formula:

[tex]C(n,k)=nC_k=\frac{n!}{k!(n-k)!}[/tex]

Where:

[tex]k\leqslant n[/tex]

In this case:

[tex]n=10\\k=4[/tex]

Therefore the number of ways that the disc jockey selction can be done is:

[tex]C(10,4)=10C_4=\frac{10!}{4!(10-4)!} =\frac{10!}{4!(6!)}=210[/tex]

Answer:

Width = (x + 8) inches.

Step-by-step explanation:

The  area of the quilt is the length times the width and if we know the area and the length we can find the width by area / length.

Area = x^2 + 18x + 80 = (x + 10)(x + 8) - now we know that the length is (x + 10) so the width must be (x + 8) inches.

Let me know if you require more explanation.

Answer:

The value of the test statistic is [tex]t = -1.44[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} \geq 432[/tex]

The alternate hypotesis is:

[tex]H_{1} < 432[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

In this problem, we have that:

[tex]X = 426, \mu = 432, \sigma = 26, n = 39[/tex]

So

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{426 - 432}{\frac{26}{\sqrt{39}}}[/tex]

[tex]t = -1.44[/tex]

The value of the test statistic is [tex]t = -1.44[/tex]

Y= -2x+10

4-(-8/3-9= -2(slope)

leaving the first option as the only viable one.

The equation of line passing through point  (9, -8) and (3, 4) : y=-2x+10

The correct option is A

Given, that line passes through points (9, -8) and (3, 4).

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope(m) =change in value of y on the vertical axis / change in value of x on the horizontal axis

Change in the value of [tex]y = y_2 - y_1[/tex]

Change in value of [tex]x = x_2 -x_1[/tex]

[tex]y_2[/tex] = final value of y

[tex]y_1[/tex] = initial value of y

[tex]x_2[/tex] = final value of x

[tex]x_1[/tex] = initial value of x

The line passes through (9,-8) and (3,4),

[tex]y_2[/tex] = 4

[tex]y_1[/tex] = - 8

[tex]x_2[/tex] = 3

[tex]x_1[/tex] = 9

Slope(m) = (4 + 8)/(3 - 9)

= 12/(- 6)

= -2

To determine the intercept, we would substitute x = 9, y = - 8 and m= - 2 into y = mx + c. It becomes

- 8 = - 2 × 9 + c = - 18 + c

c = - 8 + 18 = 10

The equation becomes

y = - 2x + 10

The correct option is A.

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Answer: 88

Step-by-step explanation:

Take [tex]12\frac{1}{2}[/tex] and change it into an improper fraction, [tex]\frac{25}{2}[/tex] divide by 100, [tex]\frac{\frac{25}{2} }{100}[/tex] this is the same as multiplying by [tex]\frac{1}{100}[/tex].

[tex]\frac{25}{2}*\frac{1}{100} =0.125[/tex]

Using a rule of 3,

[tex]\frac{x}{11}=\frac{100}{12\frac{1}{2} }[/tex]

[tex]x=\frac{11*100}{12\frac{1}{2} } \\x=88[/tex]

11 is 12 1/2% of the number 88.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

We have to find the number such that the number has the 12 1/2% as 11.

Let x be the required number.

We can write 12 1/2% as 12 + 0.5 = 12.5%.

12.5% × x = 11

(12.5 / 100) x = 11

0.125 x = 11

Dividing both sides by 0.125,

x = 11 / 0.125

x = 88

Hence the required number is 88.

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Answer:

The null hypothesis is rejected.

There is enough evidence to support the claim that the average age of the customers differs from 40 years.

The sample does not support the manager claim (the average age seems to differ from 40 years).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The manager claims that the average age of customers is 40 years. As this is an equality, we will test if the average age differs from 40. If the null hypothesis failed to be rejected, the claim of the manager is right.

Then, the claim is that the average age of the customers differs from 40 years.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=40\\\\H_a:\mu\neq 40[/tex]

The significance level is 0.05.

The sample has a size n=50.

The sample mean is M=38.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.

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

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{7}{\sqrt{50}}=0.99[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38-40}{0.99}=\dfrac{-2}{0.99}=-2.02[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=50-1=49[/tex]

This test is a two-tailed test, with 49 degrees of freedom and t=-2.02, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=2\cdot P(t<-2.02)=0.049[/tex]

As the P-value (0.049) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average age of the customers differs from 40 years.

Answer:

C. Radius

Step-by-step explanation:

Have a good day!

Answer:1

1/6 3/12 2/3

Step-by-step explanation:

3/12 = 2/6

2/3 = 4/6

1/6<2/6<2/3

Answer:

The answer is 3/12 1/6 2/3

Step-by-step explanation:

The reason why is because the denominator is larger than the rest. The larger the denominator the smaller the number. For example: 2/13 is less than 4/6 because the denominator is bigger. Now if it were 6/12 and 1/2 it would be equal since 6 is half of 12. Hope this helped!

Answer:

[tex] B = \frac{31.5}{5.25}= 6[/tex]

[tex] H = 18-6= 12[/tex]

So then Mark purchased 12 Hamburgers and 6 packages of buns

Step-by-step explanation:

For this case we can define the following notation:

B represent the number of packages buns

H represent the number of hamburgers

And from the information given we can set up the conditions into the following equations:

[tex] 6.75 H +1.50 B =90[/tex]  (1) represent the total cost

[tex] H +B =18[/tex]  (2) represent the total number of items

Solving H from equation (2) we got:

[tex] H = 18 -B [/tex]   (3)

And replacing equation (3) into equation (1) we got:

[tex] 6.75 (18-B) +1.5 B =90[/tex]

And dsitributing the terms we have:

[tex] 121.5 -6.75 B +1.5 B =90[/tex]

And solving for B we got:

[tex] 121.5-90 = 5.25 B[/tex]

And dividing by 5.25 we got:

[tex] B = \frac{31.5}{5.25}= 6[/tex]

And replacing the value of B into equation (3) we got:

[tex] H = 18-6= 12[/tex]

So then Mark purchased 12 Hamburgers and 6 packages of buns

The two equations expressing altitude y as a function of time in seconds x for Cassie and Josiah respectively are: y = 33 + 1.25x and y = 210 - 17.6x.

The subject of this problem is linear equations in algebra. We set up two equations to represent the altitude changes of Cassie and Josiah over time.

Firstly, Cassie is ascending from a base level of 33 feet at a rate of 15 inches per second. However, the rate needs to be converted to feet per second because the initial altitude and the altitude Josiah is descending from are both in feet. So, 15 inches equals 1.25 feet (since 1 foot = 12 inches). Therefore, the altitude y Cassie reaches after x seconds can be represented as y = 33 + 1.25x.

Secondly, Josiah is descending from an altitude of 210 feet at a rate of 17.6 feet per second. Thus, the altitude y reached over x seconds can be given by y = 210 - 17.6x.

The system of equations therefore is:

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Answer:

2 units

Step-by-step explanation:

As the radius is half of the  diameter. To work this out you would simply multiply 1 by 2, which gives you 2.

1) Multiply 1 by 2.

[tex]1*2=2[/tex]

Answer:

a) [tex] 78.25- 1.64 \frac{22.50}{\sqrt{40}}= 72.416[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{40}}= 84.084[/tex]

b) [tex] 78.25- 1.64 \frac{22.50}{\sqrt{75}}= 73.989[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{75}}= 82.511[/tex]

c) For this case when we increase the sample size the margin of error would be lower and then the interval would be narrower

d)   [tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

Solving for n we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

And replacing the info we have:

[tex]n=(\frac{1.640(22.50)}{5})^2 =54.46 \approx 55[/tex]

Step-by-step explanation:

Part a

For this case we have the following data given

[tex]\bar X = 78.25[/tex] represent the sample mean for the customer order totals

[tex]\sigma =22.50[/tex] represent the population deviation

[tex] n= 40[/tex] represent the sample size selected

The confidence level is 90% or 0.90 and the significance level would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 = 0.05[/tex] and the critical value from the normal standard distirbution would be given by:

[tex] z_{\alpha/2}=1.64[/tex]

And the confidence interval is given by:

[tex] \bar X -z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

And replacing we got:

[tex] 78.25- 1.64 \frac{22.50}{\sqrt{40}}= 72.416[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{40}}= 84.084[/tex]

Part b

The sample size is now n = 75, but the same confidence so the new interval would be:

[tex] 78.25- 1.64 \frac{22.50}{\sqrt{75}}= 73.989[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{75}}= 82.511[/tex]

Part c

For this case when we increase the sample size the margin of error would be lower and then the interval would be narrower

Part d

The margin of error is given by:

 [tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

Solving for n we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

And replacing the info we have:

[tex]n=(\frac{1.640(22.50)}{5})^2 =54.46 \approx 55[/tex]

Answer:

It's one infinite solutions

Step-by-step explanation:

Any number can be put in for x beings there is no set answer to the equation. if there was a set number like 3x+9+4x+x=40 for instance, there would be only one solution, but since there's not, it is infinite solutions.

Answer:8pennies,16dimes,13nickels,13quarters

Step-by-step explanation:

total number of coin=50

16% are pennies

16% of 50

16/100 x 50=(16x50)/100=800/100=8

Pennies=8

32% are dimes

32% of 50

32/100 x 50=(32x50)/100=1600/100=16

Dimes = 16

5 more nickels than pennies

Pennies=8

nickels=8+5=13

nickels=13

8+16+13=37

50-37=13

13 quarters

pennies=8,dimes=16,nickels=13,quarters=13

Answer:

7/12 of a can

Step-by-step explanation:

Answer:

Step-by-step explanation:

They sold 201 small bags

and they sold 83 large bags

hope this helps :)

Answer:

l + s = 299

4l + s = $662

121 large bags were sold.

178 small bags were sold.

Step-by-step explanation:

Quantity equation: l + s = 299. l is the amount of large bags and s is the amount of small.

Price equation: 4l + s = $662. This means each large bag earns 4 dollars and each small bag earns 1.

To solve this, you use the method elimination and subtract (l + s = 299) from 4l + s = 662.

So, after subtracting, the equation you are left with is 3l = 363. Divide both sides by 3 and you get l = 121. 121 large bags were sold.

Plug in 121 for l in the first equation, now it says 121 + s = 299. Subtract 121 from 299 and get 178. 178 small bags were sold.

Answer:

We conclude that the sodium content is same as what the nutrition label states.

Step-by-step explanation:

We are given that the nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium.

The FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams.

Let [tex]\mu[/tex] = average sodium content.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1100 milligrams      {means that the sodium content is same as what the nutrition label states}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 1100 milligrams      {means that the sodium content is different from what the nutrition label states}

The test statistics that would be used here One-sample t test statistics as we don't know about 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 average sodium content = 1088.64 milligrams

            s = sample standard deviation = 234.12 milligrams

            n = sample of packages of Oriental Spice Sauce = 40

So, test statistics  =  [tex]\frac{1088.64-1100}{\frac{234.12}{\sqrt{40}}}[/tex]  ~ [tex]t_3_9[/tex]

                              =  -0.307

The value of z test statistics is -0.307.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical values of -2.0225 and 2.0225 at 39 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the sodium content is same as what the nutrition label states.

To determine if the sodium content of the Oriental Spice Sauce is different from what the label states, a confidence interval approach can be used. A t-test is used to compare the sample mean to the hypothesized population mean. If the p-value is less than the level of significance, the null hypothesis is rejected.

To determine if the sodium content of the Oriental Spice Sauce is different from what the nutrition label states, we can use a confidence interval approach.

Step 1: Define the null and alternative hypotheses. Null hypothesis (H0): The sodium content is the same as what the nutrition label states. Alternative hypothesis (Ha): The sodium content is different from what the nutrition label states.

Step 2: Calculate the test statistic and p-value. We can use a t-test to compare the sample mean to the hypothesized population mean (the sodium content stated on the label).

Step 3: Determine the level of significance and compare the p-value to it. If the p-value is less than the level of significance, we reject the null hypothesis and conclude that there is evidence that the sodium content is different from what the nutrition label states.

Answer:

84

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

588/7=84

Answer:

123 days

Step-by-step explanation:

The minimum duration for which an empty apartment remains to update the kitchen appliances is approximately 120 days.

To find the minimum duration for which an apartment remained empty for the company to update the kitchen appliances, we need to find the duration that corresponds to the top 10% of durations. Since we know the distribution is approximately normal with a mean of 85 days and a standard deviation of 29 days, we can use z-scores to find the corresponding duration.

First, we need to find the z-score corresponding to the top 10%. We can use the z-table or a calculator to find that the z-score is approximately 1.28.

Next, we can use the formula z = (x - mean) / standard deviation to solve for x, the minimum duration:

1.28 = (x - 85) / 29.

Solving for x, we get x ≈ 120.12. Rounding to the nearest whole number, the minimum duration for which the apartment remained empty is 120 days.

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Answer:

[tex]z=\frac{0.116 -0.125}{\sqrt{\frac{0.125(1-0.125)}{2000}}}=-1.217[/tex]  

We are conducting a bilateral test then the p value would is:  

[tex]p_v =2*P(z<-1.217)=0.224[/tex]  

Since the p value obtained is higher than the significance level used of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%

Step-by-step explanation:

Information given

n=2000 represent the random sample of people

X=232 represent the people between 18-25-year-old who currently use marijuana or hashish

[tex]\hat p=\frac{232}{2000}=0.116[/tex] estimated proportion of people between 18-25-year-old who currently use marijuana or hashish

[tex]p_o=0.125[/tex] is the value that we want to verify

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic

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

Hypothesis to test

We want to verify if the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.:  

Null hypothesis:[tex]p=0.125[/tex]  

Alternative hypothesis:[tex]p \neq 0.125[/tex]  

The statistic for a proportion z test is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing into the previous formula we got:

[tex]z=\frac{0.116 -0.125}{\sqrt{\frac{0.125(1-0.125)}{2000}}}=-1.217[/tex]  

P value

We are conducting a bilateral test then the p value would is:  

[tex]p_v =2*P(z<-1.217)=0.224[/tex]  

Since the p value obtained is higher than the significance level used of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%

After conducting a statistical hypothesis test using the given data, and the chosen significance level of 0.05, there isn't enough evidence to conclude that the percentage of 18-25-year-olds who are using marijuana or hashish has significantly changed from the 1997 percentage.

The subject question concerns a statistical hypothesis testing problem, where we are testing if the proportion of 18-25 year-olds currently using marijuana or hashish is significantly different from the 1997 figure (p0=0.125). Let's denote the current proportion as p1. The null hypothesis H0: p1=p0, and the alternative hypothesis Ha: p1≠p0. The value obtained in the survey is 232/2000 (p1=0.116).

We will use a z-test for the difference of proportions here, using the formula: z = (p1- p0) / sqrt(p0(1 - p0) / n). On computation, we get z =approx -1.58.

The desired significance level is α = 0.05, a two-sided test. The critical z values for this are -1.96 and 1.96. Since -1.96 < z <1.96, we do not reject the null hypothesis at the 0.05 level of significance. This means that, according to our analysis, there is not enough evidence to conclude that the proportion of 18-25 year-olds using marijuana and hashish has significantly changed compared to the 1997 level.

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Answer:

63x

Step-by-step explanation:

3(21x)

= (3· 21)x

= 63x

Answer:63x

Step-by-step explanation:

Answer:

Step-by-step explanation:

For an explanation of vocabulary questions, consult a dictionary or vocabulary list

1) angles ending in the same place are "co-terminal."

__

2) The acute angle between the terminal ray and the x-axis is the "reference angle."

__

3) Multiply radians by 180°/π to convert to degrees.

  a) π/2 × 180°/π = 180°/2 = 90°

  b) 7π/12 × 180°/π = (7/12)(180°) = 105°

__

4) To convert from degrees to radians, multiply by π/180°.

  a) 360° × π/180° = 2π radians

  b) 315° × π/180° = 7π/4 radians

Answer:

Check the explanation

Step-by-step explanation:

1.

(a)

n>=m

(b)

n <= m

(c)

n=m

2.

(a)

let T(v1) = T(v2)

=>

T(v1)-T(v2) = 0

=>

T(v1-v2) = 0

=>

v1-v2 = 0 from the hypothesis

=>

v1=v2

=>

T is one-one

thus proved

(b)

lets assume T is onto, we already know that T is one-one, so from above problem (third case where m=n)

we should have 3=4 which is impossible

so T is NOT onto.

3.

we need to find a,b such that

T(a,b) =(a,b)

=>

a= b

=>

points on the line x=y are the required points

Answer:

x = 14

Step-by-step explanation:

If a^m = a^n, then m = n.

If two powers with equal bases are equal, then the exponents are equal.

8^(x - 4) = 8^10

x - 4 = 10

x = 14

Answer:

x = 14

Step-by-step explanation:

Looking at this problem, we see that both sides of the equation are equal. Since both numbers have the same base, this means that they must also have the same power to be equal to each other. This means:

x - 4 = 10

x = 10 + 4

x = 14