A student walk 60m on a bearing of 028 degree and then 180m due east. How is she from her starting point, correct to the nearest whole number?

Answer:

No porque si sumas los dos el resultado es más de 90 grados.

Step-by-step explanation:

Answer:

Null hypothesis H0: p = 0.01

Alternative hypothesis Ha: p < 0.01

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

The null hypothesis is that the proportion of people with colon polyps expected to die from colon cancer remains 0.01 with or without colonoscopy.

H0: p = 0.01

The alternative hypothesis is that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01.

Ha: p < 0.01

Given Information:

Mean weekly salary = μ = $490

Standard deviation of weekly salary = σ = $45

Required Information:

P(X > $525) = ?

Answer:

P(X > $525) = 21.77%

Step-by-step explanation:

We want to find out the probability that a randomly selected teacher earns more than $525 a week.

[tex]P(X > 525) = 1 - P(X < 525)\\\\P(X > 525) = 1 - P(Z < \frac{x - \mu}{\sigma} )\\\\P(X > 525) = 1 - P(Z < \frac{525 - 490}{45} )\\\\P(X > 525) = 1 - P(Z < \frac{35}{45} )\\\\P(X > 525) = 1 - P(Z < 0.78)\\\\[/tex]

The z-score corresponding to 0.78 from the z-table is 0.7823

[tex]P(X > 525) = 1 - 0.7823\\\\P(X > 525) = 0.2177\\\\P(X > 525) = 21.77 \%[/tex]

Therefore, there is 21.77% probability that a randomly selected teacher earns more than $525 a week.

How to use z-table?

Step 1:

In the z-table, find the two-digit number on the left side corresponding to your z-score. (e.g 0.7, 2.2, 1.5 etc.)

Step 2:

Then look up at the top of z-table to find the remaining decimal point in the range of 0.00 to 0.09. (e.g. if you are looking for 0.78 then go for 0.08 column)

Step 3:

Finally, find the corresponding probability from the z-table at the intersection of step 1 and step 2.

Answer:

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645*\frac{1.9}{\sqrt{4500}} = 0.04[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 5.4 - 0.04 = 5.36 years.

The upper end of the interval is the sample mean added to M. So it is 5.4 + 0.04 = 5.44 years.

The 90% confidence interval for the mean time required by all college graduates is between 5.36 years and 5.44 years.

Answer:

2x^2 -3x -8

Step-by-step explanation:

f(x) = 2x^2 - 5

g(x) = 3x + 3,

(f - g)(x)=  2x^2 - 5 -(3x + 3)

Distribute the minus sign

(f - g)(x)=  2x^2 - 5 -3x - 3

Combine like terms

            = 2x^2 -3x -8

Answer:

[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]

Step-by-step explanation:

[tex]5y^3/5y^-2[/tex]

as 5 is both in numerator and denominator it will get cancelled so we have now expression

[tex]y^3/y^-2[/tex]

we will use  law of indices wherein if there is

[tex]a^x/a^y = a^(x-y)[/tex]

which means that if the base is same in numerator and denominator then we have to subtract the power of denominator from numerator to get the reduced form using this concept

here power in numerator is 3 and power in denominator  is -2

hence we will be subtracting -2 from 3

[tex]y^3/y^-2 = y^(3-(-2) = y^(3+2) = y^5[/tex]

Thus,

[tex]5y^3/5y^-2[/tex] = [tex]y^5[/tex]

Answer:

Ashley’s backpack is the better buy.

Step-by-step explanation:

You have to calculate the price that was paid for each backpack after the discount was applied.

Ashley’s backpack: $65*0.25= $16.25

Final price= $65-$16.25= $48.75

Robbin's backpack: $75*0.3= $22.5

Final price= $75-$22.5= $52.5

According to this, the backpack that is the better buy is the one that Ashley bought because after the discounts were applied it cost $48.75 and Robbin's backpack cost $52.2 which means that Ashley's backpack was cheaper.

Answer:

Yo

Step-by-step explanation:

Answer:

The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).

Step-by-step explanation:

The question is incomplete:

"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."

We start by calculating the mean of the sample:

[tex]M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is know and is σ=24.

The sample mean is M=146.

The sample size is N=9.

As σ is known, the standard error of the mean (σM) is calculated as: [tex]\sigma_M=\dfrac{\sigma}{\sqrt{N}}=\dfrac{24}{\sqrt{9}}=\dfrac{24}{3}=8[/tex]

The z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_M=1.96 \cdot 8=15.68[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 146-15.68=130.32\\\\UL=M+t \cdot s_M = 146+15.68=161.68[/tex]

The 95% confidence interval for the population mean is (130.32, 161.68).

Answer:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]

Step-by-step explanation:

Total Number of People on Campus =1000

Let the number of people who have contracted the flu =x(t)

Therefore, the number of people who have not contracted the flu =1000-x(t)

Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.

[tex]\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)][/tex]

Introducing the proportional constant k, we obtain:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)][/tex]

At t=0, there was no infected on the campus, therefore the initial condition is given:

[tex]x(0)=0[/tex]

Therefore, a differential equation for the number of people x(t) who have contracted the flu is:

[tex]\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$ x(0)=0[/tex]

Answer:

135°, 63°, 63°, 99°

Step-by-step explanation:

Find attached the diagram used in solving the question.

We would use formula for sum of interior angles to get each exterior angle.

From the diagram, we added additional variables to be able to solve for sum of interior angles.

Sum of angle on a straight line = 180°

a° +15z° = 180°

b° +7z° = 180°

c° +7z° = 180°

d° +11z° = 180°

Where a,b,c and d are interior angles

Sum of interior angles = 180(n-2)

n = number of sides

For quadrilateral, n= 4

a°+b°+c°+d° = 180(n-2)

180-15z +180-7z+180-7z+180-11z = 180(4-2)

720-40z = 180(2)

720 - 360 = 40z

z = 360/40

z = 9

Each exterior angle:

15z = 15×9 = 135°

7z = 7×9 = 63°

7z = 7×9 = 63°

11z = 11×9 = 99°

Answer:

yes this right, it depends on what one tho

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the matrix

[tex] A = \left[\begin{matrix}4&0&0 \\ 1&3&0 \\-2&3&-1 \end{matrix}\right] [/tex]

a) To find the characteristic polynomial we calculate [tex]\text{det}(A-\lambda I)=0[/tex] where I is the identity matrix of appropiate size. in this case the characteristic polynomial is

[tex]\left|\begin{matrix}4-\lambda&0&0 \\ 1&3-\lambda&0 \\-2&3&-1-\lambda \end{matrix}\right|=0[/tex]

Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is

[tex](4-\lambda)(3-\lambda)(-1-\lambda)=(\lambda-4)(\lambda-3)(\lambda+1)=0[/tex]

which is the characteristic polynomial of A.

b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are [tex]\lambda=4,3,-1[/tex]

c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression [tex]A-\lambda I[/tex] and solve the system [tex](A-\lambda I)x =0[/tex] by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.

Consider [tex]\lambda = 4[/tex]. We get the matrix

[tex]\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right] [/tex]

The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by

[tex](x,y,z) = (5z,5z,z) = z(5,5,1)[/tex]

So, the base for this eigenspace is the vector (5,5,1).

If [tex]\lambda = 3[/tex] then the base is (0,4,3) and if [tex]\lambda = -1[/tex] then the base is (0,0,1)

Answer:

Step-by-step explanation:

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

Pearson's r is -0.140.

The critical r-value is 0.404.

Since 0.140 < 0.404, we cannot reject the null hypothesis.

Therefore, we cannot conclude that notebook computer use and grades are related.

Pearson's r is -0.140. It means that there is a weak negative relationship between notebook computer use and grades.

The coefficient of determination is 0.020. 2% of the variation in the model is explained.

The relationship is not significant.

Notebook Computer Use Final Grade for Course    

30 86      

23 88      

6 94      

0 56      

24 78      

36 72      

10 80      

0 90      

0 82      

8 60      

12 84      

18 74      

0 78      

32 66      

36 54      

12 98      

8 81      

18 74      

22 70      

38 90      

5 85      

29 93      

26 67      

10 80

r² = 0.020    

r  = -0.140    

Std. Error = 11.996    

n  = 24    

k  = 1

ANOVA table    

Source              SS              df            MS           F             p-value  

Regression    63.6652        1          63.6652   0.44           0.5129  

Residual        3,165.668     22        143.8940    

Total              3,229.333     23  

Answer:

C. Independent, 49/1296

Step-by-step explanation:

A jar contains 12 red balls, 7 green balls, 10 white balls, and 7 yellow balls.

Total balls = 12+7+10+7

Total balls= 36

Two balls are chosen at random with replacement.

The probability that the both balls are green = probability of the first ball to he green * probability of the second ball to be green

The probability that the both balls are green= 7/36 * 7/36

The probability that the both balls are green= 49/1296

The probability that the both balls are green= 49/1296

Answer: 0.0179

Step-by-step explanation:

We know that , the  standard error of the sampling distribution of sample proportion (p) is given by :-

[tex]S.E.=\sqrt{\dfrac{p(1-p)}{n}}[/tex]

where , n= sample size

Let p be the  proportion of households who have incomes in excess of $60,000 .

As per given , we have

p= 20% = 0.20

n= 500

Then,

[tex]S.E.=\sqrt{\dfrac{0.20(1-0.20)}{500}}=\sqrt{\dfrac{0.20\times0.80}{500}}\\\\=\sqrt{0.00032}\\\\=0.01788854382\approx0.0179[/tex]

Hence, the standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 is 0.0179.

The  standard error of the sampling distribution of sample proportion of households who have incomes in excess of $60,000 will be 0.0179.

Since  an actual census showed that 20% of the households in Michigan have incomes in excess of $60,000.

So here the standard error should be

[tex]\sqrt (.2\times (1-.2)\div 500) \\\\= 0.0179[/tex]

Hence, the standard error should be 0.0179.

Learn more about sample here: https://brainly.com/question/9222927

Answer:

3.00

Step-by-step explanation:

3.14 is rounded to 3.00

Answer:

141.3 m²

Step-by-step explanation:

V= πr²h

V=3.14*(6/2)²*5= 141.3 m²

Answer:

a) Surviving the year: $ -161. Not surviving: 99,839.

b) 0.9986 * -161 + (1-0.9986) * 100000 = -20.7746

c) As the expected value is negative from the male's perspective, it is positive from the insurance company's perspective. So as the number of people purchasing this insurance becomes large, the company's profit will converge to an average value of 20.7746 per male. So the company is indeed profitting.

Answer:

[tex]sin\;60 =\frac{\sqrt{3} }{2}[/tex]

Answer:

5

To find the first term

T(1)=(1×2)+3

=2+3

=5

Answer:

He needs four packs.

Step-by-step explanation:

6*4=24 there is 23 so he will need 4 packs in total.

Answer:

4 packs

Step-by-step explanation:

3 packs only gives him 18 and he needs atleast 23. The closest number that meets 23 is 24. It takes 4 packs of 6 to get 24.

Answer:

Step-by-step explanation:

Adding the numbers because that is the only step.  Making it the last operation.

Answer:

11

Step-by-step explanation:

Answer:

Y=2x-9

Step-by-step explanation:

Answer:

Length = 2.823 in (to 3 decimal places)  

Step-by-step explanation:

assuming that the box is a cubic box:

volume of box = [tex]22\frac{1}{2}[/tex] in³ = 22.5 in³

volume = Length × Length × Length = (Length)³

∴ (Length)³ = 22.5

∴ Length = ∛(22.5)

using the calculator punch ∛(22.5), and the answer is:

∴ Length = 2.823 in (to 3 decimal places)

Answer:

Step-by-step explanation:

Hello!

Hypotheses:

H₀: μ₁ = μ₂

H₁: μ₁ < μ₂  

α: 0.05

Using the following sample information:

Sample 1

n₁= 15

X[bar]₁= 10

S₁= 4

Sample 2

n₂= 27

X[bar]₂= 8

S₂= 7

This is an example of a t-test for independent samples, assuming both unknown populations variances are equal the statistic is:

[tex]t= \frac{(X[bar]_1-X[bar]_2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} } = \sqrt{\frac{14*16+26*49}{15+27-2} }= \sqrt{\frac{1498}{40} } = 6.119= 6.12[/tex]

[tex]t= \frac{(10-8)-0}{6.12*\sqrt{\frac{1}{15} +\frac{1}{27} } }= 1.01[/tex]

The p-value of this test is 0.1593

To decide using the p-value approach you have to use the following rule:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The calculated p-value is greater than the significance level, the decision is to not reject the null hypothesis.

Using a 5% significance level you can conclude that the hypothesis test is not significant and the population means of populations 1 and 2 are equal.

I hope this helps!

Answer:

Step-by-step explanation:

Answer:

Probability that 100 or fewer of these Americans could only converse in one language is 0.8599.

Step-by-step explanation:

We are given that a recent study reported that 73% of Americans could only converse in one language.

A random sample of 130 Americans was randomly selected.

Let [tex]\hat p[/tex] = sample proportion of Americans who could only converse in one language.

The z score probability distribution for sample proportion is given by;

                                 Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion of Americans who could only converse in one language = 73%

           [tex]\hat p[/tex] = sample proportion = [tex]\frac{100}{130}[/tex] = 0.77

           n = sample of Americans = 130

Now, probability that 100 or fewer of these Americans could only converse in one language is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77)

      P( [tex]\hat p[/tex] [tex]\leq[/tex] 0.77) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.77-0.73}{\sqrt{\frac{0.77(1-0.77)}{130} } }[/tex] ) = P(Z [tex]\leq[/tex] 1.08) = 0.8599                    

The above probability is calculated by looking at the value of x = 1.08 in the z table which has an area of 0.8599.

Answer:

typically, careers that require higher education levels pay higher salaries than those that require a high school diploma.

Answer:

Height h = 5 cm

Step-by-step explanation:

Given;

Volume of box V = 180 cm^3

Base area of box A = 36 cm^2

Height = h

Volume = base area × height

height = volume/base area

h = V/A

Substituting the values;

h = (180cm^3)/(36cm^2)

Height h = 5 cm