Does anyone know the slope of this line?

Answer: 151

Step-by-step explanation:

if prior population proportion is unknown , then the formula is used to find the sample size :

[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]

, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]

E = Margin of error.

Given : margin of error = 8%= .08

For 95% confidence level , two tailed critical value = 1.96

Now, the required sample size :

[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]

Hence, the size of the sample needed = 151.

Answer:

Step-by-step explanation:

A standard normal probability distribution is a normal distribution that has a mean of zero and a standard deviation of 1.

yes

Step-by-step explanation:

parallelogram are quadrilaterals with two sets of parallel sides. since square must be quadrilaterals with two sets of parallel sides ,then all squares are parallelogram ,a trapezoid is quadrilateral.

Answer:

In that year approximately 2114 thousand people visited the park.

Step-by-step explanation:

Since the expression [tex]y(x) = -7.5*x^2 + 103*x + 2142[/tex] models the number of visitors in the park, where x represents the number of years after 2007 and 2021 is 14 years after that, then we need to find "y" for that as shown below.

[tex]y(14) = -7.5*(14)^2 + 103*14 + 2142\\y(14) = -7.5*196 + 1442 + 2142\\y(14) = -1470 + 3584\\y(14) = 2114[/tex]

In that year approximately 2114 thousand people visited the park.

Answer:

2/7

Step-by-step explanation:

The numbers greater than 7 or less than 3 are 2 and 8.

2 numbers out of 7.

P(greater than 7 or less than 3) = 2/7

Answer:

2/7

Step-by-step explanation:

There are a total of 7 sample spaces also known as 2,3,4,5,6,7,8. Now we have to find a number greater than 7 and less than 3. 2 is less than 3, and 8 is greater than 7, so two numbers are selected. This would become 2/7 because out of all of the 7 outcomes, only two are selected.

Answer: -64

Step-by-step explanation: Since we know that -4 x -4 is a positive, it equals 16, then a positive plus a negative equals a negative, so 16 x -4 equals -64

Answer:

-64

Step-by-step explanation:

-4 • -4 • -4

-4*-4 = 16

16*-4

-64

Answer:

2699

Step-by-step explanation:

you do all the multiplication first

500×6= 3000

5 ×50 = 250

so it becomes

3000-51-250 = 2699

Answer:

2699

Step-by-step explanation:

Answer: 0.00153

Step-by-step explanation:

Given: An experiment consists of dealing 7 cards from a standard deck of 52 playing cards.

Number of ways of dealing 7 cards from 52 cards = [tex]^{52}C_7[/tex]

Since there are 13 clubs and 13 spades.

Number of ways of getting exactly 4 clubs and 3 spades=[tex]^{13}C_4\times\ ^{13}C_3[/tex]

Now, the probability of being dealt exactly 4 clubs and 3 spades

[tex]=\dfrac{^{13}C_4\times\ ^{13}C_3}{^{52}C_7}\\\\\\=\dfrac{{\dfrac{13!}{4!(9!)}\times\dfrac{13!}{3!10!}}}{\dfrac{52!}{7!45!}}\\\\=\dfrac{715\times286}{133784560}\\\\=0.00152850224271\approx0.00153[/tex]

Hence,  the probability of being dealt exactly 4 clubs and 3 spades = 0.00153

Answer:

Height at t = 1 sec is 1144 ft

Step-by-step explanation:

Given:

Initial height of object = 1160 feet

Height of object after t seconds is given by the polynomial:

[tex]- 16t ^2+ 1160[/tex]

Let [tex]h(t)=- 16t ^2+ 1160[/tex]

Let us analyze the given equation once.

[tex]t^2[/tex] will always be positive.

and coefficient of [tex]t^2[/tex] is [tex]-16[/tex] i.e. negative value.

It means something is subtracted from 1160 ft (i.e. the initial height).

So, height will keep on decreasing with increasing value of t.

Also, given that the object is dropped from the top of a tower.

To find:

Height of object at t = 1 sec.

OR

[tex]h (1)[/tex] = ?

Solution:

Let us put t = 1 in the given equation: [tex]h(t)=- 16t ^2+ 1160[/tex]

[tex]h(1)=- 16\times 1 ^2+ 1160\\\Rightarrow h(1) = -16 + 1160\\\Rightarrow h(1) = 1144\ ft[/tex]

So, height of object at t = 1 sec is 1144 ft.

Answer:

The required matrix is[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Step-by-step explanation:

Matrix of rotation:

[tex]P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right][/tex]

[tex]P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

x' + iy' = (x + iy)(cosθ + isinθ)

x' = x cosθ - ysinθ

y' = x sinθ + ycosθ

In matrix form:

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

The matrix stretches by 1.8 on the x axis and 0.7 on the y axis

i.e. x' = 1.8x

y' = 0.7y

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

[tex]Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right][/tex]

According to the question, the result is rotated by pi/3 clockwise radians

[tex]R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right][/tex]

[tex]R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right][/tex]

To get the matrix A, we would multiply matrices R, Q and P together.

[tex]A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Answer:

The tree was 175 centimeters tall when Vlad moved into the house.

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

Step-by-step explanation:

The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:

[tex]H(t) = H(0) + at[/tex]

In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.

He measured it once a year and found that it grew by 26 centimeters each year.

This means that [tex]a = 26[/tex]

So

[tex]H(t) = H(0) + 26t[/tex]

4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?

This means that when t = 4.5, H(t) = 292. We use this to find H(0).

[tex]H(t) = H(0) + 26t[/tex]

[tex]292 = H(0) + 26*4.5[/tex]

[tex]H(0) = 292 - 26*4.5[/tex]

[tex]H(0) = 175[/tex]

The tree was 175 centimeters tall when Vlad moved into the house.

How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

This is t for which H(t) = 357. So

[tex]H(t) = H(0) + 26t[/tex]

[tex]H(t) = 175 + 26t[/tex]

[tex]357 = 175 + 26t[/tex]

[tex]26t = 182[/tex]

[tex]t = \frac{182}{26}[/tex]

[tex]t = 7[/tex]

7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.

Answer:

a. 1/13

b. 1/52

c. 2/13

d. 1/2

e. 15/26

f. 17/52

g. 1/2

Step-by-step explanation:

a. In a deck of cards, there are 4 suits and each of them has a 7. Therefore, the probability of drawing a 7 is:

P(7) = 4/52 = 1/13

b. There is only one 6 of clubs, therefore, the probability of drawing a 6 of clubs is:

P(6 of clubs) = 1/52

c. There 4 fives (one for each suit) and 4 queens in a deck of cards. Therefore, the probability of drawing a five or a queen​​​​​​​​​​​ is:

P(5 or Q) = P(5) + P(Q)

= 4/52 + 4/52

= 1/13 + 1/13

P(5 or Q) = 2/13

d. There are 2 suits that are black. Each suit has 13 cards. Therefore, there are 26 black cards. The probability of drawing a black card is:

P(B) = 26/52 = 1/2

e. There are 2 suits that are red. Each suit has 13 cards. Therefore, there are 26 red cards. There are 4 jacks. Therefore:

P(R or J) = P(R) + P(J)

= 26/52 + 4/52

= 30/52

P(R or J) = 15/26

f. There are 13 cards in clubs suit and there are 4 aces, therefore:

P(C or A) = P(C) + P(A)

= 13/52 + 4/52

P(C or A) = 17/52

g. There are 13 cards in the diamonds suit and there are 13 in the spades suit, therefore:

P(D or S) = P(D) + P(S)

= 13/52 + 13/52

= 26/52

P(D or S) = 1/2

Answer:

The first first five terms of this sequence are

Step-by-step explanation:

[tex]a(n) = 27(0.1)^{n - 1} [/tex]

where n is the number of term

For the first term

n = 1

[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]

= 27(1)

Second term

n = 2

[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]

= 27(0.1)

Third term

n = 3

[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]

Fourth term

n = 4

[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]

Fifth term

n = 5

[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]

Hope this helps you

Answer:

A type II error is failing to reject the hypothesis that μ is equal to 2800 when in fact, μ is less than 2800.

Step-by-step explanation:

A Type II error happens when a false null hypothesis is failed to be rejected.

The outcome (the sample) probability is still above the level of significance, so it is consider that the result can be due to chance (given that the null hypothesis is true) and there is no enough evidence to claim that the null hypothesis is false.

In this contest, a Type II error would be not rejecting the hypothesis that the mean lifetime of the light bulbs is 2800 hours, when in fact this is false: the mean lifetime is significantly lower than 2800 hours.

Answer:

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Answer:

x = 7

Step-by-step explanation:

This problem can be solved using angular bisector theorem.

It states that if any angle of triangle is bisected by a line , then that line

divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.

__________________________________

Here one angle is is divided into parts theta

Thus,

using angular bisector theorem

14/21 = 6/3x-12

=> 14(3x-12) = 21*6

=> 3x-12 = 21*6/14 = 9

=> 3x = 12+9 = 21

=> x = 21/3 = 7

Thus, x = 7

Answer:

x = 15

y = 90

Step-by-step explanation:

Step 1: Find x

We use Definition of Supplementary Angles

9x + 3x = 180

12x = 180

x = 15

Step 2: Find y

All angles in a triangle add up to 180°

3(15) + 3(15) + y = 180

45 + 45 + y = 180

90 + y = 180

y = 90°

Answer:

(f o g) = x, then, g(x) is the inverse of f(x).

Step-by-step explanation:

You have the following functions:

[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]

In order to know if f and g are inverse functions you calculate (f o g) and (g o f):

[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]

[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]

(f o g) = x, then, g(x) is the inverse of f(x).

Answer:

Step-by-step explanation:

Hello!

A regression model was determined in order to predict the number of earthquakes above magnitude 7.0 regarding the year.

^Y= 164.67 - 0.07Xi

Y: earthquake above magnitude 7.0

X: year

The researcher wants to test the claim that the regression is statistically significant, i.e. if the year is a good predictor of the number of earthquakes with magnitude above 7.0 If he is correct, you'd expect the slope to be different from zero: β ≠ 0, if the claim is not correct, then the slope will be equal to zero: β = 0

The hypotheses are:

H₀: β = 0

H₁: β ≠ 0

α: 0.05

The statistic for this test is a student's t: [tex]t= \frac{b - \beta }{Sb} ~~t_{n-2}[/tex]

The calculated value is in the regression output [tex]t_{H_0}= -3.82[/tex]

This test is two-tailed, meaning that the rejection region is divided in two and you'll reject the null hypothesis to small values of t or to high values of t, the p-value for this test will also be divided in two.

The p-value is the probability of obtaining a value as extreme as the one calculated under the null hypothesis:

p-value: [tex]P(t_{n-2}\leq -3.82) + P(t_{n-2}\geq 3.82)[/tex]

As you can see to calculate it you need the information of the sample size to determine the degrees of freedom of the distribution.

If you want to use the rejection region approach, the sample size is also needed to determine the critical values.

But since this test is two tailed at α: 0.05 and there was a confidence interval with confidence level 0.95 (which is complementary to the level of significance) you can use it to decide whether to reject the null hypothesis.

Using the CI, the decision rule is as follows:

If the CI includes the "zero", do not reject the null hypothesis.

If the CI doesn't include the "zero", reject the null hypothesis.

The calculated interval for the slope is: [-0.11; -0.04]

As you can see, both limits of the interval are negative and do not include the zero, so the decision is to reject the null hypothesis.

At a 5% significance level, you can conclude that the relationship between the year and the number of earthquakes above magnitude 7.0 is statistically significant.

I hope this helps!

(full output in attachment)

Using the percentage concept, it is found that 51% of 10th graders surveyed preferred robotics, hence option B is correct.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, we have that 33% out of 65% of the students are 7th graders who preferred robotics, hence the percentage is given by:

[tex]P = \frac{33}{65} \times 100\% = 51%[/tex]

Which means that option B is correct.

More can be learned about percentages at https://brainly.com/question/14398287

#SPJ1

Answer:

It's A. 61% The dude above me is wrong.

Step-by-step explanation:

I just took the test

Answer:

  $904,510.28

Step-by-step explanation:

If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.

  P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)

where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.

Filling in your values, we have ...

  P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)

  P = $904,510.28

You need to have $904,510.28 in your account when you begin withdrawals.

Answer:

You need to have $904,510.28 in your account when you begin

Given:

An equilateral triangle JKL inscribed in circle M.

Solution:

To draw an equilateral triangle inscribed in circle follow the steps:

1: Draw a circle with any radius.

2. Take any point A, anywhere on the circumference of the circle.

3.  Place the compass on point A, and swing a small arc crossing the circumference of the circle.

Remember the span of the compass should be the same as the radius of the circle.

4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.

5. Repeat this process until you return to point A.

6. Join the intersecting points on the circle to form the equilateral triangle.

So the correct option is A. The width must be equal to the radius of circle M.

Answer:

Since RT = 12, TU = 6 and RS = 24, T and U are the midpoints of RS and TS respectively. This means that SU + UT = RT.

Answer:

su+ut=rt

Step-by-step explanation:

Answer:

The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Step-by-step explanation:

Let the random variable X represent the time it takes to wash the dishes.

The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.

The probability density function of X is as follows:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

[tex]P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx[/tex]

                           [tex]=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333[/tex]

Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

1. y² - 3x - 18

2. 4x² - 33x + 35

3. 12x² - 11x + 2

Step-by-step explanation:

All we do with these questions are expanding the factored binomials. Use FOIL:

1. y² + 3y - 6y - 18

y² - 3y - 18

2. 4x² - 28x - 5x + 35

4x² - 33x + 35

3. 12x² - 3x - 8x + 2

12x² - 11x + 2

Answer:

1) (y-6) (y+3)

=> [tex]y^2+3y-6y-18[/tex]

=> [tex]y^2-3y-18[/tex]

2) (4x-5) (x-7)

=> [tex]4x^2-28x-5x+35[/tex]

=> [tex]4x^2-33x+35[/tex]

3) (3x - 2) ( 4x - 1)

=> [tex]12x^2-3x-8x+3[/tex]

=> [tex]12x^2-11x+3[/tex]