The tallest church tower in the Netherlands is the Dom Tower in Utrecht. If the angle of elevation to the top of the tower is 77° when 25.9 m from the base, what is the height of the Dom Tower to the nearest metre.

Answer:

2) Strong Negative Correlation

Step-by-step explanation:

With the value of r we have both the information about the sign of the relationship and the strength of this relationship.

As the value of r is negative, we can conclude that the correlation between x and y is negative.

Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.

The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.

The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.

Answer:

[tex]75.6\%[/tex]

Step-by-step explanation:

Let B be the event of buying a basic model.

Given that P(B) = 41%

Let D be the event of buying a basic model.

Given that P(D) = 1 - 41% = 59%

Let E be the event of extended warranty.

Given that:

P(E [tex]\cap[/tex] B) = 31% and

P(E [tex]\cap[/tex] D) = 48%

P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)

P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103

To find: P(B/E)

Formula:

[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]

[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]

So, the correct answer is [tex]75.6\%[/tex].

Answer:

The 85% confidence interval is ( 7.7 , 8.0 )

Step-by-step explanation:

In order to find the 85% confidence interval you use the following formula:

[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]       (1)

where

[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8

σ: standard deviation = 2.2

n: sample size = 967

α: 1 - 0.85 = 0.15

Zα/2: Z factor of the density distribution = 1.44

You replace the values of all parameters in the equation (1):

[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]

Then, the confidence interval is:

[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]

Answer:

26/3 as an improper fraction in simplest form. :)

Step-by-step explanation:

Answer:

(0. 4)

(-2, 0)

Step-by-step explanation:

As per given graph,

Answer:

Rectangle C is 14 cm longer than B

Step-by-step explanation:

Let  x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,

Therefore the length of rectangle B is:

[tex]x+\frac{1}{5}x[/tex]

Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:

[tex]x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x[/tex]

The total length of all three rectangles is 133 cm.

Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm

[tex]x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm[/tex]

Therefore the length of rectangle A is 35 cm, the length of rectangle B is [tex]35+\frac{1}{5}*35=42\ cm[/tex] and the length of rectangle C is [tex]35+\frac{9}{15}*35=56\ cm[/tex]

Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B

Answer:

work is shown and pictured

Answer:

the value of x is 3

Step-by-step explanation:

Hope this helps!!!! :)

Answer:

one is a

two is c

three is b

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.

I hope this helps :))

The graph A is correct.

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

The equation is,

[tex]y=2(0.5)^{x}[/tex]

Plotting the graph, we get,

Option A

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Answer:

$3,485.48

Step-by-step explanation:

For computing the money required at the end of the account term we need to apply the Future value formula i.e be to shown in the attachment below:

Given that,  

Present value = $3,000

Rate of interest = 3% ÷ 365 days  = 0.00821917

NPER = 5 years × 365 days  = 1,825

PMT = $0

The formula is shown below:

= FV(Rate;NPER;PMT;PV;type)

So, after applying the above formula

the amount of future value is $3,485.48

Answer:

150 miles

Step-by-step explanation:

If the distance between Seattle and Boise is 400 miles and the image illustrates 4", then there must be a proportionate between the two values. Therefore, if the distance between Seattle and Portland is 1.5", then the real distance must be 150 miles.

Answer:

Lower class Limit: 20,25,30,35,40,45,50

Upper class limit: 24,29,34,39,44,49,54

Class width: 4

Class Midpoints : 22,27,32,37,42,47,52

Class Boundries : 19.5,24.5,29.5,34,5,39.5,44.5,49.5,54.5

Total Individuals: 93

Step-by-step explanation:

Lower class limit is the lowest value of a class e.g in the first class, the lowest value is 20. Similarly find lower class limit of othere classes.

Upper class limit is the highest value of a class e.g in the first class, the highest value is 24. Similarly find upper class limit of othere classes.

Class width is the difference between highest and lowest value of a class e.g 24-20=4

Class Midpoints can be found by adding lowest and highest value of a class and dividing it by 2 e.g (20+24)/2 = 22

Class boundaries are the halfway point which seperates the classes e.g for first classes, clasee boundry is (19.5,24.5)

Total individuals are founf by adding all the frequencies.

Answer:

14 ft × 14 ft × 8.75 ft

Step-by-step explanation:

A garbage company is designing an open rectangular container that should have a volume of 1,715 cubic feet.

So we have the length of the container = "x" ft, the width of the container = "y" ft and the height of the container = "z" ft

Therefore the volume of the rectangular container would be:

x * y * z = 1715 ft³

z = 1715 / x * y

The cost of making the bottom of the container is $ 5 per square foot, that is:

5 * (x * y)

Now, area of ​​all sides of the container would be:

2 * (x * z + y * z) = 2 * z * (x + y)

We know that it has been given that the cost of making all the sides of the container is = $ 4 per square foot, so:

4 * (2 * z * (x + y)) = 8 * z * (x + y)

In total the costs would be:

5 * (x * y) + 8 * z * (x + y)

If we replace z, in the previous equation we have:

5 * (x * y) + 8 * (1715 / x * y) * (x + y)

solving, and we would have that the total cost would be:

C = 5 * (x * y) + 13720 / x + 13720 / y

Now we will find the derivative of C and make it equal to zero:

dC / dx = 0; dC / dy = 0

For dC / dx = 0:

dC / dx = 5 * y + 13720 * -1 / (y ^ 2) + 13720 * 0

0 = 5 * y - 13720 / y ^ 2

5 * y = 13720 / y ^ 2

y ^ 3 = 13720/5 = 2744

y = 14

For dC / dy = 0:

dC / dy = 5 * x + 13720 * 0 + 13720 * -1 / (x ^ 2)

0 = 5 * x - 13720 / x ^ 2

5 * x = 13720 / x ^ 2

x ^ 3 = 13720/5 = 2744

x = 14

now for z:

z = 1715 / (14 * 14)

z = 8.75

Therefore, the dimensions of the container should be 14 ft × 14 ft × 8.75 ft to minimize manufacturing cost.

Answer:

y= 1/5x + 12/5

Step-by-step explanation:

Parallel line to this has same slope and passes through the point (-2, 2)

The required equation in slope- intercept form is:

Answer:

24

Step-by-step explanation:

Multiple (4)(2)= 8

-3(8) =24

Answer: 90/pi degrees

Step-by-step explanation:

It forms a 15cm arc from a circle of radius 30 cm.

The diameter is 30*2*pi = 60pi cm. So the arc is 15/60pi = 1/4pi of the way around a 360 degree circle. This is 1/4pi * 360 = 90/pi degrees.

Hope that helped,

-sirswagger21

The pendulum will swing 28.68° if the 30-cm pendulum traverses an arc of 15 cm.

It is defined as the combination of points that, and every point has an equal distance from a fixed point (called the center of a circle).

We know that relationship between arc length s and central angle θ:

s = rθ

Where r is the radius of the circle

We have s = 15 cm

r = 30 cm

15 = (30)(θ)

θ = 0.5 radians

To convert it to a degree, multiply it by 180/π

θ = 0.5(180/π)

θ = 28.647 ≈ 28.68°

Thus, the pendulum will swing 28.68° if the 30-cm pendulum traverses an arc of 15 cm.

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Answer:

4.3 units

Step-by-step explanation:

In this question we use the Pythagorean Theorem which is shown below:

Data are given in the question

Right angle

a = 3.4

b = 2.6

These two are legs of the right triangle

Based on the above information

As we know that

Pythagorean Theorem is

[tex]a^2 + b^2 = c^2[/tex]

So,

[tex]= (3.4)^2 + (2.6)^2[/tex]

= 11.56 + 6.76

= 18.32

That means

[tex]c^2 = 18.56[/tex]

So, the c = 4.3 units

Answer:

Step-by-step explanation:

(x + k) is a factor of f(x)

x+k=0 => x= -k;    -k is a root of f(x)

=> f(-k)=0

[tex](x + k) is a factor of f(x)x+k=0 = > x= -k; -k is a root of f(x)= > f(-k)=0[/tex]

So the correct option is B.fl-k)=0.

The cube root function is f(x)=3√x f ( x ) = x 3 . A radical function is a function that is defined by a radical expression. The following are examples of rational functions: f(x)=√2x4−5 f ( x ) = 2 x 4 − 5 ; g(x)=3√4x−7 g ( x ) = 4 x − 7 3 ; h(x)=7√−8x2+4 h ( x ) = − 8 x 2 + 4 7 .

The root function is used to find a single solution to a single function with a single unknown. In later sections, we will discuss finding all the solutions to a polynomial function. We will also discuss solving multiple equations with multiple unknowns. For now, we will focus on using the root function.

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Answer:

[tex]-8(y+4) =(x-6)^{2}[/tex]  

Step-by-step explanation:

The standard form of a parabola is given by the following equation:

[tex](x-h)^{2} =4p(y-k)[/tex]

Where the focus is given by:

[tex]F(h,k+p)[/tex]

The vertex is:

[tex]V=(h,k)[/tex]

And the directrix is:

[tex]y-k+p=0[/tex]

Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.

If the focus is (-6,6):

[tex]F=(h,k+p)=(6,-6)[/tex]

Hence:

[tex]h=6\\\\k+p=-6\hspace{10}(1)[/tex]

And if the directrix is [tex]y=-2[/tex] :

[tex]-2-k+p=0\\\\k-p=-2\hspace{10}(2)[/tex]

Using (1) and (2) we can build a 2x2 system of equations:

[tex]k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)[/tex]

Using elimination method:

(1)+(2)

[tex]k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)[/tex]

Replacing (3) into (1):

[tex]-4+p=-6\\\\p=-6+4\\\\p=-2[/tex]

Therefore:

[tex](x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)[/tex]

So, the correct answer is:

Option 3

Answer:

b. There's no statistically significant linear relationship between the number of miles driven and the maintenance cost

Step-by-step explanation:

The p-value for the slope estimate show us how strong is the certainty that there are a linear relationship between both variables. In this case, the p-value for the slopes shows if there is a significant relationship between the number of miles driven and the maintenance cost.

If we have a high p-value like 0.7 we can said that there is no certainty in the linear relationship. it means that there's no statistically significant linear relationship between the number of miles driven and the maintenance cost.

Answer:

Step-by-step explanation:

p(x)=2x^2

q(x)=x-3

(p•q)(x)=2(x-3)^2

2(x^2-6x+9)

2x^2-12x+18

Answer:

[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.17)=0.00076[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Step-by-step explanation:

Information provided

n=400 represent the random sample taken

X=59 represent number of defectives from the company B

[tex]\hat p=\frac{59}{400}=0.1475[/tex] estimated proportion of defectives from the company B  

[tex]p_o=0.1[/tex] is the value to verify

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

z would represent the statistic

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

Hypothesis to test

We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:  

Null hypothesis:[tex]p \leq 0.1[/tex]  

Alternative hypothesis:[tex]p > 0.1[/tex]  

The statistic would be given by:

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

Replacing the info given we got:

[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]  

The p value for this case would be given by:

[tex]p_v =P(z>3.17)=0.00076[/tex]  

For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment

Answer:

The sample proportion for the births that are girls is 0.505. It is slightly higher than the expected value of 0.5, but the right way to answer if it is an unusual proportion is by performing an hypothesis test.

The hypothesis test results in not enough evidence to claim that the outcome is unlikely. This sample result has a probability of 0.7627 of appearing by pure chance in a population with proportion p=0.5.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the proportion of girls birth differs significantly from the expected proportion (50%).

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.5\\\\H_a:\pi\neq 0.5[/tex]

The significance level is 0.05.

The sample has a size n=1100.

The sample proportion is p=0.505.

p=X/n=556/1100=0.505

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1100}}\\\\\\ \sigma_p=\sqrt{0.000227}=0.015[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.505-0.5-0.5/1100}{0.015}=\dfrac{0.005}{0.015}=0.302[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z>0.302)=0.7627[/tex]

As the P-value (0.7627) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of girls birth differs significantly from the expected proportion (50%).

Answer:

D

Step-by-step explanation:

Length × Width = Area

So we'll substitute the Area of the circle having formula, πr²

Answer:

a= 2/5

b= -3/5

Step-by-step explanation:

We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator

[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]

This simplifies to:

[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]

This further simplifies to:

[tex]\frac{-3i +2}{5}[/tex]

Can be rewritten as:

[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]

a = 2/5

b = -3/5

Answer:

0.2

Step-by-step explanation:

1/0.2 = 5

10-5 = 5

1/a = 5

a = 1/5

a = 0.2

Answer:1/5 or 0.2

Step-by-step explanation:

1/a+1/0.2=10

1/a+1/2/10=10

1/a=10/2=10

1/a+5=10

1/a=10-5

1/a=5

a=1/5 or 0.2

Answer:

2 2/3

Step-by-step explanation:

Answer:

a) The probability that the mean printing speed of the sample is greater than 17.55 ppm = 0.4247

b) The probability that more than 48.6% of the sampled printers operate at the advertised speed = 0.4197

Step-by-step explanation:

The central limit theorem explains that for an independent random sample, the mean of the sampling distribution is approximately equal to the population mean and the standard deviation of the distribution of sample is given as

σₓ = (σ/√n)

where σ = population standard deviation

n = sample size

So,

Mean of the distribution of samples = population mean

μₓ = μ = 17.35 ppm

σₓ = (σ/√n) = (3.25/√10) = 1.028 ppm

a) The probability that the mean printing speed of the sample is greater than 17.55 ppm.

P(x > 17 55)

We first normalize 17.55 ppm

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (17.55 - 17.35)/1.028 = 0.19

To determine the required probability

P(x > 17.55) = P(z > 0.19)

We'll use data from the normal probability table for these probabilities

P(x > 17.55) = P(z > 0.19) = 1 - P(z ≤ 0.19)

= 1 - 0.57535 = 0.42465 = 0.4247

b) The probability that more than 48.6% of the sampled printers operate at the advertised speed

We first find the probability that one randomly selected printer operates at the advertised speed.

Mean = 17.35 ppm

Standard deviation = 3.25 ppm

Advertised speed = 18 ppm

Required probability = P(x ≥ 18)

We standardize 18 ppm

z = (x - μ)/σ = (18 - 17.35)/3.25 = 0.20

To determine the required probability

P(x ≥ 18) = P(z ≥ 0.20)

We'll use data from the normal probability table for these probabilities

P(x ≥ 18) = P(z ≥ 0.20) = 1 - P(z < 0.20)

= 1 - 0.57926 = 0.42074

48.6% of the sample = 48.6% × 10 = 4.86

Greater than 4.86 printers out of 10 includes 5 upwards.

Probability that one printer operates at advertised speed = 0.42074

Probability that one printer does not operate at advertised speed = 1 - 0.42074 = 0.57926

probability that more than 48.6% of the sampled printers operate at the advertised speed will be obtained using binomial distribution formula since a binomial experiment is one in which the probability of success doesn't change with every run or number of trials. It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 10

x = Number of successes required = greater than 4.86, that is, 5, 6, 7, 8, 9 and 10

p = probability of success = 0.42074

q = probability of failure = 0.57926

P(X > 4.86) = P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.4196798909 = 0.4197

Hope this Helps!!!

Answer:

about $3.84

Step-by-step explanation:

you do 69.20 divided by 18

Answer:

She returned 5 gifts.

Step-by-step explanation:

36 gifts is 60% = 0.6 of all the gifts that she received. How many presents are 100% = 1?

36 gifts - 0.6

x gifts - 1

0.6x = 36

x = 36/0.6

x = 60

She received 60 gifts.

She opened the rest of the gifts and found that 25% of them were the same present

The rest is 60 - 36 = 24 gifts.

25% is (1/4)*24 = 6 duplicate figts

She returned all but one of the duplicate gifts.

That is, she returned 6 - 1 = 5 gifts.