An observer at the top of a 532 foot cliff measures the angle of depression from the top of the cliff to a point on the ground to be 4 degrees. What is the distance from the base of the cliff to the point on the ground? Round to the nearest foot.

Answer:

c. 45

Step-by-step explanation:

there are 15 participant in each category, and there are 3 categories, so total participants = 15 * 3

= 45

Hope this helps, and please mark me brainliest if it does!

Answer:

logₐ(420)

Step-by-step explanation:

Answer:

The answer is

[tex] log_{a}(420) [/tex]

Step-by-step explanation:

You have to use Logarithm Law,

[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]

* Take note, number b and c can only be multiplied when they have the same base, a

So for this question :

[tex] log_{a}(6) + log_{a}(70) [/tex]

[tex] = log_{a}(6 \times 70) [/tex]

[tex] = log_{a}(420) [/tex]

Answer:

object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .

Step-by-step explanation:

What a scale factor of 1:4 means.

Simply it means that the reals size of the object on land have been reduced in the drawing in the paper.

Now for scale factor of 1:4 in particular it means that the object have been reduced by a factor of 4 on paper or the drawing have been increased by a factor of 4 on land .

Example if the drawing has measurements of 4 inches on paper, then on land it will be 16 inches

Answer:

[tex]f(theta)=sin(theta) - cos(theta)[/tex] + C

This is my first time doing a double integral, so im only 90% sure in my answer

Step-by-step explanation:

You pretty much want to take the double integral of sinx + cosx

The anti-derivative of sinx = -cosx

The anti-derivative of cosx = sinx

So f' = -cosx + sinx

Now lets take the integral of f':

The anti-derivative of -cosx = sinx

The anti-derivative of sinx = -cosx

So, f(x) = sinx - cosx

============================================================

Work Shown:

I'll use x in place of theta since its easier to type on a keyboard.

f '' (x) = sin(x) + cos(x)

f ' (x) = -cos(x) + sin(x) + C ..... integrate both sides; dont forget the plus C

f ' (0) = 1

f ' (0) = -cos(0) + sin(0) + C

-cos(0) + sin(0) + C = 1

-1 + 0 + C = 1

C = 1+1

C = 2

So,

f ' (x) = -cos(x) + sin(x) + C

turns into

f ' (x) = -cos(x) + sin(x) + 2

----------------------------

Now integrate both sides of the first derivative to get the original f(x) function

f ' (x) = -cos(x) + sin(x) + 2

f(x) = -sin(x) - cos(x) + 2x + D .... apply integral; D is some constant

f(0) = -sin(0) - cos(0) + 2(0) + D

f(0) = 0 - 1 + 0 + D

f(0) = D - 1

f(0) = 2

D-1 = 2

D = 2+1

D = 3

We have f(x) = -sin(x) - cos(x) + 2x + D update to f(x) = -sin(x) - cos(x) + 2x + 3

----------------------------

So f '' (x) = sin(x) + cos(x) becomes f(x) = -sin(x) - cos(x) + 2x + 3 when f(0) = 2 and f ' (0) = 1

The last step is to replace every x with theta so that we get back to the original variable.

f(x) = -sin(x) - cos(x) + 2x + 3   turns into   f(θ) = -sin(θ) - cos(θ) + 2θ + 3

Answer:

65.1 and 69.1

Step-by-step explanation:

a^2+b^2=c^2

c=95

b=a+4

Solve for a^2+(a+4)^2=95^2

a=65.1

b=a+4=69.1

Answer:

65.1 and 69.1

Step-by-step explanation:

c² = a² + b²

c= 95

a - one leg

b= (a + 4) - second leg

95² = a² + (a + 4)²

9025 = a² + a² + 2*4a + 16

2a² + 8a - 9009 = 0

[tex]a= \frac{-b +/-\sqrt{b^2 - 4ac} }{2a} \\\\a = \frac{-8 +/-\sqrt{8^2 - 4*2*9009} }{2*2} \\\\a=65.1 \ and \ a=- 69.1[/tex]

A leg length can be only positive. a = 65.1

b = 65.1 + 4 = 69.1

Answer:

d) 50

Step-by-step explanation:

40 + 90 + p = 180

p = 50

Answer:

The distribution pattern that will have variance greater than mean is one where the population of species is clustered and thus far from the mean abundance of species per unit area.

This distribution pattern can be found, using the POISSON distribution.

Step-by-step explanation:

Variance is a measure of dispersion while Mean is a measure of central tendency.

The mean is the average of all values (in this case, the abundance or concentration of species per unit area). It is the sum total of all values, divided by the number of values there are.

The variance of a given set of data, on the other hand, is a measure of the spread or distance or dispersal of the data from the mean. It measures the spread between each datum/value and the mean value.

The relationship between mean and variance surely reflects the pattern that the distribution will take. The kind of distribution pattern that will have a greater variance than mean is a Poisson distribution. Sample size is usually large here. Since the variance is greater than the mean, the population is a clustered or clumped distribution.

Answer:

53.33% probability that one woman and one man will be chosen to be on the committee

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the members are chosen is not important, so we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

What is the probability that one woman and one man will be chosen to be on the committee?

Desired outcomes:

One woman, from a set of 2, and one man, from a set of 4. So

[tex]D = C_{2,1}*C_{4,1} = \frac{2!}{1!1!}*\frac{4!}{1!3!} = 8[/tex]

Total outcomes:

Two members from a set of 2 + 4 = 6. So

[tex]T = C_{6,2} = \frac{6!}{2!4!} = 15[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{8}{15} = 0.5333[/tex]

53.33% probability that one woman and one man will be chosen to be on the committee

easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

Answer:

Step 3

Step-by-step explanation:

The mistake was made in Step 3.

Step 1: Subtract the wholes. 4 - 1 = 3

Step 2: Subtract the fractions. 5/6 - 3/6 = 2/6

After Step 2, He should have added them instead of subtracting them:

3 + 2/6 = 3 2/6

So, step 3 was his mistake.

Answer:step 3

Step-by-step explanation: he should have added

Answer:

The maximum height reached by the rocket is of 938.56 feet.

Step-by-step explanation:

The height y, after x seconds, is given by a equation in the following format:

[tex]y(x) = ax^{2} + bx + c[/tex]

If a is negative, the maximum height is:

[tex]y(x_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

In this question:

[tex]y(x) = -16x^{2} + 230x + 112[/tex]

So

[tex]a = -16, b = 230, c = 112[/tex]

Then

[tex]x_{v} = -\frac{230}{2*(-16)} = 7.1875[/tex]

[tex]y(7.1835) = -16*(7.1835)^{2} + 230*7.1835 + 112 = 938.56[/tex]

The maximum height reached by the rocket is of 938.56 feet.

Answer:

[tex]y=50x+75[/tex]

Step-by-step explanation:

When writing a linear equation from a graph, we need to find two things: the y-intercept (what y is when x is 0) and the slope.

First, let us find the y-intercept.

To do this, we can just look at the graph. When x=0, y=75, so 75 is our y-intercept, which is also known as b.

To find the slope of this line, we will need to look at two points

We already know that (0,75) is a point. From the graph, we can see that (1,125) is also a point on this line.

Now, we can find the slope of this line using the following formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{125-75}{1-0} \\\\m=\frac{50}{1} \\\\m=50[/tex]

Now that we have both the y-intercept and slope, we can put them together in the form of [tex]y=mx+b[/tex]

[tex]y=50x+75[/tex]

Answer:

Slope: 50

Equation: y = 50x + 75

Step-by-step explanation:

Take two points:

(2,175)

(3,225)

Find the slope:

225 - 175/3 - 2

50/1 = 50

So we get this equation:

y = 50x + b

Now to find b, insert one of those points from before back in:

175 = 50(2) + b

175 = 100 + b

b = 75

So the equation is:

y = 50x + 75

Answer:

B.

✔ -4

Step-by-step explanation:

E 2021

Answer:

63.25 not an integer

Step-by-step explanation:

HCF(a,b)*LCM(a,b)=ab

11*368=64*x

x=11*368/64

x=63.25 not an integer, one of the given numbers must be incorrect

but you may use this method to find it yourself

Answer:

  see below

Step-by-step explanation:

The first subtraction has a zero result (blue) from the thousands digit, so we know the dividend has 4 in that place. The 5 in the 1s place of the dividend is brought down to fill the space on the bottom line. 6 goes into that number 0 times, so the final quotient digit is 0.

  4,925 = 6×820 +5

or

  4,925 ÷ 6 = 820 r5

Answer:

5

Step-by-step explanation:

[tex]\frac{7+x}{9-x}=3\\ 7+x = 3(9-x)\\7+x=27-3x\\x+3x=27-7\\4x=20\\x=5[/tex]

Answer:

11.24

Step-by-step explanation:

If she arrived at 12.15, to find the time of departure we have to deduct 33 mins and the time she spent for photos,18 mins from this to get time of departure.

Total time spent for journey

33mins +18 mins = 51mins

time of departure = 12.15 - 51mins

so the time of departure is 11.24

Answer:

You have 31.43% of your allowance left.

Step-by-step explanation:

This question can be solved using a rule of three.

Your initial amount, of 70, is 100%.

The remaining amount, of 70 - 48 = 22, is x%. So

70 - 100%

22 - x%

[tex]70x = 100*22[/tex]

[tex]x = \frac{100*22}{70}[/tex]

[tex]x = 31.43[/tex]

You have 31.43% of your allowance left.

Answer:

(71.28, 78.72)

Step-by-step explanation:

We have the following information from the statement:

mean (m) = 75

sample standard deviation (sd) = 5

Sample size (n) = 13

Significance level (alpha) = 1 - 0.98 = 0.02

Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12

The critical value would be:

t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)

Margin of error equals:

E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:

E = 2,681 * 5/13 ^ (1/2)

E = 3.72

Therefore, the interval of 98% confidence interval would be:

75 + 3.72 = 78.72

75 - 3.72 = 71.28

(71.28, 78.72)

Answer:

Step-by-step explanation:

Simple regression was employed to establish the effects of childhood exposure to lead. THe effective sample size was about 122 subjects. THe independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

Calculate the t statistic for each slope, at significance level = 0.01.

Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?

Slope Error

Highest grade achieved .061 −0.027 0.009 .008 No / Yes

Reading grade equivalent .121 −0.070 0.018 .000 No / Yes

Class standing .039 −0.006 0.003 .048 No / Yes

Absence from school .071 4.8 1.7 .006 No / Yes

Grammatical reasoning .051 0.159 0.062 .012 Yes / No

Vocabulary .108 −0.124 0.032 .000 No / Yes

Hand-eye coordination .043 0.041 0.018 .020 No / Yes

Reaction time .025 11.8 6.66 .080 No / Yes

Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No

B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.

1. No

2. Yes

[tex]t=\frac{\text {estimated slope}}{\text {std error}}[/tex]

a)

Estimated Slope           Std error              t - calculated

-0.027                            0.009                   -3

-0.070                            0.018                    -3.89

-0.006                            0.003                   -2

4.8                                  1.7                         2.82

0.159                              0.062                   2.56

-0.124                             0.032                   -3.87

0.041                              0.018                    2.28

11.8                                6.66                      1.77

-0.639                           0.36                       -1.78

b) Yes, It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.

Answer:

Descriptive statistics

Step-by-step explanation:

Descriptive statistics describes and summarizes the basic features of a given dataset. It explains features from a collection of information, it is also said to be a form of summary statistics. Here data is characterized using its properties.

In this case, I was asked to describe my approach to the initial analysis. When describing the analysis plan for the request, I would tell the interviewer to start analysis using descriptive statistics.

Answer:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]

And replacing:

[tex] \mu_{\bar X}= 5[/tex]

And the deviation:

[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]

And the distribution is given:

[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] \mu= 5. \sigma^2 =0.08[/tex]

And the deviation would be [tex] \sigma = \sqrt{0.08}= 0.283[/tex]

For this case we select a sample size of n = 5 and the distirbution for the sample mean would be:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]

And replacing:

[tex] \mu_{\bar X}= 5[/tex]

And the deviation:

[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]

And the distribution is given:

[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]

Answer:

40% of 160 is 64

Step-by-step explanation:

You can easily find the answer in one step, just multiplying the whole (160) by the percentage (40) divided by 100.

So, 40% of 160 = 160 × 0.4 = 64.

Answer:

64

Step-by-step explanation:

You first have to subtract 40% from 160 and then you subtract that amount with is 96 from 160 and you get your answer 64

Answer: provided in the explanation section

Step-by-step explanation:

The complete question says:

The time that it takes to service a car is an exponential random variable with rate 1. (a) If Lightning McQueen (L.M.) brings his car in at time 0 and Sally Carrera (S.C) brings her car in at time t, what is the probability that S.C.'s car is ready before L.M.'s car? Assume that service times are independent and service begins upon arrival of the car Be sure to: 1) define all random variables used, 2) explain how independence of service times plays a part in your solution, 3) show all integration steps. (b) If both cars are brought in at time 0, with work starting on S.C. 's car only when L.M.'s car has been completely serviced, what is the probability that S.C.'s car is ready before time 2?

Ans to this is provided in the images uploaded as it is not possible to put the symbols here...

i hope you find this helpful.

cheers !!

Answer:

I just do a' as a sample. You calculate b' and c'

Step-by-step explanation:

[tex]a'=\frac{b\times c}{a\bullet (b\times c)}, b' = \frac{c\times a}{a\bullet (b\times c)}, c' = \frac{a\times b}{a\bullet (b\times c)}[/tex]

Now, calculate b x c

[tex]\left[\begin{array}{ccc}i&j&k\\2&3&1\\1&-1&-2\end{array}\right] =<-5, 5,-5>[/tex]

[tex]a'=\frac{<-5,5,-5>}{<1, 2, 2>\bullet <-5, 5,-5>}=\frac{<-5, 5, -5>}{-5} =<1,-1,1>[/tex]

Answer:  24 square units

Explanation: The diagonals are 4+4 = 8 and 3+3 = 6 units long. Multiply the diagonals to get 8*6 = 48. Then divide this in half to get 48/2 = 24.

An alternative is to find the area of one smallest triangle, and then multiply that by 4 to get the total area of the rhombus. You should find the area of one smallest triangle to be 0.5*base*height = 0.5*4*3 = 6, which quadruples to 24.

Hey there! :)

Answer:

Price per cup: $3.5

Price for 18 cups: $63.

Step-by-step explanation:

To find the cost of a single cup of ice cream, we can set up an equation where 'x' equals the price of a cup of ice cream.

30x = 105

Divide both sides by 30:

x = $3.5.

To find the cost of 18 cups, simply multiply this price by 18:

18 × 3.5 = $63 dollars. This is the price for 18 cups of ice cream.

Answer: –55x + 570

Step-by-step explanation:

The person above me completely missed the question so this is the right one

Answer:

(d - 4) / c

Step-by-step explanation:

The slope of the line in terms of c and d is (d - 4) / c.

Here, we have,

To find the slope of the line in terms of the coordinates of the point (c, d), we can use the slope-intercept form of a line, y = mx + b, where m represents the slope.

In the given equation, y = kx + 4, we can see that the coefficient of x is k, which represents the slope of the line.

Since the line contains the point (c, d), we can substitute these values into the equation:

d = kc + 4

To isolate the slope term, we rearrange the equation:

d - 4 = kc

Now, divide both sides by c:

(d - 4) / c = k

Therefore, the slope of the line in terms of c and d is (d - 4) / c.

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Answer:

7mph

Step-by-step explanation:

Given

Time Taken to go upstream Tup = 35 min

Time Taken to go downstream Tdown=21 min.

Let the absolute speed (i.e speed relative to the stationary riverbed) be :

Vup : going upstream

Vdown: going downstream.

We know that the distance traveled upstream = distance traveled downstream, hence we can equate both distances, i.e. :

Distance Traveled Upstream = Distance Traveled Downstream

Vup · Tup = Vdown · Tdown   (substituting the values for time above)

35Vup = 21Vdown

Vup = (21/35) Vdown ------------(eq 1)

We are also given that the motorboat can travel at V = 28 mph relative to the water.

Since going upstream, we are going AGAINST the current, relative to the riverbed, we expect to be travelling slower. In fact, the absolute difference between the speed relative to the water (i.e V = 28 mph) and the speed relative to the seabed (i.e Vup), is equal to the speed of the current.

The same can be said for going downstream WITH the current, that the absolute difference between V = 28mph and Vdown is also equal to the speed of the current.

Hence we can equate the two:

28 - Vup = Vdown - 28

Vup + Vdown = 2(28)

Vup + Vdown = 56 ---------------------(eq 2)

If we solve the system of equations (eq 1) and (eq2), we will get

Vup = 21 mph and Vdown = 35 mph

(sanity check tells us that this makes sense because we expect to be going slower upstream because we are going against the current)

Hence current speed

= 28-Vup

= 28 - 21

= 7 mph. (answer)

Sanity Check:

Current speed can also be written:

= Vdown-28

= 35 - 28

= 7 mph (same as what we found above, so this checks out)

The speed of the current motorboat = 7 mph

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Speed of boat in still water = 28 mph

Let the speed of stream = w

Here, The upstream time is 35 min = 35/60 h = 7/12 h

downstream time is 21 min = 21/60 h = 7/20 hours

Since, The distance (d = vt) traveled either way is the same, but at different speeds and times.

Hence, Set upstream and downstream distances (vt) equal and solve for w as;

⇒ (28 - w)(7/12) = (28 + w)(7/20)

⇒ 20 (28 - w) = 12 (28 + w)

⇒ 5(28 - w) = 3(28 + w)

⇒ 140 - 5w = 84 + 3w

⇒ 140 - 84 = 5w + 3w

⇒ 56 = 8w

⇒ w = 7

Thus, The speed of the current = 7 mph

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