From a hot-air balloon, Grayson measures a 29^{\circ} ∘ angle of depression to a landmark that’s 1004 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.

The standard deviation of the grade points average of the college seniors is 0.57.

The given parameters:

3.2, 1.9 ,2.7, 2.4, 2.8, 2.9, 3.8, 3.0, 2.5, 3.3, 1.8, 2.5, 3.7, 2.8, 2.0, 3.2, 2.3, 2.1, 2.5, 1.9

The sum of the given data is calculated as follows;

∑x = 3.2 + 1.9 + 2.7 +  2.4 + 2.8 + 2.9 + 3.8 + 3.0 +  2.5 + 3.3 + 1.8 + 2.5 + 3.7 + 2.8 + 2.0 + 3.2 + 2.3 + 2.1 + 2.5 + 1.9

∑x = 53.3

The mean of the distribution is calculated as follows;

[tex]\bar x = \frac{\Sigma x}{N} \\\\\bar x = \frac{53.3}{20} \\\\\bar x = 2.665[/tex]

The square of the difference between the grade point and the mean;

[tex]\Sigma (x - \bar x)^2 = (3.2- 2.665)^2 + (1.9-2.665)^2 + (2.7- 2.665)^2 + (2.4-2.665)^2 \\\\+(2.8-2.665)^2 +(2.9 - 2.665)^2 + (3.8 - 2.665)^2 + (3-2.665)^2+ \\\\(2.5 -2.665)^2 + (3.3 - 2.665)^2 + (1.8-2.665)^2 + (2.5 - 2.665)^2 + \\\\(3.7-2.665)^2 + (2.8 - 2.665)^2 + (2-2.665)^2 + (3.2-2.665)^2 + \\\\(2.3 - 2.665)^2 + (2.1-2.665)^2 + (2.5-2.665)^2 + (1.9 - 2.665)^2\\\\\Sigma (x - \bar x)^2 = 6.5055[/tex]

The standard deviation of the grade points is calculated as follows;

[tex]\sigma = \sqrt{\frac{\Sigma (x-\bar x)^2}{N} } \\\\\sigma = \sqrt{\frac{6.5055}{20} } \\\\\sigma = 0.57[/tex]

Thus, the standard deviation of the grade points average of the college seniors is 0.57.

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I have no clue I just need the points have a good day tho :)

Answer:

[tex]x=-\frac{1}{2}[/tex] and [tex]x=-2[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{2x^2+5x+2}{x^2-4x+3}[/tex]

[tex]0=\frac{2x^2+5x+2}{x^2-4x+3}[/tex]

[tex]0=\frac{(2x+1)(x+2)}{(x-1)(x-3)}[/tex]

[tex]0=(2x+1)(x+2)[/tex]

[tex]2x+1=0[/tex] and [tex]x+2=0[/tex]

[tex]x=-\frac{1}{2}[/tex] and [tex]x=-2[/tex]

Answer:

See image

Step-by-step explanation:

This is to help you practice exponent rules. The rules are short cuts, which are good bc they're faster but bad bc they take away the meaning of the work. If you're trying to remember a rule, think through the meaning. See image.

So, "multiply exponents" and "product of powers" are basic two equivalent phrases! I think the answers on the image should work, but jic if not switch those two.

The Add exponents rule and Subtract are 100% correct.

The expressions are matched to the method needed to evaluate as shown below.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The first expression is 5³ × 5³.

Multiplication rule of exponents states that,

xᵃ × xᵇ = xᵃ⁺ᵇ

That is we add the exponents.

So, 5³ × 5³ = 5³⁺³ = 5⁶

The next expression is (7²)³.

We have the rule, (xᵃ)ᵇ = xᵃᵇ

So, here, multiply the exponents.

(7²)³ = 7⁶

(4x³)⁵

We can write it as,

(4x³)⁵ = 4⁵ . (x³)⁵

That is write is as product of the powers.

Division rule of exponents states that,

xᵃ / xᵇ = xᵃ⁻ᵇ

6⁹ / 6⁵ = 6⁹⁻⁵ = 6⁴

So, subtract the exponents.

Hence the expressions are matched.

Learn more about Exponents here :

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Answer:

12.4 ft

Step-by-step explanation:

Everything is done right so far.

Now to calculate the height of the tree, 12tan46, put the equation into a calculator.

Either a graphing calculator (make sure it is in degrees, not radians),

or the one on your phone (turn your phone landscape in the calculator app to get the trig functions.))

12tan46= 12.4 ft

Answer:

Step-by-step explanation:

Let x represent the amount invested at the higher rate. Then 1000-x is the amount invested at the lower rate. The total earnings are ...

  0.05(1000-x) +0.06x = 58

  50 +0.01x = 58 . . . . . . . . . . . simplify

  0.01x = 8 . . . . . . . . . . . . . . . subtract 50

  x = 800 . . . . . . . . . . . . . . . multiply by 100; amount at 6%

  (1000-x) = 200 . . . . . . . find the amount invested at 5%

Lara invested $200 at 5% and $800 at 6%.

Answer:

Step-by-step explanation:

Answer:

53.73

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

1/3*(-18) + 1 = 7

Just plug in the x which is -18, and solve with a calculator.

Hope this helps!

A. AC≅AC, Reflexive Property of Congruence

Correct. This is shared side of the triangles ABC and CDA

B. ∠ACB≅∠CAD, Alternate Interior Angles Theorem

Correct. BC and AD are parallel and AC is transversal

C. ∠BAC≅∠DCA, Alternate Interior Angles Theorem

Correct. AB and DC are parallel and AC is transversal

D. △ABC≅△CDA, SAS Triangle Congruence Theorem

Incorrect. This should be ASA as we have shown above the angles A and C and included side AC are congruent.

Answer:

The first two entries are correct since they are given. Unless you make a mistake compliling the first cell in a "given" line, they are always correct

Third one is not: they are not angles. They are segments - technically they are the SAME segment, it's in common between the two triangles.

Last one is correct, it's SSA

Answer:

A

Step-by-step explanation:

Did the test

Answer:

3 liters

Step-by-step explanation:

x>−15/2

15/2 is a fraction

Answer:

B

Step-by-step explanation:

Answer:

Im thinking its y=-2x but Im not 100% sorry if its wrong

Answer:

x=61

Step-by-step explanation:

2x-6+x+3=180

3x-3=180

3x=183

x= 61

Step-by-step explanation:

is it like this ? no diagrams ?

Answer:

y < 1

Step-by-step explanation:

In order to solve this inequality, we must isolate the y variable.

First add 5 on both sides of the inequality sign:

Now you have 8y < 8.

Then divide by 8 on both sides, to get y alone:

Now you have y < 1.

Hope this helps you :)

Answer:

The slope of the one of the top is -1/4

The slope of the one on the bottom is 1/6

Step-by-step explanation:

The one on the top goes down by 1 (negative) and goes 4 to the right (positive), which can be written as -1/4, which is the slope.

The one on the bottom goes up by 1 (positive) and goes to the right by 6 (positive), which can be written as 1/6, which is is the slope.

Answer:

B is empty

Step-by-step explanation:

Compute each probability. The strategy is to transform X, a random variable representing the weight of newborns, to another random variable Z that represents the same but scaled quantity so that Z is normally distributed with mean 0 and s.d. 1. To do this, we use the rule

X = 5.5 + 1.6 Z

or

Z = (X - 5.5)/1.6

then use a calculator to compute the probability, or look it up in a table. Multiply this probability by 800 to find the number of newborns in each category.

1.

Pr[3 ≤ X ≤ 8] = Pr[(3 - 5.5)/1.6 ≤ (X - 5.5)/1.6 ≤ (8 - 5.5)/1.6]

… ≈ Pr[-1.5625 ≤ Z ≤ 1.5625]

… ≈ 0.8818

Out of 800 babies, you would expect around 88% of them, or about 705 babies to weight between 3 and 8 pounds.

2.

Pr[X < 6] = Pr[(X - 5.5)/1.6 ≤ (6 - 5.5)/1.6]

… = Pr[Z ≤ 0.3125]

… ≈ 0.6227

Out of 800 babies, around 498 will weigh less than 6 pounds.

3.

Pr[X > 5] = Pr[(X - 5.5)/1.6 > (5 - 5.5)/1.6]

… = Pr[Z > -0.3125]

… ≈ 0.6227

same as (2) due to the symmetry of the distribution (Z is centered at zero). Out of 800 babies, you can expect around 498 in this group.

4.

Pr[5.5 ≤ X ≤ 9] = Pr[(5.5 - 5.5)/1.6 ≤ (X - 5.5)/1.6 ≤ (9 - 5.5)/1.6]

… = Pr[0 ≤ Z ≤ 2.1875]

… ≈ 0.4857

Out of 800 babies, around 388 will weigh between 5.5 and 9 pounds.

Answer:

                                 pop

                                             yes                   no             total

country            yes                  11                      38              49

                        no                       43                     8                51

                         total                54                     46               100

Hope you understand this haha

The answer is in the file. Hope it helps.

Given terms in an AP are √2,√8,√18

√8 = √(2×2×2) = 2√2

√18 = √(2×3×3) = 3√2

The AP : √2,2√2,3√2

next term = 4√2> √(4×4×2)

⇛ √32

The next term of the AP = √32.

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Which term of the AP:3, 8, 13, 18,...,is 78?

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Answer:

Step-by-step explanation:

Sorry no one answered your question sooner. First Let x = what the daughter receives

Then 180000 - x is what the son will receive. Notice that if you add these together you get the total, 180000. You write a proportion and cross multiply to solve. Since x = 80000, the son will receive 80000. The daughter will receive 100000.

Answer:

000

Step-by-step explanation:

000

Answer:

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]

Step-by-step explanation:

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = \lim_{x\to 0^+} \tan(x) - \lim_{x\to 0^+} \frac{1}{x^2} $[/tex]

and

[tex]$\lim_{x\to 0^+} \tan(x) = \tan(0) = 0$[/tex]

[tex]$\lim_{x\to 0^+} \frac{1}{x^2} = +\infty$[/tex]

Therefore,

[tex]$\lim_{x\to 0^+} \tan(x) - \frac{1}{x^2} = -\infty$[/tex]

Answer:

g(x) = (5x + 3)/ x - 7

Step-by-step explanation:

Let g(x) = y

y = (7x + 3)/x - 5

Make x the subject

xy - 5y = 7x + 3

xy - 7x = 5y + 3

x(y - 7) = 5y + 3

x = (5y + 3)/ y - 7

Therefore, the inverse of the function = (5x + 3)/ x - 7