A vertical radio tower is 645 feet high above level ground. How far would you need to be from the base of the tower so that the angle of elevation to the top of the tower would be 35.0°? (The “angle of elevation” is the angle measured from level ground up to the top of the tower.)

Answer:

Function

Step-by-step explanation:

A function is a relation where each x-value has only one y-value. In this problem, all the x-values have a y-value of 3. It is a function because even though they all share the same y-value, they don't have more than one y-value. It would be a relation but not a function if one x-value had two y-values.

Hope this helps. :)

Answer:

Step-by-step explanation:

Factors of 12

2, 3 , 6 , 4, 1, 12

Answer:

Step-by-step explanation:

Let x represent the rate of the freight train. If the rate of the passenger train is 15 MPH faster than the rate of the frieght train, it means that the rate of the passenger train is x + 15

Time = distance/speed

Time that it will take a passenger train to travel 245 miles is

245/(x + 15)

Time that it will take a fright train to travel 200 miles is

200/x

Since both times are the same, it means that

245/(x + 15) = 200/x

Cross multiplying, it becomes

245x = 200(x + 15)

245x = 200x + 3000

245x - 200x = 3000

45x = 3000

x = 3000/45 = 66.67 mph

Rate of freight train is 66.67 mph

Rate of passenger train is 66.67 + 15 = 81.67 mph

Answer:

The following combination describes a regression line that is a good fit for the data

a. Larger R-sq and small Se

Step-by-step explanation:

In regression analysis, we measure the goodness of fit in terms of two parameters.

1. R² ( R-squared or also called the coefficient of determination)

2. SE ( Standard Error)

1. R-squared

The R-squared indicates the relative measure of the percentage of the variance with respect to the dependent variable.

R-squared is measured in percentage so it doesn't have any unit.

The greater the R-squared percentage, the better is the goodness of fit.

2. Standard Error

The SE basically indicates that on average how far the data points are from the regression line.

The unit of the standard error is the same as the dependent variable.

The lower the SE, the better is the goodness of fit.

Therefore, the correct option is (a)

a. Larger R-sq and small Se

Answer:

Where is the table because I dont see it up here?

Answer:

4. 9.1 – 10 = 0.2x

X= -4.5

Step-by-step explanation:

Let's solve for x in the equations given below

1. 9.1 = -0.2x + 10

9.1 - 10 = -0.2x

-0.9= -0.2x

-0.9/-0.2= x

4.5 = x

2. 10 = 9.1 + 0.2x

10-9.1 = 0.2x

0.9= 0.2x

0.9/0.2 = x

4.5 = x

3. 10 – 0.2x = 9.1

10-9.1= 0.2x

0.9= 0.2x

0.9/0.2= x

4.5 = x

4. 9.1 – 10 = 0.2x

-0.9 = 0.2x

-0.9/0.2= x

-4.5 = x

The different equation is equation 4

Reason because it's answer gave a negative value of x while others gave a positive value of x.

But in magnitude they all have same value of x

Answer:Its D

Step-by-step explanation:

I just did it on ed

━━━━━━━☆☆━━━━━━━

▹ Answer

#3. 1.89/100

▹ Step-by-Step Explanation

1.89 → hundreths place so..

1.89/100 is the correct answer

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex]\boxed{\sf \ \ \ a = 1 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

saying that [tex]x-\sqrt{a}[/tex] is a factor means that [tex]\sqrt{a}[/tex] is a zero which means

[tex]2(\sqrt{a})^4-2a^2(\sqrt{a})^2-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=> 2a^2-2a^3-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=>3-3*\sqrt{a}=0\\\\<=>\sqrt{a}=\dfrac{3}{3}=1\\\\<=> a = 1[/tex]

so the solution is a = 1

Do not hesitate if you have any question

Answer:

B

Step-by-step explanation:

Answer:

The nth term rule of the quadratic sequence is [tex]2n^{2} +5n-3[/tex].

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by =  [tex]an^{2}+bn+c[/tex]

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a  =  [tex]\dfrac{4}{2}[/tex] = 2

SO, the first term of the nth term rule equation is [tex]an^{2}[/tex] = [tex]2n^{2}[/tex].

Now, in the term [tex]2n^{2}[/tex], put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then [tex]2n^{2}[/tex] = [tex]2 \times (1)^{2}[/tex] = 2

If n = 2, then [tex]2n^{2}[/tex] = [tex]2 \times (2)^{2}[/tex] = 8

If n = 3, then [tex]2n^{2}[/tex] = [tex]2 \times (3)^{2}[/tex] = 18

If n = 4, then [tex]2n^{2}[/tex] = [tex]2 \times (4)^{2}[/tex] = 32

If n = 5, then [tex]2n^{2}[/tex] = [tex]2 \times (5)^{2}[/tex] = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is [tex]2n^{2} +5n-3[/tex].

Answer:

Step-by-step explanation:

[tex]x/a=1+x/b \\Make- x -subject- of- formula\\Multiply -both-sides-by ; ab\\bx =ab+ax\\bx-ax=ab\\x(b-a) =1ab\\\frac{x(b-a)}{(b-a)} = \frac{ab}{(b-a)} \\x = \frac{ab}{(b-a)}[/tex]

[tex]x/a=1+x/b\\Make ; b -subject-of-formula\\\frac{x}{a} -1=\frac{x}{b} \\Multiply-both-sides-by ; b\\\\b(\frac{x}{a} -1) = x\\\frac{b(\frac{x}{a} -1)}{(\frac{x}{a} -1)} = \frac{x}{(\frac{x}{a} -1)} \\\\b = \frac{x}{(\frac{x}{a} -1) }[/tex]

Step-by-step explanation:

x÷a = 1 + x÷b

To make x subject of the formula

x÷a = 1 + x÷b

x/a - x/b = 1

(xb - xa)/ab = 1

xb - xa = ab

x(b - a) = ab

x = ab/(b-a)

To make b subject of the formula

x÷a = 1 + x÷b

x/a - 1 = x/b

(x - a)/a = x/b

b(x-a) = ax

b = ax/(x-a)

Step-by-step explanation:

[tex] \frac{2}{ \sqrt{9} } [/tex]

[tex] \frac{2 \times \sqrt{9} }{ \sqrt{9} \times \sqrt{9} } [/tex]

[tex] \frac{2 \sqrt{9} }{9} [/tex]

Answer:

[tex]\frac{2\sqrt{9} }{9}[/tex]

Step-by-step explanation:

[tex]\frac{2}{\sqrt{9} } \\[/tex]

[tex]\frac{2}{\sqrt{9} } * \frac{\sqrt{9} }{\sqrt{9} }[/tex]

[tex]\frac{\sqrt{9} }{\sqrt{9} }[/tex]  is equal to 1, so it doesn't change the value, just helps us simplify.

[tex]\frac{2\sqrt{9} }{9}[/tex]

There are no common factors between 2 and root 9, so we are done

The mass of the lamina is 6 units.

The center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Here,

To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.

The mass (M) of the lamina is given by the double integral of the density function over the region D:

M = ∬_D ρ(x, y) dA

where dA represents the differential area element.

The center of mass (X,Y) of the lamina can be calculated using the following formulas:

X = (1/M) ∬_D xρ(x, y) dA

Y = (1/M) ∬_D yρ(x, y) dA

Now, let's proceed with the calculations:

The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:

0 ≤ x ≤ 2

0 ≤ y ≤ 3 - (3/2)x

Now, let's calculate the mass (M):

M = ∬_D ρ(x, y) dA

M = ∬_D 2(x + y) dA

We need to set up the double integral over the region D:

M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx

Now, integrate with respect to y first:

M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx

M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx

M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx

Now, integrate with respect to x:

[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]

So, the mass of the lamina is 6 units.

Next, let's calculate the center of mass (X,Y):

X = (1/M) ∬_D xρ(x, y) dA

X = (1/6) ∬_D x * 2(x + y) dA

We need to set up the double integral over the region D:

X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx

Now, integrate with respect to y first:

X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx

X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx

X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx

X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx

Now, integrate with respect to x:

[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]

Next, let's calculate Y:

Y = (1/M) ∬_D yρ(x, y) dA

Y = (1/6) ∬_D y * 2(x + y) dA

We need to set up the double integral over the region D:

Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx

Now, integrate with respect to y first:

Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx

Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx

Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx

Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx

Now, integrate with respect to x:

[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]

So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Learn more about mass here

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Answer:

It is a 9/10 chance of having at least one boy. The probability is also high enough for the couple to be very confident in having at least one boy in 9 children.

Step-by-step explanation:

I listed all of the possible combinations below

GGGGGGGGG           BGGGGGGGG

BBGGGGGGG           BBBGGGGGG

BBBBGGGGG           BBBBBGGGG

BBBBBBGGG            BBBBBBBGG

BBBBBBBBG             BBBBBBBBB

Total number of combinations with at least one boy is 9/10

This is a very high percentage, which means the couple is very likely to have at least one boy.

Answer:

Step-by-step explanation:

Given the encoded message defined by the function f(x) = x³-1,  the inverse function that the decoder would need when the message is received can be expressed as thus:

let the inverse of the function be represented as y such that y = x³-1.

Making x the subject of the formula from the equation above;

x³ = y+1

Taking the cube root of both sides:

∛x³ = ∛(y+1)

x = ∛(y+1)

replacing y with x:

y = ∛(x+1)

f⁻¹(x) = ∛(x+1)

The encoded message is the inverse function ∛(x+1)

Answer:

B. 35%

Step-by-step explanation:

P(winning $1.00)=40%

P(winning $5.00)=20%

P(winning $10.00)=5%

In a probability distribution, the sum of the probability must always be equal to 1.

Therefore:

P(winning $0.00)=1-(40%+20%+5%)

=1-(0.4+0.2+0.05)

=1-0.65

=0.35

The probability of winning nothing at all is 35%.

Answer:

For 90% CI = (0.428, 0.572)

For 98% CI = (0.399, 0.601)

The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 66/132 = 0.50

Number of samples n = 132

Confidence level = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

0.50 +/- 1.645√(0.50(1-0.50)/132)

0.50 +/- 1.645√(0.001893939393)

0.50 +/- 0.071589436011

0.50 +/- 0.072

(0.428, 0.572)

The 90% confidence level estimate of the true population proportion of students who responded "yes" is (0.428, 0.572)

For 90% CI = (0.428, 0.572)

For 98% CI = (0.399, 0.601)

The confidence interval (and Margin of error) reduces when 90% confidence level is used compared to when 98% confidence level is used.

Answer:

50 %

Step-by-step explanation:

p not greater than 5 means 5 or <5

so half of spinner means probability 50 %

Answer:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Step-by-step explanation:

For this problem we have the following set:

E = { x l x is a perfect square <36}

And we can rewrite it taking in count the list of all the perfect squares less than 36 and we have:

1= 1*1

4= 2*2

9 = 3*3

16 =4*4

25= 5*5

And we can rewrite the set on this way:

E= {1,4,9,16,25}

Answer:

A. 2x

Step-by-step explanation:

Step 1: Factor out a 2

2(2x³ - x² + 4x)

Step 2: Factor out an x

2x(2x² - x + 4)

So our answer is B.

Answer: 13.5

Step-by-step explanation:

30% = 0.3.

Thus, simply do 0.3*45 to get 13.5.

Hope it helps <3

Answer:

for us to be able to ascertain whether a function has no limit we approach from two points which are from zero and infinity.

Step-by-step explanation:

the two best path to approach a function is to approach from zero and approach from infinity, literary what we are trying to do is approach from the smallest to the greatest and it each point we can conclude with certainty whether the function has a limit or not.

Step-by-step explanation:

Net $103.92 [$25.98 ÷ 20%]

List. $129.90 [ $103.92 + $25.98]

Answer:

Step-by-step explanation:

Given the expression [tex]log_81000 = log_210[/tex], to prove this expression is true using the properties of logarithm, we will follow the following steps.

Starting from the Left Hand Side:

Answer:

Step-by-step explanation:

First we must first find the LCM

The LCM of x² + 3x + 2 and (x + 2)(x + 1 ) is

x² + 3x + 2

So we have

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

Hope this helps you

Answer:

The answer is OPTION D!

Step-by-step explanation:

HoPe ThIs HeLpS!

Answer:

7/8

Step-by-step explanation:

The numbers that are not 3 are 1, 2, 4, 5, 6, 7, and 8.

7 out of 8 numbers.

P(not 3) = 7/8

Answer:

7/8

Step-by-step explanation:

There are a total of 8 cards, and one of the cards is 3.

Their cards that are not 3 are 1,2,4,5,6,7,8. Therefore, there is a total of 7 cards that are not 3.

Now, let’s find the probability of drawing a card that is not 3.

P(not 3)= numbers that are not 3 / total numbers

There are 7 numbers that are not 3 and 8 total number cards.

P(not 3)= 7/8

Answer:

20% probability that a box weighs more than 32.2 ounces

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X higher than x is given by the following formula.

[tex]P(X > x) = \frac{b-x}{b-a}[/tex]

Uniform distribution ranging from 31 to 32.5 ounces.

This means that [tex]a = 31, b = 32.5[/tex]

What is the probability that a box weighs more than 32.2 ounces?

[tex]P(X > 32.2) = \frac{32.5 - 32.2}{32.5 - 31} = 0.2[/tex]

20% probability that a box weighs more than 32.2 ounces

Answer:

Her temperature is 97.27ºF.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 98.2, \sigma = 0.62[/tex]

Z = -1.5. What is her​ temperature?

Her temperature is X when Z = -1.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.5 = \frac{X - 98.2}{0.62}[/tex]

[tex]X - 98.2 = -1.5*0.62[/tex]

[tex]X = 97.27[/tex]

Her temperature is 97.27ºF.

Answer:

x=3 and y=1

Step-by-step explanation:

First find the deteminant

That is ad-bc

ᵃ ᵇ

ᶜ ᵈ