Sameena measures the angle from the ground to the top of a building from two locations. The angle of elevation from the first point is 45°, and the angle of elevation from the second point is 60°. The distance from the second point to the top of the building is 150 ft.


[Not drawn to scale]

What is the distance from the first observation point to the top of the tower (x)? Round the answer to the nearest tenth.
122.5 ft
183.7 ft
244.9 ft
501.9 ft

Answer:

[tex]\frac{57}{16}[/tex] lb

Step-by-step explanation:

[tex]\frac{7}{8} +1\frac{3}{4} +\frac{15}{16}[/tex]

Change the mixed fraction into an improper fraction,

[tex]\frac{7}{8} +\frac{7}{4} +\frac{15}{16}[/tex]

Now convert the denominator to 16 (since 8 and 4 are factors of 16)

And remember that what you do to the denominator, you must do the same to the numerator!

[tex]\frac{14}{16} +\frac{28}{16} +\frac{15}{16}[/tex]

Now that we have all fractions with the same denominator, we can simply add all the numerators together,

= [tex]\frac{57}{16}[/tex]

It cannot be simplified any further, so this is your answer!

Hope this helped!!

Answer:

A'(-1,-3)

B'(-2,-2)

C'(-4,-3)

Step-by-step explanation:

The rotation by 90° counterclockwise about the origin has the rule

[tex](x,y)\rightarrow (-y,x)[/tex]

So, the vertices of the triangle ABC have the images:

[tex]A(-3,1)\rightarrow A'(-1,-3)\\ \\B(-2,2)\rightarrow B'(-2,-2)\\ \\C(-3,4)\rightarrow C'(-4,-3)[/tex]

see attached diagram for details.

[tex]\bf (b^4)^2\implies b^{4\cdot 2}\implies b^8[/tex]

Answer:

The sample should be a random sample from the entire set of students and should include enough students to be reliable. Small samples have more variation, which leads to less reliable inferences.

To find out how many sixth through eighth grade students are interested in joining a running club, you can conduct a survey among these students. Choose a sample by randomly selecting a certain number of students from the list, ensuring diversity. Contact the selected students to ask about their interest in joining the club and calculate the percentage of interested students.

To find out how many sixth through eighth grade students are interested in joining a running club, you would need to conduct a survey or questionnaire among the students in these grades. Here's how you can choose a sample that will give you a good representation of the whole population:

Answer:

20

Step-by-step explanation:

The two given and marked angles add up to 90.

A = x

B = 3x + 10

A + B = 90          Substitute for A and B. A and B are just letters I gave things.

x + 3x + 10 = 90        Combine the left

4x + 10 = 90              Subtract 10 from both sides.

4x +10-10 = 90-10     Combine

4x = 80                      Divide by 4

4x/4=80/4

x = 20

Answer:

x=20

Step-by-step explanation:

The two angles are complementary angles.  Complementary angles add to 90 degrees

x + 3x+10 = 90

Combine like terms

4x+10 = 90

Subtract 10 from each side

4x+10-10 = 90-10

4x= 80

Divide each side by 4

4x/4 = 80/4

x = 20

Answer:

The metric system is a called a decimal-based system because it is based on multiples of ten.

Answer:

Number of cats in the kennel = 8

Step-by-step explanation:

Let

c denote the number of cats and

d be the number of dogs

Given that the ratio of dogs to cats is 3 to 2

So,

d:c=3:2

Sum of ratio is 5.

And the total number of cats and dogs is 20.

So in order to find the number of cats, following formula will be used:

[tex]Numbr\ of\ cats=\frac{ratio\ of\ cats}{sum\ of\ ratio}*Total\ number\ of\ animals\\ =\frac{2}{5}*20\\ =2*4\\=8[/tex]

So, there are 8 cats in the kennel ..

The number of cats in the kennel can be found using the given ratio of dogs to cats, 3 to 2. Each part in this ratio represents 4, since the total number of animals is 20. Therefore, since the number of cats is represented by 2 parts in the ratio, there are 2 * 4, or 8 cats.

This question can be solved using the concepts of ratios and proportions. In this case, the ratio of the number of dogs to the number of cats at the kennel is given as 3 to 2. This means for every 3 dogs, there are 2 cats.

The total number of dogs and cats at the kennel is given as 20. We need to find out how many of these are cats.

To find the number of cats, we first find the total parts of the ratio by adding 3 (for dogs) and 2 (for cats), which equals 5 parts. Since the total number of animals is 20, each part in the ratio represents 20 divided by 5, which is 4. Therefore, since the number of cats is represented by 2 parts in the ratio, the number of cats is 2 multiplied by 4, which equals 8.

Therefore, there are 8 cats in the kennel.

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Answer:

D.  

individual retirement account

Step-by-step explanation:

The account that will be beneficial to Victor, to ensure he has enough funds during his old age, is the  individual retirement account(IRA).

Answer:

The most appropriate answer option is D. Individual Retirement Account.

Step-by-step explanation:

We know that Victor is a mechanic and he wants to make sure that he has enough funds during his old age.

For this purpose, an Individual Retirement Account (IRA) would be the most suitable and beneficiary for him.

An Individual Retirement Account is a type of account that is tax advantaged and aims to help people save for their post retirement life.

Answer:

14%

Step-by-step explanation:

If the selected student is a male, that reduces the population to consider, to 14 (4 + 6 + 2 + 2).

How many male juniors?  2

So, the chance for the random student to be a junior if he's a male, are 2 out of 14.

P = 2/ 14 = 1/ 7 = 14.29%

Rounded to the nearest whole percent: 14%

Answer: After 1 year = $15085.85168

After 5 years = $20339.34789

After 10 years = $29549.21947

After 25 years = $90609.34284

Step-by-step explanation:

14000e^.0747 (however many years)

Answer:

The balance after 1 year, 5 years, 10 years, 25 years are 15085.85, 20339.35, 29549.22 and 90609.34 respectively.

Step-by-step explanation:

It is given that the principle amount is $14,000 and interest rate is 7.47%.

The formula for amount is

[tex]A=Pe^{rt}[/tex]

Where, P is principle, r is rate of interest and t is time in years.

Substitute P=14000 and r=0.0747 in the above equation.

[tex]A=14000e^{0.0747t}[/tex]         ..... (1)

Substitute t=1 in equation (1) to find the balance after 1 year.

[tex]A=14000e^{0.0747(1)}=15085.851678\approx 15085.85[/tex]

Substitute t=5 in equation (1) to find the balance after 5 year.

[tex]A=14000e^{0.0747(5)}=20339.3478896\approx 20339.35[/tex]

Substitute t=10 in equation (1) to find the balance after 10 year.

[tex]A=14000e^{0.0747(10)}=29549.2194696\approx 29549.22[/tex]

Substitute t=25 in equation (1) to find the balance after 25 year.

[tex]A=14000e^{0.0747(25)}=90609.3428426\approx 90609.34[/tex]

Therefore the balance after 1 year, 5 years, 10 years, 25 years are 15085.85, 20339.35, 29549.22 and 90609.34 respectively.

Answer:

[tex]x =38.7\°[/tex]

Step-by-step explanation:

By definition, the tangent of a x-angle is defined as

[tex]tan(x) =\frac{opposite}{adjacent}[/tex]

For this case

[tex]opposite = 8[/tex]

[tex]adjacent = 10[/tex]

Therefore we have that

[tex]tan(x) =\frac{8}{10}[/tex]

[tex]x =arctan(\frac{8}{10})[/tex]

The answer is:

[tex]x =38.7\°[/tex]

Answer:

Step-by-step explanation:

D

Answer:

19 inches each I believe but I'll stand corrected if Im wrong.

Step-by-step explanation:

Answer:

Scale factor is [tex]\frac{1}{2}[/tex]

Dimension for each channel is 46 in × 38 in

Step-by-step explanation:

Given,

The original dimension of television = 92 in × 76 in

Let A represents the area of the television,

So, after splitting the screen of television into 4 channels,

The area of each channel = [tex]\frac{A}{4}[/tex]

We know that, the scale factor is equal to the square root of the ratio of areas of the figures ( new over old ),

If x represents the scale factor,

[tex]\implies x=\sqrt{\frac{A/4}{A}}=\sqrt{\frac{1}{4}}=\frac{1}{2}[/tex]

Hence, scale factor in the given situation is [tex]\frac{1}{2}[/tex]

Also, the dimension of each channel will get after multiplying each dimension of the TV by the scale factor ( i.e. 1/2 ),

Therefore, the dimension of each channel would be 46 in × 38 in

Answer:

The first choice is the one you want

Step-by-step explanation:

Use geometric means to solve for a first. The formula is

[tex]8^2=15a[/tex] and 64 = 15a and a = 64/15

That one was quite easy.  Finding b is a bit more difficult.

The formula for finding b is

[tex]\frac{a}{b}=\frac{b}{15+a}[/tex]

Solving for b:

[tex]b^2=a(15+a)[/tex]

Filling in we have

[tex]b^2=15(\frac{64}{15})+(\frac{64}{15})^2[/tex] and

[tex]b^2=64+\frac{4096}{225}[/tex] and

[tex]b^2=\frac{18496}{225}[/tex] so b = 136/15

Answer: I think the correct answer is B

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The given expression is

[tex](4x^2+3x-7)(x-2)[/tex]

If a ,b, c are three real number, then by distributive property,

[tex]a(b+c)\Leftrightarrow ab+ac[/tex]

Using distributive property, then given expression can be written as

[tex](4x^2+3x-7)(x)+(4x^2+3x-7)(-2)[/tex]

Option A is not a correct way to rewrite the given expression and option C represents a correct way to rewrite the given expression.

Using distributive property, then given expression can be written as

[tex](4x^2)(x-2)+(3x)(x-2)+(-7)(x-2)[/tex]

Option D represents a correct way to rewrite the given expression.

Again using distributive property in the above expression, we get

[tex](4x^2)(x)+(4x^2)(-2)+(3x)(x)+(3x)(-2)+(-7)(x)+(-7)(-2)[/tex]

Option B represents a correct way to rewrite the given expression.

Therefore the correct option is A.

Answer:

6

Step-by-step explanation:

I think you mean |v|... you wouldn't need dot product for that...

It is just sqrt(6^2)=6

Answer:

d

Step-by-step explanation:

You cannot use the dot product on a single vector

To find the magnitude of v = - 6i, then

| v | = [tex]\sqrt{(-6)^2}[/tex] = [tex]\sqrt{36}[/tex] = 6 → d

Answer:

Step-by-step explanation:

The residual is the difference between the actual value and that predicted by the model.

1. actual - predicted = 5.2 - 4.8 = 0.4

__

2. actual - predicted = 20 - (4·3 +10) = 20 -22 = -2

Answer:

right 3 units and down 1 unit

Step-by-step explanation:

we know that

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

Is the equation of a vertical parabola open upward with vertex at (0,0)

and

[tex]f(x)=(x-3)^{2}-1[/tex]

Is the equation of a vertical parabola open upward with vertex at (3,-1)

so

The rule of the translation of

(0,0) -----> (3,-1)

is equal to

(x,y) -----> (x+3,y-1)

That means ----> the translation is right 3 units and down 1 unit

Answer:

C.right 3 units and down 1 unit

Step-by-step explanation:

Answer:

  1. C, E, G

  2. A, D, H

Step-by-step explanation:

Compare each equation to the form ...

  f(x) = 1/(4p)(x -h)^2 +k

In this form, p is the distance from the vertex to the focus (positive is up), and (h, k) is the location of the vertex. The focus is (h, k+p); the directrix is y=k-p.

1. The equation tells us ...

  (h, k) = (1, 4)

  1/(4p) = (-1) . . . ⇒ . . . p = -1/4

So, we have ...

--

2. The equation tells us ...

  (h, k) = (-1, 4)

  1/(4p) = 2 . . . ⇒ . . . p = 1/8

So, we have ...

Answer:

Step-by-step explanation:

Answer:

  230

Step-by-step explanation:

The function simplifies to ...

  f(t) = 230

This will be the value for any value of t, so ...

  f(2) = 230

Let the point (1,3) be (x1, y1)

Let the point (5,2) be (x2, y2)

The distance between the two points would be √((x2-x1)²+(y2-y1)²)

Substitute the numbers into the  points

distance: √((5-1)²+(2-3)²)

=√(4²+(-1)²)

=√(16+1)

=√17

Answer:5 but its probaly not right bc im just looking for points

Step-by-step explanation:

Answer:

Im not this sure but i think its 25/40 so its 62.5%

Step-by-step explanation:

23 Take psychology but 8 takes both so 23-8=15

18-8=10

7 dont take any

this is where im not sure, im not sure if i add the 8 who take both of the classes. I Didnt so its

15+10=25

25/40

Hope this help??

Answer:

Step-by-step explanation:

This is a Venn Diagram problem.

23 - 8 = 15 take just AP Psychology

18 - 8 = 10 take just AP Calculus

I think this question is likely done by adding all three areas together to get 33

15 + 10 + 8

33

The probability is therefore 33/40 = 0.825

Answer:

t = 6162 years

Step-by-step explanation:

This equation takes the form of

[tex]N=N_{0}e^{kt}[/tex]

We are given everything but the amount of C-14 at time t = 0.  But we can figure it out from the info we ARE given.  We are told that when the spear head is found it contains 54% of its original amount of C-14.  Notice we are dealing in percents.  If 54% remains when it is found, it started out with 100% of its amount.  That's our N value.  Filling in:

[tex]100=54e^{.0001t}[/tex]

Our goal is to get that t down from the exponential position that it is currently in.  To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication.  So we take the natural log of both sides.  On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone.  Before that, though, we will simplify by dividing both sides by 54.  100/54 = 1.851851852.  So, altogether...

[tex]ln(1.851851852)=.0001t[/tex]

Simplifying by plugging the log of that number into our calculator, we get

.6161861395 = .0001t  and

t = 6161.8613

Rounding to the nearest year, t = 6162 years

Answer:  (f·g)(x) = -5x³ - 31x² + 62x + 18

               (f·g)(1) = 44

Step-by-step explanation:

f(x) = x² + 8x + 2          g(x) = -5x + 9

(f·g)(x) = (x² + 8x + 2)(-5x + 9)

          = -5x³ + 9x²

                    - 40x² + 72x

                                - 10x + 18

          = -5x³ - 31x² + 62x + 18

(f·g)(1)= -5(1)³ - 31(1)² + 62(1) + 18

         =  -5     -   31    + 62   + 18

         =  44

Answer:

[tex]19.22\:<\:\mu\:<\:44.78[/tex]

Step-by-step explanation:

Tthe population is normally distributed and the sample size is [tex]n=22\:<\:30[/tex].

Since the population standard deviation [tex]\sigma[/tex] is unknown and the sample standard deviation [tex]s[/tex], must replace it, the t distribution must be used for the confidence interval.

Hence with degrees of freedom of 21, [tex]t_{\frac{\alpha}{2} }=3.527[/tex].(Read from the t distribution table)

The 98% confidence interval can be constructed  using the formula:

[tex]\bar X-t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )\:<\:\mu\:<\:\bar X+t_{\frac{\alpha}{2}}(\frac{s}{\sqrt{n} } )[/tex].

From the question the sample mean is [tex]\bar X=32[/tex]dollars and the sample standard deviation is [tex]s=17[/tex] dollars.

We substitute the values into the formula to get

[tex]32-3.527(\frac{17}{\sqrt{22} } )\:<\:\mu \:<\:32+3.527(\frac{17}{\sqrt{22} } )[/tex]

[tex]19.22\:<\:\mu\:<\:44.78[/tex]

Therefore, we can be 98% confident that the population mean is between is between 19.22 and 44.78 dollars.

Answer:

1. 0.1367

2. 0.0709

3. 0.1766

Step-by-step explanation:

The probability of success is p=0.6, then the probability of a failure is q=1-0.6=0.4.

1. The probability that there are exactly 13 successes in 24 trials is

[tex]C^{24}_{13}p^{13}q^{24-13}=\dfrac{24!}{13!(24-13)!}\cdot (0.6)^{13}\cdot (0.4)^{11}\approx 0.1367[/tex]

2. The probability that there are exactly 9 successes in 20 trials is

[tex]C^{20}_{9}p^{9}q^{20-9}=\dfrac{20!}{9!(20-9)!}\cdot (0.6)^{9}\cdot (0.4)^{11}\approx 0.0709[/tex]

3. The probability that there are exactly 6 failures in 12 trials is

[tex]C^{12}_{6}q^{6}p^{12-6}=\dfrac{12!}{6!(12-6)!}\cdot (0.4)^{6}\cdot (0.6)^{6}\approx 0.1766[/tex]

Answer:

Option D. 90°

Step-by-step explanation:

we have

[tex]D(5, 7),E(4, 3),F(8, 2)[/tex]

Plot the vertices

see the attached figure  

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance DE

[tex]D(5, 7),E(4, 3)[/tex]

substitute

[tex]d=\sqrt{(3-7)^{2}+(4-5)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(-1)^{2}}[/tex]

[tex]DE=\sqrt{17}\ units[/tex]

step 2

Find the distance EF

[tex]E(4, 3),F(8, 2)[/tex]

substitute

[tex]d=\sqrt{(2-3)^{2}+(8-4)^{2}}[/tex]

[tex]d=\sqrt{(-1)^{2}+(4)^{2}}[/tex]

[tex]EF=\sqrt{17}\ units[/tex]

step 3

Find the distance DF

[tex]D(5, 7),F(8, 2)[/tex]

substitute

[tex]d=\sqrt{(2-7)^{2}+(8-5)^{2}}[/tex]

[tex]d=\sqrt{(-5)^{2}+(3)^{2}}[/tex]

[tex]DF=\sqrt{34}\ units[/tex]

step 4

The triangle DEF is a right triangle because satisfy the Pythagoras theorem

so

[tex](\sqrt{34})^{2}=(\sqrt{17})^{2}+(\sqrt{17})^{2}[/tex]

[tex]34=34[/tex] -----> is true

therefore

The measure of angle DEF is a right angle

Answer:

The combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].

Step-by-step explanation:

Consider the provided expression:

[tex]20(-1.5r+0.75)[/tex]

Use the distributive property: [tex]a(b + c) = ab + bc[/tex]

[tex]-30r + 15[/tex]

After using distribution property there are no more like terms. Thus, [tex]-30r + 15[/tex] is the simplest form.

Hence, the combined like terms to create an equivalent expression [tex]20(-1.5r+0.75)[/tex] is [tex]-30r + 15[/tex].

Based on the information, the simplified expression is -30r + 15.

Given expression:

20(-1.5r+0.75)

Applying the distributive property:

= 20(-1.5r) + 20(0.75)

= -30r + 15

Therefore, the simplified expression is -30r + 15.

Use the distributive property to distribute the 20 to each of the terms inside the parentheses.

Simplify the expression by combining the like terms.

The simplified expression is -30r + 15.

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Answer:

$6.40

Step-by-step explanation:

We first multiply 1.20 by 3 so we can find the price for 3 parcels. We then subtract the result by 10 to get the change Late should get

10-3(1.20)

=10-3.60

=6.40

The required change is $ 6.40

So price of 3 parcels = $3(1.20) = $ 3.60

So, the change = $ {  10-3.60  }

= $ 6.40

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A = (-3, 2) → (-3 + 2, 2 - 4) → (-1, - 2)

B = (1, 5) → (1 + 2, 5 - 4) → (3, 1)

C = (2, -3) → (2 + 2, -3 - 4) → (4, -7)

A’ = (-1, -2)

B’ = (3, 1)

C’ = (4, -7)