IZ) Samantha wants to determine the height of a flagpole at school. Her eye level is 4.6 feet from the ground and
she stands 26 feet from the flagpole. If the angle of elevation is about 68°, what is the height of the flagpole to
the nearest tenth foot?

Answer:

f(x) = (8/3)^x

Step-by-step explanation:

Since f increasing, the base value must be greater than 1.

8/3 is the only base value greater than 1.

The base (3/8) would be a decreasing graph because it is less than 1.

The base (-3/8) would result in a wavering graphing passing the x-axis many times. (Because whether the result is negative depends on if x is odd or even.)

in (8/3)^(-x), it is the same as (3/8)^x by applying the negative exponent rule a^(-x) = 1/(a^x).

Answer:

The standard error of distribution for n = 4 is 5 and for n = 25 is 2.

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Population mean = 72

Standard deviation  =  10

Sample₁ = 4

Sample₂ = 25

2. For finding the standard error of the mean, we use the following formula:

Standard error = Standard deviation / √Size of the sample

Standard error for Sample₁ = 10/√4

Standard error for Sample₁ = 10/2 = 5

Now, let's find the standard error for Sample₂

Standard error for Sample₂ = 10/√25

Standard error for Sample₂ = 10/5 = 2

Answer:

10657.5

Step-by-step explanation:

We can start by finding the area of the larger triangle. Using the Pythagorean theorem, we can say that 251²-105²=the bottom side², and  251²-105²=51976, so the bottom side of the larger triangle is √51976 , or approximately 228. Then, the area of the larger triangle is √51976 * 105/2 = 11969 (approximately). Then, the area of the smallest triangle (the largest triangle - the one that we're trying to find the area of) is 105*(√51976-203)/2 = approximately 1312. Then, subtracting that from the total area, we get (√51976 * 105 -  105*(√51976-203))/2 = 105*203/2 = 10657.5

ALTERNATIVELY, upon further review, we can just see that the height is 105 and the base is 203, so we multiply those two and divide by 2, as is the formula for the area of a triangle, to get 10657.5

[tex]\bf x^2+4=0\implies x^2=-4\implies x = \pm\sqrt{-4}\implies x = \pm\sqrt{-1\cdot 2^2} \\\\\\ x = \pm\sqrt{-1}\cdot \sqrt{2^2}\implies x = \pm 2i[/tex]

Answer:

[tex]x=0,x=\pi,x=\frac{\pi}{3},x=\frac{2\pi}{3},x=\frac{4\pi}{3},x=\frac{5\pi}{3}[/tex]

Step-by-step explanation:

This is a trigonometric equation where we need to use the cosine of the double-angle formula

[tex]cos4x=2cos^22x-1[/tex]

Replacing in the equation

[tex]cos4x - cos2x = 0[/tex]

We have

[tex]2cos^22x-1 - cos 2x = 0[/tex]

Rearranging

[tex]2cos^22x - cos 2x-1 = 0[/tex]

A second-degree equation in cos2x. The solutions are:

[tex]cos2x=1,cos2x=-\frac{1}{2}[/tex]

For the first solution

cos2x=1 we find two solutions (so x belongs to [0,2\pi))

[tex]2x=0, 2x=2\pi[/tex]

Which give us

[tex]x=0,x=\pi[/tex]

For the second solution

[tex]cos2x=-\frac{1}{2}[/tex]

We find four more solutions

[tex]2x=\frac{2\pi}{3},2x=\frac{4\pi}{3},2x=\frac{8\pi}{3},2x=\frac{10\pi}{3}[/tex]

Which give us

[tex]x=\frac{\pi}{3},x=\frac{2\pi}{3},x=\frac{4\pi}{3},x=\frac{5\pi}{3}[/tex]

All the solutions lie in the interval [tex][0,2\pi)[/tex]

Summarizing. The six solutions are

[tex]x=0,x=\pi,x=\frac{\pi}{3},x=\frac{2\pi}{3},x=\frac{4\pi}{3},x=\frac{5\pi}{3}[/tex]

Answer:

-0.37

Step-by-step explanation:

The total amount of liquid in the three beakers is 0.6 liters.

Calculating Total Volume of Liquid

To determine the total amount of liquid in 3 beakers, we need to multiply the volume of liquid in each beaker by the number of beakers.

So, the total amount of liquid in the three beakers is 0.6 liters.

Answer:

3

Step-by-step explanation:

Given: [tex]$  (\frac{1}{4} + \frac{5}{4} )^{2} + \frac{3}{4} $[/tex]

This is equivalent to: [tex]$ ( \frac{6}{4}) ^2 + \frac{3}{4} $[/tex]

⇒  [tex]$ (\frac{3}{2})^2 + \frac{3}{4} $[/tex]

⇒ [tex]$ \frac{9}{4} + \frac{3}{4} $[/tex]

⇒ [tex]$\frac{12}{4} = 3$[/tex]

Therefore,  [tex]$(\frac{1}{4} + \frac{5}{4} )^{2} + \frac{3}{4} = 3 $[/tex]

Answer:

(1/4 + 5/4)^2 +3/4 = 12

Step-by-step explanation:

To solve the problem given, we will follow the steps below;

(1/4 + 5/4)^2 +3/4

First, we will find the value of  (1/4 + 5/4)^2

1/4 + 5/4 = 6/4

(1/4 + 5/4)^2   =   (6/4)^2 =  [tex]\frac{36}{16}[/tex]

 [tex]\frac{36}{16}[/tex]  can be reduced to   [tex]\frac{9}{4}[/tex]

This implies that ; (1/4 + 5/4)^2    =   [tex]\frac{9}{4}[/tex]

Then, we can now add  [tex]\frac{9}{4}[/tex]   and [tex]\frac{3}{4}[/tex]  together  

(1/4 + 5/4)^2 +3/4    =   [tex]\frac{9}{4}[/tex]   +  [tex]\frac{3}{4}[/tex]   =  [tex]\frac{12}{3}[/tex]   = 4

Therefore    (1/4 + 5/4)^2 +3/4 = 12

Answer:

The distance is 7 (approximately).

Step-by-step explanation:

Given:

Point A, (2,3) and point B, (-4,6).

Now, to find the distance between the points using the formula:

Let A = (2,3) be [tex](x_{1}, y_{1})[/tex] and B = (-4,6) be [tex](x_{2}, y_{2})[/tex] and d = distance.

Putting the distance formula to find:

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

[tex]d=\sqrt{(-4-2)^{2} +(6-3)^{2}}[/tex]

[tex]d=\sqrt{(-6)^{2} +(3)^{2}}[/tex]

[tex]d=\sqrt{36 +9}[/tex]

[tex]d=\sqrt{45}[/tex]

[tex]d=6.71[/tex]

Distance = 6.71

Therefore, the distance is 7 (approximately).

Answer:

The answer is 24/2=36/3=66/5.5=108/9=180/15.

Step-by-step explanation:

Given:

24/2=_/3=_/5.5=108/_=_/15.

Now, we need to solve this by putting [tex]x[/tex] in the place of _ and then continue:

[tex]\frac{24}{2} =\frac{x}{3}[/tex]

By cross multiplication we get:

[tex]72=2x[/tex]

By dividing with 2 we get:

[tex]36=x[/tex]

Now, we will continue like this process:

[tex]\frac{36}{3}=\frac{x}{5.5}[/tex]

[tex]198=3x[/tex]

[tex]x=66[/tex]

And, then again:

[tex]\frac{66}{5.5}=\frac{108}{x}[/tex]

[tex]66x=594[/tex]

[tex]x=9[/tex]

And, last:

[tex]\frac{108}{9}=\frac{x}{15}[/tex]

[tex]9x=1620[/tex]

[tex]x=180[/tex]

Therefore, the answer is 24/2=36/3=66/5.5=108/9=180/15.

Answer:

x=6/31, y=147/31. (6/31, 147/31).

Step-by-step explanation:

y=-22x+9

y=40x-3

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

-22x+9=40x-3

9=40x-(-22x)-3

9=40x+22x-3

9=62x-3

62x=9+3

62x=12

x=12/62

simplify,

x=6/31

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

y=40(6/31)-3=240/31-3=240/31-93/31=147/31

x=6/31, y=147/31.

16/36=4/9

(16)(9)=(36)(4) cross multiply

144=144 proportional

After cross-multiplying the ratios 16/36 and 4/9 and finding that both products are equal (144), it is determined that these ratios are proportional.

The question asks to classify the pair of ratios 16/36 and 4/9 as either proportional or not proportional. We can determine if two ratios are proportional by cross-multiplying and checking if the products are equal. In this case, for the ratios 16/36 and 4/9, we cross-multiply:

Since the products are equal (144 = 144), this confirms that the ratios 16/36 and 4/9 are indeed proportional.

Answer:

a.   s = 0.9r

not very sure about b

Step-by-step explanation:

Answer:

Part a) [tex]6x+4y=48[/tex]

Part b) The graph in the attached figure

Part c) (6,3) and (4,6)

Step-by-step explanation:

Part a) Write a linear equation to represent the number of items you can buy if she spends $48

Let

x ----> number of package of cupcakes you can buy

y ---> number of package of cookies you can buy

we know that

The number of package of cupcakes you can buy multiplied by it cost ($6 for a package) plus the number of package of cookies you can buy multiplied by it cost ($4 for a package) must be equal to $48

so

The linear equation that represent this problem is

[tex]6x+4y=48[/tex]

Part b) Graph the equation

To graph the line we need two points

Find the intercepts

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

[tex]6x+4(0)=48[/tex] ----> [tex]x=8[/tex]

the x-intercept is the point (8,0)

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]6(0)+4y=48[/tex] ----> [tex]y=12[/tex]

the y-intercept is the point (0,12)

Plot the intercepts and join the points to graph the line

see the attached figure

Part c) State two possible solutions in the context of the problem

1) First possible solution

the ordered pair (6,3)

That means

You can buy 6 package of cupcakes and 3 package of cookies

Verify in the linear equation

[tex]6(6)+4(3)=48[/tex]

[tex]48=48[/tex] ---> is true

therefore

The ordered pair is a solution of the linear equation

2) Second possible solution

the ordered pair (4,6)

That means

You can buy 4 package of cupcakes and 6 package of cookies

Verify in the linear equation

[tex]6(4)+4(6)=48[/tex]

[tex]48=48[/tex] ---> is true

therefore

The ordered pair is a solution of the linear equation

Answer: The answer is B.

Step-by-step explanation:

Final answer:

The correct transformation that carries the figure onto itself is Option B: reflecting across the line y=1 and rotating 1080° clockwise about the point (-7,1), as the 1080° rotation is a multiple of 360° and does not change the figure's orientation.

Explanation:

The question is asking to identify the transformation that can be applied to a figure such that the figure maps onto itself. We're given various options that involve a reflection and a rotation. Reflection across a line like y=1 would flip the figure over this horizontal line. A rotation of 1080° clockwise about a point is equivalent to a full 360° rotation three times (since 1080° = 360° × 3), which would bring the figure back to its original position, effectively leaving it unchanged.

The correct answer is Option B, which includes a reflection across the line y=1 and a 1080° clockwise rotation about the point (-7,1). This is because the 1080° rotation, being an integer multiple of full circles, results in no net rotation, so the figure looks exactly the same after this operation. The reflection flips the figure across the line y=1 but, when combined with the rotation, it results in the figure mapping onto itself.

Options A and C suggest a 990° rotation, which is not a multiple of 360° and therefore would not result in the figure mapping onto itself. Option D suggests reflecting across the line x=-6, which is not in the given options for the reflection, and a 1080° rotation about the point (-7,1), which would rotate the figure back onto itself after the reflection, but the reflection line is incorrect.

Answer:

convert 17 meters into feet and then write it down to teh nearest 10thof a foot

Step-by-step explanation:

Answer: 24 people are in the class

I am sorry I don’t know the equation but I hope this helps.

Step-by-step explanation:

3. 18. 18

- =. —. =. —-

4. ? 24

They need to babysit for 10 hours to have same money each day.

Step-by-step explanation:

On Thursday;

Charges = $3 per hour

Initial fee = $40

let x be the number of hours.

T(x) = 3x+40

On Friday;

Charges = $4 per hour

Initial fee = $30

F(x)= 4x+30

The cost will be same when;

T(x) = F(x)

[tex]3x+40=4x+30\\40-30=4x-3x\\10=x\\x=10[/tex]

They need to babysit for 10 hours to have same money each day.

Keywords: functions, addition

Learn more about functions at:

#LearnwithBrainly

Answer:

-1/10

Step-by-step explanation:

1/2 - 3/5

Find common denominator. in this case, it'll be 10

1/2 * 5/5 = 5/10

3/5 * 2/2 = 6/10

5/10 - 6/10 = -1/10

Answer:

A=(5/2x+10)(5/2x+5)

Step-by-step explanation:

A=LW

A=(5/2x+10)(5/2x+5)

Answer:

0.6808

Step-by-step explanation:

First, find the standard deviation of the sample.

s = σ / √n

s = 3 / √49

s = 0.429

Next, find the z-score.

z = (x − μ) / s

z = (28.8 − 29) / 0.429

z = -0.467

Use a calculator or z-score table to find the probability.

Using a table:

P(x > -0.47) = 1 − 0.3192 = 0.6808

Using a calculator:

P(x > -0.467) = 0.6796

The probability that the average mileage of the fleet is greater than 28.8 mpg is approximately 0.680.

Step 1

In order to determine the likelihood that a fleet of 49 automobiles will get more than 28.8 mpg on average, we must apply the Central Limit Theorem, which states that the sample mean's sampling distribution will be roughly normally distributed.

Given:

- Mean [tex](\(\mu\))[/tex]= 29 mpg

- Standard deviation [tex](\(\sigma\))[/tex] = 3 mpg

- Sample size [tex](\(n\))[/tex] = 49 cars

- Sample mean [tex](\(\bar{x}\))[/tex]= 28.8 mpg

Step 2

First, we find the standard error of the mean (SEM):

[tex]\[\text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{49}} = \frac{3}{7} \approx 0.4286\][/tex]

Next, we convert the sample mean to a z-score to find the probability:

[tex]\[z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{28.8 - 29}{0.4286} \approx \frac{-0.2}{0.4286} \approx -0.466\][/tex]

We can use a calculator or the conventional normal distribution table to find the probability using the z-score.

With a z-score of -0.466, one may calculate the cumulative probability to be roughly 0.3204. This is the likelihood that the mileage will be on average less than 28.8 mpg.

We deduct this figure from 1 to get the likelihood that the average mileage is higher than 28.8 mpg:

Step 3

[tex]\[P(\bar{x} > 28.8) = 1 - P(\bar{x} < 28.8) = 1 - 0.3204 = 0.6796\][/tex]

Therefore, the probability that the average mileage of the fleet is greater than 28.8 mpg is approximately 0.680 (rounded to three decimal places).

Answer:

$2853.5

Step-by-step explanation:

Let us assume that the interest rate of both the investments of Haley is simple interest.

So, $16820 amounts of investment in nine-year CD bearing 5.8% interest will get interest of [tex]16820 \times \frac{5.8}{100} \times 9 = 8780[/tex] dollars.

Again, $21950 amounts of investment in an online savings account giving 3% interest will give interest of [tex]21950 \times \frac{3}{100} \times 9 = 5926.5[/tex] dollars.

Therefore, the nine-year CD will give more interest by $(8780 - 5926.5) = $2853.5. (Answer)

Answer:

C. $2,853.54

Step-by-step explanation:

I just answered it correct

Answer:

Subtract the second equation from the first one.

The solution is (1.71, 0.93).

Step-by-step explanation:

2x + 3y = 7

2x = 4y - 5

2x + 3y - 2x = 7 - (4y - 5)   So we eliminate the x term:

3y =  -4y + 12

7y = 12

y = 12/7 = 1.714

Plug this into the first equation:

2x + 3(1.714) = 7

2x = 1.858

x = 0.929.

Answer:

Step-by-step explanation:

Answer:

The range of g(x) =  {-11,-9,-7,-5}.

Step-by-step explanation:

Given:

g(x) = x – 13 over the domain {2, 4, 6, 8).

Now, to evaluate:

Putting [tex]x=2[/tex]

[tex]g(2)=2-13=-11[/tex]

Putting [tex]x=4[/tex]

[tex]g(4)=4-13=-9[/tex]

Putting[tex]x=6[/tex]

[tex]g(6)=6-13=-7[/tex]

Putting [tex]x=8[/tex]

[tex]g(8)=8-13=-5[/tex]

So, the range is {-11,-9,-7,-5}.

Therefore, the range of g(x) =  {-11,-9,-7,-5}.

Answer:

Thomas still has 1 3/5 suitcases available for his own belongings.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Number of souvenirs bought by Thomas = 6

Space that each souvenir takes of Thomas suitcase = 1/15

Number of Thomas suitcases = 2

2.  How much room is left for his own belongings in his suitcases?

Let's find out how much space the souvenirs take:

Number of souvenirs * Space that each souvenir takes

6 * 1/15 = 6/15 = 2/5 (Dividing by 3 the numerator and the denominator)

The souvenirs take 2/5 of one suitcase.

Now, we can calculate the room that is left for Thomas' belongings.

2 Suitcases - 2/5 for the souvenirs

2 - 2/5 = 10/5 - 2/5 = 8/5 = 1 3/5

Thomas still has 1 3/5 suitcases available for his own belongings.

Answer:

1 9/15

Step-by-step explanation:

Step-by-step explanation:

denominator separately

[tex]277 \sqrt{3} [/tex]

the below 160 Number 2) Same thing with the first one Multiply the Fraquetions, then multiply the numerator and denominator separately so

[tex] \frac{590}{160} \sqrt{17} [/tex]

then change to

[tex]590 \sqrt{17} [/tex]

the below that is a 5 and above it on the top right corner out 160

Answer:

$60

Step-by-step explanation:

75% divided by 100 x 80 = 60

              OR

$80 divided by 100 x 75 = 60

Answer:

The probability of picking the first boyis 14/26 and the probability of picking another boy is 13/25. The combined probability is thus 14/26 x 13/25 = 7/25

Step-by-step explanation:

The probability the teacher picks 2 boys in a row is 7/13.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.

Given that, there are 12 girls and 14 boys in math class.

Here, total number of outcomes = 12+14

= 26

Number of favorable outcomes = 14

Now, probability = 14/26

= 7/13

Therefore, the probability the teacher picks 2 boys in a row is 7/13.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ3

Answer:

The temperature at noon is 6ºF.

Step-by-step explanation:

3:00am: -10ºF

               -12ºF

6:00am: -22ºF

              +8ºF

9:00am: -14ºF

              +20ºF

Noon:     6ºF

So at 6:00 a.m. the temperature is 33 F

12:00 p.m. the temperature increased by 10 F so it is 43 F

3:00 p.m. the temperature increased by another 12 F making it 55 F

At 10:00 p.m. it would decrease by 15 F making it 40 F.

The temperature would need to fall/decrease 7 F to reach the original temperature of 33 F so it would be A.

Hope this helps!

Can u plz mark me as brainliest? I really need it!

Answer:

The length of the side of the square is 6 feet.

Step-by-step explanation:

Given,

Length of side of square = [tex](24 - 3x)\ feet[/tex]

According to question, x = 6

So we have to substitute x with 6 in the given expression.

Length of side of square = [tex](24-3x)= 24-3\times6=24-18=6\ feet[/tex].

Thus the length of the side of the square is 6 feet.

Final answer:

To find the length of the side of the square when x is 6, substitute 6 for x into the given expression (24 - 3x). Thus, the length of the side is calculated as 6 feet.

Explanation:

The student asked for the length of the side of the square when x = 6. To find this, we substitute x with 6 into the expression representing the side length of the square, which is (24 - 3x) feet.

Replacing x with 6, we get:

The length of the side of the square when x is equal to 6 is therefore 6 feet.