3. A power line extends from a light pole 43 meters to the ground and makes an angle of 60 degrees with the ground. To the nearest tenth of a meter, how tall is the light pole? (2 points)

(6•4m) + (6•5)= 24m + 30

The correct answer is 30

Here’s how you solve it!

First multiply what’s in the parentheses

6✖️4m➕6✖️5

Now calculate the produce

24m➕6✖️5

Now multiply 6 and 5 then add the number to 24m

Then you are left with your answer:

24m➕30

Hope this helps! :3

Answer: transformation 5 units right

Step-by-step explanation: the preimage mapped to the image is moved 5 units to the right.

the algebraic expression is (x,y)-->(x+5,y)

Answer: M.A.T.H was translated (-5, 0) units; or five units to the left

Step-by-step explanation:

Point A is moved to the left to become A'.

Similarly, Points M, H, and T have moved to the left to become M', H', and T', respectively.

This type of transformation, in which all the points in a figure move in the same direction and by the same amount, is called a translation (moving sideways).

Each point has moved five units to the left.

Answer:

Step-by-step explanation:

For x use the Pythagorean theorem:

[tex]x^2+6^2=10^2[/tex]

[tex]x^2+36=100[/tex]              subtract 36 from both sides

[tex]x^2=64\to x=\sqrt{64}\\\\x=8[/tex]

We know: x + y = 20. Substitute:

[tex]8+y=20[/tex]              subtract 8 from both sides

[tex]y=12[/tex]

Answer:

[tex]5,500\ g[/tex]

Step-by-step explanation:

we know that

[tex]1\ kg=1,000\ g[/tex]

step 1

Find the difference between the kilograms of apples and the kilograms of pears

[tex]8-2.5=5.5\ kg[/tex]

step 2

Convert to grams

[tex]5.5\ kg=5.5*1,000=5,500\ g[/tex]

Answer:

$75000

Step-by-step explanation:

5% of $60000 is $3000 and $3000 x 5 is $15000 and $15000 + $60000 is $75000

To calculate the total salary over 5 years with an initial salary of $60,000 and a 5% annual raise, you add the salary of each year considering the raise. The salaries over 5 years will be $60,000; $63,000; $66,150; $69,457.50; $72,930.38 respectively, amounting to a total of $331,537.88, which is approximately $331,538.

The question asks how much money you would earn total after 5 years of working at a company starting with a $60,000 salary and receiving a 5% raise each year. This is a problem of geometric progression in mathematics. To calculate the total amount earned over 5 years, we have to apply the formula for the sum of a geometric series because the salary increases by a fixed percentage each year. The salary each year is as follows: Year 1 - $60,000, Year 2 - $60,000*1.05, Year 3 - $60,000*(1.05)^2, Year 4 - $60,000*(1.05)^3, and Year 5 - $60,000*(1.05)^4.

Here is the calculation step-by-step:

Now, add up the salaries for each year to find the total earnings:

Add up these amounts to get the total earnings after 5 years:

Total = $60,000 + $63,000 + $66,150 + $69,457.50 + $72,930.38 = $331,537.88, which can be rounded to approximately $331,538.

Therefore, the correct answer is: $331,538.

Answer:

  2.34 grams

Step-by-step explanation:

The first 3 digits of the number are 2, 3, 3. The next digit is 5, which is more than 4, so 1 is added to the digit to its left and all digits to the right of the first three are dropped.

2.33 becomes 2.34 because of the 5 in the thousandths place.

Your rounded measurement is 2.34 grams.

Answer:

  y = tan(x -π) -1

Step-by-step explanation:

It looks like a straight tangent function shifted down one unit. Since the tangent function has a period of π, ...

  tan(x -π) = tan(x)

so you're only looking for the function that has a translation downward of 1 unit. Of course that translation is accomplished by adding -1 to the original function.

The appearance of the graph is of ...

  y = tan(x) -1

The choice that is equivalent to this is ...

  y = tan(x -π) -1

Answer:

y = tan (x-pi)-1

Step-by-step explanation:

The function in the graph is a periodic function with intervals of pi and having discontinuities at regular intervals.

Hence this must be a transformation of the original trignometric funciton

tan x.   y intercept is at -1 which shows that there is a vertical shift of 1 unit down.

Hence the funciton is y = tanx-1

But tan x is not given in any of the options.

Let us check which is equivalent to tan x-1

We find that tan(x-pi) = -tan (pi-x) = -(-tanx) = tanx

Hence the option 3 is the right answer

Hey there!

Let's start by adding 6 to both sides of the equation to eliminate the -6.

3y^2 = 48

Next, let's divide both sides by 3 to eliminate the 3.

y^2 = 16

Find the square root of both sides.

y = ±4

It can be both positive or negative 4 because -4 x -4 and 4 x 4 both equal 16.

The value of y is ±4.

Hope this helps!

Answer:

Part a) [tex]m<HIG=40\°[/tex]

Part b) IHG is a semicircle and GJI is a semicircle

Part c) HIJ is a major arc and HIJG is a major arc

Part d) [tex]arc\ GH=80\°[/tex]

Part e) [tex]arc\ GJI=180\°[/tex]

Step-by-step explanation:

Part a) Give an inscribed angle

we know that

The inscribed angle measures half that of the arc comprising

so

in this problem m<HIG is an inscribed angle

[tex]m<HIG=\frac{1}{2}(arc\ HG)[/tex]

[tex]arc\ HG=80\°[/tex] ----> by central angle

substitute

[tex]m<HIG=\frac{1}{2}(80\°)=40\°[/tex]

Part b) Give a semicircle

we know that

The diameter divide the circle into two semicircles

so

GI is a diameter

therefore

IHG is a semicircle

GJI is a semicircle

Part c) Give a major arc

we know that

The measure of a major arc is greater than 180 degrees

therefore

HIJ is a major arc

HIJG is a major arc

Part d) Measure of arc GH

we know that

[tex]arc\ GH=m<HFG[/tex] ----> by central angle

so

[tex]arc\ GH=80\°[/tex]

Part e) Measure of arc GJI

we know that

[tex]arc\ GJI=180\°[/tex] ----> the arc represent a semicircle

First find the value of the two vertical angles which have x in them.

Vertical angles are the same so you have:

4x = x +36

subtract 1x from each side:

3x = 36

Divide both sides by 3:

x = 36/3

x = 12

Now replace x with 12 to solve for the angles:

4x = 4(12) = 48 degrees.

All 4 angles need to equal 360 degrees, so now subtract 48 +48 from 360:

360 - 96 = 264

Y and the angle above it are vertical angles, so you can divide 264 by 2 to find y:

Y = 264 /2

Y = 132 degrees.

Answer:

The answer would be C

Final answer:

No, (-2n)⁴ is not equal to -8n⁴ because when -2 is raised to the fourth power, it results in a positive 16, making the correct evaluation of the expression 16n⁴. The correct answer is option (C).

Explanation:

The question is whether (-2n)⁴ is equal to -8n⁴. To evaluate the expression (-2n)⁴, you must raise both -2 and n to the fourth power. Since the exponent is even, the negative sign in front of 2 will become positive after being raised to the fourth power: (-2n)⁴ = (-2)⁴ × n⁴ = 16n⁴

So, the correct statement is No; for values other than 0, (–2n)⁴ = 16n⁴ not equal to  –8n⁴. When raising a negative number to an even power, the result is positive, and (-2)⁴ equates to 16, not -8. Therefore, the option C is correct.

As a result, the misconception that -2 times 4 makes -8 is incorrect when dealing with exponents, as the negative sign is squared, turning it positive.

To calculate the probability of an adult female's pulse rate being between 72 and 80 bpm, additional information like mean and standard deviation is necessary if using a normal distribution or population data for a simple probability.

To find the probability that an adult female's pulse rate is between 72 beats per minute and 80 beats per minute, we need additional information such as the mean and standard deviation if the pulse rates follow a normal distribution, or the percentage of females with pulse rates in that range if the data is available in simple probability form.

Without this information, it's not possible to provide an exact answer. However, we can reference typical heart rate data or use estimation techniques to provide a rough idea of the probability. Health organizations often provide guidelines on normal heart rates for adults that could be used as a proxy in the absence of specific data points.

Answer:

  C)  78 ft

Step-by-step explanation:

The side opposite the angle has the ratio to the hypotenuse:

  Sin = Opposite/Hypotenuse

Then the solution to this problem is found by substituting the given information and solving for the height.

  sin(45°) = height/(110 ft)

  (110 ft)·sin(45°) = height ≈ 77.7817 ft

Rounded to the nearest foot, the crane can raise material to a height of 78 ft.

Answer:

see explanation

Step-by-step explanation:

Isolate r² by dividing both sides by πh

r² = [tex]\frac{V}{h\pi }[/tex]

Take the square root of both sides

r = ± [tex]\sqrt{\frac{V}{h\pi } }[/tex]

The negative part can be  discarded as r > 0, hence

r = [tex]\sqrt{\frac{V}{h\pi } }[/tex]

Answer:

Athena

Step-by-step explanation:

Squares are rhombuses but rhombuses are not squares

Answer:

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

(X^3+2x^2) +(5x+10)

X^2(x+2) +5(x+2)

(X^2+5)(x+2)

Answer:

[tex](x+2)\text{ and }(x^2+5)[/tex] are the factors of given polynomial,    

Step-by-step explanation:

We are given the following information in the question:

We are given a polynomial:

[tex]x^3 + 2x^2 + 5x + 10[/tex]

We have to factor this polynomial with the help of grouping method.

Grouping can be dine with the help of taking the common factors.

Working:

[tex]\text{Taking } x^2 \text{ common from the first two terms and 5 from the other two terms, we have}\\\Rightarrow x^2(x + 2) +5(x + 2)\\\text{Aain taking the common term}\\\Rightarrow (x+2)(x^2+5)[/tex]

Hence, the two factors of the given polynomial are:

[tex](x+2)\text{ and }(x^2+5)[/tex]

Answer:

75 pieces

Step-by-step explanation:

1. determine how many pieces per ounce by dividing 45 by 6 (# of pieces in a 6 oz bag)

    45/6= 7.5 pieces per ounce

2. multiply 7.5 (for one ounce) by 10

    7.5*10 = 75

Answer:

75

Step-by-step explanation:

just answer it

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{u^{\frac{2}{5}}}{r^{\frac{1}{2}}}\implies \cfrac{1}{u^{\frac{1}{2}}\cdot u^{-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{1}{2}-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{5-4}{10}}}\implies \cfrac{1}{u^{\frac{1}{10}}}\implies u^{-\frac{1}{10}}[/tex]

Answer:

B. (0,6)

Step-by-step explanation:

To solve this question, you'll need to figure out what the final point is after reflecting each point. A quick way to figure this out is by multiplying (-1) to the x-coordinate.

When you reflect A. (2,0) over the y-axis, the point becomes (-2,0).

When you reflect C. (3,3) over the y-axis, the point becomes (-3,3).

When you reflect D. (5,5) over the y-axis, the point becomes (-5,5).

The only answer that does not change location is B. (0,6) as it stays at (0,6). If you multiply 0 by any number, it will always stay 0.

Multiplying the x-coordinate by (-1) to find the reflection point only works if you are reflecting it over the y-axis. You would multiple the y-coordinate by (-1) if you were reflecting over the x-axis.

Answer:

[tex]\large\boxed{-6y^2+12y+4}[/tex]

Step-by-step explanation:

[tex](2y^2+7y+11)-(8y^2-5y+7)\\\\=2y^2+7y+11-8y^2-(-5y)-7\\\\=2y^2+7y+11-8y^2+5y-7\qquad\text{combine like terms}\\\\=(2y^2-8y^2)+(7y+5y)+(11-7)\\\\=-6y^2+12y+4[/tex]

Answer:

Translated to the left 5 units and up 5 units and compressed horizontally by 2 units.

Step-by-step explanation:

The  parent function given is [tex]f(x)=x^2[/tex]

This function has its vertex at the origin.

If we move this function 5 units  to the left and 5 units up, then its vertex will now be at [tex](-5,5)[/tex].

If the parent function is then compressed horizontal by a factor of 2, then the transformed function will now have equation.

[tex]g(x)=2(x+5)^2+5[/tex]

Answer: [tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]

Step-by-step explanation:

The slope-intercept form of a equation of the line is:

[tex]y=mx+b[/tex]

Where m is the slope and b the y-intercept-

If the lines are parallel then they have the same slope:

[tex]m=\frac{5}{8}[/tex]

You can find the value of b by substituting the point given and the slope into the equation and solving for b:

[tex]3=\frac{5}{8}*2+b\\b=\frac{7}{4}[[/tex]

Then the equation is:

[tex]y=\frac{5}{8}x+\frac{7}{4}}[/tex]

Answer:

[tex]y = \frac{5}{8} x+\frac{7}{4}[/tex]

Step-by-step explanation:

We are to write the slope intercept form of the equation which passes through the point (2, 3) and is parallel to the line [tex]y = \frac{5}{8} x-7[/tex].

We know that the standard (slope-intercept) form of an equation of a line is given by: [tex]y=mx+c[/tex]

where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept.

Since we are to find the equation of the line parallel to the given equation so its slope will be same as of [tex]y = \frac{5}{8} x-7[/tex].

Finding the y-intercept:

[tex]y=mx+c[/tex]

[tex]3=\frac{5}{8}(2)+c[/tex]

[tex]c=\frac{7}{4}[/tex]

Therefore, the equation will be [tex]y = \frac{5}{8} x+\frac{7}{4}[/tex].

Answer:

48

Step-by-step explanation:

The sample space of the experiment contains all the possible outcomes of all events.

There are 3 events that are taking place.

Rolling a die which has 6 possible outcomes.

Flipping a coin which has 2 possible outcomes.

Spinning a spinner which has 4 possible outcomes.

Since the outcome of each event is independent of the other, the total possible outcomes will be equal to the product of outcomes of each event.

i.e.

Total outcomes = 6 x 2 x 4 = 48

The sample space of the experiment contains all the possible outcomes. so the number of elements in the sample space of this experiment will be 48

Answer:

48

Step-by-step explanation:

In the given experiment, three events take place which include rolling a die, flipping a coin and spinning a spinner.

The possible outcomes of each of these events are as follows:

Rolling a die - 6

Flipping a coin - 2

Spinning a spinner - 4

Therefore, by multiplying their possible outcomes, we can find the number of elements in the sample space of this environment.

Number of elements = 6 × 2 × 4 = 48

Answer: The price of a book increased from $20 to $25. What is the markup rate?

Answer:

N is a population parameter; the estimate of N is a statistic.

Step-by-step explanation:

A measure of a population is called a parameter.  The population is the entire set we are measuring.  In this problem, N is the total number of warplanes fielded by the Germans.  Since it is the total, it is a population, making it a parameter.

A measure of a sample is a statistic.  This means an estimate of N based on a sample would be a statistic.

In the context of the RAF's scenario, N is a population parameter representing the number of German warplanes in World War II. However, using the observed serial numbers to estimate N would produce a statistic, which may not be accurate as it corresponds to a sample rather than the total population.

In the given scenario, N is a population parameter. It represents the total number of warplanes built by Germany. A parameter represents a factual characteristic about a population. Estimating N from the observed serial numbers on the warplanes is a statistic. A statistic is derived from a sample, and it is used to estimate a population parameter when we don't have access to the full population.

For instance, suppose the RAF captures some German warplanes, and the highest observed serial number is 5000. They might then estimate that the Germans produced around 5000 planes (which would be a statistic). But this estimate could be incorrect since they're basing it on a sample rather than the total population of German warplanes (i.e., all the planes built by Germany).

This method for estimating N is similar to a technique called mark and recapture in biology, where scientists mark a number of individuals in a population, release them back into their natural environment, and later recapture a number of individuals. Using the ratio of marked to unmarked individuals in the recaptured sample, scientists can estimate the total population size.

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Answer:

The answer is A for sure

Step-by-step explanation:

And this is why

n ≥ 20

n + 5 ≥ 25

n + 5 − 5 ≥ 25 − 5

n ≥ 20

Inequality shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

The inequality that represents the solutions set is

n ≥ 20.

Option A is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Jim wants to collect at least 25 coins for his coin collection. He has already collected 5 coins.

The inequality shows the above situation.

n + 5 ≥ 25

Subtract 5 on both sides.

n ≥ 25 - 5

n ≥ 20

Thus,

The inequality that represents the solutions set is

n ≥ 20.

Option A is the correct answer.

Learn more about inequalities here:

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Answer:

2√5

Step-by-step explanation:

Use a factor tree to break down 20 into it's prime roots.

20 = 2 x 10

20 =  2 x 2 x 5

These are the prime factors of 20, so we can rewrite √20 as

(√2)(√2)(√5)

         (√2)(√2) = √(2x2) = √4 = 2, so we have

2√5

Scholarships and grants do not need to be paid back.

Government loans and private loans do need to be paid back.

She has 2 loans. $5,000 and $6,000.

She needs to pay back $11,000