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?

Answer:

  B

Step-by-step explanation:

The question asks why you can use the argument that two angles are congruent. Hence, you want to have a statement that involves two angles in the two triangles. Only statement B is such a statement.

_____

Multiple choice questions often answer themselves, if you understand what you're reading.

Answer:

Step-by-step explanation:

We have alternative external corners.

The lines m and n are parallel. That is why the alternative external angles are congruent (they have the same measure).

In the triangle RTS we have angles:

[tex]4x^o,\ 54^o,\ 2x^o[/tex]

We know: The sum of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

[tex]4x+54+2x=180[/tex]            subtract 54 from both sides

[tex]6x=126[/tex]           divide both sides by 6

[tex]x=21[/tex]

Answer:

The answer is ⇒ No, because Deon starts with less bacteria,

but it grows at a faster rat than Cameron's bacteria

Step-by-step explanation:

* Lets study the graph and the equation

- At t = 0

# Cameron's population = 200

# Deon population = 100

- At t = 5

# From the equation b(5) = 200(1 + 0.08)^5 ≅ 294

# From the graph b(5) ≅ 200

∴ Cameron's population > Deon's population

- The increase of the Cameron's population ≅ 94

  (294 - 200 = 94)

- The increase of the Deon's population ≅ 100

  (200 - 100 = 100)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 8

# From the equation b(8) = 200(1 + 0.08)^8 ≅ 370

# From the graph b(8) ≅ 300

∴ Cameron's population > Deon's population

- The increase of the Cameron's population ≅ 76

  (370 - 294 = 76)

- The increase of the Deon's population ≅ 100

  (300 - 200 = 100)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 11

# From the equation b(11) = 200(1 + 0.08)^11 ≅ 466

# From the graph b(11) ≅ 500

∴ Cameron's population < Deon's population

- The increase of the Cameron's population ≅ 96

  (466 - 370 = 96)

- The increase of the Deon's population ≅ 200

  (500 - 300 = 200)

∴ The rat of increase of Deon > The rat of increase of Cameron

- At t = 14

# From the equation b(14) = 200(1 + 0.08)^14 ≅ 587

# From the graph b(14) ≅ 700

∴ Cameron's population < Deon's population

- The increase of the Cameron's population ≅ 121

  (587 - 466 = 121)

- The increase of the Deon's population ≅ 200

  (700 - 500 = 200)

∴ The rat of increase of Deon > The rat of increase of Cameron

* From all these calculations the rate of increase of

 Cameron's population is less than the rate of increase

 of Deon's population

∴ Cameron is not right because Deon starts with less bacteria,

   but it grows at a faster rat than Cameron's bacteria

Answer:

The answer is C

Step-by-step explanation:

The answer is c)

Here’s why:

Answer: D. [tex] 7t^2+3+6[/tex]

Step-by-step explanation:

Given: The function 'a' represents the cost of manufacturing product A, in hundreds of dollars, and the function 'b' represents the cost of manufacturing product B, in hundreds of dollars.

[tex]a(t)=5t+2\\\\b(t)=7t^2-2t+4[/tex]

The expression that describes the total cost of manufacturing both products will be ,

[tex] a(t) + b(t)=5t+2+7t^2-2t+4[/tex]

Combining like terms, we  get

[tex] a(t) + b(t)=7t^2+5t-2t+4+2\\\\\Rightarrow\ a(t) + b(t)=7t^2+3+6[/tex]

Answer:

49.1 cm^2

Step-by-step explanation:

The appropriate area formula is ...

area = (1/2)(side 1)(side 2)(sin(angle between))

= (1/2)(10 cm)(12 cm)·sin(55°) = 60·sin(55°) cm^2

area ≈ 49.1 cm^2

The probability that a randomly chosen card from a standard 52-card deck is either an ace or a heart is approximately 31%.

In a standard deck of 52 cards, there are 4 suits and each suit has 13 cards: hearts, clubs, diamonds, spades. Therefore, the total number of heart cards in the deck is 13 and the total number of aces in the deck is 4 (one for each suit).

To compute the probability P (A or H), the probability that Anthony chooses a card which is either an ace or a heart, we first need to calculate individual probabilities. The probability of drawing a heart P(H) is 13/52 = 0.25, and the probability of drawing an ace P(A) is 4/52 = 0.077. However, as the aces also include one heart (Ace of Hearts), the probabilities overlap.

To correct this, we use the rule of sum for probabilities which says that the probability that A or B will happen is the probability that A will happen plus the probability that B will happen, minus the probability that both A and B will happen. Applying this, P ( A or H) = P(A) + P(H) - P(A and H) = 0.077 + 0.25 - 0.019 = 0.308, or approximately 31%

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Final answer:

The probability of drawing either an ace or a heart from a standard deck of cards is 11/26.

Explanation:

To find the probability of choosing either an ace or a heart card, we need to calculate the individual probabilities of each event and then subtract the probability of neither event happening.

There are 4 aces in a deck of 52 cards, so the probability of picking an ace is 4/52, which simplifies to 1/13.

Similarly, there are 13 hearts in a deck, so the probability of picking a heart is 13/52, which simplifies to 1/4.

Since the events are mutually exclusive (a card can't be both an ace and a heart), we can add the probabilities together to find the probability of either event happening: 1/13 + 1/4 = 4/52 + 13/52 = 17/52.

Finally, to find the probability of either an ace or a heart, we subtract the probability of neither event happening (the probability of picking a card that is neither an ace nor a heart):

P(A or H) = 17/52 - 39/52 = 22/52, which simplifies to 11/26.

To find out how many games Natalie and her friends played, we subtracted the total shoe rental cost for 6 people from the $21 spent and divided the remainder by the cost per game, which gave us a result of 3 games played.

The question asks us to solve a real-world math problem where Natalie and her friends go bowling and spend a total of $21. The cost to play one game is $3 and shoe rental is $2 per person.

To determine the number of games they played, we need to calculate the cost of shoe rental for all people and then figure out how much of the $21 was left for the games.

First, we calculate the shoe rental for 6 people (Natalie and her 5 friends):

Next, we subtract the shoe rental cost from the total amount spent to find the amount spent on games:

Finally, we divide the amount spent on games by the cost per game to find the number of games played:

Natalie and her friends played 3 games of bowling.

I think the last one is maybe ten, maybe

Answer:

Step-by-step explanation:

no

Answer:

  18 minutes 34.8 seconds

Step-by-step explanation:

We assume the minutes of commercials are proportional to the minutes of television, so we have ...

  (6 minutes of commercials)/(6 + 25 minutes of television) = x/(96 minutes of television)

Multiplying by 96, we get ...

  x = 96·6/31 = 576/31 = 18 18/31 . . . . minutes of commercials

That's about 18 minutes, 34.8 seconds of commercials in 1 hour 36 minutes of television.

let's firstly convert the mixed fractions to improper fractions and then add them up.

[tex]\bf \stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}~\hfill \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{4}+\cfrac{9}{8}\implies \stackrel{\textit{using and LCD of 8}}{\cfrac{(2)39~~+~~(1)9}{8}}\implies \cfrac{78+9}{8}\implies \cfrac{87}{8}\implies 10\frac{7}{8}[/tex]

Answer:

  buying in packets of 100

Step-by-step explanation:

Adding the given numbers results in a total that is twice the total number of cards the girls have. That total is 1256, so the total of the girls card collections is 628 cards.

  Mai has 628 -371 = 257 cards, so will need ceiling(257/9) = 29 pages

  Ellen has 628 -481 = 147 cards, so will need ceiling(147/9) = 17 pages

  Lora has 628 -404 = 224 cards, so will need ceiling(224/9) = 25 pages

Together, the girls need 29 +17 +25 = 71 pages.

If they were to buy packets of 10, they would need 8 packets, or 80 pages at 0.20 per page, for a cost of $16.00.

If they were to buy packets of 100, they would need 1 packet, or 100 pages at 0.15 per page, for a cost of $15.00.

Buying their pages in packets of 100 will cost the girls less.

First, we figure out how many cards each girl has, then determine how many pages they need in total. Comparing the costs, it is clear that it would cost less for the girls to buy the packets of 100 pages.

To answer this question, the first step is to find out how many cards each girl has. From the question, we understand that Ellen and Lora together have 371 cards and Lora and Mai together have 481 cards. The sum of Ellen's and Mai's cards totals to 404. By using these equations, we can determine that Lora has 227 cards, Ellen has 144 cards, and Mai has 254 cards.

Next, we need to find out how many pages each girl needs. Since each page has 9 pockets, Lora needs 26 pages (227 divided by 9, rounded up), Ellen requires 16 pages and Mai requires 29 pages. Altogether, they need 71 pages.

Now, let's get to the cost. At .20 cents per page, packets of 10 would cost $2, and they need 8 packets, which totals to $16. Alternatively, a packet of 100 costs .15 cents per page, which equals to $15.

Therefore, buying pages in packets of 100 will save the girls money as compared to buying in smaller packs of 10.

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Answer:

C) 7 ft 4 in

Step-by-step explanation:

Shadows are assumed to be proportional to the height of the object casting them. Hence the brother's shadow will satisfy ...

shadow/(6 ft) = (5.5 ft)/(4.5 ft) = 11/9 . . . . . reduce the fraction

shadow = (6 ft) · (11/9) . . . . . . . . . . . . . . . . . multiply by 6 ft

shadow = 7 1/3 ft = 7 ft 4 in

100:40

=2.5

1200 : 2.5

=480

About 480 people out of the 1,200 customers are likely satisfied with their service.

To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.

Find the proportion of satisfied customers in the survey:

Number of satisfied customers in the survey: 40

Total number of people surveyed: 100

Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)

Proportion of satisfied customers = 40 / 100 = 0.4 or 40%

Apply this proportion to the entire customer base:

Total number of the company's customers: 1,200

Estimate of satisfied customers = Proportion of satisfied customers × Total customers

Estimate of satisfied customers = 0.4 × 1,200 = 480

The second value in a set of parenthesis is the y value, so B is true.

If you multiplied each value of W by -2, you would get the values for V, so C is also true.

The answer is B and C.

Answer:

Option B and C are correct.

Step-by-step explanation:

Given the vectors V = (8, -4) and W = (-4,2)

we have to check the following options.

Option A: V x W = 40

[tex]A\times B=\begin{vmatrix}i&j&k\\8&-4&0\\-4&2&0\end{vmatrix}=0i+0j+k(16-16)=0i+0j+0k[/tex]

Hence, not true

Option B: The y-component of W is 2

W = (-4,2)

x-component is -4

y-component is 2

Hence, true

Option C:  V = -2W

W=(-4, 2)

V=-2(-4,2)=(8,-4)

which is true

Option D: The x-component of V is 4

V = (8,-4)

x-component is 8

y-component is -4

which is not true.

hence, the option B and C are correct.

Answer:

option H

457.9 CM squared

Step-by-step explanation:

Given that,

base of parallelogram = 30 cm

side of parallelogram = 18 cm

one of the angle of parallelogram = 58°

Formula to calculate area of parallelogram is

To calculate height we will use trigonometry identity  

sin(58) = height / 18

height = 15.27

Area = 30 x 15.27

         = 457.9 cm²

so the area of parallelogram is 457.9 cm²

whats the question? ill help you out i just wanna Answer the right question

Answer:

C.  Each additional t-shirt being printed will increase the total cost by $11.

Step-by-step explanation:

We know that the total cost of custom t-shirts, y, in dollars, for x t-shirts is given by:

[tex]y = 11x + 25[/tex]

Here 11 is the price of the shirt, x is the number of shirts that are printed and 25 might be some additional charges.

For each additional shirt that is printed, the total price, y, will increase by $11 so the correct answer option is C.

Answer: it should be will receive a refund of $278

Step-by-step explanation:

That’s just what was on my test though

Hope that helps somebody

The amount Ms. Wilson will receive after she figures out her tax for the year is; $999.88

The tax bracket Ms. Wilson falls into demands that she pays 12% of her taxable income in tax.

Hence, the tax she's supposed to pay is;

Hence, she will receive after she figures her taxes for the year is; $5344 - $4,344.12 = $999.88

Read more on federal tax rate;

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Answer:

Step-by-step explanation:

f and g will be inverses if f(g(x)) = x.

A — f(g(x)) = 5(0.2x -2) +10 = x -10 +10 = x . . . . . inverses

B — f(g(x)) = (±√x+3)^2 +3 = x ±6√x +9 +3 ≠ x . . . . . not inverses

  (even if it is g(x) = ±√(x+3), the functions are still not inverses)

C — 1/2(2x -7) +7 = x -7/2 +7 = x +7/2 ≠ x . . . . . not inverses

D — 1/4(4x +4) -1 = x +1 -1 = x . . . . . inverses

We know that, usually,

[tex] c^2 = a^2+b^2 [/tex]

In this case, we also know that

[tex] c^2 = 2ab [/tex]

We deduce that

[tex] a^2+b^2 = 2ab [/tex]

If we subtract 2ab from both sides, we get

[tex] a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b [/tex]

So, the triangle is an isosceles right triangle, and so the angles are 90-45-45

Answer:

 1) Methods:

-  Quadratic formula.

- Factorization.

- Completing the square.

2) If the determinant is less than zero ([tex]D<0[/tex]) then there are two roots that are complex conjugates.

Step-by-step explanation:

 Methods:

-  Quadratic formula

Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex], you can solve it with the quadratic formula:

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

- Factorization

You must find two expression that when you multply them, you get the original quadratic equation. For example:

[tex]x^2+6x+8=0[/tex]

Find two number whose sum is 6 and whose product is 8. These are 2 and 4. Then:

[tex](x+2)(x+4)=0[/tex]

When you make the multiplication indicated in [tex](x+2)(x+4)=0[/tex], you obtain [tex]x^2+6x+8=0[/tex]

- Completing the square

Given the quadratic equation in Standard form [tex]ax^2+bx+c=0[/tex],, you must turn it into:

[tex]a(x+d)^2+e=0[/tex]

Where:

[tex]d=\frac{b}{2a}\\\\e=c-\frac{b^2}{4a}[/tex]

Once you get that form, you must solve for x.

You can predict if the quadratic function will have a complex solution with the determinant:

[tex]D=b^2-4ac[/tex]

If [tex]D<0[/tex] then there are two roots that are complex conjugates.

Quadratic equations can be solved by several methods including the quadratic formula. The concept of a discriminant, calculated by b² - 4ac, can indicate if a function has a complex solution. A negative discriminant means the equation will have complex solutions.

Quadratic equations, or second-order polynomials, take on the form ax²+bx+c = 0. There are several methods to solve these equations, for instance, factoring, completing the square, using the quadratic formula or graphically.

The most general method is the quadratic formula: -b ± √b² - 4ac / 2a.

Indicator for a complex solution is called the discriminant(b² - 4ac). If the discriminant is negative, the equation will have complex solutions rather than real ones. This is because you'd be attempting to find the square root of a negative number, which is not possible within the set of real numbers, and hence the answer is in the form of a complex number.

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Answer:

b

Step-by-step explanation:

100%

The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.

Each term of an arithmetic sequence can be found using the formula:

a_n = a + (n-1)d

The given sequence is 5, -3, -1, 1, 3.

From this, we can see that the value of:

a = -5

d = -3 - (-5) = -3 + 5 = 2

∴ The explicit formula can be written as:

a_n = -5 + (n - 1)2

Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.

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Answer:

73.19

Step-by-step explanation:

4 * (1/2)* (6.5) * (5.63)

Answer:

Part a) [tex]\$17,622.72[/tex]

Part b) [tex]\$20,442.36[/tex]

Part c) [tex]\$23,713.13[/tex]

Part d) [tex]\$27,507.23[/tex]

Step-by-step explanation:

we know that  

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part a) How much would you have at the end of 1 year?

in this problem we have

[tex]t=1\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*1}=\$17,622.72[/tex]

Part b) How much would you have at the end of 2 year?

in this problem we have

[tex]t=2\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*2}=\$20,442.36[/tex]

Part c) How much would you have at the end of 3 year?

in this problem we have

[tex]t=3\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*3}=\$23,713.13[/tex]

Part d) How much would you have at the end of 4 year?

in this problem we have

[tex]t=4\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*4}=\$27,507.23[/tex]

Answer:

6 to the power of 1 over 6

Answer:

The correct option is 4.

Step-by-step explanation:

The given interpretation is square root of the cube root of 6. The mathematical expression is

[tex]\sqrt{\sqrt[3]{6}}[/tex]

It can be written as

[tex]((6)^{\frac{1}{3})^{\frac{1}{2}}[/tex]

Using the property of exponent, we get

[tex](6)^{\frac{1}{3}\times \frac{1}{2}}[/tex]         [tex][\because (x^m)^n=(x)^{mn}][/tex]

Now simplify the power.

[tex](6)^{\frac{1}{6}}[/tex]

The simplified form of given expression is 6 to the power of 1 over 6. Therefore the correct option is 4.

Answer: c. Exponential

Answer:

  graph D

Step-by-step explanation:

You want to choose the graph with a y-intercept of 70 and an x-intercept of 140. Graph D matches that.

___

Comment on graph D

The horizontal scale is a bit weird in that the numbers don't correspond to hash marks on the horizontal axis. The hash mark between the numbers 120 and 160 will correspond to a distance of 140 ft. That is where the graph touches the horizontal axis, so that is one indication it is the graph you want.

Answer:

Failing to pay debt

Step-by-step explanation:

Final answer:

Defaulting on a debt, failing to pay debt, and building a credit history are crucial aspects of managing one's financial health.

Explanation:

Defaulting on a debt occurs when a borrower fails to repay the loan according to the terms agreed upon with the lender. This can lead to serious consequences such as damage to one's credit score and possible legal actions taken by the lender.

One of the contributing factors to defaulting is failing to pay debt on time. This affects a person's credit history and the lender's trust in the borrower's ability to repay borrowed money.

It is important to build a credit history by responsibly managing credit accounts, paying bills on time, and avoiding opening too many accounts rapidly to maintain a good credit score and prevent defaulting.

Give each month a number:

January = 0

February = 1

March = 2

April = 3

Now set X to 3 in the equation ad solve for t.

t = -30cos(x/6) +60

t = -30cos(3/6) +60

t = 33.672 degrees. ( Round as necessary)

You would need to change the +60 to a new starting point based on what the rise in temperature is due to global warming.

The model predicts a maximum afternoon temperature of around 33.67°C in April. To adjust for the impact of global warming, one can increase the constant term in the equation based on observed data. For instance, if there's a 2°C increase, the modified equation would be: t = -30cos(x/6) + (60 + 2).

Find the maximum temperature in April and how the model would change due to global warming:

Finding the maximum temperature in April:

Plug in x = 3: Since April is the fourth month (x = 0 for January), we need to substitute x with 3 in the equation:

t = -30cos(3/6) + 60

Calculate the temperature:

t = -30cos(0.5) + 60 ≈ 33.67°C

Therefore, the model predicts a maximum afternoon temperature of approximately 33.67°C in April.

Impact of global warming:

If the maximum temperature in April starts rising due to global warming, the model needs to be adjusted to account for the increase. Here's how:

Increase the constant term: The constant term in the equation (currently 60) represents the average temperature across all months. To account for a general rise in temperatures, we can increase this value.

Adjust the increase based on the observed data: The amount of increase should be based on observed data on how much the temperature has risen in April compared to the historical average.

For example, if observations show that the average April temperature has increased by 2°C due to global warming, we can modify the equation as follows:

t = - 30cos(x/6) + (60 + 2)  // Increase the constant term by 2

This new equation would then account for the simulated effect of global warming on the maximum afternoon temperature in April.

Answer:

Step-by-step explanation:

a) The image A'B'C'D' is smaller than the original ABCD, so the dilation is a reduction. The image is reduced in size from the original.

__

b) Each image point is 1/2 the distance of the original point from the origin. Count the grid squares to see this, or compare coordinates:

  A'(-1, 2) = 1/2·A(-2, 4)

Thus the scale factor is 1/2.