divisibility rule for 4.

Answer:

The length of the ladder is 14.5 ft

Step-by-step explanation:

For a right triangle

sinx = opposite / hypotenuse

Since we know the angle and the opposite side, we can calculate the hypotenuse

sin 64 = 13/ hypotenuse

Multiply each side by the hypotenuse

hypotenuse * sin 64 = 13

Divide by sin 64

hypotenuse = 13/sin 64

hypotenuse=14.4638

Rounding to the nearest tenth

14.5

The problem asks for the length of the ladder that forms a triangle with the house. The length of the ladder, which represents the hypotenuse of the triangle, can be calculated using the sine function and the given angle of 64 degrees and the opposite side of 13 feet. The calculated length of the ladder, rounded to the nearest tenth of a foot, is 14.2 feet.

The subject of this question falls under the branch of Mathematics, specifically trigonometry. The problem statement defines a right-angled triangle with a 64-degree angle, a known opposite side (13 ft), and we are asked to find the hypotenuse or the length of the ladder.

To find the length of the ladder, we will use the sine function which in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In mathematical form, Sin(θ) = Opposite / Hypotenuse. To find the hypotenuse, we will rearrange the formula to Hypotenuse = Opposite / Sin(θ).

Substituting the known values: Hypotenuse = 13 ft / Sin(64 degrees). Therefore, the length of the ladder is approximately 14.2 feet rounding to the nearest tenth.

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Answer:

10 2/15 hours

Step-by-step explanation:

If we have a candle that is 11 2/5 inches tall

It burns 1 1/8 inches per hour.  We need to divide to see how long the candle will last

11 2/5 ÷ 1 1/8

I will convert the mixed numbers to improper fractions

11 2/5 = (5*11+2)/5 = 57/5

1 1/8 = (8*1+1)/8 = 9/8

57/5 ÷ 9/8

Copy dot flip

57/5 * 8/9

456/45

Now we change it back to a mixed number

45 goes into 456  10 times with 6 left over

10 6/45

This simplifies to 10 2/15

Answer: My expected value would be of $10

Step-by-step explanation The way you can determine the expected value is by thinking about the lowest price and how much you paid. I think I would get $10 because They wouldn't make it very easy to get a big prize like $100. Pleas mark this brainliest and I will be glad to help you anytime.

The expected value of buying a ticket in this raffle is -$0.348, meaning you're expected to lose about 35 cents per ticket. Thus, in terms of expected financial return, this game is not favorable to play.

The expected value, in probability theory, is the average result of an experiment repeated many times. In this case, to calculate the expected value of the game, we will multiply each outcome by the probability of that outcome, and then sum these values. The outcomes here are $100, $50, $10, and -$1 (the cost of the ticket), and the respective probabilities are 1/250, 1/250, 1/250, and 247/250 (the probability of not winning anything).

Here's the calculation: ($100 x (1/250)) + ($50 x (1/250)) + ($10 x (1/250)) + (-$1 x 247/250) = $0.40 + $0.20 + $0.04 - $0.988 = -$0.348. That indicates that, on average, for each ticket you buy, you're expected to lose about $0.35. Therefore, in terms of pure expected value, it's not a favorable game to play. However, decisions to participate in games like this often consider more than just expected financial return, such as the thrill of participation or the opportunity to support a charitable cause.

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Answer:

168km

Step-by-step explanation:

132/11=12km per litre

12*14=168km

Adam can cover [tex]\boxed{{\mathbf{168 km}}}[/tex]  with [tex]14{\text{ liters}}[/tex]  of fuel.

Further explanation:

The direct relationship is the relationship between two quantities in which one quantity decreases then the other quantity also decreases and vice versa. The examples are supply function and speed distance function.

The direct relationship of the variables [tex]a{\text{ and }}b[/tex]  as

[tex]\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}[/tex]                   ......(1)

Here, [tex]{a_1},{a_2}[/tex]  are the quantities of the variable [tex]a[/tex]  and [tex]{b_1},{b_2}[/tex]  are the quantities of the variable [tex]b[/tex]  

Given:

Adam covered the distance [tex]132{\text{km}}[/tex]  by car with 11 liters of fuel.

Step by step explanation:

Step 1:

The provided data can be written in the table form as,

It can be seen that data is direct relationship.

Here, [tex]{a_1}=132,{a_2}=a,{b_1}=11{\text{ and }}{{\text{b}}_2}=14[/tex]

Step 2:

Now put the values [tex]{a_1}=132,{a_2}=a,{b_1}=11{\text{ and }}{{\text{b}}_2}=14[/tex] in equation (1) to get the value of [tex]a[/tex] .

[tex]\begin{gathered}\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}\hfill\\\frac{{132}}{a}=\frac{{11}}{{14}}\hfill\\\end{gathered}[/tex]

Now calculate the further equation by the cross multiplication method.

[tex]\begin{aligned}\frac{{132}}{a}&=\frac{{11}}{{14}}\\132\times14&=11a\\1848&=11a\\a&=168\\\end{aligned}[/tex]

Thus, Adam can cover [tex]168{\text{ km}}[/tex]  distance with [tex]14{\text{ liters}}[/tex]  of fuel.

Learn more:  

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Comparing quantities

Keywords: Adam, car, fuel, distance, direct relationship, speed, positive relationship, increase, decrease, equation, cross multiplication method, variables, quantity, substitute.

Answer:

It Is 175% Of 88.

Step-by-step explanation:

154 ÷ 88 = 1.75

To Convert A Decimal Into Percent, You Multiply By 100.

1.75 · 100% = 175%

Therefore, The Answer Is 175%.

The answer is 57.14%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here 88/154 and therefore in percentage terms it is 88/154 × 100

                                                                                                 = 57.14%

Hence, The answer is 57.14%

Learn more about percentages here:

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The question is about solving the equation 4/3x+2=5x and identifying the corresponding graph. There appears to be a mix-up with unrelated information about proportions and graphing the equation y = 9 + 3x. The correct approach to solve the equation was described, but without graphical context, a specific graph cannot be identified.

The student asked which graph represents the solution for the equation 4/3x+2=5x. To solve this equation algebraically, we need to isolate the variable x. However, it seems that the information provided in the question does not directly relate to the solution of the given equation. Instead, there is a mix-up with an example of setting up a proportion, finding the slope of a line, and graphing the equation y = 9 + 3x.

For the equation 4/3x+2=5x, we would solve for x by first combining like terms or using inverse operations to get all x terms on one side and constants on the other. The correct approach would be to subtract 4/3x from both sides of the equation and subtract 2 from both sides, which simplifies to 0 = 5x - 4/3x - 2, giving us a single-variable linear equation that can be solved for x. However, without a clear graph or further context, this explanation cannot indicate which specific graph represents the solution to the original equation.

Answer:

1.12

Step-by-step explanation:

1.6 x 0.7

Answer:

8

Step-by-step explanation:

Read a little bit at a time.

Equation

Solution

Answer:

x=8

Step-by-step explanation:

4x+30 =70-x

Add x to each side

4x+x+30 =70-x+x

4x+x +30 =70

5x +30 = 70

Subtract 30 from each side

5x +30 -30 =70-30

5x = 40

Divide each side by 5

5x/5 = 40/5

x = 8

These lines are perpendicular since their slopes are negative reciprocals. If you multiply a slope times its negative reciprocal, the result is always -1. ... Let's prove that perpendicular lines have negative reciprocal slopes, AND that negative reciprocal slopes imply perpendicular lines.

[tex]\text{If}\ x_1,\ \text{and}\ x_2\ \text{are zeros of a polynomial function, then the function}\\\text{has equation}:\\\\f(x)=a(x-x_1)(x-x_2).\\----------------------------\\\\11.\ \text{We have the zeros}\ 3\ \text{and}\ i:\\\\f(x)=(x-3)(x-i)=(x)(x)+(x)(-i)+(-3)(x)+(-3)(-i)\\\\=x^2-xi-3x+3i=\boxed{x^2-(3+i)x+3i}\\\\12.\ \text{We have the zeros}\ -2\ \text{and}\ 2i:\\\\f(x)=(x-(-2))(x-2i)=(x+2)(x-2i)\\\\=x^2-(2i)^2=x^2-2^2i^2=x^2-4(-1)=\boxed{x^2+4}\\\\\text{used}\\\\(a-b)(a+b)=a^2-b^2\\\\i=\sqrt{-1}\to i^2=-1[/tex]

Answer:

Hope this helps, sorry for my horrible handwriting. If you have any questions feel free to ask me!

Step-by-step explanation:

Answer:

your answer is h=2.65 hours

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=2(x-0) \\\\\\ y-5=2x\implies y=2x+5[/tex]

Answer:

This winds up being a 4% decrease.

Step-by-step explanation:

For an example, we will take an object that costs $100. If we mark it up by 60%, the new cost will be $160.

Now we want to take the cost of $160, and subtract 40%. First we need to find 40% of $160. We can do that by multiplying them together.

$160*40% = $64

Now we will subtract that from the cost of the item after the increase.

$160 - $64 = $96.

Even though the percent decrease was less, the order in which we do it causes this to be an overall decrease

The net effect of a 60 percent increase followed by a 40 percent decrease is a 4 percent decrease from the initial value.

The student is asking about the net effect of a 60 percent increase followed by a 40 percent decrease on a value. To solve this, one would typically express these percentages as factors; an increase of 60% would be represented as multiplying by 1.60 (100% original + 60% increase), and a decrease of 40% as multiplying by 0.60 (100% original - 40% decrease). If we call the initial value 'x', then after the increase, the value becomes 1.60x.

Then, applying the 40 percent decrease, we multiply by 0.60: 1.60x * 0.60 = 0.96x. Thus, the net effect of a 60 percent increase followed by a 40 percent decrease results in a 4 percent decrease of the initial value.

Answer: Hello there!

We know that Jada has 12 books checked out, and Han has one third less than that.

one-third of a number is equal to the number divided by 3, in this case, we have the number 12, so a third of 12 is: 12/3 = 4

then if Han has a third less than 12, Han has 12 - 4 = 8 books checked out.

Answer:

21 girls

Step-by-step explanation:

Boys: girls

5:7

Multiply each number by 3

15: 21

There will be 15 boys and 21 girls

Answer:

$2,000

Step-by-step explanation:

Since she has $440 dollars and adds $65 dollars a week, the equation will be 440+65(24)=X

Answer:

2000

Step-by-step explanation:

Let's go:

The centroid of a triangle is the point of intersection of its medians. The distance from de centroid to some vertex of triangle to which it belongs is equal to 2/3 of the length of its median:

BM = 18/3 = 6

I hope I helped you.

Answer:

A

Step-by-step explanation:

because -4 is x and -3 is y

Answer:

A

Step-by-step explanation:

the solution to a system of equations graphically is the point of intersection of the 2 lines.

The point of intersection = (- 4, - 3) → A

Answer: 2 pairs of angles

As the name "angle angle" suggests, we need 2 pairs of angles proven congruent in order to prove that two triangles are similar. Each "angle" refers to a pair of angles between the two triangles, which are corresponding angles. We could use the third pair, but it's extra unnecessary work. This theorem is often written as "AA similarity" or something along those lines.

One way to check for similar triangles is to compare the ratios of the sides. If the corresponding sides divide to the same value, then you have similar triangles. This method only works of course if you know the side lengths.

The formula of an area of a triangle:

[tex]A_{\triangle}=\dfrac{1}{2}bh[/tex]

b - base

h - height

We have b = 8in and h = 3in. Substitute:

[tex]A_{\triangle}=\dfrac{1}{2}(8)(3)=(4)(3)=12\ in^2[/tex]

The formula of an area of a rectangle:

[tex]A_{\boxed{\ }}=lw[/tex]

l - length

w - width

We have l = 8in and w = 5in. Substitute:

[tex]A_{\boxed{\ }}=(8)(5)=40\ in^2[/tex]

The area of a shaded region:

[tex]A=A_{\boxed{\ }}-A_{\triangle}\\\\A=40\ in^2-12\ in^2=28\ in^2[/tex]

Answer:

Graph A.

Step-by-step explanation:

The given graph in the question is y = (x + 2)  (x + 7)

or y = x² + 2x + 7x + 14

      = x² + 9x + 14

Now we convert this equation of parabola in vertex form

[tex]y=(\frac{x+9}{2})^{2}-\frac{81}{4}+14[/tex]

  [tex]=(x+4.5)^{2}-6.25[/tex]

This equation is in the form of y = (x-h)² + k where (h,k) is the vertex.

So in the given equation y = (x + 4.5)² - 6.25

Vertex should be (-4.5, 6.25) which lies in third quadrant.

Therefore, option A. is the graph.

[tex]\left\{\begin{array}{ccc}x-4y=28\\2x+y=2&\text{multiply both sides by 4}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-4y=28\\8x+4y=8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad9x=36\qquad\text{divide both sides by 9}\\.\qquad\boxed{x=4}\\\\\text{Put the value of x to the second equation:}\\\\2(4)+y=2\\8+y=2\qquad\text{subtract 8 from both sides}\\\boxed{y=-6}\\\\Answer:\ \boxed{x=4\ and\ y=-6\to(4,\ -6)}[/tex]

Answer:

2

Step-by-step explanation:

8% is the same thing as multiplying something by 0.08.

25 x 0.08 = 2

Hope this helps :)

Answer:

8 is 2 percent of 25

Step-by-step explanation:

we can prove this as

=[tex]\frac{25}{100}[/tex]×8

=[tex]\frac{2oo}{100}[/tex]

=2

hence proved

To find the discounted price of the sweater, multiply the original price $84 by 30% to get the discount amount of $25.20. Subtract this from the original price to find that the sweater will cost $58.80 after the discount.

To calculate the cost of a sweater that is on sale for 30% off its ticketed price of $84, you will need to find 30% of $84 and then subtract that amount from the original price.

Therefore, after a 30% discount, the sweater will cost $58.80.

Answer:

Her guinea pig is 210 millimeters longer than her fish

Step-by-step explanation:

1.Convert centimeters into millimeters

2.Subtract 40 from 250

3.You have the answer!

I hope this was helpful

Answer:

$120.

Step-by-step explanation:

We have been given that Libby sold $60 worth of vegetables at the farmer's market.

Jess sold 3/4th of what Libby sold. Let us find 3/4 of 60.

[tex]\text{Jess sold}=60\times \frac{3}{4}[/tex]

[tex]\text{Jess sold}=15\times 3[/tex]

[tex]\text{Jess sold}=45[/tex]

Therefore, Jess sold $45 worth of vegetables.

We are told that Stephanie sold 1/3rd of what Jess sold. So let us 1/3rd of 45.

[tex]\text{Stephanie sold}=45\times \frac{1}{3}[/tex]

[tex]\text{Stephanie sold}=15[/tex]

Therefore Stephanie sold $15 worth of vegetables.

Now let us add amounts of money earned by Libby, Jess and Stephanie to get the total money earned by all.

[tex]\text{The total money earned by Libby, Jess and Stephanie}=60+45+15[/tex]

[tex]\text{The total money earned by Libby, Jess and Stephanie}=120[/tex]

Therefore, they all sell $120 worth of vegetables together.

Answer:

As per the statement: Libby sold $60 worth of vegetables at the farmer's market.

⇒ Libby sold vegetables at the farmers market = $60

Jess sold 3/4th of what Libby sold.

⇒ Jess sold = [tex]\frac{3}{4} \times 60 = \$45[/tex]

Also, Stephanie sold 1/3rd of what Jess sold.

⇒ Stephanie sold = [tex]\frac{1}{3} \times 45 = \$15[/tex]

To find how much did they all sell together.

Together they all sell together = Libby sold + Jess sold + Stephanie sold

                                                    =$60 + $45+$15 = $120

Therefore, they all sell together is, $120                                                                                

Answer:

17²

Step-by-step explanation:

to find the perfect square take the square root of 289

[tex]\sqrt{289}[/tex] = 17 ⇒ 17² = 289

Answer:

17

Step-by-step explanation:

The defenition of a perfect square is "the product of a rational number multiplied by itself."

If you multiply 17 by itself you get 289, so the answer is 17.