Mr. Norris is paid a 5% commission on each boat he sells. What is his commission on a boat that he sells for $125,000?

Answer:

9=1.375 10=1.625 11=3.3125 12=4.45

Answer: 54.4°

Step-by-step explanation:

If the spotlight is mounted 7.3 meters high, its height will be 7.3meters.

If A is 10.2 meters from the base of the pole, the base of the pole to the parking area will be 10.2meters

The angle of the depression will be facing the base directly therefore, the base will be the opposite of the triangle formed and the height of 7.3m will be the adjacent.

To get the depression angle, we use the trigonometry identity SOH, CAH, TOA

Since we have opposite and adjacent, we will use "TOA" which means

Tan theta = Opposite/Adjacent

Opposite = 10.2m Adjacent = 7.3

Tan theta = 10.2/7.3

Tan theta = 1.39

theta = arctan 1.39

Theta = 54.4°

The angle of depression that the spotlight should aim at is 54.4°

To find the angle of depression for the spotlight to illuminate point A, one takes the inverse tangent of the ratio of the height of the pole to the distance from the pole to point A (7.3 meters / 10.2 meters).

The student has asked to determine the angle of depression that a spotlight should be aimed at to illuminate a specific point on the ground. To find this angle, we use trigonometry, specifically the tangent function, which relates the opposite side (the height of the pole) to the adjacent side (the distance from the base of the pole to point A).

The tangent of the angle of depression (θ) is equal to the opposite side divided by the adjacent side. That is, tan(θ) = height / distance = 7.3 meters / 10.2 meters.

Using a calculator, the angle of depression θ can be found by taking the inverse tangent (or arctan) of 7.3/10.2. Therefore, θ = arctan(7.3/10.2).

Once you calculate this value, you will have the angle of depression at which to aim the spotlight to illuminate point A.

Answer:

Yumiko should multiply the other equation by 3.

If she adds the two equations she would be left with the variable 'x'.

Step-by-step explanation:

Given the two equations are as follows:

[tex]$ 2x - 3y = 12 \hspace{5mm} \hdots (1) $[/tex]

[tex]$ 5x + 6y = 18 \hspace{5mm} \hdots (2) $[/tex]

It is given that she multiplies the first equation by 6. Therefore, (1) becomes

[tex]$ 12x - 18y = 72 \hspace{15mm} \hdots (a) $[/tex]

Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.

The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.

Therefore, Equation (2) becomes:

[tex]$ 15x + 18y = 54 \hspace{5mm} \hdots (b) $[/tex]

Now, we add Equation (a) and Equation (b).

[tex]$ \implies 12x - 18y + 15x + 18y = 72 + 54 $[/tex]

[tex]$ \implies 27x = 126 $[/tex]

Factor: 3

Equation: 27x = 126

The slope of the line that passes through two points is

(the difference in 'y') divided by (the difference in 'x').

The two points are:  (3, -4) and (5, -7)

The difference in 'y' is . . . (-7) - (-4) = -3

The difference in 'x' is . . . (5) - (3) = 2

The slope of the line through those two points is (-3) / (2) .

That's the 3rd choice on the list.

Answer:

The slope of the line that passes through two points is

(the difference in 'y') divided by (the difference in 'x').

The two points are:  (3, -4) and (5, -7)

The difference in 'y' is . . . (-7) - (-4) = -3

The difference in 'x' is . . . (5) - (3) = 2

The slope of the line through those two points is (-3) / (2) .

That's the 3rd choice on the list.

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Answer:1 and 2:4

Step-by-step explanation: Because  if it's fair you have  a 50 percent chance of heads or tails. and if u write it as a ratio you would get 2_4 you will most likely learn this in 7th grade or 6th

Answer:

a

Step-by-step explanation:

the x of each point in order from least to greatest makes up the domain

Part a) Wayen's saving before he spend $28 is $30

Part b) Steph's saving after she spend $28 is $8

Step-by-step explanation:

Ratio of Wayen's saving to stephs saving: 5:5

After spending $28

Ratio of Wayen's saving to Stephs saving: 1:4

We can write ratio as:

[tex]\frac{W}{S}=\frac{5}{6}\\Cross\,\,multiply\\6W=5S\,\,eq(1)[/tex]

After spending $28

[tex]\frac{W-28}{S-28}=\frac{1}{4}\\Cross\,\,multiply\\4(W-28)=S-28\,\,eq(2)[/tex]

Part a) Find Wayen's saving before he spend $28

Using both equations to find value of W

Putting value of S from eq(1) into eq(2)

6W/5=S

[tex]4W-112+28=S\\4W-84=S\\Putting\,\,value\,\,of\,\,S\\4W-84=\frac{6W}{5}\\ Multiply\,\,both\,\,sides\,\,by\,\,5\\20W-420=6W\\20W-6W=420\\14W=420\\W=420/14\\W=30[/tex]

So, Wayen's saving before he spend $28 is $30

Part b) Find Steph's saving after she spend $28

First Steph's saving before spending $28 is:

[tex]S=\frac{6W}{5}\\S=\frac{6*30}{5} \\S=36[/tex]

Now, After spending $28

S-28 we get:

36-28= $8

So, Steph's saving after she spend $28 is $8

Keywords: Ratio and proportion

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Answer:

24

Step-by-step explanation:

18-6=12

24=12x2

12-24= -12

Answer:

Helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.

Step-by-step explanation:

We are given the following in the question:

A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).

The attached image shows the path of helicopter.

Distance Formula:

[tex](x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Distance traveled by helicopter =

[tex]d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}[/tex]

If the helicopter goes directly:

[tex]d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}[/tex]

Difference in distances =

[tex]19 - 13.45 = 5.55\text{ units}[/tex]

Thus, helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.

Answer:

i had this question in a quiz on edge and got a 100% on the quiz

here is your answer

Step-by-step explanation:

Answer:

b= 8.5

Step-by-step explanation:

To find b, subtract 4.1 to both sides.

12.6= b+4.1

- 4.1      -4.1

8.5= b

Answer:

7.5 = b

Step-by-step explanation:

12.6 - 4.1 = b + 4.1 - 4.1

8.5 = b

The Total number of students at the school is 1240.

The given ratio is 11 boys : 9 girls,

Let 11x = boys and

9x = girls.

As 124 more boys are there than girls, so

11x - 9x = 124.

2x = 124

x = 62

The actual number of boys = 11x = 11 × 62 = 682

The actual number of girls = 9x = 9 × 62 = 558

Total number of students at the school = 682 boys + 558 girls = 1240 students

Answer:

4/15 or in decimal form its 0.26

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.26

Answer:

4

Step-by-step explanation:

6 - 2 = 4

Jake ate 2 less than 6 which is how many Harry ate.

Answer:

4

Step-by-step explanation:

the answer is 4 because 6 minus 2 would be 4 so the answer is four

Answer:

y = - 4.4

Step-by-step explanation:

from the question

y = -6.6

x = 9.9

y∝ x

y = kx ..... where k is introduced as a constant of proportionality

solve for k

y=-6.6 and x = 9.9

we have,

-6.6 = k × 9.9

-6.6 = 9.9k

divide both sides by 9.9

-6.6/ 9.9 = 9.9k/9.9

-0.667= k

therefore k = - 0.667

now, find y when x = 6.6

from the equation y = kx

y = -0.667 × 6.6

y = - 4.4

Answer:

-4.4

Step-by-step explanation:

x : y

9.9 : -6.6

6.6 : y

9.9/-6.6 = 6.6/y

y = 6.6 × -6.6/9.9

y = -4.4

Answer: y = 3/4 + 8.25

Step-by-step explanation:

1. You already know the slope, 3/4, and the coordinates (-7,3). We could plug these into a y=mx+b equation: 3=3/4(-7) + b

2. Next you need to solve for b. Then you get your answer of 8.25. (I attached my work for that)

3. You plug in 8.25 as your y-intercept or b: y=3/4 + 8.25

Answer:

Yes

Step-by-step explanation:

The tablecloth is large enough as when you multiply 4×8=32 square feet. Thus meaning a 56 square foot table cloth would be enough.

4×8=32

It's easier to figure it out when both fractions have the same denominator, so let's fix that:

17/40*15/15 is 255/600

8/15*40/40 is 320/600

Notice we are multiplying by a factor of 1 to get equivalent fractions

So 8/15 is bigger

Hope this helped!

8/15

when you divide it it comes out to be 0.533 repeating

but when you divide 17/40 it comes out to be 0.425

so .5 is larger then .4

The combination is solved and the number of ways of choosing the contestants is 10

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Out of the 7 people in the front row, we need to choose 3 people to be contestants, and we want to count the number of ways that both you and your friend are chosen.

Since we are choosing 3 people, there are 3 positions to be filled. We can think of this as a combination problem, where we need to choose 2 people out of the 5 remaining people in the front row, to fill the two remaining positions after you and your friend are chosen.

The number of ways to choose 2 people out of 5 is given by the combination formula:

C(5, 2) = 5! / (2! (5 - 2)!) = 10

Hence , there are 10 ways to choose you and your friend, and then choose two additional people to fill the remaining positions

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Answer:

1/4  4/16 8/32 16/64

Step-by-step explanation:

Answer:

a simplified fraction is 1/4

Step-by-step explanation:

2/8 (divided by) 2/2= 1/4

Answer:

Step-by-step explanation:

The roots are the values of x that make y=0.

  0 = -16x^2 +4x = -4x(4x -1)

The values of x that make the factors zero are solutions to this equation:

  x = 0

  x = 1/4 . . . . . makes the factor (4x-1) equal to zero

The roots of the equation are x=0 and x=1/4.

__

Since y is height and x is time, when y=0, the frog is on the ground. The roots, then, are the times when the frog is on the ground.

The smaller root is the time when the frog leapt.

The larger root is the time when the frog landed.

The roots of the equation y = -16x² + 4x are x = 0 and x = 1/4,

The given equation y = -16x² + 4x models the height y of the frog as a function of time x in seconds.

To find the roots of this equation when y = 0, we need to solve:

0 = -16x² + 4x

This is a quadratic equation.

Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula.

In this case, factoring is straightforward:

0 = x(-16x + 4)

This gives us two solutions

x=0

x=4/16=1/4

The roots are x = 0 and x = 1/4 seconds.

Interpreting the Roots

The numbers are 37 and -18.

Step-by-step explanation:

Step 1:

Let the numbers be x and y. Given their sum = 19 and difference = 55. Form equations out of it.

⇒ x + y = 19 --------- (1)

⇒ x - y = 55 --------- (2)

Subtract eq(2) from eq(1)

⇒ 2x = 74

⇒ x = 37

Step 2:

Find y.

⇒ y = 19 - x = 19 - 37 = -18

Answer:

x=21

Step-by-step explanation:

Each measurment is multiplied by three, so 7 multiplied by 3 is 21

Answer:75

Step-by-step explanation: 50 + 25

Use the formula c = λν to determine wavelength

299792458=689.46λ

434822.1188=λ

Hope this helped!

Answer:

try different keywords

Step-by-step explanation:

The area under the standard normal curve corresponding to Z > -1.62 is approximately 0.9474.

The question asks for the area under the standard normal curve corresponding to Z > -1.62. Using standard normal distribution tables, we can find this area by finding the area corresponding to Z = -1.62 and subtracting it from 1. Since standard normal distribution tables provide the area to the left of the Z-score, we need to subtract the area from 1 to get the area to the right of the Z-score.

By looking up Z = -1.62 in the standard normal distribution table, we find the area to the left (or below) the Z-score is approximately 0.0526. Therefore, the area to the right (or above) the Z-score is approximately 1 - 0.0526 = 0.9474.

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Answer: 74beats/per minute

Step-by-step explanation:

Divide 518 by 7

The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

    quadrilateral is 360°

- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = [tex]\frac{40}{100}[/tex] × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = [tex]\frac{12.5}{100}[/tex] × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = [tex]\frac{25}{100}[/tex] × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

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Answer:

x^2-25

Step-by-step explanation:

rewrite 25 as 5^2

x^2-5^2

since both terms are perfect squares, factor using the difference of square s formula, a^2-b^2=(a+b)(a-b) where a=x and b=5

(x+5)(x-5)

plz mark me as brainliest if this helped :)

Answer:

[tex]\[(x+5)*(x-5)\][/tex]

Step-by-step explanation:

Given polynomial expression is [tex]\[x^{2}-25\][/tex]

[tex]\[=> x^{2}-5^{2}\][/tex]

This is of the form [tex]\[a^{2}-b^{2}\][/tex]

An expression of this form can be factorized as [tex]\[(a+b)*(a-b)\][/tex]

Here, a = x and b = 5.

Hence the factorized form of the given polynomial expression can be represented as the following product:

[tex]\[(x+5)*(x-5)\][/tex]