Please help me with this word problem!

[tex]\bf r=\sqrt{\cfrac{A}{P}}-1~~ \begin{cases} P=425\\ A=470 \end{cases}\implies r=\sqrt{\cfrac{470}{425}}-1\implies r=\sqrt{\cfrac{94}{85}}-1 \\\\\\ r\approx 0.051609\implies \stackrel{\textit{converting it to percentage}}{r\approx 0.051609\cdot 100}\implies r\approx 5.1609\implies \stackrel{\textit{rounded up}}{r=5.2}[/tex]

Answer:

It is not likely that you will choose a person whose favorite color is red.

It is most likely that you will choose a person whose favorite color is something other than red.

Step-by-step explanation:

The probability that you choose a student who picked red as his or her favorite color is 45%, but the probability that you choose a person who picked another color is 55%.

It is not likely that you will choose a person whose favorite color is red. It is most likely that you will choose a person whose favorite color is blue. The probability that you choose a student who picked red as his or her favorite color is 10%, but the probability that you chose a person who picked another color is 90%.

To solve this problem, we need to analyze the given percentages of students who chose each color as their favorite. The percentages provided are as follows:

- Red: 10%

- Blue: 40%

- Green: 20%

- Yellow: 15%

- Purple: 10%

- Orange: 5%

The total probability of all possible outcomes must equal 100%. In this case, the sum of the percentages of all colors equals 100%, confirming that the probabilities are correctly distributed among the color choices.

Now, let's address the first part of the question: It is/is not likely that you will choose a person whose favorite color is red. Since red has the lowest percentage (10%), it is the least likely choice among all the colors. Therefore, it is not likely that you will choose a person whose favorite color is red.

Next, we determine which color is most likely to be chosen. Since blue has the highest percentage (40%), it is the most likely choice. Thus, it is most likely that you will choose a person whose favorite color is blue.

To calculate the probability of choosing a student who picked red as their favorite color, we use the given percentage for red, which is 10%. This is the probability of randomly selecting a student who prefers red.

Finally, to find the probability of choosing a person who picked any color other than red, we subtract the probability of choosing red from the total probability (100%). This gives us 100% - 10% = 90%. Therefore, the probability that you chose a person who picked another color is 90%.

In conclusion, the probability of choosing a student who likes red is 10%, and the probability of choosing a student who likes any other color is 90%. The most likely color to be chosen is blue.

The answer is:

It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.

To find how many seconds Ella took to do a push-up and a sit-up we must write two equations using the given information.

Let be "x" the time needed to push-ups and "y" be the time needed to do sit-ups.

So, writing the equations we have:

First equation,

If she can do 13 push-ups and 7 sit-ups in 60 seconds, we have:

[tex]13x+7y=60[/tex]

Second equation,

If she can do 13 push-ups and 19 sit-ups in 96 seconds, we have:

[tex]13x+19y=96[/tex]

Now, creating a system of equations, and using the reduction method to solve it, we have:

[tex]\left \{ {{13x+7y=60} \atop {13x+19y=96}} \right.[/tex]

Multiplying the first equation by -1, we have:

[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right.[/tex]

[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right\\\\12y=36\\\\y=\frac{36}{12}=3[/tex]

Then, substituting "y" into the first equation, we have:

[tex]13x+7y=60[/tex]

[tex]13x+7(3)=60[/tex]

[tex]13x+21=60[/tex]

[tex]13x=60-21=39[/tex]

[tex]x=\frac{39}{13}=3[/tex]

Hence, we have that It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.

Have a nice day!

Answer:

200 divided by 1700=.1176

move decimal two to the right =11.76% or 12% commission

The y axis? As the graph is symmetrical on either side of it

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\bf \left( -\cfrac{5}{2(3)}~~-2-\cfrac{5^2}{4(3)} \right)\implies \left(-\cfrac{5}{6}~~,~~-2-\cfrac{25}{12} \right)\implies \stackrel{\stackrel{axis~\hfill }{coordinate\qquad }}{\left(-\cfrac{5}{6}~~,~~-\cfrac{49}{12} \right)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=-\cfrac{5}{6}}~\hfill[/tex]

let's notice, that the squared variable is the "x", and therefore this is a vertical parabola whose axis of symmetry is the vertical line equation of the x-coordinate of its vertex.

Answer:   100%

Step-by-step explanation:

100 + 80 + 80+ 80 = 340  (total scores of 4 tests)

340 divided by the number of tests 4 = 85

George would need to score 100% on his next test to bring his test average from 80 to 85.

Using the law of tangents:

Tan(angle) = Opposite leg / Adjacent leg

Tan(30) = b / 8

Rewrite to solve for b:

b = 8 * tan(30)

The first answer is correct.

Answer:

b = 8 * Tan 30

Step-by-step explanation:

Points to remember

Trigonometric ratio

Tan θ = Opposite side/Adjacent side

From the figure we can see that a right angled triangle ABC

Bc = 8ft, <C = 90° and  <B = 30°

To find the equation of finding the b

We have,

Tan θ = Opposite side/Adjacent side

Tan 30 = AC/BC  = b/8

b = 8 * Tan 30

sin(155)º = sin(180 - 25)º =  sin(25)º

=> B) sin25º

Answer:

The plywood that is closest to three over four-inch thick is thirteen over sixteen inches thick

Step-by-step explanation:

we have

3/4 in

Verify each value

case A) 13/16 in

we know that

3/4 in=12/16 in ----> multiply by (4/4)

Find the difference

13/16-12/16=1/16 in

case B) 11/32 in

we know that

3/4 in=24/32 in ----> multiply by (8/8)

Find the difference

24/32-11/32==13/32 in

case C) 1/2 in

we know that

1/2 in=2/4 in ----> multiply by (2/2)

Find the difference

3/4-2/4=1/4 in

case D) 3/8 in

we know that

3/4 in=6/8 in ----> multiply by (2/2)

Find the difference

6/8-3/8=3/8 in

Compare the values of the difference and find the less value

we have

case A) 1/16=2/32 in

case B) 13/32 in

case C) 1/4=8/32 in

case D) 3/8=12/32 in

The less value is case A) 2/32 in

therefore

The plywood that is closest to three over four-inch thick is thirteen over sixteen inches thick

Answer:

[tex]\boxed{\text{a. 111.1 m; b. 56 575 m}^{3}}[/tex]

Step-by-step explanation:

a. Height

(i) Height of prism

The height of the prism is 70 m.

(ii) Height of pyramid

Consider the red triangle in the diagram.

The diagonal of the square base is given by

d² = a² + a² = 2a²

d² = 2(26)² = 2 ×676 = 1352 m²

d = √1352 = 36.77 m

The base of the triangle R is

R = ½d = ½ × 36.77 = 18.38 m

Now,

h² + R² = e²

h² + 18.38² = 45²

h² + 338  = 2025  

h² = 1687

h = 41.07 m

(iii) Total height

Total height = height of prism + height of pyramid = 70 + 41.07 = 111.1 m

b. Volume

(i) Volume of prism

V = lwh

V = 70 × 26 × 26 = 47 320 m³

(ii) Volume of pyramid

The formula for the volume of a square pyramid is  

V = ⅓a²h

V = ⅓ × 26² × 41.07 = 9255 m³

(iii) Total volume

Total volume = volume of prism + volume of pyramid

V = 47320 + 9255 = 56 575 m³

The total height of the building is [tex]\boxed{\textbf{111.1 m}}[/tex]

The total volume of the building is [tex]\boxed{\textbf{56 575 m}^{3}}[/tex]

Answer:

112.5 km

Step-by-step explanation:

The lorry needed 45 minutes to travel the remaining 0.4 of the journey and was traveling at 60 km/hr.

First, convert minutes to hours:

45 min × (1 hr / 60 min) = 0.75 hr

Now use distance equation:

distance = rate × time

0.4d = 60 × 0.75

d = 112.5

The distance between the towns is 112.5 km.

they are all the same???

Answer:

a

Step-by-step explanation:

Hello There, the answer is C. 55%!

To solve, get the total (11 boys + 9 girls = 20 total students). Put the number of boys over the total, representing it as a fraction, 11/20. Now convert this t  a precent by dividing 11 by 20 and multiplying the result by 100.

11 divided by 20 = 0.55

0.55 times 100 = 55%

So, 55% is your final answer. I hope this helps and have a great day!

The percent of the class that are boys is Option(C) 55% .

It is given that a class had 11 boys and 9 girls in it.

Thus the total number of students in the class is = (11 + 9) = 20

The percent of boys is given by -

(Number of boys / Total number of students) * 100 %

⇒ Percent of boys = 11/20 * 100 %

∴  Percent of boys = 55%

Therefore, the percent of the class that are boys is Option(C) 55% .

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Answer:

[tex]\boxed{\text{15.8 cords}}[/tex]

Step-by-step explanation:

Step 1. Calculate the volume of the room

V = lwh =  5 yd × 5 yd × 3 yd = 75 yd³

Step 2. Convert cubic yards to cubic feet

3 ft = 1 yd

[tex]V = \text{75 yd}^{3} \times \left(\dfrac{\text{3 ft}}{\text{1 yd}} \right)^{3} = \text{2025 ft}^{3}[/tex]

Step 3. Convert cubic feet to cords

128 ft³ = 1 cord

[tex]V = \text{2025 ft}^{3} \times \dfrac{\text{1 cord}}{\text{ 128 ft}^{3}} = \textbf{15.8 cords}\\\\\text{You could fit }\boxed{\textbf{15.8 cords}} \text{ of wood into the room.}[/tex]

Answer:

Slope = 6

Step-by-step explanation:

Taking two points on line l to find its slope: (0, 3) and (6, 2).

Slope of line l = [tex]\frac{3-2}{0-6} =-\frac{1}{6}[/tex]

We know that the slope of a line which is perpendicular to another line has a slope which is a negative reciprocal of the other line.

Therefore, the slope of the line which is perpendicular to line l will have a slope of 6.

Answer: 6

Step-by-step explanation: I just got it right lol

Answer:

circle

Step-by-step explanation:

The equation

x² + y² = r²

Represents a circle centred at the origin with radius r

x² + y² = 25 ← is in this form and

is a circle centre (0, 0) with r = 5

ANSWER

circle

EXPLANATION

The given equation is

[tex] {x}^{2} + {y}^{2} = 25[/tex]

To determine the type of conic, we analyze the coefficient and sign of the quadratic terms.

If the coefficient of the quadratic terms are equal and have the same sign,then the conic is a circle.

If the coefficient of the quadratic terms are equal and have opposite signs,then the conic is a hyperbola.

If the coefficient of the quadratic terms are not equal and have the same sign,then the conic is an ellipse.

Since the coefficients are all 1 and the signs are positive, the given conic is a circle.

Hi, it should be written as y = mx + b.

The answer should be:

y = (3/2)r - (5/2)

Answer:

[tex]a_n=78-6n[/tex]

[tex]a_{14}=78-6(14)[/tex]

Step-by-step explanation:

To solve this, we are using the formula for the nth term of an arithmetic progression:

[tex]a_n=a_1+(n-1)d[/tex]

where

[tex]a_1[/tex] is the first term of the progression

[tex]d[/tex] is the difference

[tex]n[/tex] is position of the term in the progression

We know for our problem that the bottom row contains 72 bricks, so [tex]a_1=72[/tex]. We also know that each row above decreases by 6 bricks, so the difference is -6 ([tex]d=-6[/tex]).

Replacing the values:

[tex]a_n=72+(n-1)(-6)[/tex]

[tex]a_n=72-6n+6[/tex]

[tex]a_n=72-6n+6[/tex]

[tex]a_n=78-6n[/tex]

Where [tex]n[/tex] is the row

Since we want to now the number of bricks in the 14th row, [tex]n=14[/tex]:

[tex]a_{14}=78-6(14)[/tex]

[tex]a_{14}=78-84[/tex]

[tex]a_{14}=-6[/tex]

Since bricks can't be negative, we can conclude that this is an impossible real-life situation.

Answer:

The value of x is 1

Step-by-step explanation:

Remember that

The radius of the circle is perpendicular to the lines that are tangent to the circle

Applying the Pythagoras Theorem

[tex]6.1^{2}+(10x)^{2}=6.1^{2}+(9x+1)^{2}[/tex]

Simplify

[tex](10x)^{2}=(9x+1)^{2}[/tex]

[tex]10x=(9x+1)\\ \\ 10x-9x=1\\ \\x=1[/tex]

Answer:

x = 114

Step-by-step explanation:

Answer:

92.4% or 73/79

Step-by-step explanation:

You have to add up all the individual songs, which is 158. Then add up the number of songs that aren't classical, which is 146. Then divide 146 by 158 which gives you your answer.

To find the probability that a randomly selected song from Suki's playlist is not a classical song, follow these steps:
1. **Find the total number of songs**: Add up the number of rock songs, dance songs, and classical songs to get the total number of songs in Suki's playlist.
  Total number of songs = Number of rock songs + Number of dance songs + Number of classical songs
  Total number of songs = 54 rock songs + 92 dance songs + 12 classical songs
  Total number of songs = 158 songs
2. **Calculate the probability of selecting a classical song**: To calculate the probability of selecting a classical song, divide the number of classical songs by the total number of songs.
  Probability of selecting a classical song = Number of classical songs / Total number of songs
  Probability of selecting a classical song = 12 / 158
3. **Calculate the probability of not selecting a classical song**: The probability of not selecting a classical song is the complement of the probability of selecting a classical song. To get this probability, subtract the probability of selecting a classical song from 1.
  Probability of not selecting a classical song = 1 - Probability of selecting a classical song
  Probability of not selecting a classical song = 1 - (12 / 158)
4. **Compute the final probability**: Perform the subtraction from step 3 to get the final probability.
  Probability of not selecting a classical song = 1 - (12 / 158)
  Probability of not selecting a classical song ≈ 0.92405 (rounded to five decimal places)
Therefore, when Suki's music player randomly selects a song, the probability that the song will not be a classical song is approximately 0.92405, or 92.405%.

Answer:

15. h⁻¹ (x) = 5x-6/2

16. (g.f)x = 4x^2 -2x -1

Step-by-step explanation:

15. Find Inverse of h(x) =  2x+6 /5

Let y = 2x+6/5 we need to find value of x

Multiplying both sides with 5

5y = 2x+6

Adding -6 on both sides

5y -6 = 2x

Dividing both sides by 2

5y-6/2 = x

Now replace y with x our answer will be:

h⁻¹ (x) = 5x-6/2

16. f(x) =2x-1 and g(x) = x^2 -2 find (g.f)x

(g.f)x can be written as: g(f(x))

We know f(x) = 2x-1 so, put value of f(x) into x of g(x).

Putting values we get:

(g.f)x = g(f(x))= (2x-1)^2 -2

                   = 4x^2 -2x +1 -2

                   = 4x^2 -2x -1

so, (g.f)x = 4x^2 -2x -1

your answer would be B. 5

Answer:

5

Step-by-step explanation:

Given a matrix [tex]\left[\begin{array}{ccc}a&b&\\c&d&\\\end{array}\right][/tex]

Then the determinant = ad - bc

For the matrix [tex]\left[\begin{array}{ccc}2&3&\\1&4&\\\end{array}\right][/tex]

determinant = (2 × 4) - (3 × 1) = 8 - 3 = 5

Answer:

Single Solution of 3.2 (16/5)

Step-by-step explanation:

3x = 8x -16 <--- I combine like terms.

-5x = -16

-16/-5 = x

x = 3.2

BTW Negative times a Negative equals a positive.

To find the solutions to the equation -6y + 13 + 9y = 8y - 3, combine like terms, isolate the variable, and solve for y. The equation has one solution, which is y = 3.2.

To find the solutions to the equation -6y + 13 + 9y = 8y - 3, we need to simplify the equation and solve for y. First, combine like terms by adding the y terms on the left side and the constant terms on the right side. This gives us 3y + 13 = 8y - 3. Next, subtract 3y from both sides to isolate the variable term on the right side. This gives us 13 = 5y - 3. Then, add 3 to both sides to isolate the variable term. This gives us 16 = 5y. Finally, divide both sides by 5 to solve for y. This gives us y = 16/5 or y = 3.2.

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Answer:

x=11

Step-by-step explanation:

y= 1/4x

5x-8y=33

5x-8(1/4x)=33

x=11

Answer:

11

Step-by-step explanation:

Given that ,

⇒ y = 1/4x and

⇒ 5x - 8y = 33

We can write 1st equation as ,

⇒ 4y = x

Put x = 4y in 2nd Equation ,

⇒ 5*4y - 8y = 33

⇒ 20y - 8y = 33

⇒ 12y = 33

⇒ y = 33/12

Put this in 1st ,

⇒ 33/12 = 1/4 x

⇒ x = 33/12 × 4

⇒ x = 33/3

⇒ x = 11 .

Answer:

5 rolls

Step-by-step explanation:

If the perimeter around the square footage of the ceiling is equal to 12 + 12 + 12 + 12 = 48, even though the number is 48, in order to have all of the footage covered, Katie would need to buy (at least) 5 rolls.

Hope I helped and please give me brainliest!

Let A = adult and s = student.

Multiply the cost of an adult ticket by number of adults: 13a.

Do the same for students: 9s

Add those together to get total money made:

13a + 9s = $2130

Then add the number of each tickets sold to get total sold:

a +s = 210 tickets.

13a + 9s = $2130, a +s = 210

The last answer is correct.

Answer:

x=22

Step-by-step explanation:

2(x+5)=3(x-4)

2x+10=3x-12

-x=-22

x=22

Step 1: Distribute the numbers outside the parentheses to each number inside the parentheses

(2 * x) + (2 * 5) = (3 * x) + (-4 * 3)

2x + 10 = 3x - 12

Step 2: Combine like terms

2x goes with 3x. To do this subtract 2x to both sides (subtraction is the opposite of addition)

(2x - 2x) + 10 = (3x - 2x) - 12

0 + 10 = x - 12

10 = x - 12

10 goes with -12. To do this add 12 to both sides (addition is the opposite of subtraction)

10 + 12 = x + (-12 + 12)

22 = x + 0

22 = x

Check:

2(22 + 5) = 3(22 - 4)

2(27) = 3(18)

54 = 54

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The answer is 42%.

Step-by-step explanation:

If we make a Venn diagram, we get 12% in the middle, meaning that 12% of people chose both coffee and juice.

54% is the total amount of people who chose coffee, including the % of people who chose coffee as well as juice.

So, we need to subtract 12% from 54%, therefore giving us 42%.

The percentage of people choose coffee only is 42%.

We have given that,

At a breakfast buffet, 54% of people choose coffee for their beverage while 16% choose juice. Also, 12% choose both coffee and juice.

If we make a Venn diagram, we get 12% in the middle, meaning that 12% of people chose both coffee and juice.

This free percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.

54% is the total amount of people who chose coffee, including the % of people who chose coffee as well as juice.

So, we need to subtract 12% from 54%, therefore giving us 42%.

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median because there is and outlier

Final answer:

The best measure of spread for the first period is the range, which is found by subtracting the smallest value from the largest value in the dataset.

Explanation:

The best measure of spread for the first period is the range.

The range is found by subtracting the smallest value from the largest value in a dataset. For the first period, the smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.

The range is a good measure of spread because it gives the distance between the minimum and maximum values, providing an idea of how much the data values vary.