Sebastian swam laps every day in the community swimming pool. He swam an hour each day, 5 days each week, for 12 weeks. In
that time, he swam 1,800 laps. What was his average rate in laps per hour?

Answer: 6 children

Step-by-step explanation:

Given:

Children - 24

Groups - 4

Number of children per group - x

Solve:

24 ÷ 4 = x

x = 6

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In 1st month let she exercised h hours

in second month she exercised h+4 hours

in third month she exercised h+4-3=h+1 hours

Now

Answer:

Let's say the unknown variable is h

In 1st month let she exercised h hours

in the 2nd month she exercised h+4 hours

in the 3rd month she exercised h+4-3=h+1 hours

Now, to display the sequence:

h+h+4+h+1=101

3h+5=101

3h=96

h=32hours

uhm i dont know sorry but i can't help you

The equation on the graph is shown (I really hope this helps)

Equation of the translated graph is;

⇒y = cos(x - 30) - 1

What is equation of translated graph?

Equation of the translated graph is solved as;

g(x) = f(x + k) + C

Where, k and C are points.

Given that;

The equation is;

y = cos x

Since, Graph of function y = cosx is translated by (30, -1).

So, Equation of translated graph will be;

y = cos(x - 30) - 1

Hence, The equation of the translated graph will be;

⇒ y = cos(x - 30) - 1

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Answer:

all rhombuses are parallelograms, all trapezoids are quadrilaterals 

Step-by-step explanation:

rhombuses have all equal sides, 2 sets of parallel lines and are a diamond shape. a quadrilateral is a shape with 4 sides (quad means 4) therefore, all rhombuses are parallelograms. we know that all trapezoids have 4 sides, so we can conclude that all trapezoids are quadrilaterals i hope this helped because i know that end of year tests are super hard.

Answer:

18

Step-by-step explanation:

Here,

given,

a=3 and b=6

Then

4a+b=?

Put respective values on 4a+b

4*3+6

=12+6

=18

Answer:

18

Step-by-step explanation:

step 1:4a+b=

step 2:(4x3)+6=

step 3:12+6=

answer=18

hope this helps

Answer:

2 5/8 inches

Step-by-step explanation:

There are 2 pieces 5 3/4 inches long.

There is 1 piece 5 1/2 inches long.

There are 4 pieces 5 1/4 inches long.

The seventh longest piece is one of the pieces measuring 5 1/4 inches.

Juan's piece is 1/2 as long as 5 1/4 inches.

1/2 × 5 1/4 inches = 1/2 × 21/4 = 21/8 inches = (16/8 + 5/8) = 2 5/8 inches

Answer:

[tex]5 \leqslant x \leqslant 8[/tex]

Answer:

B. 75%

Step-by-step explanation:

If about a quarter ( 25% ) do like non-fiction, then we know that the rest do not prefer it ( 75% )

75 + 25 = 100

The quotient of the expressions (9.6 x 10⁻⁸) and (3.2 x 10⁴) is 3.0 × 10⁻¹². Then the correct option is D.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The expressions are given below.

(9.6 x 10⁻⁸) and (3.2 x 10⁴)

Then the quotient of the expressions will be

⇒ (9.6 x 10⁻⁸) / (3.2 x 10⁴)

⇒ (3 x 10⁻⁸) / (10⁴)

⇒ 3 x 10⁻⁸ x 10⁻⁴

⇒ 3 x 10⁻⁸⁻⁴

⇒ 3 x 10⁻¹²

Then the correct option is D.

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Answer:

27,032 Rupees

Step-by-step explanation:

$1.09 x 400 = $436

$436 x 62 = 27,032

(Hope this helps and that it's not wrong ^-^)

Answer:

vertex

Step-by-step explanation:

Step-by-step explanation:

profit amount=150000-120000

profit amount=30000

profit %= profit amount/cost price*100

therefore profit percent=30000/120000*100

there for profit %=25%

The percentage of profit will be equal to 25%

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

The profit percentage will be calculated as:-

Profit amount =  150000-120000

Profit amount  =  30000

Profit %= profit amount/cost price*100

Profit percent=30000/120000*100

Profit percentage = 25%

Therefore the percentage of profit will be equal to 25%

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Step-by-step explanation:

If you know, the sine. You must find the cos ratio, using the Pythagorean trig theorem.

Next, you use the half angle identity for sin

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos(a) }{2} } [/tex]

Example.

[tex] \sin( \alpha ) = \frac{ \sqrt{3} }{2} [/tex]

We must find

[tex] \sin( \frac{ \alpha }{2} ) [/tex]

First, use the Pythagorean identity

[tex] \sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1[/tex]

[tex]( \frac{ \sqrt{3} }{2} ) {}^{2} + \cos {}^{2} (a) = 1[/tex]

[tex] \frac{3}{4} + \cos {}^{2} (a) = 1[/tex]

[tex] \cos {}^{2} (a) = \frac{1}{4} [/tex]

[tex] \cos( \alpha ) = \frac{1}{2} [/tex]

Now use the half angle identiy

[tex] \sin( \frac{ \alpha }{2} ) = \sqrt{ \frac{1 - \cos( \alpha ) }{2} } [/tex]

[tex] = \frac{ \sqrt{1 - \frac{1}{2} } }{ \sqrt{2} } [/tex]

[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } [/tex]

[tex] = \frac{ \sqrt{ \frac{1}{2} } }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{ \sqrt{1} }{ \sqrt{4} } = \frac{1}{2} [/tex]

So the answer for our example is 1/2

This shows that the number of quarts she should you buy to stain the wheelchair ramp is 9 quart

This the sum of all the area of the surfaces. The given figures is made of 3 rectangles and 2 triangles

Determine the surface area

TSA = (25*25) + (2 * 5*301/12) + (5*2.08333)

TSa = 625 + 258.33333 + 10.41665

TSA = 893.74995

If a quart of stain covers 100 square feet, the total nuber to buy is given as:

Number to buy = 894/100 = 8.94

This shows that the number of quarts she should you buy to stain the wheelchair ramp is 9 quart

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The measure of the angle B from the isosceles triangle is equal to 28°. (Correct choice: D)

In this problem we have the case of an isosceles triangle, that is, a triangle with two sides of equal length and two angles of same measure. By properties from isosceles triangles, we know that the measures of sides AC and BC are the same and angles B and C are the same.

Then, if we know that AC = AB = 10 and m ∠C = 28°, then the measure of the angle B is equal to 28°.

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The ordered pairs of the equation are

The equation is given as

3x + 8y = 6000

We have x = number of tables

y = number of chairs

When x = 0

3(0) + 8y = 6000

8y = 6000

y = 750

When y = 0

3x + 8(0) = 6000

3x = 6000

x = 2000

The ordered pairs of the products are:

0 table 750 chairs

200 tables, 0 chairs.

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Answer: 63.63  m²

Explanation:

Area of circle:

Here given:

radius: (diameter/2) = (9/2) = 4.5 m

π should be taken as 3.142

So area of circle:

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the area of this circle.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

→ [tex]\bf{Area_{circle}=\pi r^{2}}[/tex]

Notice that we are asked to use 3.142 for [tex]\pi[/tex] (pi).

The radius isn't given to us;  what we have instead is...the diameter.

To find the radius, we divide the diameter by 2.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{\bf{To\;find\;the\;radius,\;we\;divide\;the\;diameter\;by\;2}}[/tex]

Thus, the radius is

[tex]\bf{9\div2=4.5}[/tex]

Now substitute the values (3.142 for pi and 4.5 for r):

[tex]\bf{A=3.142\times4.5^{2} }[/tex]

Simplifying,

[tex]\bf{A=3.142\times20.25}[/tex]

Simplifying,

[tex]\bf{A=63.6255\:m}[/tex]

Rounding to 2 decimal places (D.P.):

[tex]\bf{A=63.63\:m}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

~Just a smiley person helping fellow students :)

There are 11 elements are in (A U B)

The given parameters are:

n(A) = 4

n(B) = 7

The number of elements in (A U B) is calculated using:

n(A U B) = n(A) +n(B) - n(A U B)

Given that the sets have distincts elements, we have:

n(A U B) = 4 + 7 - 0

Evaluate

n(A U B) = 11

Hence, there are 11 elements are in (A U B)

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Answer: There are 11 elements are in (A U B)

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Find the value of x and the measure of angleMNQ.

3x − 11°62°

The value of x is

90

° and the measure of angleMNQ is

180

°.

A ratio shows us the number of times a number contains another number. Caitlin is right.

A ratio shows us the number of times a number contains another number.

The ratio of the ages of Mandy and Sandy is 2:5. Therefore, the ratio will be,

M/S = 2/5

M = 2S/5

After 8 years, their ages will be in the ratio 1:2, therefore,

(M+8)/(S+8) = 1/2

2M + 16 = S + 8

2M - S = -16 + 8

Substitute the value of M,

2(2S/5) - S = -8

-0.2S = -8

S = 40

Now, if we substitute the value of S in the first ratio,

M/S = 2/5

M/40 = 2/5

M = 16

Now, if we take the difference in their ages the difference will be 24(40-16).

Since the difference is 24, we can conclude that Caitlin is right.

Hence, Caitlin is right.

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Answer:

32 times

Step-by-step explanation:

the probability in getting a certain number is you first find out the chance of rolling one side on a die. There are six sides, and there is two numbers on it you want a 3 and a 1. so you would get 2/6 would be the fraction of what you what most likely get, so you would multiply 95 by 2/6 you get the correct answer

The ratio of adults to children at a party is 3:5. There are 72 people at the party. Find out number of children.

In this question we are provided with the ratio of adult and children 3 : 5 respectively. It is given that 72 people are there at the party. We are asked to calculate number of children.

We are asked to calculate number of children

Let us assume number of adults and children as 3x and 5x

It is given that total number of people are 72.

According To Question

3x + 5x = 72

→ 8x = 72

→ x = 72/8 = 9

x = 9

Adults = 3x = 3 × 9 = 27 people

Children = 5x = 5 × 9 = 45 people

By using the triangular inequality, we conclude that the other side must measure more than 3 inches and less than 13 inches.

Remember that the triangular inequality says that the sum of any two sides on a triangle is larger than the other side of the triangle.

If we define the missing side of the triangle as x, then we must have:

5 + x > 8

8 + x > 5

8 + 5 > x

From the third inequality we get the upper bound:

13 > x.

From the first inequality we get the lower bound:

x > 8 - 5 = 3

Then:

3 < x < 13

This means that the other side of the triangle must measure more than 3 inches and less than 13 inches.

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[tex]\sf Sine \ Rue : \ \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

Given following:

Solve for b (distance between school and mall):

[tex]\dashrightarrow \sf \dfrac{\sin 56}{38} = \dfrac{\sin 77}{b}[/tex]

[tex]\dashrightarrow \sf b= \dfrac{38\sin 77}{\sin 56}[/tex]

[tex]\dashrightarrow \sf b= 44.6615 \quad \approx \quad 45[/tex]

Answer:

Marked price: Rs. 4875

Cost price: Rs. 3750

Explanation:

(i) Cost price: 100%

(ii) Marked price: (100% + 30%) = 130%

(i) Let the cost price be p

(ii)  Marked price: 130% × p = 1.3p

Given, 20% discount then sold at 80%

Discount price: (130% × 80%) × p = 1.04p - discounted price

Gain price: 1.04p - p = 0.04p

Cost price:

0.04p = 150

p = 150/0.04 = 3750 ← This is the cost price.

Marked price:

1.3p  =  1.3(3750) = Rs. 4875

Answer:

[tex]x \: = \: \boxed{ \bold{ - 4 }}\: \: \text{or} \: \: x \: = \: \boxed{ \bold{ 8}}[/tex]

Step-by-step explanation:

[tex](x \: - \: 2 {)}^{2} \: + \: 2 \: = \: 38[/tex]

[tex] {x}^{2} \: - \: 4x \: + \: 4 \: + \: 2 \: = \: 38[/tex]

[tex] {x}^{2} \: - \: 4x \: + \: 6 \: = \: 38[/tex]

[tex] {x}^{2} \: - \: 4x \: + \: 6 \: - \: 38 \: = \: 0[/tex]

[tex] {x}^{2} \: + \: 4x \: - \: 8x \: - \: 32 \: = \: 0[/tex]

[tex]x \: \times \: (x \: + \: 4) \: - \: 8(x \: + \: 4) \: = \: 0[/tex]

[tex](x \: + \: 4) \: \times \: (x \: - \: 8) \: = \: 0[/tex]

[tex]x \: + \: 4 \: = \: 0 \\ x \: - \: 8 \: = \: 0[/tex]

[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]

[tex]x \: = \: - 4 \\ x \: = \: 8[/tex]

Answer: x (x - 1)

Step-by-step explanation:

[tex]2x^{2} - x^{2} -x[/tex]

[tex]x^{2} -x[/tex]

x (x - 1)