Jack wants to know how much water a sphere can hold with a diameter of 16 cm. Find the volume. Use 3.14 for pi.

We're given:

Let a represent the number of children who swam.

Let b represent the number of adults who swam.

Because we've set two variables, we need two equations to be able to find the answers.

One of the equations will regard price while the other will regard the number of people, as those are the two things given in the question.

Number of people:

[tex]a+b=478[/tex]

Price:

[tex]1.75a+2.25b=975[/tex]

We can solve this question using substitution, where we plug one equation into the other.

Isolate a in the first equation:

[tex]a+b=478\\a=478-b[/tex]

Plug the first equation into the second equation by replacing a:

[tex]1.75a+2.25b=975\\1.75(478-b)+2.25b=975[/tex]

Solve for b:

[tex]1.75(478-b)+2.25b=975[/tex]

⇒ Open up the parentheses:

[tex]836.5-1.75b+2.25b=975\\836.5-0.5b=975[/tex]

⇒ Subtract 836.5 from both sides to isolate b:

[tex]-0.5b=138.5[/tex]

⇒ Divide both sides by -0.5:

[tex]b=277[/tex]

Solve for a:

[tex]a+b=478[/tex]

⇒ Replace b with 277:

[tex]a+277=478\\a=201[/tex]

There were 201 children and 277 children at the pool that day.

Answer:

brody worked 58 hrs

Answer:

A: [tex]12x+15y=60[/tex] B: [tex]12x+15y\leq 60[/tex]

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

substitute 510 with 1000 and multiply by 10 to get 10,000

Answer:

[tex]a)\ \frac{3}{20}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} \div 5\\\\\frac{3}{4}*\frac{1}{5}\\\\\frac{3}{20}[/tex]

Hope this helps!

Your answer is 3/20

3/4 divided by 5 is 3/20

Hope this helps

Answer:

y≤3

Step-by-step explanation:

5y+4≤22−y

Step 1: Simplify both sides of the inequality.

5y+4≤−y+22

Step 2: Add y to both sides.

5y+4+y≤−y+22+y

6y+4≤22

Step 3: Subtract 4 from both sides.

6y+4−4≤22−4

6y≤18

Step 4: Divide both sides by 6.

6y/6≤18/6

y≤3

Hey there!

Let's solve your inequality step-by-step.

[tex]\fbox{5y+4≤22−y}[/tex]

Step 1: Simplify both sides of the inequality.

[tex]\fbox{5y+4≤−y+22}[/tex]

Step 2: Add y to both sides.

[tex]\fbox{5y+4+y≤−y+22+y}[/tex]

[tex]\fbox{6y+4≤22}[/tex]

Step 3: Subtract 4 from both sides.

[tex]\fbox{6y+4−4≤22−4}[/tex]

[tex]\fbox{6y≤18}[/tex]

Step 4: Divide both sides by 6.

[tex]\fbox{6y/6 ≤ 18/6}[/tex]

[tex]\fbox{y≤3}[/tex]

Answer:

[tex]\fbox{y≤3}[/tex]

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Answer:

[tex]4^{2}[/tex]

Step-by-step explanation:

so when you multiply two numbers with the same constant, and different exponents, just add the exponents!

so it is 5 - 3 = 2

so its [tex]4^{2}[/tex]

Answer:

A) 4²

Step-by-step explanation:

[tex](4^5)(4^{-3})\\\\4(^{5-3})\\\\4^2\\\\16[/tex]

Hope this helps!

1/4 of cookies

Cost of one cookies =2.95

Total cost

Answer:

$41.3

Step-by-step explanation:

Each cookie costs,

→ a = $2.95

Lemon cookies (1/4) of 56 cookies is,

→ b = 1/4 × 56

→ b = 56/4

→ [ b = 14 lemon cookies ]

The money made if she sell the lemon cookies alone will be,

→ a × b

→ 2.95 × 14

→ $41.3

Hence, the money made is $41.3.

Answer:

Step-by-step explanation:

The radius of cone = 9 cm

Step-by-step explanation:

Formula : Volume of a cone =  , where r= radius , h= height of the cone.

Given: Volume = 1,017.36 cubic centimeters

h = 12 centimeters

Substitute these values in formula , we get

Hence, the radius of cone = 9 cm

Answer:

Explanation:

11x5=55

11x13=143

5x13/2=32.5

55+32.5+143=230.5

230x185 5/8 m²=42 693.75 m2

230x219 3/8 m²=50 456.25 m2

230x247 1/2 m²=56 925 m2

230x292 1/2 m²=67 275 m2

I DO NOT 100% KNOW IF THESE ARE CORRECT

Answer:

247 1/2 m 2

Step-by-step explanation:

have  a good day

Answer:

Step-by-step explanation:

Since the dilation is centered at the origin, we can multiply each of the coordinates by the scale factor. This gives us that D'(36,0).

Answer:

Step-by-step explanation:

400

Answer:

3,969

Step-by-step explanation:

If n is a perfect square, then the last digits of the prefect square must be 3 or 7  because n ends in 9.

Since n is 4 digits the number can only land between 33 and 97.

(33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, 87, 93, 97)

squared- 1089, 1369, 1849, 2209, 2809, 3249, 3969, 4486, 5329, 5939, 6889, 7569, 8649, 9409

possible answers- 2209, 3969, 4486, 5939, 6889, 9409

2+2+0+9 = 13

3+9+6+9 = 27

4+4+8+6 = 22

5+9+3+9 = 26

6+8+8+9 = 31

9+4+0+9 = 22

Answer:

0

Step-by-step explanation:

So,0= the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.

Hence, the values for different conditions were calculated with the help of trigonometric functions.

Part A

θ=kπ

Where k is an integer k=0,1,2..

Part B

θ=[tex]k\frac{\pi }{2}[/tex]

Where k is an integer k=0,1,2..

Part C

θ=kπ

Where k is an integer k=0,1,2..

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths

Part A

Given that,

f(x)=2sinθ+[tex]\sqrt{2}[/tex]

Non compressed length = [tex]\sqrt{2}[/tex]

Then

2sinθ+[tex]\sqrt{2}[/tex]=[tex]\sqrt{2}[/tex]

2sinθ=0

sinθ=0

Therefore θ is the integer multiple of π

θ=kπ

Where k is an integer k=0,1,2..

Part B

Here angle is doubled

Then,

2sin2θ+[tex]\sqrt{2}[/tex]=[tex]\sqrt{2}[/tex]

2sin2θ=0

sin2θ=0

Here θ will be the integer multiple of [tex]\frac{\pi }{2}[/tex]

θ=[tex]k\frac{\pi }{2}[/tex]

Where k is an integer k=0,1,2..

Part C

g(x)=1-[tex]cos^{2}[/tex]θ+[tex]\sqrt{2}[/tex]

Here

f(x)=g(x)

2sinθ+[tex]\sqrt{2}[/tex]=1-[tex]cos^{2}[/tex]θ+[tex]\sqrt{2}[/tex]

2sinθ=1-[tex]cos^{2}[/tex]θ

we know that [tex]1-cos^{2}[/tex]θ=[tex]sin^{2}[/tex]θ

2sinθ=[tex]sin^{2}[/tex]θ

sinθ=0

Therefore θ is the integer multiple of π

θ=kπ

Where k is an integer k=0,1,2..

Hence, we have solved that

Part A

θ=kπ

Where k is an integer k=0,1,2..

Part B

θ=[tex]k\frac{\pi }{2}[/tex]

Where k is an integer k=0,1,2..

Part C

θ=kπ

Where k is an integer k=0,1,2..

Learn more about Trigonometric functions here

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Answer:

1/3

Step-by-step explanation:

add all of the totals including the missing pair

we now have 24

7+1 is 8

24 minus 8 is 16

24 can be split into 2 groups of 8

and we have 2/3 left. which makes our solution 1/3

Answer:

Given that Elena is currently e years  old and Katie is k years old. Now, nine years ago, Katie was twice as old as Elena was.

So, k - 9 = 2(e - 9)

⇒ k - 2e + 9 = 0 .............. (1)

And, in four years, Elena will be as old as Katie is now.

So, k = e + 4

⇒ k - e - 4 = 0 ............... (2)

Therefore, the equations (1) and (2) matches the conditions. (Answer)

Answer:

B. $1.34

Step-by-step explanation:

5.36 ÷ 4

=536×1/4×1/100

=536/400

=1.34

Answer:

145

Step-by-step explanation:

angle 2 = angle 3

=>          angle 3 = 35

now, we have

=>         35+angle 5 = 180

=>         angle 5 = 180 - 35

=>         angle 5  = 145

Answer:

145°

Step-by-step explanation:

line m || line (Given)

[tex]m\angle 2 = 35\degree ......(1)[/tex] (Given)

[tex]m\angle 3 = m\angle 2 ......(2)[/tex] (vertical angles)

From equations (1) and (2)

[tex]\implies m\angle 3 = 35\degree[/tex]

[tex]m\angle 3 +m\angle 5 = 180\degree[/tex] (interior angles on the same side of transversal)

[tex] \implies 35\degree +m\angle 5 = 180\degree[/tex]

[tex] \implies m\angle 5 = 180\degree-35\degree[/tex]

[tex] \implies m\angle 5 = 145\degree[/tex]

Answer:

-4

Step-by-step explanation:

vertical opposite angles are equal

110=x+114

=-4+114

Answer:

-4 the answer is -4

Answer:

$43 million

Step-by-step explanation:

15.4 million = 0.36 (T)

15,400,000 / 0.36 = T

42,777,777.78 = T

$42.8 million ≈ $43 million (rounded)

The final answer rounded to the nearest million is $43 million. This makes sense since $15.4 was only 36% of this total. Checking our math, 36% of $43 million is $15.4 million!

Hope this helps :)

Answer:

These would be complementary angles.

Step-by-step explanation:

Complementary angles are angles that add up to 90 degrees.

supplementary angles are when two angles sum up to 180 degrees.

∠x and ∠y are supplementary angles

===============

Answer:

64°

Step-by-step explanation:

Supplementary angles are two angles that add up to 180°.

∠x + ∠y = 180° <== substitute 116° for ∠y

∠x + 116° = 180° <== subtract 116 from both sides

     - 116    - 116

∠x = 64° <== measure of ∠x

Therefore, the measure of ∠x is 64°

Hope this helps!

4.44/37= 0.12

1.80/15= 0.12

3.12/26= 0.12

3.60/30= 0.12

2.16/18= 0.12

1. She donates 12% of her income to charity

2. The quantity, d, would be the better choice for the dependent variable (y) the cost of the donation, depends on her income, if her income increases, the amount donated would increase.

3. d = 0.12m

(my apologize if this is incorrect)

Answer:

Step-by-step explanation:

Answer:

15 because there are 15 squares i counted

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

that is a right triangle

90-18=72

Answer:

there are so many ways

Step-by-step explanation:

such as observing day by day and checking its height with a scale everyday etc

The number of ways of combining different growth factors to form a level is 80.

The act of organizing all the components of a set into some sequence or order is known as permutation. Permuting, in other words, is the act of reordering the components of a set that has previously been sorted.

A permutation is the selection of r items from a collection of n items without replacement, with the order of the items being significant.

nPr = (n!) / (n-r)!

The combination is a method of picking elements from a collection in which the order of selection is irrelevant (unlike permutations).

A combination is a selection of r items from a collection of n items with no replacements and no regard for order.

nCr = (n!)/{(r!)((n-r)!)}

We are given that Jenny is studying the growth of a particular type of plant. She is testing the effects of three growth factors: lighting, age, and temperature. Here are the levels she's testing for each.

Growth factor Levels

Lighting: Low, Medium, High, Very high.

Age: 1 month, 2 months, 3 months, 4 months, 5 months.

Temperature: 20°, 22°, 24°, 26°.

We are asked to find the number of ways in which she can combine different levels to form one level.

We first check the number of combinations for each factor and then multiply them all to get the total number of ways possible.

Lighting: 4 (∵ All the 4 levels are possible, so the combinations are 4P1 = 4).

Age: 5 (∵ All the 5 levels are possible, so the combinations are 5P1 = 5).

Temperature: 4 (∵ All the 4 levels are possible, so the combinations are 4P1 =4).

∴ Total number of ways of combining different growth factors to form a level = 4*5*4 = 80

∴ The number of ways of combining different growth factors to form a level is 80.

Learn more about permutations and combinations at

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