Hope plans to run one day this week, play tennis one day, swim one day, and play soccer one day. A tree diagram would show different combinations in which she can do these.

Using proportions, it is found that the number of cups per student is of 1.97. hence there will not be enough for each student to have 2 cups.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each gallon is worth 16 cups, hence, since each grade is given 15 gallons of water, and the trip consists of three grades, the number of cups is given by:

C = 3 x 15 x 16 = 720.

There is a total of 370 students, hence the number of cups per student is given by:

n = 720/370 = 1.97.

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The value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2

For a system of equation to have no solution, the expression on both sides must be different.

Given the system of equation

6x-5y=3 and

3x+ay=1

For the equations to have no solution, the a1/a2= b1/b2

Substitute

6/3 = -5/a

Cross multiply

2 = -5/a

a= -5/2

Hence the value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2

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The u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 5.

From the information given about the population and sample mean, the values include:

u=27 o=5 n=14

The standard deviation will be:

= 5/✓14

= 5/3.74

= 1.34

Therefore, u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 1.34.

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Answer:

y = 6

Step-by-step explanation:

-7 (4) + y = -22

-28 + y = - 22

+28 + 28

y = 6

Answer:

x = sqrt(403)

Step-by-step explanation:

Use Pythagorean Theorem for right triangles

x^2 + 9^2 = 22^2

   x = sqrt 403

Answer:

2 good scoops

Step-by-step explanation:

I got you I think

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The correct answer that is an example of a permutation is; D: The number of ways 7 books can be selected from 50.

Formula for permutation is;

nPr = n!/(n - r)!

Now, permutation is defined as the arrangement of objects in a definite order. Thus, looking at the given options, the only one that depicts permutation is Option D.

Thus, the correct answer is the number of ways 7 books can be selected from 50.

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Answer:

25

Step-by-step explanation:

When multiplying a whole number by a fraction, the first step is to multiply the whole number by the numerator. Then, you divide by the denominator. For example, on the left side, 5 x 5 = 25. You are left with 25/6. Finally, when you divide by 6, you are left with 4.166.....

If the denominator is the same (6) on both sides, to get the same answer, you somehow need to get the numerator (25) the same. So, what whole number can be multiplied by 1 to get 25? This number is 25. Therefore, the missing number is 25. This answer is correct because 25 x 1 = 25. You would be left with 25/6 and get a final answer of 4.166....

Answer:

  a)  ΔCED ~ ΔCAB

  b)  157.5 m

Step-by-step explanation:

The similarity statement for geometric figures lists the corresponding vertices in the same order. Corresponding sides of similar figures are proportional. That fact can be used to find the missing side length.

__

The right angles are corresponding. Angle C corresponds to itself, so the similarity statement can be written ...

  ΔCED ~ ΔCAB

__

Corresponding sides are proportional, so we can write ...

  AB/AC = ED/EC

  AB/(50+160) = 120/160 . . . . . using the numerical values

  AB = 210 × 120/160 = 157.5 . . . meters

The length of the lake is 157.5 meters.

Using function concepts, it is found that the correct statements are given by:

It gives the amount of garbage, in tons, produced by a city in t years after 2000.

The amount depends on the number of years, hence:

Hence, the correct statements are given by:

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Step-by-step explanation:

See the attached pics it explains everything

Answer:

Corresponding Angles Theorem

When a straight line intersects 2 parallel lines, the angles in the same relative position are congruent (equal).

Alternate Exterior Angles Theorem

When a straight line intersects 2 parallel lines, the alternate exterior angles are congruent (equal).

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Q1.   As  s ║ c  we can apply the Corresponding Angles Theorem:

⇒ 11x - 5 = 116

⇒ 11x - 5 + 5 = 116 + 5

⇒ 11x = 121

⇒ 11x ÷ 11 = 121 ÷ 11

⇒ x = 11

Q2.   As  s ║ c  we can apply the Alternative Exterior Angles Theorem:

⇒ 12x - 4 = 148

⇒ 12x - 4 + 4 = 148 + 4

⇒ 12x = 152

⇒ 12x ÷ 12 = 152 ÷ 12

⇒ x = 38/3 = 12.7 (nearest tenth)

Q1.   As  j ⊥ r  then the sum of the angles is 90°

⇒ 4x + 6x + 10 = 90

⇒ 10x + 10 - 10 = 90 - 10

⇒ 10x = 80

⇒ 10x ÷ 10 = 80 ÷ 10

⇒ x = 8

Q2.  As  j ⊥ r   we can apply the Vertical Angles Theorem:

⇒ 5x - 10 = x + 70

⇒ 5x - 10  + 10 = x + 70 + 10

⇒ 5x = x + 80

⇒ 5x - x = x + 80 - x

⇒ 4x = 80

⇒ 4x ÷ 4 = 80 ÷ 4

⇒ x = 20

The mean and median of the given set of data are respectively; The mean age is 38.28. The median age is 38.

The mean simply means the average of the set of data. Thus;

Mean = ∑x/n

∑x = 22 + 24 + 28 + 28 + 30 + 31 + 31 + 32 + 32 + 35 + 36 + 37 + 38 + 41 + 42 + 42 + 44 + 44 + 45 + 46 + 46 + 47 + 47 + 49 + 50

∑x = 957

Mean = 957/25

Mean ≈ 38.28

B) Median is the midterm when arranged in ascending order. When we arrange in ascending order, we get;

22, 24, 28, 28, 30, 31, 31, 32, 32, 35, 36, 37, 38, 41, 42, 42, 44, 44, 45, 46, 46, 47, 47, 49, 50

Thus, the median is 38.

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Answer:

see the attachment photo!

Based on the calculations below, the weekly gross pay of John Pelson is $1,339.90.

Let G represents weekly gross pay. The gross pay can now be calculated as follows:

Net pay = G – FIT – SIT – CIT - Health insurance – Charity ……………….. (1)

Substitute all the relevant values into the equation (1) and solve as follows:

$972.11 = G – $185.00 – 0.05G – 0.02G – $64.00 – $25.00

$972.11 + $185.00 + $64.00 + $25.00 = G – 0.05G – 0.02G

$1,246.11 = (1 – 0.05 – 0.02)G

$1,246.11 = 0.93G

G = $1,246.11 / 0.93

G = $1,339.90

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The computation shows that the greatest number of each wing that she can purchase with her money will be 28 wings.

From the information, Jessie goes to the mall, she alwavs makes sure to have $10 for lunch at the food.

In this case, he cannot be able to buy boneless wings a it cost $50.45. Therefore, the number of bone in wing that can be bought will be:

= 10/0.35

= 28

Therefore, the computation shows that the greatest number of each wing that she can purchase with her money will be 28 wings.

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Answer:

P (blue) = 23 / 82

Step-by-step explanation:

There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls

or,

23 / 82

So, the probability of a blue ball being chosen is  23/82  

(or a 28% chance [rounded])

The factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)

The expression is given as:

x = a²b² + 2a + a⁴

Factor out a from the expression

x = a(ab² + 2 + a³)

The above expression cannot be further factorized.

Hence, the factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)

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Answer:

A ≈ 43.3 cm²

Step-by-step explanation:

the area (A) of an equilateral triangle is calculated as

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is a side of the triangle )

given perimeter = 30 cm , then

s = 30 cm ÷ 3 = 10 cm

then

A = [tex]\frac{10^2\sqrt{3} }{4}[/tex] = [tex]\frac{100\sqrt{3} }{4}[/tex] = 25[tex]\sqrt{3}[/tex] ≈ 43.3 cm² ( to the nearest tenth )

Answer:

Step-by-step explanation:

Formula:

[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]

Then

[tex]p\left( A|B\right) =\frac{\frac{2}{9} }{\frac{1}{3} } =\frac{2}{9} \times \frac{3}{1}=\frac{6}{9}=\frac{2}{3}[/tex]

Answer:

y=-1/7+48/7

Step-by-step explanation:

You want to isolate the Y so you subtract the x to the other side.

Next you divide both numbers on the right hand side by 7 and that gives you

y=-1/7+48/7

Answer + Step-by-step explanation:

CE bisects AB

CE ⊥ AB

Then

CE is the perpendicular bisector of AB.

Therefore

CA = CB and DA = DB

…………………………………

we have :

CA = CB

DA = DB

CD is a common side of the two triangles ACD and BCD

Hence , ΔACD ≅ ΔBCD

⇒ ∠CAD ≅ ∠CBD.

Answer:

294[tex]m^2[/tex]

Step-by-step explanation:

The area of one face of the cube would be 7 x 7 = 49 [tex]m^2[/tex]

Since there are 6 faces on a cube, the total surface area would therefore be 49 x 6 = [tex]294m^2[/tex]

Answer:

True

Step-by-step explanation:

Rays have one endpoint and one arrow, which means that they extend forever in one direction.

The cosine ratio is given as:

[tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex]

See attachment for the graph of [tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex] under the domain of [0,∞)

From the graph, we can see that some values of [tex]\theta[/tex] when [tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex] are:

[tex]\theta = \frac{\pi}{6}[/tex]    [tex]\theta = \frac{11\pi}{6}[/tex] and [tex]\theta = \frac{13\pi}{6}[/tex]

We have:

θ = 495°

Convert to radians

[tex]\theta = 495 * \frac{\pi}{180}[/tex]

Evaluate

[tex]\theta = \frac{11\pi}{4}[/tex]

The value of sec θ is then calculated as:

[tex]\sec(\theta) = \sec(\frac{11\pi}{4})[/tex]

Using a calculator, we have:

[tex]\sec(\theta) = -1.414[/tex]

Hence, the value of [tex]\sec(\theta)[/tex] is -1.414

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Answer: 400,000

Step-by-step explanation:

The product is the result of multiplication. In other words, you would multiply 80×5,000.

I hope this helps!! :)

Answer:

Radius:3.14

Circumference: 6.28

Step-by-step explanation:

C=2(pi)(r)

replace r with 1

and you get 6.28

R=(pi)(r)^2

Replace r with 1

multiply and you get 3.14

Answer:

players on both teams are about the same height on average

Step-by-step explanation:

because both are same

Answer:

No because Us is powerful country canada is also powerful but U S ever sale to candians

The mathematical symbol for the line XY is XY(a line on top it) . The first option

There are so many mathematical symbols use in geometry. They include ∠(angles), ⊥(perpendicular line), Δ(triangle), ≅(congruency) and many more.

Therefore, the symbol for the line XY is as follows;

XY(a line on top it)

It means line segment "XY"

In words, it is the line segment between X and Y

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