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xxTIMURxx [149]
2 years ago
7

The table shows expressions to represent the number of students involved in different activities. The number of students involve

d in sports and student council is equal to the number of students involved in band and drama club. Model the situation with an equation. Select the correct expression for each box. Then solve the equation.​

Mathematics
1 answer:
Maurinko [17]2 years ago
6 0

Answer:

6n + 7 = 7n

Step-by-step explanation:

Number of students involved in sports = 5n + 7

Number of students involved in student council = n

Number of students involved in sports and student council = (5n + 7) + n = 5n + 7 + n = 6n + 7

Number of students involved in band = 3n - 2

Number of students involved in drama club = 2(2n + 1)

Number of students involved in band and drama club = (3n - 2) + 2(2n + 1) = 3n - 2 + 4n + 2 = 7n

Equation to model number of students involved in sports and student council which equal number of students involved in band and drama club:

6n + 7 = 7n

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The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets contain 190 calories, and 114 calorie
PIT_PIT [208]
The percent of total calories from fat is 60%

Step-by-step work:

190 calories is the total amount of calories in the chicken nuggets and 114 calories are from fat so you could write that as:

114/190

now remember that a “/“ also means divide, so divide the fraction:

114/190 = 0.6

0.6 is the decimal form of 114/190

then since percentages are out of 100, you multiply it by 100:

0.6 • 100 = 60

and 60% is your final answer!
4 0
1 year ago
Read 2 more answers
Points X(6, 8), Y(3, 3), and Z(13, –3) form a triangle. What is the area of △XYZ?
Rufina [12.5K]

Answer:

23(6,8)(3,3)(13-3)(-3-)

Step-by-step explanation:

8-3=3-6

+13-3=

23

5 0
1 year ago
Toni and Nicky each earn a weekly salary
Reil [10]

Answer:

10,000

Step-by-step explanation:

800 + .07x = 600 + .09x

200 = .02x

10000 = x

4 0
1 year ago
The geometric sequence a i a i ​ a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 ​ =8a, start subscr
frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0
1 year ago
CHEGG When testing the claim that bags of M&M candies will have less than 3% broken pieces, which of the following would be
Vadim26 [7]

Answer:

H0: p ≥ 0.03 Ha: p < 0.03

Step-by-step explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

On this case we want to test is p, where:

p represent the true proportion for the population of broken pieces

What we want to proof need's to be on the alternative hypothesis and the complement on the null hypothesis.

So the correct system of hypothesis for this case would be:

Null hypothesis: p\geq 0.03

Alternative hypothesis: p < 0.03

H0: p ≥ 0.03 Ha: p < 0.03

5 0
1 year ago
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