. Which of the following situations is best represented by the equation y = x + 15?

1 Each student begins the candy hunt with 15 pieces of candy in their bag.
2 Emery earns $15 per hour babysitting.
3 Joshua spent $15 of his money at the movie theatre.
4 Each homeroom class has at least 15 students.

Answer:

x=c-6

Step-by-step explanation:

6+x=c

-6    -6

x=c-6

Answer:

Angles and sides are the main differences! In a rectangle, all angles will be 90 degrees. In a rhombus, opposite angles will always be congruent. And, all sides in a rhombus are congruent, while in a rectangle, opposite sides are congruent

Step-by-step explanation:

here

Answer:x=11/2+y/2

Step-by-step explanation:

The solution of the given system of equation would be (6, 2)

Two or more equations to be solved together, i.e., the solution must satisfy all the equations in the system.

We have Given the equations, 3x + 2y = 22

-x + 4y = 2

Solving by elimination, Multiplying the second equation by 3,

3x+2y = 22

-3x + 12y = 6

Adding the equation, we get;

2y+12y = 22+6

24y = 28

y = 2

Putting y=2 we get;

3x+2*2=22

3x+4 = 22

3x = 18

x = 6

Hence, The solution is (6, 2)

For more references on system of equations, click;

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Answer:

6 and 20

Step-by-step explanation:

Answer:

0.0625 should be the answer of .5 to the fourth power.

Answer:

30

Step-by-step explanation:

If CUB is 78 and that’s the full angle just to 48 minus 78 and you get your answer.

Answer:

x = 1

Step-by-step explanation:

It is given that,

∠A and ∠B are vertical angles.

∠A = (5x – 4) and ∠B = (2x – 1)

We need to find the value of x.

We know that, the vertical angles are equal. So,

∠A=∠B

(5x – 4)=(2x – 1)

Taking like terms together,

5x-2x = 4-1

3x=3

x = 1

So, the value of x is equal to 1.

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

[tex]Event\ 1 = \{1,2,3,4,5,6\}[/tex]

Next, we list out the sample space of F

[tex]Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\[/tex]

[tex]6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]

In (1): the sample space of E is:

[tex]E = \{1\}[/tex]

So:

[tex]P(E) = \frac{n(E)}{n(Event\ 1)}[/tex]

[tex]P(E) = \frac{1}{6}[/tex]

In (2): the sample space of F is:

[tex]F = \{5,5,5,5\}[/tex]

So:

[tex]P(F) = \frac{n(F)}{n(Event\ 2)}[/tex]

[tex]P(F) =\frac{4}{36}[/tex]

[tex]P(F) =\frac{1}{9}[/tex]

For E and F to be independent:

[tex]P(E\ and\ F) = P(E) * P(F)[/tex]

Substitute values for P(E) and P(F)

This gives:

[tex]P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}[/tex]

[tex]P(E\ and\ F) = \frac{1}{54}[/tex]

However, the actual value of P(E and F) is 0.

This is so because [tex]E = \{1\}[/tex] and [tex]F = \{5,5,5,5\}[/tex] have 0 common elements:

So:

[tex]P(E\ and\ F) = 0[/tex]

Compare [tex]P(E\ and\ F) = \frac{1}{54}[/tex] and [tex]P(E\ and\ F) = 0[/tex].

These values are not equal.

Hence: the two events are not independent

Answer:

Correct Answer - It shows the unit rate of the graph in miles per hour.

Step-by-step explanation:

hope this helps

Answer:

-9

Step-by-step explanation:

Given

See attachment for number line

Required

What does the arrow integer

Represent the value of the arrow with x.

The arrow is on number -9.

This number is what the arrow represents.

Hence:

[tex]x = -9[/tex]

Answer:

80 +30h

Step-by-step explanation:

Answer:

80 + 30h

Step-by-step explanation:

Distribute the 10 over the (8 + 3h). This means: multiply 10 by 8 and by 3h.

10 x 8 = 80

10 x 3h = 30h

10(8 + 3h) = 80 + 30h

Answer:

20.5

Step-by-step explanation:

Hi there! :)

[tex]\large\boxed{\text{ x = 0, or (0, 2)}}[/tex]

The solution of g(x) = 3x + 2 and f(x) = |x - 1| + 1 is where the two lines intersect.

According to the graph, the functions intersect at the point (0, 2), or x = 0. This is the solution to the system of equations.

We could also prove this algebraically by setting the two equations equal to each other:

3x + 2 = | x - 1 | + 1

Assume the absolute value function is negative:

3x + 2 = -(x - 1) + 1

Simplify:

3x + 2 = -x + 2

Add x to both sides:

4x + 2 = 2

Subtract 2 from both sides:

4x = 0

x = 0. This is the solution to the system.

Answer:

Step-by-step explanation:

2 to 5 or 2:5

      or

2 to 3 or 2:3

The thing before the square root means that the answer can be positive and negative.

Answer:

First blank: Divide

Second blank: Multiply

Third blank: 25

Step-by-step explanation:

For the first part, you would divide to get X as itself

For the second part, you would multiple to cancel out the fraction and be left with whole numbers, which is much easier to work with

1.3 x 25 = 32.5, so that would be that answer

Answer:

i so want to know this aswell

Step-by-step explanation:

Answer:

4182

Step-by-step explanation:

I gotten this question so I decided to find the answer but I still got it wrong and it said the answer was 4182

Answer:

We fail to reject the null

Step-by-step explanation:

Given the data: 1298; 1229.96; 1193.07; 1279; 1224.98; 1229.97; 1269.98; 1248

Mean price, μ = 1249

Standard deviation, σ = 25

Variance, σ² =

Null hypothesis, H0 : σ² = 25²

Alternative hypothesis, H1 : σ² > 25

Using calculator, the sample standard deviation :

Sample standard deviation = s = 34.072

Sample size, n = 8

For chi² distribution :

X² = [(n - 1)s²] ÷ σ²

X² = [(8 - 1)*34.072^2] ÷ 25^2

X² = (7 * 1160.901184) / 625

X² = 13.002093

Using the Pvalue from Chisquare calculator, df = 8 - 1 = 7; α = 0.05

Pvalue =0.07206

0.07206 > 0.05

Since , Pvalue > α

We fail to reject the null; there is insufficient evidence to conclude that standard devuatue do selling a computer is greater than 25

Answer:

Associative

Step-by-step explanation:

Answer:

Line b and line c are perpendicular.

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, and -1/2 and 2 are opposite reciprocals.

Answer:

[tex]\mathbf{\theta = 0.0875 \ radians}[/tex]

Step-by-step explanation:

Given that:

The distance between city A and city B = 350 miles; &

The radius of the earth = 4000 miles

We all know that:

l = rθ

[tex]\theta = \dfrac{l}{r}[/tex]

[tex]\theta = \dfrac{350}{4000}[/tex]

[tex]\mathbf{\theta = 0.0875 \ radians}[/tex]

From l = rθ; recall that l = a

so;

a = rθ

350 = 4000×θ

θ = 350/4000

θ = 35/400 degree

In radians;

θ = (35/400) × (π/180)

θ = (7π /800× 180) radians

Answer:

The proportion of children in this age range between 70 lbs and 85 lbs is of 0.9306.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A study suggested that children between the ages of 6 and 11 in the US have an average weightof 74 lbs, with a standard deviation of 2.7 lbs.

This means that [tex]\mu = 74, \sigma = 2.7[/tex]

What proportion of childrenin this age range between 70 lbs and 85 lbs.

This is the pvalue of Z when X = 85 subtracted by the pvalue of Z when X = 70. So

X = 85

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{85 - 74}{2.7}[/tex]

[tex]Z = 4.07[/tex]

[tex]Z = 4.07[/tex] has a pvalue of 1

X = 70

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 74}{2.7}[/tex]

[tex]Z = -1.48[/tex]

[tex]Z = -1.48[/tex] has a pvalue of 0.0694

1 - 0.0694 = 0.9306

The proportion of children in this age range between 70 lbs and 85 lbs is of 0.9306.

Answer:

a. [tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex] b. 7.44 s

Step-by-step explanation:

a. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min.

Let m(t) be the mass of salt in the tank at any time, t.

Now, since a brine solution flows in at a rate of 4 L/min and has a concentration of 0.2 kg/L, the mass flowing in per minute is m' = 4 L/min × 0.2 kg/L = 0.8 kg/min

Now, the concentration in the tank of volume 100 L at any time, t is m(t)/100 L. Since water flows out at a rate of 3 L/min, the mass flowing out per minute is

m(t)/100 × 3 L/min = 3m(t)/100 kg/min

Now the net rate of change of mass of salt in the tank per minute dm/dt = mass flowing in -mass flowing out

dm/dt = 0.8 kg/min - 3m(t)/100 kg/min

So, dm/dt = 0.8 - 0.03m(t)

The initial mass of salt entering m(0) = 0 kg

dm/dt = 0.8 - 0.03m(t)

separating the variables, we have

dm/[0.8 - 0.03m(t)] = dt

Integrating, we have

∫dm/[0.8 - 0.03m(t)] = ∫dt

-0.03/-0.03 × ∫dm/[0.8 - 0.03m(t)] = ∫dt

1/(-0.03)∫-0.03dm/[0.8 - 0.03m(t)] = ∫dt

-1/0.03㏑[0.8 - 0.03m(t)] = t + C

㏑[0.8 - 0.03m(t)] = -0.03t - 0.03C

㏑[0.8 - 0.03m(t)] = -0.03t + C'  (C'= -0.03C)

taking exponents of both sides, we have

[tex]0.8 - 0.03m(t) = e^{-0.03t + C'} \\0.8 - 0.03m(t) = e^{-0.03t}e^{C'}\\0.8 - 0.03m(t) = Ae^{-0.03t} A = e^{C'}\\0.03m(t) = 0.8 - Ae^{-0.03t}\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\when t = 0 \\m(0) = 0\\m(0) = 26.67 - \frac{A}{0.03} e^{-0.03(0)}\\\\0 = 26.67 - \frac{A}{0.03} e^{0}\\26.67 = \frac{A}{0.03} \\\frac{A}{0.03} = 26.67\\\frac{A}{0.03} = 6.67\\A = 26.67 X 0.03\\A = 0.8\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\\\m(t) = 26.67 - \frac{0.8}{0.03} e^{-0.03t}\\[/tex]

So, the mass of the salt after t min is

[tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex]

b. When will the concentration of salt in the tank reach 0.1 kg/L?

When the concentration of the salt reaches 0.1 kg/L, m(t) = 0.1 kg/L

Solving the equation for t,

[tex]m(t) = 26.67 - 6.67e^{-0.03t}\\0.1 = 26.67 - 26.67e^{-0.03t}\\26.67e^{-0.03t} = 26.67 - 0.1\\26.67e^{-0.03t} = 26.57\\e^{-0.03t} = 26.56/26.67\\e^{-0.03t} = 0.9963\\[/tex]

taking natural logarithm of both sides, we have

-0.03t = ㏑0.9963

-0.03t = -0.0038

t = -0.0038/-0.03

t = 0.124 min

t = 0.124 × 60 s

t = 7.44 s

Answer:

a)

initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]  

b)

S(0) = 1

Therefore; S(0)  is 1 million dollar

S(1) = 1.105170918075647

Therefore; S(1)  is 1.105170918075647 million dollar

Step-by-step explanation:

Given that;

Initial salary of football coach = 1 million dollar

raise of 10% every year (so exponential growth model) r = 10% = 0.10

a) initial value problem to represent the salary

lets S represent salary in millions dollars and t represent time in years.

S(t) = S₀[tex]e^{rt}[/tex]

so,

at S₀ = 1 million dollars } { r = 0.10 }

S(t) = 1.[tex]e^{0.10t}[/tex]  

Therefore, initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]  

b) What is s(0) and s(1)

at s(0)

S(t) = 1.[tex]e^{0.10t}[/tex]  

we substitute

S(0) = 1.[tex]e^{0.10*0}[/tex]

S(0) = 1.[tex]e^{0}[/tex]

S(0) = 1

Therefore; S(0)  is 1 million dollar

at s(1)

S(t) = 1.[tex]e^{0.10t}[/tex]  

we substitute

S(1) = 1.[tex]e^{0.10*1}[/tex]

S(1) = 1.[tex]e^{0.10}[/tex]

S(1) = [tex]e^{0.10}[/tex]

S(1) = 1.105170918075647

Therefore; S(1)  is 1.105170918075647 million dollar

Answer:

discount=25%

selling price=$449

original price=?

Step-by-step explanation:

we have

original price=selling price + discount% of original price

original price-discount% of original price=$449

original price (1-25/100)=$449

original price=$449/0.75=$598.66

Answer:

7.48

Step-by-step explanation:

find what 6% of 7.95 is and then subtrct that from 7.95 which gives u ur answer

Answer:

124

Step-by-step explanation:

You can find this answer by simply multiplying 62 by 2. lol