It cost Faith $9.10 to send 91 text messages. How many text messages did she send if she spent $17.60?

Answer:

Step-by-step explanation:

Answer:

\(7x - 4y = 42\)

Step-by-step explanation:

Given

\((x_1,y_1) = (6,0)\)

\((x_2,y_2) = (2,-7)\)

Required

Determine the equation in standard form

First, calculate the slope (m) using:

\(m = \frac{y_2 -y_1}{x_2 - x_1}\)

This gives:

\(m = \frac{-7 -0}{2 - 6}\)

\(m = \frac{-7}{-4}\)

\(m = \frac{7}{4}\)

The equation in standard form is calculated using:

\(y - y_1 = m(x - x_1 )\)

This gives:

\(y - 0 = \frac{7}{4}(x - 6)\)

\(y = \frac{7}{4}(x - 6)\)

Cross Multiply

\(4y = 7(x - 6)\)

Open bracket

\(4y = 7x - 42\)

Subtract 7x from both sides

\(-7x + 4y = 7x - 7x - 42\)

\(-7x + 4y = - 42\)

Multiply through by -1

\(-1(-7x + 4y) = - 42*-1\)

\(7x - 4y = 42\)

a)The probability of the computer breaking down during the next month is 0.27

b) The probability that the time between two consecutive breakdowns is longer than 2 weeks is 0.135

c)The probability that the time between two consecutive breakdowns is longer than 2 weeks (or 0.5 months) is 0.778

d)The probability of having zero breakdowns in a 2-week period is 0.607.

e)The probability that X is greater than 2 is 0.25.

a) The number of breakdowns in a month can be modeled as a Poisson distribution with parameter

λ=2,

since we are given the average rate of breakdowns per month.

Therefore, the probability of the computer breaking down during the next month is:

P(X = 1) = (e^-λ) * (λ^1) / 1! = (e^-2) * (2^1) / 1! ≈ 0.27

(b) We can use the exponential distribution with parameter

λ=2

to model the waiting time between two consecutive breakdowns in weeks.

The probability that the time between two consecutive breakdowns is longer than 2 weeks is:

P(X > 2)

= e^(-2*2)

≈ 0.135

(c) We can convert the waiting time between two consecutive breakdowns in weeks to months by dividing by 4, since 4 weeks constitute a month.

Therefore, the waiting time between two consecutive breakdowns in months can be modeled by an exponential distribution with parameter

λ=2/4

=0.5.

The probability that the time between two consecutive breakdowns is longer than 2 weeks (or 0.5 months) is:

P(X > 0.5)

= e^(-0.5*0.5)

≈ 0.778

(d) We can model the number of breakdowns per week by a Poisson distribution with parameter

λ=2/4

=0.5,

since there are 4 weeks in a month.

The probability that the time between two consecutive breakdowns is longer than 2 weeks is equivalent to the probability of having zero breakdowns in a 2-week period.

Therefore, we need to find:

P(X = 0)

where X is the number of breakdowns in a 2-week period

P(X = 0)

= e^(-0.5*2) * (0.5^0) / 0!

≈ 0.607

(e) We can also model the waiting time between two consecutive breakdowns in weeks using a geometric distribution,

where X is the number of weeks until the next breakdown.

The probability that the time between two consecutive breakdowns is longer than 2 weeks is equivalent to the probability that X is greater than 2.

Therefore, we need to find:

P(X > 2) = (1 - p)^2

where p is the probability of a breakdown in a given week

p = 2/4 = 0.5

since the computer breaks down on average 2 times per month

P(X > 2) = (1 - 0.5)^2 = 0.25

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The polynomial that represents the area of the shaded region is given as follows:

x² - 3x + 36.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

For the entire region, the area is given as follows:

A = (x + 1)(x + 1)

A = x² + 2x + 1.

The area of the white region is given as follows:

Aw = 5(x - 7)

Aw = 5x - 35.

Then the area of the shaded region is given as follows:

As = A - Aw

A = x² + 2x + 1 - (5x - 35)

A = x² + 2x + 1 - 5x + 35

A = x² - 3x + 36.

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Answer:

60 Km / hour

Step-by-step explanation:

average speed (S) is calculated as

S = \(\frac{D}{T}\) ( D is distance and T time in hours )

here D = 180 and T = 3 , then

S = \(\frac{180}{3}\) = 60 Km / hour

Answer:

The probability of getting exactly 2 soles is 0.375.

Step-by-step explanation:

The question is:

If you toss a fair coin 4 times, what's the probability that you get exactly 2 soles?

Solution:

A fair coin has two parts.

On tossing a coin once there is 50-50 odds of both the sides.

So, the probability of one side is, p = 0.50.

It is provided that a fair coin is tossed n = 4 times.

The event of any of the sides showing up after the toss are independent of each other.

The random variable X defined as soles, follows a Binomial distribution with parameters n = 4 and p = 0.50.

The probability mass function of X is:

\(P(X=x)={4\choose x}\ (0.50)^{x}\ (1-0.50)^{4-x};\ x=0,1,2,3,4\)

Compute the probability of getting exactly 2 soles as follows:

\(P(X=2)={4\choose 2}\ (0.50)^{2}\ (1-0.50)^{4-2}\)

                \(=6\times 0.25\times 0.25\\\\=0.375\)

Thus, the probability of getting exactly 2 soles is 0.375.

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

Answer: b=7

Step-by-step explanation:

Answer:

o 1)

\(Y= 6x + 11 \\ \\ 6x = Y - 11 \\ \\ x = \frac{Y - 11}{6} \\ \\ x = \frac{Y}{6} - \frac{11}{6} \)

___o__o__

o 2)

\(A = \frac{1}{2} bh \\ \\ bh = A \div \frac{1}{2} \\ \\ bh = A \times 2 \\ \\ bh = 2A\)

\(b = \frac{2A}{h} \)

\(h = \frac{2A}{b} \)

By converting the mixed numbers to decimals is an essential skill in mathematics, and it allows us to represent fractional quantities in a more concise and precise manner.

The point on the number line that shows the number of miles Emily rides her bike can be represented as a decimal. To convert the given mixed number 2 5/10 to a decimal, we first convert the fractional part to a decimal.

To do so, we divide the numerator 5 by the denominator 10:

5 ÷ 10 = 0.5

Therefore, the fractional part of the mixed number 2 5/10 is equal to 0.5.

Next, we add the integer part 2 to the decimal equivalent of the fraction:

2 + 0.5 = 2.5

Hence, the decimal that correctly represents the point on the number line is 2.5.

In the context of Emily riding her bike, this decimal can represent the distance that she has traveled in miles. For example, if she starts at 0 miles and rides her bike for 2.5 miles, she would end up at the point on the number line that corresponds to the decimal 2.5.

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Answer:

Step-by-step explanation:

perimeter is the sun of all sides, so, (x)+(x+3)+(x-4)+(2x)

                                                            = x+x+3+x-4+2x

                                                            = 5x-1 is the answer

Answer:

the second option.

a policy that pays to get your vehicle replaced or repaired incase of an accident.

Step-by-step explanation:

Answer:

All of the above.

Step-by-step explanation:

All of the above are equal to 5,2. I hope this cleared things up! ^w^

Answer:

root of 64, root of 71,pie squared

Step-by-step explanation:

Answer:

Step-by-step explanation: a= E

b=D

c=A

Answer:

A. E

B. D

C. A

Step-by-step explanation:

y=25x-400

so we can conclude that the slope of the line represents the rate per hour

Step 1

set the equation:

a)let x represent the total hours and let y represents the total income ,so

if the rate is $25 per hour of tutoring service, the total will be:

i

therefore, the equation is y= 25x-400

b)

a slope of a line is the change in y coordinate with respect to the change in x coordinate, so for our problem the rate is the change in the income to the change in the number of hours,

so we can conclude that the slope of the line represents the rate per hour

I hope this helps you

Answer:

24p = 72

Step-by-step explanation:

The product refers to multiplication.

Let the number be p.

The product of p and 24 is 72.

24 × p = 72

24p = 72

Answer:

Step-by-step explanation:

the ration of boys to girls will be:

36/12=3/1

choice b

another way

36 boys.........................12 girls  divide by 6

6 boys.............................2 girls   divide by 2

3 boys.............................1 girl

The base of the function given 2(4)ˣ+5 is 4ˣ

The base of an exponential function. If f(x) = ax, then we call a the base of the exponential function. The base must always be positive. Base 1. If f(x) is an exponential function whose base equals 1 – that is if f(x)=1x.

Given is a function, 2(4)ˣ+5, we need to find the base of the function,

With the multiplication of 4ˣ with 2, the rate at which f(x) changes is 2 times larger. Now it is added by 5, by adding 5 the value of f(x) is always 5 greater than the value of f(x).

This reverses the value of y for each corresponding value of x and increases the rate at which f(x) changes 8 times that of the original function.

Hence, the base of the function given 2(4)ˣ+5 is 4ˣ

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The percentages of each snack type that were sold are given as follows:

A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.

Hence the percentages for each type are obtained as follows:

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Answer:

x = 6+b

Step-by-step explanation:

-6 = -x+b

Subtract b from each side

-6-b = -x+b-b

-6-b = -x

Multiply each side by -1

6+b = x

Answer:

I believe it a I just believe and please make me brailnest

Answer:

The answer is the "Null hypothesis and Alternative hypothesis".

Step-by-step explanation:

The null hypothesis is almost like a hypothesis test, which indicates the certain demographic characteristics which aren't varied.

The alternative presumption will be that the hypothesis besides making predictions is opposite to the void assumption. Its posts are generally taken as a result of a meaningful effect.

Difference:

The null hypothesis is indeed a gross generalization, which specifies there is no relation between different phenomenons under evaluation. There is no association between the two groups. An alternate solution hypothesis is a statement, that defines there is a relation between different chosen variables in this study.

Answer:

No

But it us Near though

Step-by-step explanation:

9/15 or 3/5 =60%

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

3/8 against 5/12

expand 3/8 to get 9/24

expand 5/12 to get 10/24

so, julie lives closer

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

122 degrees

Step-by-step explanation:

The two intersecting lines are parallel for this problem, which means that the angle next to angle3 is the same degree measure as the one that is 58 degrees.

Also, remember that two angles next to each other on a straight line are supplementary, meaning that they add to 180 degrees.

When keeping these two things in mind, you can solve like this:

180 = angle3 + 58

180 - 58 = angle3

angle3 = 122

122 degrees

Given:

Vin says in 4,346, one 4 is 10 times as great as the other 4.

To check:

Vin's statement is correct or wrong.

Explanation:

The place value of one 4's is 40. Because it is in the tens place.

The place value of another 4's is 4000. Because it is in thousands plance.

From this, we observe that 40 is 100 times as great as 4000.

Therefore, Vin's statement is incorrect.

Final answer:

No, Vin's statement is incorrect.