Travel back in time to the year 2008, when text messages were charged per text. Some carriers charged $59 for a basic text package of 200 texts and 20 cents per text after that. Today, most packages include unlimited text and data but cost closer to $100 a month.

Write and solve an inequality to determine the range of text messages you can send with the 2008 plan without spending more than $100.
If you have a phone, look at your data summary. Is this range your average daily number, weekly number, or monthly number of texts? Determine how much you would have paid for the month if you had the 2008 text plan? Write this as an equation and solve it. If you do not have a phone, you can use a family member's information or make a hypothesis.

a) B represents a boy and G represents a girl.

b) The probability that 2 of the 3 children are boys is 3/8 or 0.375.

a) Here's one way to create a sample space for the number of boys in the family:

S = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

Where B represents a boy and G represents a girl.

b) Counting outcomes in the sample space doesn't tell you the probability that there are 2 boys because each outcome in the sample space is equally likely to occur, but not all outcomes have the same probability. For example, the outcome BBB has a probability of 1/8, while the outcome BGG also has a probability of 1/8. Therefore, you need to assign probabilities to each outcome in the sample space before you can calculate the probability of a specific event like "there are 2 boys".

c) Another way to create a sample space is to use the binomial distribution which models the number of successes in a fixed number of independent trials. In this case, success is having a boy and failure is having a girl. The sample space would be:

S = {0, 1, 2, 3}

where 0 represents the number of boys being 0, 1 represents the number of boys being 1, and so on.

The probability of getting exactly 2 boys out of 3 children can be calculated using the binomial distribution formula:

P(X=2) = (3 choose 2) * (1/2)^2 * (1/2)^1 = 3/8

where (3 choose 2) is the number of ways to choose 2 boys out of 3 children, (1/2)^2 is the probability of getting 2 boys, and (1/2)^1 is the probability of getting 1 girl.

Therefore, the probability that 2 of the 3 children are boys is 3/8 or 0.375.

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Answer: 5 * cube root of 7

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

I am going to assume that one doesn't know what an inconsistent or consistent system of equations is, let alone what a dependent and independent system of equation is. Well an inconsistent system is one that have no solutions, while a consistent system of equations has solutions. A consistent dependent system has infinite solutions, while a consistent independent system has 1 solution.

_______________________________________________________

This system of equations has one solution, as the slopes are not the same nor a multiple of one another ( no solution ) , and the equations are not the same either, nor a multiple of one another ( infinite solutions ). Thus, the system of equations is consistent, independent - Option C

I hope that clarified any questions that you had, as the answer was not Option D!

Answer:

No, because for each input there is not exactly one output

Step-by-step explanation:

Each input, x-coordinate, must have one and only one output (y-coordinate) to be a function.

Since 3/4 is used as an x-coordinate twice, the input 3/4 has two different outputs, -2 and -1/2. That means this relation is not a function.

Answer: No, because for each input there is not exactly one output

Answer: is A

Step-by-step explanation:

Answer:

Each small truck can hold a total of 110 boxes.

Step-by-step explanation:

It says three small delivery trucks can hold 330. That meant all three together. So you just have to do 330 divided by 3 and you get 110. So that's the number of boxes ONE small truck can hold. Also, If u do it backward, 3 x 110 =330.

Answer:

\(m = \frac{0 - ( - 3)}{12 - 3} = \frac{3}{9} = \frac{1}{3} \)

\(slope(m) = \frac{y2 - y1}{x2 - x1} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 3 - 0}{3 - 12} \\ \\ \: \: \: \: \: \: \: \: \: \: \: = \frac{ - 3}{ - 9} \\ \\ \: \: \: \: \: \: \: = \frac{1}{3} \)

Answer:

hope u get it............

Answer: ↓↓↓

Step-by-step explanation:

1. a = ?   b = 16  c = 18

a² + b² = c²

a² + (16)² = (18)²

a² +  256 = 324

     - 256   -256

a² = 68

√a² = √68

a ≈ 8.25

2. a = 4     b = 8     c = ?

a² + b² = c²

(4)² + (8)² = c²

16 + 64 = c²

80 = c²

√c² = √80

c ≈ 8.94

Option - D : The probability of selecting a random sample of 36 scores with a sample mean greater than 64 is  .0228 or 2.28%

60 is the population's average, while 12 is its standard deviation. The likelihood of choosing a random sample of 36 scores with a sample mean larger than 64 is what we are interested in.

To get a general idea of the sample mean distribution, we may utilise the central limit theorem. Regardless of how the population is distributed, the central limit theorem asserts that the distribution of sample means for a sizeable sample is roughly normal.

We may assume that the distribution of the sample mean is roughly normal since the sample size, n = 36, is fairly big. The population mean, which is 60, is the same as the mean of the sampling distribution of the sample mean. The standard error of the mean, which is computed as follows, is the deviation from the sample mean.

Standard deviation divided by the square root of the sample size (12/sqrt) yields the standard error of the mean (36)

The mean's standard deviation is two.

The z-score for a sample mean of 64 may now be determined as follows:

Standard error of the mean is equal to (sample mean - population mean) / z.

z = (64 - 60) / 2

z = 2

The likelihood of a z-score larger than 2 is around 0.0228 or 2.28%, according to a conventional normal distribution table.

Option d, or 0.0228 or 2.28%, is the appropriate response.

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Answer:

See explanations below

Step-by-step explanation:

Given the function

f(x) = 3x+12

Let y = f(x)

y = 3x+12

Replace y with x

x = 3y+12

Make y the subject

3y = x-12

y = (x-12)/3

Hence the required inverse is!

g(x) = (x-12)/3

b) To show that the functions are inverses, we must show that f(g(x)) = g(f(x))

f(g(x)) = f((x-12)/3)

Replace x in f(x) with x-12/3

f(g(x)) = 3(x-12)/3 +12

f(g(x)) = x-12+12

f(g(x)) = x

Similarly for g(f(x))

g(f(x)) = g(3x+12)

g(f(x)) = (3x+12-12)/3

g(f(x)) = 3x/3

g(f(x)) = x

Since f(g(x)) = g(f(x)) = x, hence they are inverses of each other

c) Given f(g(x)) = x

f(g(–2)) = -2

The domain is the input variable of the function. Hence the domain is -2

Answer:

-2

Step-by-step explanation:

coefficient is the number without a letter next to it

The solution of given simultaneous equations is x = 2 and y= 3

"It is set of all points (x, y) on the coordinate plane that makes equation true."

"It is a statement that consists of equal symbol between two algebraic expressions."

For given question,

We have been given two equations,

y = 5 - x and

y = x + 1

The graph of above two equations is as shown below.

The solution of given equations is the point of intersection of the lines    y = 5 - x and y = x + 1.

Therefore, the solution of given simultaneous equations is :

x = 2 and y= 3

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Answer:

then get social media

Step-by-step explanation:

Answer:

-------------------

Heron's formula states that the area of a triangle with side lengths a, b, and c is:

We have a triangle with side lengths:

We can first find the semi-perimeter:

Then we can plug this into Heron's formula to find the area:

So the area of the triangle is approximately 82.41 square units.

The final result of the integral is ln|sin(x)| - ln|sin(x) + 1| + C

To find the integral of cos(x) / (sin^2(x) + sin(x)) dx, we can make a substitution to simplify the integrand. Let u = sin(x), then du = cos(x) dx. Rearranging the equation, dx = du / cos(x).

Substituting these expressions into the integral, we have ∫(cos(x) / (sin^2(x) + sin(x))) dx = ∫(1 / (u^2 + u)) du.

Now we can work on simplifying the integrand. Notice that the denominator can be factored as u(u + 1). Thus, we can rewrite the integral as ∫(1 / (u(u + 1))) du.

To decompose the fraction into partial fractions, we express it as A/u + B/(u + 1), where A and B are constants. Multiplying both sides of the equation by the common denominator (u(u + 1)), we get 1 = A(u + 1) + Bu.

Expanding the right side and collecting like terms, we have 1 = Au + A + Bu. Equating the coefficients of u and the constants on both sides, we find A + B = 0 (for the constant terms) and A = 1 (for the coefficient of u). Solving these equations simultaneously, we get A = 1 and B = -1.

Now we can rewrite the original integral using the partial fractions: ∫(1 / (u(u + 1))) du = ∫(1/u - 1/(u + 1)) du.

Integrating each term separately, we have ∫(1/u) du - ∫(1/(u + 1)) du = ln|u| - ln|u + 1| + C,

where C is the constant of integration.

Substituting back u = sin(x), we obtain ln|sin(x)| - ln|sin(x) + 1| + C as the antiderivative.

Thus, the final result of the integral is ln|sin(x)| - ln|sin(x) + 1| + C.

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Answer:

550

Step-by-step explanation:

first we find what 10 percent of 500 is by multiplying 500 by 0.10

500 x 0.10

50

and not we add the increase

500+50

550 students

hopes this helps please mark brainliest

The probability of having 0 girls is 0.1372, the probability of having 1 girl is 0.4992, and the probability of having 2 girls is 0.2304. These probabilities can be calculated using the formula P(X) = nCr.

The tree diagram and binomial distribution table are incorrect. The tree diagram should have four branches, not three. For the binomial distribution table, the probabilities should be multiplied by two, since there are two children in the family. The correct tree diagram would look like this: Boy (0.52) Girl (0.48) Boy (0.52) Girl (0.48).The correct binomial distribution table would look like this: P(X) 0 (0.52)(0.52)(0.52) 0.13721(0.52)(0.52)(0.48) + (0.52)(0.48)(0.52) + (0.48)(0.52)(0.52) 0.49922(0.48)(0.48)(0.48) 0.2304The probability of having 0 girls is 0.1372, the probability of having 1 girl is 0.4992, and the probability of having 2 girls is 0.2304. These probabilities can be calculated using the formula P(X) = nCr.

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\(\rule{300}{3}\)

\(\text{Hi!}\)

To find the cost per item (or in your case "rolls"), you will first have to divide the cost of the lunch rolls  \((2.50)\)  by the amount of lunch rolls there are \((5)\).

So in this case, it would look like

\( \textbf{$2.50/5} \)\(\text{$2.50 ÷ 5}\)\(\text{$2.50 / 5}\)\(\text{2.50}\) ÷ \(\text{5}\)

\(\text{=$0.50}\)= \(\text{\ 0.50}\)

\(\boxed{\$0.50{}}\)

\(\rule{300}{3}\)

Step-by-step explanation:

Simplifying 4x4 + -12x2 + 8 = 0 Reorder the terms: 8 + -12x2 + 4x4 = 0 Solving 8 + -12x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -3x2 + x4) = 0 Factor a trinomial. 4((1 + -1x2)(2 + -1x2)) = 0 Factor a difference between two squares. 4(((1 + x)(1 + -1x))(2 + -1x2)) = 0 Ignore the factor 4.

Subproblem 1

Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Subproblem 3

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-1.414213562, 1.414213562, -1, 1}

The apprοximate prοbability that Ankit will make all three shοts is 0.405 οr 40.5%. Thus, option a is correct.

A prοbability distributiοn knοwn as the binοmial distributiοn is used tο characterize the number οf successes in a certain number οf independent trials, where each trial has οnly οne οf twο pοtential οutcοmes (success οr failure) and the chance οf success is cοnstant acrοss all trials. Fοr determining the likelihοοd οf achieving a certain number οf successes in a set number οf trials, it is utilised.

Given, Ankit makes 74% οf the free thrοws.

Using binοmial distributiοn we have:

\($\rm P(X=k)= (^nC_k) \times p^{k} \times (1-p)^{(n-k)}$\)

Fοr k = 3 we have:

\($ \rm P(X=3)=(^3C_3) \times 0.74^{3} \times (1-0.74)^{(3-3)}$\)

\($ \rm P(X=3)=0.74^{3}$\)

P(X=3) ≈ 0.405

Hence, the apprοximate prοbability that Ankit will make all three shοts is 0.405 οr 40.5%.

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Answer:

10 Minutes

Step-by-step explanation:

At roughly 10 minutes, the y-axis meets a point at the x-ais that can be shown as (40,10)

Answer:

80%

Step-by-step explanation:

We need to find the percent of change from 3,545 pt to 709 pt.

Original value is 3,545

Changed value is 709

Percent change is given by :

\(\%=\dfrac{\text{difference in values}}{\text{original value}}\times 100\\\\\%=\dfrac{3545-709}{3545}\times 100\\\\\%=80\%\)

So, there is 80% of change from 3,545 pt to 709 pt.

Answer:

688.1 cm

Step-by-step explanation:

Area of circle = (π)r^2

Area= π × 14.8^2

Area = 688.1 cm^2 (to the nearest tenth)

Supply and demand are two factors that affect how much a country's currency is worth.

The supply and demand of a country's currency determine the value of that currency in a free-floating currency exchange market. A currency improves in value or appreciates when demand for it rises. A currency loses value or depreciates when there is less demand for it.

Money's demand determines how much it is worth. When there is still a strong demand for treasuries, the US dollar increases. The value of a currency determines both its supply and demand. For instance, if a nation prints a lot of currency, the value relative to other currencies will drop because supply exceeds demand. Inflation will happen if the cost of products rises or the value of money declines in comparison to other assets.

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Answer:

Midpoint of side EF would be (-.5,4.5)

Step-by-step explanation:

We know that the coordinates of a mid-point C(e,f) of a line segment AB with vertices A(a,b) and B(c,d) is given by:

e=a+c/2,f=b+d/2

Here we have to find the mid-point of side EF.

E(-2,3) i.e. (a,b)=(2,3)

and F(1,6) i.e. (c,d)=(1,6)

Hence, the coordinate of midpoint of EF is:

e=-2+1/2, f=3+6/2

e=-1/2, f=9/2

e=.5, f=4.5

SO, the mid-point would be (-0.5,4.5)

Answer:Number of miles Erin jogged altogether= 7 miles

Step-by-step explanation:

Number of miles jogged on Monday =2 miles

Number of miles jogged on Wednesday =3 miles

Number of miles jogged on Friday =2 miles

Number of miles jogged altogether= 2 miles+3 miles+2 miles=7 miles

The simplified form of sin x / (1-cos x) is not in the provided options. The final form is  (1 + cos x)^(1/2).

To find the simplified form of sin x / (1-cos x), we will use the following identity:

sin^2(x) + cos^2(x) = 1
Now, we can rewrite sin^2(x) as (1 - cos^2(x)).

Then, we will factor in the numerator:
sin x / (1 - cos x) = (1 - cos^2(x))^(1/2) / (1 - cos x)
Next, we factor the denominator by using the difference of squares formula:
(1 - cos^2(x))^(1/2) / (1 - cos x) = [(1 + cos x)(1 - cos x)]^(1/2) / (1 - cos x)
Now, we can simplify by canceling out the common factor (1 - cos x):
[(1 + cos x)(1 - cos x)]^(1/2) / (1 - cos x) = (1 + cos x)^(1/2)

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We have the given equation for the remaining Tylenol in her body.

Where n represents the number of hours.

We need to find the remaining Tylenol in her body after 4 hours. Therefore, set n=4.

Replacing on the formula:

The value is rounded to the nearest hundredth.

Hence, Jane will have 14.99 mg's of Tylenol remaining in her body after 4 hours.

Answer:

\(9m^8t^1^0/ 2t ^7\)

Step-by-step explanation:

Hope this helped :)

The null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.

A study has been carried out to determine the relationship between gratitude and prosocial attitudes. JASP is used to run a Pearson correlation test between gratitude and prosocial attitudes. The null hypothesis of this study is that there is no correlation between gratitude and prosocial attitudes.

In this investigation, the Pearson correlation is used. This research aims to identify the relationship between gratitude and prosocial attitudes. It can be difficult to determine whether or not there is a correlation between two variables. Pearson's correlation is a statistical method that can be used to examine the correlation between two variables.

This research is carried out with the hypothesis that there is a relationship between gratitude and prosocial attitudes. In this study, the null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.

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