Jo goes to the store to get school supplies. She buys two notebooks for $3.75 each and 5 pens. The amount of money she spent can be represented by the equation $10.50 = $7.50 + 5p.

What does the 5 represent in the equation?

Answer: 5/26

Step-by-step explanation:Hope this is helpful

a) The probability that a randomly chosen college student has a GPA of at least 2.30 is approximately 0.099, or 9.9%.

b) The probability that exactly nine out of ten independently selected college students have a GPA of at least 2.30 is approximately 0.0000001768, or 1.768 x 10^-7.

a. To find the probability that a randomly chosen college student has a GPA of at least 2.30, we need to calculate the area under the normal distribution curve to the right of 2.30.

Using the standard normal distribution (z-distribution), we can convert the GPA value of 2.30 to a z-score using the formula:

z = (x - μ) / σ

where x is the GPA value, μ is the mean, and σ is the standard deviation.

In this case:

x = 2.30

μ = 2.84

σ = 0.42

Calculating the z-score:

z = (2.30 - 2.84) / 0.42 ≈ -1.2857

Now, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of -1.2857. The probability can be obtained by finding the area to the right of the z-score.

Looking up the z-score in the standard normal distribution table or using a calculator, we find that the probability corresponding to a z-score of -1.2857 is approximately 0.099.

Therefore, the probability that a randomly chosen college student has a GPA of at least 2.30 is approximately 0.099, or 9.9%.

b. If ten college students are independently selected, we can use the binomial distribution to calculate the probability that exactly nine of them have a GPA of at least 2.30.

The probability of success (p) is the probability that a randomly chosen college student has a GPA of at least 2.30, which we calculated as 0.099 in part a.

Using the formula for the binomial distribution:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where X is the random variable representing the number of successes, n is the number of trials, k is the number of desired successes, C(n, k) is the number of combinations, p is the probability of success, and (1 - p) is the probability of failure.

In this case:

n = 10 (number of college students)

k = 9 (desired number of college students with GPA at least 2.30)

p = 0.099 (probability of success from part a)

Calculating the probability:

P(X = 9) = C(10, 9) * (0.099)^9 * (1 - 0.099)^(10 - 9)

Using the combination formula C(n, k) = n! / (k! * (n - k)!):

P(X = 9) = 10! / (9! * (10 - 9)!) * (0.099)^9 * (1 - 0.099)^(10 - 9)

P(X = 9) = 10 * (0.099)^9 * (1 - 0.099)^1 ≈ 0.0000001768

Therefore, the probability that exactly nine out of ten independently selected college students have a GPA of at least 2.30 is approximately 0.0000001768, or 1.768 x 10^-7.

To learn more about probability

https://brainly.com/question/13604758

#SPJ11

Answer:

D=(-1, -2)=(xd, yd); xd=-1, yd=-2→A'=(yd, -xd)=(-2, -(-1))→A'=(-2, 1)

E=(0, -1)=(xe, ye); xe=0, ye=-1→B'=(ye, -xe)=(-1, -0)→B'=(-1, 0)

F=(0, 1)=(xf, yf); xf=0, yf=1→C'=(yf, -xf)=(1, -0)→C'=(1, 0)

Step-by-step explanation:

pls give creds to Professor1994

Answer: .416666667

Step-by-step explanation: Take 80 and divide it by 192.0= .416666667

A real life example of an acute angle is the angle that's made in letter V.

It should be noted that an acute triangle simply means an angle that measures less than 90 degrees.

In this case, the real life example of an acute angle is the angle that's made in letter V. Other examples include slizing a pizza into different shapes.

Learn more about acute angles on:

brainly.com/question/17335144

#SPJ1

Answer:

1000

Step-by-step explanation:

The easiest way to go about this is by turning our number into ABCD.

A will be in the 1000th spot, B 100th, C 10th, and D 1st.

A has to be ≥ 5. So 5, 6, 7, 8, 9.

B has to be a prime number. 2, 3, 5, 7.

C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Since the number is odd, D has to be 1, 3, 5, 7, 9.

A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000

Step-by-step explanation:

1) So you can get a similar denominator by multiplying by 5 and 4:

5(5x-4)+4(3x+2) / 20

And then simplify:

25x-20+12x+8 / 20

ANSWER: 37x-12/20

2) g is a function here so I'm not sure how to solve this, but in case it's f(g(x))...

5(-3x+1)-2

-15x+5-2

ANSWER (if f(g(x))): -15x+3

I'm not sure about the last one though, sorry. Hope this helped though. -w-

Answer:

See below:

Step-by-step explanation:

Hello! I hope you are having a nice day.

We can solve the problem in 2 steps, one being Solving, and the second being Comprehending. I'll start with comprehending.

Comprehending

We can start by analyzing the problem and creating an equation to then begin solving.

So, we know that a number, which we will call \(x\) has a discount of 10% to get the current price of $810. We know that when there is a discount, we need to find what the 10 percent is then add it to the current price;$810.

We can create a formula and steps by doing the following:

\(x*0.9=810\)

We have 0.9 as there is a 10% discount (0.1) and we subtract 1.00 by 0.1 to get 0.9. (Which is 90%).

This states that 90% of a number is equal to 810.

Now that we have an equation, we can begin solving.

Solving

We can solve the problem by using basic algebra.

\(x*0.9=810\\x*\frac{9}{10}=810\\x=(810*10)\div 9\\x=8100 \div 9\\x=900\)

On step 1, we convert the decimal to a fraction for easy simplification/solving.

On step 2, we split the fraction into two and since we're dividing, we can flip the fraction and multiply by 10 and divide by 9.

On step 3, we use basic algebra and after step 4 we get our answer.

We can double check out answer by doing the following:

\(900-(900*0.10)=810?\\900-90=810?\\810=810\)

We have checked our answer and gotten our answer of $900.

Cheers!

Answer:

See attached image.  82 and 98 degrees.

Step-by-step explanation:

On attached document.

Answer:

The domain is found depending on the information you're given. In a table, the domain is found by taking all the x values given and listing them least to greatest. Same with ordered pairs. In a graph, the domain is found by first seeing if there are any restrictions and then find the x values that work and have one output.

The range is found the same way, but with the y values.

Hope this helps!!

If λ is an eigenvalue of matrix A and x is the corresponding eigenvector, then for any positive integer m, λ^m is an eigenvalue of A^m, and x is the corresponding eigenvector of A^m.

Let λ be an eigenvalue of matrix A with eigenvector x. This means that Ax = λx. Now, consider the matrix A^m, where m is a positive integer. By multiplying both sides of the eigenvector equation by A^(m-1), we have A^(m-1)Ax = A^(m-1)(λx), which simplifies to A^mx = λA^(m-1)x.

Since A^mx = (A^m)x and A^(m-1)x = λ^(m-1)x, we can rewrite the equation as (A^m)x = λ^(m-1)(Ax). Using the initial eigenvector equation Ax = λx, we have (A^m)x = λ^(m-1)(λx), which further simplifies to (A^m)x = λ^m x.

Therefore, we have shown that if λ is an eigenvalue of A with eigenvector x, then for any positive integer m, λ^m is an eigenvalue of A^m with the same eigenvector x. This result demonstrates the relationship between eigenvalues and matrix powers, illustrating that raising the matrix to a power corresponds to raising the eigenvalue to the same power while keeping the eigenvector unchanged.

Learn more about matrix here:

https://brainly.com/question/29132693

#SPJ11

The function of the table will be y = 5x.

And, The graph of the function is shown in figure.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Jalyn made a table of how much money she will earn from babysitting as;

1, 5

2, 10

3, 15

4, 20

Now,

Find the function of the table as;

Take two points of the table are,

(x, y) = (1, 5), (2, 10)

We know that;

The equation of function is find as;

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 5 = (10 - 5) / (2 - 1)  (x - 1)

⇒ y - 5 = 5 (x - 1)

⇒ y - 5 = 5x - 5

⇒ y = 5x - 5 + 5

⇒ y = 5x

Thus, The function of the table will be y = 5x.

And, The graph of the function is shown in figure.

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ2

Answer:

2 11/12 cups of flour

Step-by-step explanation:

well 2 recipes is 2 1/2 cups of flour

1/3 is 1/3 x 1 1/4= 1/3 + 1/12= 5/12

so 2 11/12 cups of flour

The complete statements are:

The complete question is added as an attachment

The roots are given as:

x = 0 second

and

x = 9.8 seconds

x = 0 implies that the height of the arrow was 0 meters above his bow after 0 seconds

x = 9.8 implies that  it takes approximately 9.8 seconds for the arrow to return to the height of the bow.

The x-value of the vertex is

x = (0 + 9.8)/2

Evaluate

x = 4.9

Approximate

x = 5

This means that the vertex is approximately 5 seconds

Read more about quadratic functions at:

https://brainly.com/question/1214333

#SPJ1

Answer: x< -30

Step-by-step explanation:

Answer:

x=k/6-c/6

hope this helps

Step-by-step explanation:

The inequality that represents the situation is 8.50x < 35 and the pounds of shrimp Luna can buy is 4.

Inequality is a statement that two or more mathematical expressions are unequal.

Inequalities are represented as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), and not equal to (≠).

The cost price of shrimp per pound = $8.50

The total spending budget = $35

Let the number of pounds of shrimp Luna can buy = x

8.50x < 35

x = 4

Thus, the total amount Luna can spend on shrimp is $34 (4 x $8.50), which is less than $35.

Learn more about inequalities at https://brainly.com/question/25275758

#SPJ1

The probability is approximately 0.9544 or 95.44%.

To solve this problem, we need to calculate the z-scores for both values of interest and use a standard normal distribution table or calculator to find the probability.

The z-score for a score of 70 is:

z = (70 - 80) / 5 = -2

The z-score for a score of 90 is:

z = (90 - 80) / 5 = 2

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected student scored between -2 and 2 on the standard normal distribution. This probability is approximately 0.9544.

However, we need to adjust this probability to account for the fact that the scores are not rounded. Since the distribution is continuous, we need to use the probability of the interval between 70 and 90, inclusive, which is:

P(70 ≤ X ≤ 90) = P(X ≤ 90) - P(X < 70)

where X is the random variable representing the exam score.

Using the z-scores we calculated earlier, we can find these probabilities as:

P(X ≤ 90) = P(Z ≤ 2) ≈ 0.9772

P(X < 70) = P(Z < -2) ≈ 0.0228

So, the probability of a randomly selected student scoring between 70 and 90 on the exam is:

P(70 ≤ X ≤ 90) = P(X ≤ 90) - P(X < 70) ≈ 0.9772 - 0.0228 = 0.9544

Therefore, the probability is approximately 0.9544 or 95.44%.

Learn more about probability

brainly.com/question/30034780

#SPJ11

Answer: 12.85

Step-by-step explanation:

It will cost $375 to hire the doctor for 45 minutes

The doctor charges $500 for an hour

60 minutes makes 1 hour

60 minutes= $500

Therefore the amount that will be charged for 45 minutes can be calculated as follows

60 minutes= $500

45 minutes= x

Cross multiply both sides

60x= 500×45

60x= 22500

x= 22500/60

x= 375

Hence it will cost $375 to hire the doctor for 45 minutes

Please see the link below for more information

https://brainly.com/question/15696369?referrer=searchResults


#SPJ1

The probability of vowel or letter D is determined as 4/9.

The probability of vowel or letter D is calculated by applying the formula for probability of an event as follows;

Mathematically, the formula for probability is given as;

P (E) = number of outcomes in event E / total number of outcomes in sample space

If the lucky wheel is divided into 9 sectors of equal size lettered A through I, the number of outcomes include the following;

number of outcomes = A, B, C, D, E, F, G, H, I

vowels in the outcome = A, E, I

letter D in the outcome = D

number of outcomes = {A, E, I} or {D}

P(vowel or D) = 3/9 or 1/9

P(vowel or D) = 3/9 + 1/9

P(vowel or D) = 1/3 + 1/9

P(vowel or D) = 4/9

Learn more about probability here: https://brainly.com/question/25870256

#SPJ1

Answer: \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Step-by-step explanation:

The given expression: \(\sqrt{\dfrac{16n}{m^3}}\)

'

since \(16=4^2\)

\(m^3=m^{2+1}= m^2\times m\)   [\(a^{n+m}=a^n\times a^m\)]

Now, the given expression becomes,

\(\sqrt{\dfrac{4^2n}{m^2\timesn}}=\dfrac{4\sqrt{n}}{m\sqrt{m}}\)

Since there is root in denominator , so we need to rationalize

\(\dfrac{4\sqrt{n}}{m\sqrt{m}}\times\dfrac{\sqrt{m}}{\sqrt{m}}=\dfrac{4\sqrt{mn}}{m\times\sqrt{m}\times\sqrt{m} }\\\\=\dfrac{4\sqrt{mn}}{m\times m}\\\\=\dfrac{4\sqrt{mn}}{m^2}\)

Hence, the correct option is \(4.\ \ \ \dfrac{4\sqrt{mn}}{m^2}\) .

Mia, this is the solution to the exercise:

Let's recall the formula of the area of a rhombus:

• Area = (Diagonal 1 * Diagonal 2)/2

Now, let's also recall the formula of the area of a kite:

• Area = (Diagonal 1 * Diagonal 2)/2

Thus, the correct answers are:

• B. Kite

• D. Rhombus

Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

Your answer is  x=-13/3

Step-by-step explanation:

RS and QT are equal knowing this your equation would be x=4x+13. you get -3x=13 when 4x get cancelled out, divide both side by 3 and you get -13/3

The number of different colors that Sam can use for the triangle is given as follows:

60 different colors.

The Fundamental Counting Theorem (also known as the multiplication rule) is a fundamental principle in combinatorics that describes how to count the number of possible outcomes in a sequence of events.

The theorem states that if there are m ways that one event can occur and n ways that a second event can occur, then there are m x n ways that both events can occur.

The parameters for this problem are given as follows:

Hence the number of options is obtained as follows:

5 x 4 x 3 = 60 options.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751

#SPJ1

Answer:

10-4=6

Step-by-step explanation:

The range is the difference between the biggest and smallest number. In this case, 10 is the biggest number and 4 is the smallest. So we do 10-4, which gives us 6, so 6 is the range.