Determine the probability of the event, given the following information. Express as a reduced fraction.

A drawer contains 30 pens of various colors: 4 are black, 10 are blue, 3 are red, 6 are green, 6 are blue and red, and 1 is white

A green pen is removed from the drawer and replaced before a black pen is removed.

To solve the system of equations y=x^2-3x+2 and y=-9x-3, set them equal and solve the resulting quadratic equation using the quadratic formula to obtain the solutions for x; then substitute back to find y.

To solve the system of equations given by y = x2 - 3x + 2 and y = -9x - 3, we must find the values of x and y that satisfy both equations simultaneously. Since both expressions are equal to y, we can set them equal to each other to find the x-values that satisfy both equations:

x2 - 3x + 2 = -9x - 3

Rearrange the equation by adding 9x and 3 to both sides:

x2 + 6x - 1 = 0

This is a quadratic equation, which we can solve by factoring, completing the square, or using the quadratic formula. In this case, factoring is not straightforward, so we may opt for the quadratic formula:

x = (-b ± √(b2 - 4ac)) / (2a)

Here, a = 1, b = 6, and c = -1. Plugging these into the quadratic formula gives us:

x = (-6 ± √(36 + 4)) / 2

x = (-6 ± √(40)) / 2

x = (-6 ± 2√(10)) / 2

x = -3 ± √(10)

So the solutions for x are x = -3 + √(10) and x = -3 - √(10). To find the corresponding y-values, substitute these x-values back into either of the original equations.

The solution to the system of equations is:
(x, y) = (-1, 6) and (-5, 42)

To solve the system of equations:

1. Substitute the expression for y from the second equation into the first equation. This gives us:

x^2 - 3x + 2 = -9x - 3

2. Rearrange the equation to bring all terms to one side, setting the equation equal to zero:

x^2 - 3x + 9x + 2 + 3 = 0

x^2 + 6x + 5 = 0

3. Factor the quadratic equation:

(x + 1)(x + 5) = 0

4. Apply the zero product property to find the values of x that satisfy the equation:

x + 1 = 0 or x + 5 = 0

x = -1 or x = -5

5. Substitute these values of x back into either equation to find the corresponding values of y. Let's use the second equation:

For x = -1:
y = -9(-1) - 3 = 9 - 3 = 6

For x = -5:
y = -9(-5) - 3 = 45 - 3 = 42

Therefore, the solution to the system of equations is:
(x, y) = (-1, 6) and (-5, 42)

Answer:

y = 6x

Step-by-step explanation:

Using [tex]\frac{rise}{run}[/tex] formula,

[tex]\frac{6}{1}[/tex] is the rise and run

This equals 6.

Hope this helps.

Answer:

3 42/48 + 6 12/48

Step-by-step explanation:

Final answer:

To find the equivalent expression, convert the mixed numbers to improper fractions, subtract the fractions, and then convert the result back to a mixed number.

Explanation:

The expression equivalent to 3 7/8 - 6 1/4 is:

Step 1: Convert the mixed numbers to improper fractions: 3 7/8 = 31/8 and 6 1/4 = 25/4.

Step 2: Subtract the fractions: 31/8 - 25/4 = 31/8 - 50/8 = -19/8.

Step 3: Convert the result back to a mixed number: -19/8 = -2 3/8.

Answer:

C. 22x

Step-by-step explanation:

7x+15x=22x

Answer:

C. 22x

Step-by-step explanation:

7x + 15x = 22x

You simply need to add 7 and 15 and you get 22x.

Answer:

31

Step-by-step explanation:

The function given in this problem is described by the expression

[tex]f(x)=3x+1[/tex]

In this problem, we want to find

[tex]f(10)[/tex]

Which means that we want to evaluate the function when the value of x is 10, so when

[tex]x=10[/tex]

To solve the problem, we just need to substitute x = 10 into the expression of f(x). By doing so, we find:

[tex]f(10)=3\cdot 10 +1 = 30+1 = 31[/tex]

Therefore, the correct option is

31

Answer:

31

Step-by-step explanation:

Answer:

$9865.76¢

Step-by-step explanation:

Please kindly check the attached file for explanation.

Using compound interest, it is found that the amount in the account is of $9,865.76.

Compound interest:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

In this problem:

The amount in the equation is:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]A(8) = 6500(1 + \frac{0.0525}{4})^{32}[/tex]

[tex]A(8) = 9865.76[/tex]

The amount is of $9,865.76.

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Answer:

20 minutes

Step-by-step explanation:

40% = 8 minutes

40% x 2.5 = 100%

8 minutes x 2.5 = 20 minutes

Answer:

8m = 0.4

Step-by-step explanation:

I think thats the equation you are looking for. or i may be late to answer this question.

Final answer:

Cruz's running speed is 10 mph, and his biking speed is 16 mph, which we found by setting up an equation representing the total distance he covered and the time spent on each activity at their respective speeds.

Explanation:

To determine Cruz's biking and running speeds, we can use the information given about the total distance and the ratio of his speeds. The information tells us that Cruz ran for 1.5 hours (from 6:00 to 7:30) and biked for 2.25 hours (from 7:30 to 9:45). If we let r represent his running speed, then his biking speed would be 1.6r because it's said to be 1.6 times his running speed.

Cruz's total running distance would then be r × 1.5 hours, and his biking distance would be 1.6r × 2.25 hours. We know that the total distance covered is 51 miles, so we can set up the following equation:

1.5r + 1.6r × 2.25 = 51

Now, solve for r:

1.5r + 3.6r = 51

5.1r = 51

r = 51 / 5.1

r = 10 miles per hour

Therefore, Cruz's running speed is 10 mph, and his biking speed is:

1.6 × 10 mph = 16 mph

Cruz's running speed is 10 mph, and his biking speed is 16 mph.

Answer: x=8

Width=8 inches

Length=13 inches

Final answer:

The width of the rectangle is 8 inches and the length is 13 inches, as determined by solving the quadratic equation representing the area of the rectangle.

Explanation:

To solve for the dimensions of the rectangle, we need to find the value of x, which represents the width of the rectangle. The quadratic equation we have is x² + 5x - 104 = 0.

Factoring this equation, we are looking for two numbers that multiply to -104 and add to 5.

These numbers are 13 and -8, so the equation factors to (x + 13)(x - 8) = 0. Setting each factor equal to zero gives us two possible solutions for x: x = -13 or x = 8.

Since a width cannot be negative, the only sensible solution for this problem is x = 8 inches. Given that the length is 5 inches more than the width, the length will be 8 inches + 5 inches = 13 inches.

Dimensions of the rectangle:

Width = 8 inches

Length = 13 inches

Answer:

the first and 5th  

Step-by-step explanation:

this is right

a) The difference in the distances the boys ran, so this is a subtraction problem

d) The equation is s - 2.3 = 6.8

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the distance ran be Dean be represented as d

Let the distance ran be Sam be represented as s

And , Dean ran 2.3 fewer kilometers than Sam

So , difference in the distances the boys ran, so this is a subtraction problem  

On simplifying , we get

s - 2.3 = d   be equation (1)

And , when d = 6.8 km

s - 2.3 = 6.8

Adding 2.3 km on both sides of the equation , we get

s = 9.1 km

Therefore , the value of s is 9.1 km

Hence , the distance ran be Sam is 9.1 km

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Answer:

The correct option is;

(x, y) → (215·x, 215·y)

Step-by-step explanation:

An enlargement is a form of transformation involving an alteration of the size of the shape. When a shape is to be enlarged, the center of the shape is noted and the enlargement of the dimensions of the shape from that center is by multiplication of each point by the factor of the enlargement or the scale factor.

Therefore, based on the requirement for enlargement, and given the dimension of the point from the center as (x, y) the enlargement then is (215·x, 215·y), where 215 is the scale factor.

Answer:

A. (x, y) → (215x, 215y)

Step-by-step explanation:

Enlargement of a figure is the process of increasing the size of a given figure by the use of a scale. It requires the use of a scale factor that is greater than 1 to form an image. This is called dilation in transformation.

Transformation is the process of manipulating the size or orientation of a figure. To enlarge a shape, a center of enlargement is required.

Thus, the rule that signifies enlargement of a figure is ;

(x, y) → (215x, 215y)

This implies multiplying the initial coordinate x and y by a factor of 215 to produce a required size of an image.

Answer:

200 are on screen 1

125 are on screen 2

175 went to screen 3

Step-by-step explanation:

10% is 50 so 50 x 4 =200

25% of 500 is 12, divide 500 by 4

35% is 25% + 10% = 125 + 50 = 175

Answer:

The surface area is 294 ft^2 (please give branliest)

Step-by-step explanation:

area of one side 49

multiply by 6 sides

The surface area of the cube is equal to 294 square inches.

How to calculate the surface area of the cube

In this problem we find the representation of a cube, whose surface area, that is, the sum of the areas of all faces of the cube, must be computed in accordance with this formula:

A = 6 · l²

Where:

If we know that l = 7 in, then the surface area of the cube is equal to:

A = 6 · (7 in)²

A = 6 · 49 in²

A = 294 in²

The cube has a surface area of 294 square inches.

Answer:

no

Step-by-step explanation:

A set of three integers that can be the lengths of the sides of a right triangle is called a Pythagorean triple. The simplest Pythagorean triple is the set “3, 4, 5.” These numbers are the lengths of the sides of a “3-4-5” Pythagorean right triangle. The list below contains all of the Pythagorean triples in which no number is greater than 50.

3, 4, 5

5, 12, 13 6, 8, 10

7, 24, 25 8, 15, 17 9, 12, 15 9, 40, 41 10, 24, 26 12, 16, 20 12, 35, 37

14, 48, 50 15, 20, 25 15, 36, 39 16, 30, 34 18, 24, 30 20, 21, 29 21, 28, 35 24, 32, 40 27, 36, 45 30, 40, 50

Example Problems

Find the length of the missing side.

13 25 x7

12 x

From the list above, the missing From the list above, the missing side is “5” side is “24”

Show why the set “6,8,10” is a Pythagorean triple.

c2 = a2 + b2 102 =82 +62 100 = 64 + 36 100 = 100

Since the Pythagorean equation is satisfied, the set “6,8,10” is a Pythagorean triple.

Answer:

NO.

Step-by-step explanation:

By the Pythagoras theorem if 30^2 = 12^2 + 18^2 it is a right triangle.

30^2 = 900

12^2 = 144

18^2 = 324

Adding 12^2 + 18^2 = 468  so the answer is no.

Answer:

16.49 cubic inches.

Step-by-step explanation:

Given:

A waffle cone has a height of 7 inches and a diameter of 3 inches.

Question asked:

What is the volume of ice cram that can be contained within the cone?

Solution:

First of we will find the radius ;-

Diameter = 3 inches

Radius, r = [tex]\frac{Diameter}{2} =\frac{3}{2} =1.5\ inches[/tex]

As we know:

[tex]Volume\ of\ cone=\frac{1}{3} \pi r^{2} h[/tex]

                          [tex]=\frac{1}{3} \times3.14\times1.5\times1.5\times7\\ \\ =\frac{49.455}{3} \\ \\ =16.485[/tex]

Thus, volume of ice cream will be 16.49 cubic inches.

Answer:

30

Step-by-step explanation:

x(45) = 27(50) -->

45x = 1350 -->

x = 30

Answer:

The answer to your question is slope = -2

Step-by-step explanation:

Data

A = (5, 9)

B = (4, 11)

slope = m = ?

Slope means the steepness of a line.

Process

1.- Write the formula to calculate the slope

   m = (y2 - y1) / (x2 - x1)

   x1 = 5   y1 = 9   x2 = 4   y2 = 11

2.- Substitution

    m = (11 - 9) / (4 - 5)

3.- Simplification

    m = 2/-1

4.- Result

    m = -2

Answer: AB=5.66, AC=4

Step-by-step explanation:

So this triangle is a 45-45-90 triangle, meaning it has one 90 degree angle and two 45 degree angles.

If you remember from geometry, the sides that have the same angle have the same length, and seeing as angle A is 45 degrees and side BC is 4, we can know for certain that angle B is 45 degrees and side AC is also 4.

This is because angle C is already marked as the 90 degree angle due to the square symbol in it.

Now to find side AB, we would use our friend the Pythagorean Theorem, which states that [tex]a^2+b^2=c^2[/tex].

Let a = side BC and b = side AC, meaning c = side AB.

Now plug in the values and solve:

[tex]4^2+4^2=c^2[/tex]

[tex]32=c^2[/tex]

[tex]\sqrt{32} =\sqrt{c^2}[/tex]

[tex]5.65685=c[/tex]

Answer:

7 out of 8

Step-by-step explanation:

Answer:

A: 8x-12

B: 5(n+3)

Step-by-step explanation:

A) Distribute 4 to the numbers inside the parenthesis.

4 x 2x= 8x

4 x -3= -12

8x-12

B) 5 is divisible to 15, so you can divide it with both numbers.

5/5=1

15/5=5

5(n+3)

Answer:

first one is 4×2x-4×3 while the second is 5(n+3)

Step-by-step explanation:

you needed to expand letter a. and simplify letter b.

Answer: (2,8)

Step-by-step explanation:

Answer:

deeznuts

Step-by-step explanation:

Answer:

[tex]20[/tex]

Step-by-step explanation:

GIVEN: Tina, Sijil, Kia, vinayash Alisha and shifa are playing game by forming two teams Three players in each team.

TO FIND: how many different ways can they be put into two teams of three players.

SOLUTION:

Total number of players [tex]=6[/tex]

total teams to be formed [tex]=2[/tex]

total players in one team [tex]=3[/tex]

we have to number of ways of selecting [tex]3[/tex] players for one team, rest [tex]3[/tex] will go in other team.

Total number of ways of selecting [tex]3[/tex] players [tex]=^6C_3[/tex]

                                                                      [tex]=\frac{6!}{3!3!}[/tex]

                                                                     [tex]=20[/tex]

Hence total number of different ways in which they can be put into two different teams is [tex]6[/tex]

Anything to the power of zero should always equal 1.

There shouldn't be any reason why it will be undefined.

Answer:

(-16,24)

Step-by-step explanation:

In this problem, we have segment PR, where the endpoins have coordinates

P (-22, 32)

R (5, -4)

We want to find point Q along the segment such that

PQ : QR = 2 : 7 (1)

We can write the coordinates of point Q as

[tex]Q(x_P,y_P)[/tex]

So we can now rewrite eq(1) for both the x- and y- variable:

[tex]\frac{x_Q-x_P}{x_R-x_Q}=\frac{2}{7}[/tex] (2)

[tex]\frac{y_Q-y_P}{y_R-y_Q}=\frac{2}{7}[/tex] (3)

We start by solving eq(2) to find the coordinate x of point Q:

[tex]7(x_Q-x_P) = 2(x_R-x_Q)\\7x_Q-7x_P=2x_R-2x_Q\\9x_Q=2x_R+7x_P\\x_Q=\frac{2x_R+7x_P}{9}=\frac{2(5)+7(-22)}{9}=-16[/tex]

While for the y-coordinate:

[tex]7(y_Q-y_P) = 2(y_R-y_Q)\\7y_Q-7y_P=2y_R-2y_Q\\9y_Q=2y_R+7y_P\\y_Q=\frac{2y_R+7y_P}{9}=\frac{2(-4)+7(32)}{9}=24[/tex]

So the coordinates of Q are (-16,24).

The coordinate of Q is [tex]Q=(-16,4)[/tex]

To understand more, check below explanation.

To find the coordinate of Q, we use section formula,

                             [tex]Q=(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} )[/tex]

It is given that,

           [tex](x_{1},y_{1})=(-22,32),(x_{2},y_{2})=(5,-4), m_{1}=2,m_{2}=7[/tex]

Substitute above values in above section formula,

             [tex]Q=(\frac{(2*5)+(7*-22)}{2+7}, \frac{(2*32)+(7*-4)}{2+7})\\\\Q=(-\frac{144}{9} ,\frac{36}{9} )\\\\Q=(-16,4)[/tex]

Therefore, the coordinate of Q is [tex]Q=(-16,4)[/tex]

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Answer:

He earned $9.25

Step-by-step explanation:

First, you have to create an equation.

346.88= 37.5h

Then divide 346.88 by 37.5

You get 9.25=h

Rodrick earned $9.25 per hour.

Rodrick earned approximately $9.25 per hour.

To find out how much Rodrick earns per hour, we need to divide his total pay by the number of hours worked. In this case, Rodrick worked for 37.5 hours and earned $346.88. So, to find his earnings per hour, we divide $346.88 by 37.5:

Earnings per hour = Total pay / Number of hours

Earnings per hour = $346.88 / 37.5

Earnings per hour ≈ $9.25

Therefore, Rodrick earned approximately $9.25 per hour.

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Answer:

You can either factor or use quadratic formula to find where h(x)=0

Step-by-step explanation:

Remember that the ball is on the ground when h(x)=0 since that is the height. There will be two zeros,  one is a negative number so would be before you kicked the ball, the other one will be when the ball comes back down.

Answer:

The exponents of a start at n and decrease until they reach 0 . The exponents of b start at 0 and increase until they reach n

Step-by-step explanation:

The general formula for [tex](a+b)^n[/tex] is:

[tex]a^n + C_1a^{n-1}b + C_2a^{n-2}b^2 + ... + C_{n-1}a^2b^{n-2} + C_nab^{n-1} + b^n[/tex]

Therefore, the exponents of a start at n and decrease until they reach 0 . The exponents of b start at 0 and increase until they reach n

Answer:

The balance of Laura's account at the end of 3 years will be $4,870.

Step-by-step explanation:

Formula of simple interest:

[tex]I[/tex]=Prt

[tex]I[/tex] =  simple interest

P= Principal

r = rate of interest

t= time in year.

Amount after t years (A)= P+[tex]I[/tex].

Given that,

Laura deposits $4,000 at a rate 7.25%  simple interest.

Here, P=$4,000, r=7.25%= 0.0725, t=3 years

[tex]I[/tex]=Prt

 =$(4,000×0.0725×3)

=$870

The balance of Laura's account at the end of 3 years will be =$(4,000+870)

=$4,870                                                                                                    

To find the probability that the mean benefit for a random sample of 25 patients is less than $3920, we calculate the z-score and use the z-table to find the probability. The probability is approximately 0.0749, or 7.49%.
To find the probability that the mean benefit for a random sample of 25 patients is more than $4230, we follow the same steps and find that the probability is approximately 0.0179, or 1.79%.

To find the probability that the mean benefit for a random sample of 25 patients is less than $3920, we need to use the standard deviation and the sample size. The formula we'll use is:

Z = (X - μ) / (σ / sqrt(n))

Where Z is the z-score, X is the value we're interested in, μ is the mean, σ is the standard deviation, and n is the sample size.

Z = (3920 - 4064) / (460 / sqrt(25))

Z = -1.44

P(X < 3920) = P(Z < -1.44)

Z = (4230 - 4064) / (460 / sqrt(25))

Z = 2.13

P(X > 4230) = P(Z > 2.13)

Using the z-table, we find that the probability is approximately 0.0179, or 1.79%.

The probable question may be:

The average yearly Medicare hospital insurance benefit per person was $4064 in a recent year. Suppose the benefits are normally distributed with a standard deviation of $460. Round the final answers to four decimal places and intermediate Z value calculations to two decimal places.

Find the probability that the mean benefit for a random sample of 25 patients is less than $3920

P(X <3920) =

Find the probability that the mean benefit for a random sample of 25 patients is more than $4230

P (X> 4230) =

Average yearly Medicare hospital insurance benefits below $4500: z-score ≈ 0.95, probability ≈ 0.8289. About 82.89% benefits fall below this threshold.

let's break down the steps to solve this problem:

Given:

- Average yearly Medicare hospital insurance benefit [tex](\( \mu \))[/tex] = $4064

- Standard deviation[tex](\( \sigma \))[/tex] = $460

We are asked to find the probability of Medicare hospital insurance benefits being below a certain value, which requires calculating the z-score.

The z-score formula is given by:

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

Where:

- ( X ) is the value we want to find the probability for,

[tex]- \( \mu \)[/tex] is the mean,

[tex]- \( \sigma \)[/tex] is the standard deviation.

Let's say we want to find the probability for Medicare hospital insurance benefits below $4500. Substituting the values into the formula:

[tex]\[ z = \frac{{4500 - 4064}}{{460}} \][/tex]

[tex]\[ z = \frac{{436}}{{460}} \][/tex]

[tex]\[ z \approx 0.95 \][/tex]

Now, we need to find the probability corresponding to the z-score we calculated. We can use a standard normal distribution table or a calculator for this purpose. The z-score of 0.95 corresponds to a probability of approximately 0.8289.

This means that approximately 82.89% of Medicare hospital insurance benefits are below $4500.

The probability of Medicare hospital insurance benefits being below $4500 is approximately 0.8289 or 82.89%.