Liz flips a coin 70 times. The coin lands heads up 21 times and tails up 49 times. Complete each statement. The theoretical probability of the coin landing heads up is what%.

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: 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]

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%.

Answer:

1. 26.6

2. 12.3

3. 23.3

4. 10.9

Step-by-step explanation:

1. tan(31) = 16/x

x = 16/tan(31)

x = 26.62847172

2. sin(43) = x/18

x = 18sin(43)

x = 12.27597048

3. cos(53) = 14/x

x = 14/cos(53)

x = 23.26296198

4. cos(33) = x/13

x = 13cos(33)

x = 10.90271738

Answer:

1. 26.6 units

2. 12.3 units

3. 23.3 units

4. 10.9 units

Step-by-step explanation:

1. We have the opposite and adjacent sides here for angle 31 degrees. So we need to use tangent, which is opposite / adjacent:

[tex]tan(31)=16/x[/tex]

[tex]x=16/(tan(31))[/tex] ≈ 26.6 units

2. We have the opposite and hypotenuse sides here for angle 43 degrees. So we need to use sine, which is opposite / hypotenuse:

[tex]sin(43)=x/18[/tex]

[tex]x=18*sin(43)[/tex] ≈ 12.3 units

3. We have the adjacent and hypotenuse sides here for angle 53 degrees. So we need to use cosine, which is adjacent / hypotenuse:

[tex]cos(53)=14/x[/tex]

[tex]x=14/(cos(53))[/tex] ≈ 23.3 units

4. We have the adjacent and hypotenuse sides here for angle 33 degrees. So we need to use cosine, which is adjacent / hypotenuse:

[tex]cos(33)=x/13[/tex]

[tex]x=13*cos(33)[/tex] ≈ 10.9 units

Hope this helps!

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                                                                                                    

Answer:

Step-by-step explanation:

This is an increase of 9

Or, as a percentage (rounded to two decimal places):

an increase of 50%

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:

113.1

Step-by-step explanation:

V=[tex]\frac{4}{3}[/tex]πr³

Answer: Four is the exterior angle.

Step-by-step explanation:

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:

To calculate the area of Spencer's 7x7 quilt, each square patch measuring 1 3/4 inches is calculated for area (3.0625 sq. in.) and then multiplied by the total number of patches (49), resulting in a total quilt area of 150.0625 square inches.

Spencer made a quilt for his cousin's doll with a 7x7 array of square patches. To find the area of the whole quilt, we need to calculate the area of one patch and then multiply by the total number of patches. The length of each patch is 1 3/4 inches, which can also be represented as 1.75 inches.

First, we find the area of one patch:

Since there are 49 patches in total (7 patches per row × 7 rows), we then find the total area:

Therefore, the area of Spencer's quilt is 150.0625 square inches.

Final answer:

The area of Spencer's quilt is 150.0625 square inches.

Explanation:

Spencer made a quilt for his cousin's doll that had a 7x7 array of square patches, each measuring 1 3/4 inches in length. To find the area of the quilt, you would calculate the area of one patch and then multiply it by the total number of patches in the quilt.

First, convert the inches to a decimal to make the calculation easier:

Area of one square patch = length × width

Since the patches are square, the length and width are the same:

Area of one patch = 1.75 inches × 1.75 inches = 3.0625 square inches

To find the total area of the quilt:

Total area of quilt = area of one patch × number of patches

There are 7 rows and 7 columns in the quilt:

Total patches = 7 × 7 = 49

Total area of quilt = 3.0625 square inches × 49 = 150.0625 square inches

Therefore, the area of the whole quilt is 150.0625 square inches.

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:

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:

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.

The dependent variable is muscle mass.

The dependent variable in this relationship is muscle mass.

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Answer:

hunter

Step-by-step explanation:

Final answer:

Hunter is correct that the hypotenuse of a right triangle acts as the diameter of its circumcircle, with the circumcenter located at the midpoint of the hypotenuse.

Explanation:

When constructing a circumcircle of a right triangle, Hunter's assertion is correct. According to a well-known theorem, the hypotenuse of a right triangle will be the diameter of the circumcircle that can be drawn around the triangle. This is because the center of the circumcircle, known as the circumcenter, is equidistant from all vertices of the triangle, and for a right triangle, this point is the midpoint of the hypotenuse.

Since the circumcenter is the midpoint of the hypotenuse, and the hypotenuse is the longest side of a right triangle, it will also serve as the diameter of the circumcircle. The radius of the circle, therefore, extends from this midpoint to any of the triangle’s vertices. Daniel's statement that the circumcenter would be located inside the triangle is incorrect for a right triangle, though it might be true for acute or obtuse triangles.

Answer:

option A is the correct one

Step-by-step explanation:

The product of the expression negative 9 x (5 minus 2x) is 18x² - 45x.

The correct option is c) negative 18 x minus 45 x.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given expression:

Negative 9 x (5 minus 2x).

To find the product:

First, we simplify the expression,

-9x (5 - 2x)

Solving the parenthesis,

-9 (5 - 2x)

= -45x + 18x².

= 18x² - 45x.

= 18 x squared minus 45 x

Therefore, 18x² - 45x is the required expression.

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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:

[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]

Answer: 205 buttons

Step-by-step explanation:

Garcia has 2 button collections. One has 321 buttons in it. The other has 704 buttons. The total button collection will be:

= 321 + 704 = 1025

Since she wants to divide it equally among 5 friends, we divide 1025 by 5. This will be:

= 1025 ÷ 5

= 205

Each friend will get 205 buttons.

Answer:

Each friend will receive 205 buttons

Step-by-step explanation:

In this question, we are tasked with calculating the number of buttons each of 5 Garcia's friend will receive

Firstly, we will need to find the total number of buttons available

That would be 321 + 704 = 1025 buttons

Now to find the distribution per friend, we simply divider the total by 5

That would be 1025 buttons ÷ 5 = 205 buttons

This means that each of the five friends will receive 205 buttons each

An expression for the profit of the company is 26x - 0.0002x^2 - 120,000.

To find the expression for the profit of a company, we need to subtract the cost from the revenue.

The cost of the company is given by the expression 14x + 120,000, where x represents the quantity of the product being produced or sold.

The revenue of the company is given by the expression 40x - 0.0002x^2, where x represents the quantity of the product being produced or sold.

To find the profit, we subtract the cost from the revenue:

Profit = Revenue - Cost

Profit = (40x - 0.0002x^2) - (14x + 120,000)

To simplify the expression, we distribute the negative sign:

Profit = 40x - 0.0002x^2 - 14x - 120,000

Combining like terms:

Profit = (40x - 14x) - 0.0002x^2 - 120,000

Simplifying further:

Profit = 26x - 0.0002x^2 - 120,000

Therefore, an expression for the profit of the company is 26x - 0.0002x^2 - 120,000.

Final answer:

The profit of a company is the difference between its total revenue and costs, and can be calculated using the formula P = R - (14x - 0.0002x²), where P is profit, R is revenue, and x is the number of units.

Explanation:

To calculate the expression for the profit of the company, we need to find the difference between the total revenue and the total cost.

Given the cost can be modeled by 14x - 0.0002x2, and assuming the revenue is R, the profit P can be represented as:

P = R - (14x - 0.0002x²)

If we are given a specific value for the revenue, we would substitute it in place of R to find an explicit expression for P. For instance, if the revenue is $200,000, the profit formula would be:

P = $200,000 - (14x - 0.0002x²)

It's important to note that the profit decreases as the cost increases, and when costs exceed revenue, the company experiences a loss.

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: 2m+5=15

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2x+5=15 can represent this situation. 15-5=10... 10/2= 5

Answer:

Therefore I would earn $532,761 more on the first investment than in the second investment.

Step-by-step explanation:

The formula of compound interest

[tex]A=P(1+r)^n[/tex]

Compound interest [tex]I=A-P[/tex]

A= Amount after n years

P= Principal

r=Rate of interest

n= Number of years

First investment,

P₁=$22,000, r=12%=0.12 and n=30 years

[tex]A_1= 22,000(1+0.12)^{30}[/tex]

    =659,118.28

   ≈$659,118

[tex]I_1[/tex]= [tex]A_1[/tex]-P₁

  =$(659,118-22,000)

 =$637,118

Second investment,

P₂=$22,000, r=6%=0.06 and n=30 years

[tex]A_1= 22,000(1+0.06)^{30}[/tex]

    =126,356.81

   ≈$126,357

[tex]I_2[/tex]= [tex]A_2[/tex]-P₂

  =$(126,357-22,000)

  =$104357

[tex]I_1-I_2[/tex]

=$(637,118-104,357)

=$532,761

Therefore I would earn $532,761 more on the first investment than in the second investment.

Answer:

30

Step-by-step explanation:

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

45x = 1350 -->

x = 30

Anything to the power of zero should always equal 1.

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

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:

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:

They can be chosen in 6,840 different ways

Step-by-step explanation:

In this question, we are tasked with calculating the number of ways in which the 1st, 2nd and 3rd students can be chosen.

For the first position, we have 20 people vying for the position and we are to select only one for the position.

The number of ways this is achievable is 20C1 ways = 20 ways

For the second position, we are left with 19 students vying for the position and we are to select only one for the position. The number of ways this is possible is 19C1 ways = 19 ways

For the third position, we are left with 18 students vying for the position. The number of ways this is possible is 18C1 ways = 18 ways

Thus, the total number of ways this cane be done is; 20 ×19 ×18 = 6,840 ways