Find the length of AC if PQ is a segment bisector.
Show work.

The length of the line segment with is 9.9 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points B =  (3, 5) and A (-4, -2) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

x₂ = -4

x₁ = 3

y₂ = -2

y₁ = 5

substituting the values to formula

d =√{(-4 - 3)² + (-2 -5)²}

d =√{(-7)² + (-7)²}

d =√{49 + 49}

d = √98

d = 7√2

d = 9.9 units

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Answer:

$2618.52

Step-by-step explanation:

we multiply each monthly payment by the total amount of monthly payments to figure out the overall cost

218.51*12 = 2618.52

Answer:

57/10 is the simplest form

Step-by-step explanation:

To divide fractions you need to do the reciprocal rules.

You also need to convert any mixed numbers to improper to make them easier to divide.

4 3/4 and 5/6 are your fractions.

4 3/4 converted into an improper fraction is 19/4

This is because the rule with this is that you take your whole number multiply it by the denominator and take the product and add it to the numerator.

19/4 divided by 5/6.

You need to flip 5/6 to 6/5 due to the reciprocal rules and also change the division sign to a multiplication sign.

19/4 x 6/5

You can multiply straight across!

19 x 6 and 4 x 5

19 x 6 = 114

4 x 5 = 20

Our answer: 114/20

We still need to simplify this answer

We can divide this result into 2/2.

114/20 = 57/10

57/10 is the simplest form. If you were to divide more, you will get involved with decimals.

Answer: 57/10 is the simplest form

Step-by-step explanation:

You also need to convert any mixed numbers to improper to make them easier to divide.

4 3/4 and 5/6 are your fractions.

4 3/4 conerted into an improper fraction is 19/4

This is because the rule with this is that you take your whole number multiply it by the denominator and take the product and add it to the numerator.

19/4 divided by 5/6.

You need to flip 5/6 to 6/5 due to the reciprocal rules and also change the division sign to a multiplication sign.

19/4 x 6/5

19 x 6 and 4 x 5

19 x 6 = 114

4 x 5 = 20

Our answer: 114/20

We still need to simplify this answer

We can divide this result into 2/2.

114/20 = 57/10

57/10 is the simplest form. If you were to divide more, you will get involved with decimals.

The answer to this Question based on probability is 0.49

What is probability of a event?

It is just defined as number of favourable outcomes divided by the total number of outcomes.

Solution:

We can take example of 100 people to solve the problem easily

P(Bench) = P(B) = 0.56

P(Offecnce) = P(O) = 0.68

P(B U O) = 0.75

we need to find P(B intersection O) = let it denote by P(A) which is probability of selecting a random player and player will be a starter and playing offence

0.75 = 0.56 + 0.68 - P(A)

P(A) = 1.24 - 0.75

P(A) = 0.49

which is required answer

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Answer:

x = 0.5

Step-by-step explanation:

When we add up the distance between the apartment and park with the distance between the park and the coffee shop, the total will equal nine miles.

Our equation will look like this:

(5x + 2) + (25x - 8) = 9

Add up the like terms

5x + 2 + 25x - 8 = 9

30x - 6 = 9

Add 6 to both sides

30x - 6 = 9

      + 6  + 6

30x = 15

Divide both sides by the coefficient, 30, to isolate the variable, x

30x/30 = 15/30

x = 15/30

Reduce

x = 1/2

Answer:

The width is 72

Step-by-step explanation:

The probability that Y is greater than 1 is approximately 0.0228 or 2.28%.

To find the probability that a normally distributed random variable Y with a mean of -1 and a standard deviation of 2 is greater than 1, we can standardize the variable and use the standard normal distribution. First, we calculate the z-score, which represents the number of standard deviations away from the mean: z = (1 - (-1)) / 2 = 2. Next, we look up the probability of z being greater than 2 in the standard normal distribution table. From the table, we find that Pr(Z > 2) is approximately 0.0228. Since Y is normally distributed, the probability that Y is greater than 1 is equal to the probability that Z is greater than 2. Therefore, Pr(Y > 1) ≈ 0.0228. The probability that Y is greater than 1 is approximately 0.0228 or 2.28%.

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Answer:

x+y= idk

Step-by-step explanation:

sorry i need the points

Answer:

15

Step-by-step explanation:

so you know that the hypotenuse for the triangle with "x"'s is 5 square root two, and because we know that the triangle is an isoceles triangle we know the other two side are equal and as a result x=5. Now for the next triangle it is 5 square root 2 on both sides and that is also an isoceles triangle and y is the hypotenuse so it 5 square root 2 times square root 2 which just becomes 2 so then it is 5 times 2 which is 10. So Y=10 and X=5 so X+Y=15.

Answer:

2909

Step-by-step explanation:

Answer:

So the answer for your question is Sarah is correct because square root 2 is irrational:)

Step-by-step explanation:

Rational numbers are numbers that can be expressed as a fraction or part of a whole number. (examples: -7, 2/3, 3.75) Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers.

√  means square root. Square root means a number which produces a specified quantity when multiplied by itself. SO for example 7 is a square root of 49...

Example of another irrational and rational number: 74 is rational. Irrational number would be  3.14:)

Hope this helped...yeah I wrote a lot of stuff, I hope you understand it;)

Answer:

x + 35 = 70

   -35    -35

–––––––––––

     x = 35

Step-by-step explanation:

35 + 35 = 70

:))

The expression that represents the correct factorization of the polynomial 8x³  +  125 exists (2x + 5) (4x²  -  10x  +  25)

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

A polynomial is not an expression that contains a variable with exponents that are negative or fractional, divides by a variable, or has a variable inside a radical.

Let the given polynomial expression be 8x³  +  125

The expression 8x³  +  125 can be rewritten as (2x)³ + 5³

By using the sum of cubes formula, we get

(2x)³ + 5³  =  (2x  + 5)( ((2x)² - 2x(5) + 5²)

8x³  +  125 = (2x + 5) (4x²  -  10x  +  25)

Therefore, the expression that represents the correct factorization of the polynomial 8x³  +  125 is (2x + 5) (4x²  -  10x  +  25)

The complete question is:

A polynomial expression of degree three is shown below. 8x^3 + 125 Which expression represents the correct factorization of the polynomial?

A (2x + 5)(4x + 10x + 25)

B (2x + 5)(4x + 10x-25)

C (2x + 5)(4x - 10x +25)

D (4x + 25)(2x - 10x+5)

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Answer:

So 13 x 3=  39

Step-by-step explanation=

your just gonna multiply 13x3 to get your answer

Hope this helped :D

Answer:

between 0 cm and 21 cm

Step-by-step explanation:

BC could be anything between zero and 8+13=21 as per triangle inequality theorem:

0 < BC < AB+AC or

0 cm < BC < 21 cm

Answer:

11.73

Step-by-step explanation:

Converting 8 miles per hour to feet per second, the answer would be 11.73 feet per second

Answer:

m = -7

Step-by-step explanation:

Answer:

Final temperature of the solution is 14°C.

Step-by-step explanation:

Given that,

Initial temperature of the solution, \(T_i=31^{\circ}\ C\)

The change in temperature of the solution, \(\Delta T=-17^{\circ}\ C\)

We need to find the final temperature of the solution.

Change in temperature = Final temperature - initial temperature

\(\Delta T=T_f-T_i\\\\T_f=\Delta T+T_i\\\\T_f=-17+31\\\\T_f=14^{\circ} C\)

So, the final temperature of the solution is 14°C.

The Sweet Drip Beverage Co sells cans of soda popo in machines, and the company has observed that when the price per can is 50 cents, the average monthly sales are 26,000 cans. For each nickel (5 cents) increase in price, the company experiences a decrease of 1,000 cans in monthly sales.

This information suggests an inverse relationship between the price of the cans and the number of cans sold per month. For every nickel increase in price, the company experiences a decrease in sales of 1,000 cans. This implies that customers are sensitive to price changes, with higher prices leading to lower demand for the product. The relationship can be described by a linear equation, where the number of cans sold per month is a function of the price. The specific equation can be determined by using the given data points and applying linear regression techniques.

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Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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Here we have some given restrictions that affect the number of medals, using these, we want to find the maximum number of bronze medals that can be awarded.

We will find that:

The maximum number of bronze medals that can be awarded is 535

Now let's see how we can get that.

Let's define the variables:

G = number of gold medals.

S = number of silver medals.

B = number of bronze medals.

Now we can see what information we have.

There are 2021 participants.

The number of silver medals is at least twice the number of gold medals.

S ≥ 2*G

The number of bronze medals is at least twice the number of silver medals:

B ≥ 2*S.

The number of all medals is not more than 40% of the number of participants.

The total number of medals is (G + S + B)

40% of the total number of participants is:

(40%/100%)*2021 = 0.4*2021 = 808.4

Then we have:

G + S + B ≤ 808.4

We can rewrite the above inequality as:

G + S + B ≤ 808.

Then we have 3 inequalities:

S ≥ 2*G

B ≥ 2*S

G + S + B ≤ 808

Now we want to maximize the number of gold medals.

This means that the total number of medals should be exactly 808 (the maximum number of total medals) so we have:

G + S + B = 808.

Also, if we want to maximize the number of gold medals, then we need to minimize the number of silver medals and the number of bronze medals, such that we get:

S = 2*G

B = 2*S

Now we have 3 equations:

G + S + B = 808

S = 2*G

B = 2*S

Replacing the third equation in the first one, we get:

G + S + 2*S = 808

G + 3*S = 808

Now we can replace:

S = 2*G

in the above equation to get:

G + 3*(2*G) = 808

G + 6*G = 808

7*G = 808 =

G = 808/7 = 115.43

But we can have 0.43 of a gold medal, so we need to round down to the next whole number:

G = 115

Now, with this restriction, we want to find the maximum number of bronze medals.

This means that we need to minimize the number of silver medals, so we use:

S = 2*G = 2*115 = 230

And the number of bronze medals will be such that:

B + G + S  = 880

B + 115 + 230 = 880

B = 880 - 115 - 230 = 535

The maximum number of bronze medals that can be awarded is 535

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According to fraction, another way to express 8 feet is written as 2 ²/₃ yards.

In math the term fraction refers the numerical values that are a part of the whole.

As we have given that a clothesline rope is 8 feet long.

Now, we have to find another way to express 8 feet.

The process of converting a foot measurement to a yard measurement, here we have to divide the length by the conversion ratio.

As we all know that one yard is equal to 3 feet, therefore, here you can use this simple formula to convert:

=> feet ÷ 3 = 1 yard

As the given feet measurement is 8 feet.

Then the equivalent yard measurement is written as,

=> 8/3 feet = yards

After the simplification, that is convert it into mixed fraction form, then we get the resulting yards as 2 ²/₃ yards.

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Answer:

(a+6)²

by identity (a+b)²=a²+2ab+b²

(a+6)²= a²+ 2×a×6 + 6²

= a²+ 12a + 36

(2a)²+5a = 4a²+5a

Answer:

64

Step-by-step explanation:

16 chapters per hour times 4 hours is 64 chapters

Answer:

kay

Step-by-step explanation:

Let us first understand what is meant by the term probability of happening of an event. The term probability of an event happening tells us about the extent or how many times it is likely to happen in a given number of tries. For example, if we throw a die of six faces, then the probability of a number to come on the top of the dice tells us about the extent to which that is likely to occur.

The probability of an event to occur in an experiment is equal to the ratio of the outcomes in which this event happens to the total number of outcomes of the experiment. A pack of cards contains 52 total cards. Therefore, when we pick a card from the set there can be 52 different outcomes.

(i) A pack of cards contains 13 red cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a red card is 1352=14.

(ii) A pack of cards contains 13 black cards. Therefore, out of those 52 outcomes, 13 outcomes are required. Hence, the probability of getting a black card is 1352=14

(iii) A pack of cards contains 4 black cards. Therefore, out of those 52 outcomes, 4 outcomes are required. Hence, the probability of getting an ace is 452=113.

Note: Note that probability is not always sure or it doesn’t guarantee that the specific event will surely happen in those number of trials. This means that the probability of getting an ace card does not mean that in four tries we will surely get an ace. Probability just tells us how likely the event may happen.

Answer:

6+9 is the two numbers

Step-by-step explanation:

Answer:

6 and 9

Step-by-step explanation:

We can write out all possible numbers

1 and 14 (difference is 13, not 3) X

2 and 13 (difference is 11, not 3) X

3 and 12 (difference is 9, not 3) X

4 and 11 (difference is 7, not 3) X

5 and 10 (difference is 5, not 3) X

6 and 9 (difference is 3, checks out!) ✔

7 and 8 (difference is 1, not 3) X

The reduced gradient is analogous to the residual for linear models.

In linear regression, the residual represents the difference between the observed values and the predicted values of the dependent variable. Similarly, in optimization, the reduced gradient represents the difference between the current solution and the optimal solution. It is a measure of how far the current solution is from the optimal solution in the direction of the search. By minimizing the reduced gradient, we can move closer to the optimal solution.

The reduced gradient is a widely used optimization technique in non-linear programming that allows for efficient computation of the descent direction at each iteration while accounting for constraints. It involves calculating a partial derivative of the objective function with respect to the variables that are not restricted by the constraints, and then projecting the resulting gradient onto the space defined by the constraints. The resulting vector is called the reduced gradient, and it points in the direction of the steepest descent that is feasible.

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Answer:

192 cm

Step-by-step explanation:

3.5+4.5=8

8*24=192

Answer:

she would have to go 30 miles per hour or less to make this possible

Step-by-step explanation:

if it went over 35 31 miles per hour they would run out of gas before they got there

The  the volume of the solid paraboloid z=48−3x2−3y2z=48−3x2−3y2d is 1/2(2304π) cubic units

To find the volume of the solid above the xy-plane using polar coordinates, we will integrate the volume element dv over the region of the paraboloid in the xy-plane using double integral.The paraboloid will intersect the xy plane where z = 0, hence we substitute z with 0 to find the equation of the circle given by the intersection of the paraboloid and the xy-plane.

0 = 48 - 3x² - 3y²3x² + 3y² = 48x² + y² = 16

Hence the radius of the circle is √16 = 4.

The equation of the circle is x² + y² = 16.

We will then take the projection of the paraboloid on the xy-plane, the region D is a circle of radius 4.

Limits of integration 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π

The volume element in cylindrical coordinates is given by dv = r dr dθ dz

Volume of solid is given by ∭ dv

Where the region of integration D is the region in the xy-plane enclosed by the circle x² + y² = 16.

Using polar coordinates

x = r cosθ,

y = r sinθ,

z = zr r^2 + z^2 = 48 - 3x^2 - 3y^2r^2 + z^2 = 48 - 3(r^2 cos²θ) - 3(r^2 sin²θ)r^2 + z^2 = 48 - 3r^2cos²θ - 3r^2sin²θr^2 + z^2 = 48 - 3r^2(cos²θ + sin²θ)r^2 + z^2 = 48 - 3r²r² + z² = 48 - 3r²r² = 48 - 3r² - z²z = √(48 - r²)0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π∭ dv = ∫∫∫ r dr dθ dzwhere r varies from 0 to 4, θ varies from 0 to 2π and z varies from 0 to √(48 - r²)∭ dv = ∫₀²π∫₀⁴r√(48 - r²)drdθ= 1/2(48)²π= 1/2(2304π) cubic units.

Therefore, the volume of the solid is 1/2(2304π) cubic units.

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