Find f(10) for this piecewise-defined function.
f(x) = { -4x + 1 if x < 3
{2/5x -3 if x > 3


Write your answer as an integer or as a fraction in simplest form.
f(10) =

Answer:

Let x be the first unknown angle, and y be the second unknown angle.

We know that the sum of the three angles in a triangle is 180 degrees, so:

85 + 9kx + 10kx = 180

where k is a constant representing the ratio of the other two angles.

Simplifying the equation, we get:

19kx = 95

Dividing both sides by 19k, we get:

x = 5/k

Since the ratio of the other two angles is 9:10, we know that:

y = 9kx = 9k(5/k) = 45

So the measures of the two unknown angles are:

x = 5/k and y = 45

We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:

5/k + 45/k = 95

50/k = 95

k = 50/95

Using this value of k, we can find the measures of x and y:

x = 5/k = 5/(50/95) = 9.5

y = 9kx = 9(50/95)(9.5) = 47.37

Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).

Step-by-step explanation:

Answer:

(x,y) ——-> ( - x ,  y )

Step-by-step explanation:

When reflected across the y-axis, the sign of the x will change. So, the answer to this is (x,y) ——-> ( - x ,  y )

The time period required is 31.91 months(Approx)

The monthly payments based on the given information would be $129.88

Putting into a financial calculator;

PV=-1245

PMT=50

I/Y=(19/12)=1.58333333%

Solving for N;we get N=31.91

Hence time period required=31.91 months(Approx)

b.Putting into a financial calculator;

PV=-2456.80

N=(2*12)=24

I/Y=(23.99/12)=1.99916667%

Solving for PMT;we get PMT=129.88

Hence monthly payments=$129.88(Approx)

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You should invite at least 23 guests to your party to have at least a 2/3 chance of having a guest with the same birthday as yours.

For your party, you need to invite at least 23 randomly chosen guests in order to have a probability of 2/3 or higher of having a guest with the same birthday as yours. This is known as the birthday paradox and it is based on the probability of two people having the same birthday. To calculate the number of guests needed for the probability of having at least one match, you can use the following formula:

P(at least one match) = 1 - (365/365)^n

where n is the number of guests you invite.
So, to solve for n, you would rearrange the equation to:

n = ln(1-P) / ln(365/365)

When P = 2/3, this equation gives us n = 23.

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A.

by simply putting the suggested solution into the equation and see if it stays true. if yes, it is a solution.

(5 + 2i)² - 10(5 + 2i) = -29

25 + 20i - 4 - 50 - 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution.

B. for a parabola the 2 solutions are usually symmetrical around the center line.

so, I suspect 5 - 2i to be a solution too.

(5 - 2i)² - 10(5 - 2i) = -29

25 - 20i - 4 - 50 + 20i = -29

21 - 50 = -29

-29 = -29 true

yes, it is a solution too.

C.

nowhere.

with 2 complex solutions there are no real number solutions left. and that means there is no intersection with the x-axis.

every quadratic equation must have 2 and only 2 solutions. a solution is normally an intersection with the x-axis (the x- value when y = 0).

Answer: A. (x,y)----->(x,-y)

because their x coordinates are all -6. But their y coordinates are 6 and -6.

Answer:

The equation of the ellipse is:

(x^2)/16 + (y^2)/4 = 1

Step-by-step explanation:

An ellipse is a set of points on a plane, the sum of whose distances from two fixed points (called foci) is constant. The distance between the foci of an ellipse is denoted by 2c, and the distance between the center of the ellipse and one of its vertices is denoted by a.

In this problem, the foci are located at (2,0) and (-2,0), so the distance between the foci is 2c = 4, which means that c = 2. The major vertices of the ellipse are located at (4,0) and (-4,0), so the distance between the center and one of the vertices is a = 4.

The formula for the equation of an ellipse centered at the origin is:

(x^2)/(a^2) + (y^2)/(b^2) = 1

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. Since the center of this ellipse is at the origin and the major axis lies on the x-axis, we know that b = a, so we can substitute a for b in the equation:

(x^2)/(a^2) + (y^2)/(a^2) = 1

To find a, we use the fact that c^2 = a^2 - b^2:

a^2 - b^2 = c^2

a^2 - a^2 = 4

b^2 = 4

b = 2

Now we can substitute a = 4 and b = 2 into the equation:

(x^2)/(16) + (y^2)/(4) = 1

This is the equation of the ellipse.

Answer:

= 75 cubic units

Step-by-step explanation:

Volume = height * width * length

Then:

volume = 4 1/2 * 3 1/3 * 5

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

Then:

volume = 9/2 * 10/3 * 5/1

volume = (9*10*5) / (2*3*1)

volume = 450 / 6

Volume = 75 cubic units

Step-by-step explanation:

Example 1:

Given pair: (3;2)

{2x + 3y = 12,

{x - 4y = -5;

Make x the subject from the 2nd equation:

x = -5 + 4y

Replace x in the 1st equation:

2 × (-5 + 4y) + 3y = 12

-10 + 8y + 3y = 12

11 y = 12 + 10

11y = 22 / : 11

y = 2

y = 2x = -5 + 4 × 2 = -5 + 8 = 3

The answer: (3;2)

The given pair is the solution of the system of equations

.

Example 2:

Given pair: (0; -4)

{x + y = -4,

{x - 5y = 20;

x = -4 - y

(-4 - y) - 5y = 20

-4 - y - 5y = 20

-6y = 20 + 4

-6y = 24 / : (-6)

y = -4

y = -4x = -4 - (-4) = -4 + 4 = 0

The answer: (0; -4)

The given pair is the solution

.

Example 3:

Given pair: (3;3)

{x + 2y = 9,

{4x - y = 15;

x = 9 - 2y

4(9 - 2y) - y = 15

36 - 8y - y = 15

-9y = 15 - 36

-9y = -21 / : (-9)

[tex]y = 2 \frac{1}{3} [/tex]

[tex]x = 9 - 2 \times 2 \frac{1}{3} = 9 - 2 \times \frac{7}{3} = 9 - \frac{14}{3} = \frac{13}{3} = 4 \frac{1}{3} [/tex]

The given pair is not the solution

.

Example 4:

Given pair: (1; -2)

{2x - 3y = 8,

{3x + 2y = -1;

2x = 8 + 3y / : 2

x = 4 + 1,5y

3(4+1,5y) + 2y = -1

12 + 4,5y + 2y = -1

6,5y = -1 - 12

6,5y = -13 / : 6,5

y = -2

y = -2x = 4 + 1,5 × (-2) = 4 - 3 = 1

The given pair is the solution

.

Example 5:

Given pair: (1;5)

{5x - 2y = -5,

{3x - 7y = -32;

-2y = -5 - 5x / : (-2)

y = 2,5 + 2,5x

3x - 7(2,5 + 2,5x) = -32

3x - 17,5 - 17,5x = -32

-14,5x = -32 + 17,5

-14,5x = -14,5 / : (-14,5)

x = 1

x = 1y = 2,5 + 2,5 × 1 = 5

The given pair is the solution

.

Example 6:

Given pair: (-1; -3)

{3x + y = -6,

{2x = 1 + y;

y = -6 - 3x

2x = 1 + (-6 - 3x)

2x = 1 - 6 - 3x

2x + 3x = 1 - 6

5x = -5 / : 5

x = -1

x = -1y = -6 - 3 × (-1) = -6 + 3 = -3

The given pair is the solution

To find how many times larger the diameter of the Sun is than the diameter of the Earth, we need to divide the diameter of the Sun by the diameter of the Earth:

(1.3 x 10^6 km) / (1.3 x 10^4 km)

Simplifying:

= (1.3 / 1.3) x (10^6 / 10^4)

= 100

Therefore, the diameter of the Sun is 100 times larger than the diameter of the Earth.

I explained step by step I hope it was helpful

The visitor should run 1.2 miles to minimize the time it takes to reach the island.

Consider the following figure.

Let us assume that x (CD) represents the distance covered when visitor runs at a rate of 5 mph

So, the time taken by visitor would be:

t₁ = x/5

Let the distance covered 10 - x when visitor swims at a rate of 3 mph

From figure consider right triangle ABC.

Using Pythagoras theorem,

BC² = 7² + (10 - x)²

BC = [tex]\sqrt{49 + (10-x)^2}[/tex]

Now the times taken by visitor when he swims at a rate of 3 mph,

t₂ =  [tex]\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]

so, the total time would be:

t = t₁ + t₂  

[tex]t=\frac{x}{6}+\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]

Differentiating with respect to x we get,

[tex]\frac{dt}{dx}=\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}[/tex]

consider dt/dx = 0

[tex]\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}=0[/tex]

If we solve above equation for x we get, x = 11.2 and x = 8.8

The distance the visitor should run to minimize the time would be:

10 - 8.8 = 1.2 miles

Therefore, the required distance is 1.2 miles

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Thomas can fill 35 of these 1/4 gallon containers with the light-blue mixture.

To find out how many 1/4 gallon containers Thomas can fill with the light-blue mixture, we need to divide the total volume of the mixture by the volume of one container.

The total volume of the mixture can be found by adding the volumes of blue and white paint that Thomas mixed

Total volume = 4 3/8 gallons + 6 5/8 gallons

To add these mixed numbers, we need to find a common denominator, which is 8

Total volume = (4 x 8 + 3) / 8 gallons + (6 x 8 + 5) / 8 gallons

Total volume = 35/8 gallons

Now we can set up the two equations

Total volume = number of containers x volume per container

We know the total volume is 35/8 gallons, and the volume per container is 1/4 gallon, so we can write

35/8 = (1/4) x number of containers

Number of containers = total volume / volume per container

We can rearrange the above equation to solve for the number of containers

Number of containers = total volume / volume per container

Number of containers = 35/8 / 1/4

Number of containers = 35/8 x 4

Number of containers = 35

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The given question is incomplete, the complete question is:

Thomas has some leftover paint that he would like to sell. he mixes 4 3/8 gallons of blue paint with 6 5/8 gallons of white paint. then, he pours this light-blue mixture into 1/4 gallon containers. find out how many of these 1/4 gallon containers he can fill?

you know that i have gave wrong Ans  

explanation: because i need points

Answer:

Step-by-step explanation:

where’s the figure ?

Answer:

26.4

Step-by-step explanation:

You can add Y together because they have the same variable making it 10y

The equation is now 10y - 84 = 180

Add 84 to 180 since on the left side it was -84 (Imagine it crossed a magic bridge and become the opposite of what it is)

The equation is now 10y = 264

Divide the equation by 10 because 10 crossed a "magic bridge" to the other side and became division instead of multiplication

The equation is now solved = 26.4

We can cross check this by adding it to the first equation

3(26.4) + 7(26.4) - 84

which gives us 180

Hope this helps

Answer: y=26.4

Step-by-step explanation:

First we need to simplify 3y+7y .... that would be 10y.

Now we have 10y-84=180. We can add 84 to both sides of the equation

So now we have 10y= 180+84 = 10y= 264

Divide both sides by 10= y= 26.4

Now we can check this answer by inputting 26.4 to all the y values in the equation.

(3*26.4) +(7*26.4) - 84=180

79.2 + 184.8 -84=180

180=180    so we know 26.4 is the correct answer

Answer:

4%

Step-by-step explanation:

The formula for simple interest is I = Prt, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.

In this case, we know that:

P = £500 (the principal amount)

I = £40 (the interest earned)

t = 2 years (the time the money was invested)

We can rearrange the formula to solve for r:

r = I / Pt

Substituting the given values, we get:

r = 40 / (500 x 2)

r = 0.04 or 4%

Therefore, the simple interest rate per annum is 4%.

Answer:x = 4

Step-by-step explanation:

Answer:

Median: 19

Mean: 18

Step-by-step explanation:

Numbers: 19, 20, 40, 3, 17, 5, 22

Number in order from least to greatest: 3, 5, 17, 19, 20, 22, 40

The median is the number in the middle of a data set.

The median is: 19

The mean is the average of a set of data.

The mean is: [tex]\frac{3 + 5 + 17 + 19 + 20 + 22 + 40}{7}[/tex] = 18

So, Median is 19

      Mean is 18

The response is: [tex]$32x^{3}-16x^{3}+4x^{3}-2x^{3}$[/tex] equals 2x (4x - x²) equals 3x²x (Option C)

An expressiοn is a grοup οf digits, variables, and mathematical οperatοrs (such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, etc.) that depicts a quantity οr relatiοnship. Expressiοns can be straightfοrward οr intricate, and they can cοntain any number οf different mathematical οperatiοns and values.

Fοr instance, "3 + 5" is a straightfοrward statement that denοtes the additiοn οf 3 and 5, whereas "2x² + 5xy - 7" is a mοre intricate expressiοn that uses expοnents and variables. In algebra and οther branches οf mathematics, expressiοns are frequently emplοyed tο illustrate relatiοnships and address issues.

Let's first simplify each phrase that appears after the square rοοt:

√32x^3 = √(16x²) * √(2x) = 4x√2x √16x³ = √(16x²) * √x = 4x√x 4√x³ = 4√(x²) * √x = 4x√x √2x³ = √(2x²) * √x = √2x * x√x

Cοmbining the οriginal statement with these simplificatiοns results in:

32x³ - 16x³ + 4x³ - 2x³ = 4x²x - 4xx + 4xx - xx = 4x²x - xx = 2x (4x - x²).

As 4x and x2 are bοth nοn-negative because x 0, their difference is alsο

non-negative.

Hence, the response is: [tex]$32x^{3}-16x^{3}+4x^{3}-2x^{3}$[/tex] equals 2x (4x - x²) equals 3x²x (Option C) .

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Answer:

The difference between the price after value added tax (VAT) and the price after discount of an article gives us the actual amount of money saved by the customer.

The price after VAT is the price of the item including the tax imposed by the government, whereas the price after discount is the price of the item after any promotional or discounted price reduction. By subtracting the price after discount from the price after VAT, we can determine the actual amount saved by the customer, which is the discount amount minus any VAT paid on the original price.

For example, if an item originally cost $100 with a 10% VAT, the price after VAT would be $110. If the item was discounted by 20%, the price after discount would be $80. The difference between the price after VAT and the price after discount would be $30, which is the actual amount saved by the customer ($20 discount minus $10 VAT paid on the original price).

Step-by-step explanation:

To calculate the actual amount saved by the customer, we need to follow these steps:

Determine the original price of the item. For example, let's say the original price of the item is $100.

Calculate the VAT amount paid on the original price. To do this, multiply the original price by the VAT rate as a decimal. For example, if the VAT rate is 10%, then the VAT amount would be:

VAT amount = original price x VAT rate

VAT amount = $100 x 0.1

VAT amount = $10

So, the VAT amount paid on the original price of $100 is $10.

Determine the discounted price of the item. For example, let's say the item is discounted by 20%, so the discounted price is:

Discounted price = original price - (original price x discount rate)

Discounted price = $100 - ($100 x 0.2)

Discounted price = $80

So, the discounted price of the item is $80.

Calculate the actual amount saved by the customer. To do this, subtract the discounted price from the price after VAT. For example:

Actual amount saved = price after VAT - discounted price

Actual amount saved = $110 - $80

Actual amount saved = $30

So, the actual amount saved by the customer is $30, which is the discount amount minus the VAT paid on the original price.

The measure of angle m∠KSP is 14⁰.

A special property of a parallelogram is that opposite angles are equal in measure. This means that if you take any two angles of a parallelogram that are opposite each other, they will have the same degree measure.

The measure of angle m∠KSP is calculated as follows;

The measure of angle P and R = ¹/₂[ 360 - (76 x 2)] (sum of angles in quadrilateral )

The measure of angle P and R = 104

The measure of QPK = 180 - (76 x 2) (sum of angles in a triangle )

The measure of QPK =  28⁰

Angle P consists of QPK plus KPS

KPS = 104 - QPK

KPS = 104 - 28

KPS = 76

The measure of angle m∠KSP is calculated as;

KSP = 180 - (90 + 76) ( sum of angles in a triangle)

KSP = 14⁰

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Answer:

38

Step-by-step explanation:

We know that Q and P are supplementary because they are parallelograms.

So,

180 - < Q = < P                               Use substitution

180 - 76 = < P                                 Solve

180 - 76 = 104

104 = < P

Since we know that < QPK and < KPS are congruent and are apart of < P we can multiply < P by 1/2 to find either < QPK or < KPS.

So,

1/2(104)                                           Simplify using distributive property

52

If a shape is a triangle, then it’s interior angles all add up to 180.

< KPS + < PKS + < KSP = 180        Use substitutions

52 + 90 + < KSP = 180                  Move variables to one side

< KSP = 180 - 52 - 90                    Simplify  
< KSP = 38

And there’s your answer: 38

Answer:

15) surface area = 791.68, volume = 1693.32

16) surface area = 138.23, volume = 113.1

17) surface area = 650.87, volume = 1073

18) surface area = 34.87, volume = 10.52

19) surface area = 153.94, volume = 179.59

20) surface area = 314.16, volume = 523.6

Step-by-Step Explanation:

sorry I didn't add the cm or inches or km in my answers :)

0.148 is the probability that they are both democrats.

In one town, 39% of all voters are democrats.

If two voters are randomly selected for a survey, the probability that they are both democrats can be calculated as follows.

P(A) = 0.39 is the probability of selecting a democrat in the first draw.

P(B|A) = 0.38

is the probability of selecting a democrat in the second draw if the first draw selects a democrat.

P(B|A') = 0.39 is the probability of selecting a democrat in the second draw if the first draw does not select a democrat.

The probability that both voters are democrats is:

P(A) x P(B|A) = 0.39 x 0.38 = 0.1482

The result is 0.1482, which means the probability that two voters are both democrats in one town is 0.1482 to the nearest thousandth.

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Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .

The amount of money earned or charged on a principal sum of money over time is referred to as interest in mathematics. In financial transactions like loans, investments, and savings accounts, it is frequently utilized.  Simple interest is calculated for the full time period as a fixed percentage of the principal amount. For instance, after a year, you would owe $50 in interest if you borrowed $1,000 at a simple interest rate of 5% per year.

given

We can use the following formula for simple interest to determine the interest rate given the principal, period, and simple interest:

I = P * r * t

where r is the interest rate expressed as a decimal, P is the principal, I is the simple interest, and t is the amount of time in years.

This formula can be changed to account for the interest rate:

r = I / (P * t)

In this instance, the principal, period, and simple interest are all provided. These values can be plugged in to find the interest rate:

r = I / (P * t)

r = 600 / (4000 * 5)

r = 0.03

Hence, the interest rate is 0.03 percent, or 3%. it is expressed as a percentage .

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The inequality in the expression [tex]41-x < 17[/tex] is the less than inequality

The solution to the inequality is [tex]x > 24[/tex]

The inequality is given as:

[tex]41-x < 17[/tex]

Subtract 41 from both sides of the inequality

[tex]41 - 41 -x < 17 - 41[/tex]

Evaluate the difference

[tex]-x < -24[/tex]

Multiply both sides by -1

[tex]-1 \times -x < -24 \times -1[/tex]

Evaluate the product

[tex]x > 24[/tex]

The standard deviation of demand over the lead time is 23.72.

The demand over lead time is normally distributed with a mean of 80. The reorder point for a 95% service level is 119. To calculate the standard deviation of demand over the lead time, we need to use the following formula:

z = (x - μ) / σ, where z is the number of standard deviations from the mean, x is the reorder point for a 95% service level, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To solve for σ, we need to first find the z-score for a 95% service level, which can be obtained from the standard normal distribution table.

The z-score for a 95% service level is 1.645.

Substituting the given values in the formula, we get:

1.645 = (119 - 80) / σ

Solving for σ, we get:σ = (119 - 80) / 1.645

σ = 23.72

Therefore, the standard deviation of demand over the lead time is 23.72.

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Answer:

  x = 10

Step-by-step explanation:

You want to find the value of x, where a chord of segment lengths 9 and x crosses a chord of segment lengths 6 and 15.

The product of the segment lengths is the same for intersecting chords:

  9x = 6·15

  x = 90/9 . . . . divide by 9

  x = 10

The equation for the cost of ticket 13.50 = 1.5m is and the price for a matinee movie ticket is $9.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's use "m" to represent the price of a ticket to a matinee movie.

From the given information, we know that the cost of a ticket to an evening movie is 1.5 times more than a ticket for a matinee movie.

This means that -

Cost of an evening movie ticket = 1.5 × Cost of a matinee movie ticket

We also know that the cost of a ticket to an evening movie is $13.50.

Substituting this value into the equation above, we get -

$13.50 = 1.5m

To solve for "m", we can divide both sides of the equation by 1.5 -

$13.50 / 1.5 = m

m = $9

Therefore, the price of a ticket to a matinee movie is $9.

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Answer:

Step-by-step explanation:

The mean is found by adding the numbers and dividing by how many numbers there are.

              [tex]Mean=\frac{-2+3+0-15+5-20-4}{7} =\frac{-33}{7} =-4\frac{5}{7}[/tex]