If William has 5 different shirts and 7 different pairs of pants, how many different combinations could he wear?

Answer:

x   = 5 sqrt(6)/3

 y= 10 sqrt(6)/3

Step-by-step explanation:

We know sin 60 = opposite/hypotenuse

    sin 60 = 5 sqrt(2) /y

 Multiply each side by y

y sin 60 = 5 sqrt(2)

Divide each side by sin 60

y sin 60/ sin 60 = 5 sqrt(2)/ sin 60

y = 5 sqrt(2) / sin 60

y = 5 sqrt(2) / sqrt(3) /2)

y   = 10 sqrt(2)/ sqrt(3)

You cannot leave a sqrt in the denominator

 y=   10 sqrt(2)/ sqrt(3) * sqrt(3)/sqrt(3)

   y= 10 sqrt(6)/3

tan 60 = oppositve/ adjacent

tan 60 = 5 sqrt(2)/ x

Multiply each side by x

x tan 60 = 5 sqrt(2)

Divide by tan 60

x = 5 sqrt(2)/tan 60

x =5 sqrt(2)/sqrt(3)

You cannot leave a sqrt in the denominator

x = 5 sqrt(2)/sqrt(3) * sqrt(3)/sqrt(3)

x   = 5 sqrt(6)/3

Answer:

Price $0.75 per ounce of confetti

Step-by-step explanation:

Given the statement: Yuki bought a pound of confetti for $12.

⇒[tex]1 pound = \$ 12[/tex]                 ......[1]

Also, it is given that there are 16 ounces in 1 pound.

⇒ 16 ounces = 1 pound                       .....[2]

To calculate the price, in dollars per ounce of confetti.

From [1] and [2] we have;

[tex]16 ounces = \$12[/tex]

then;

1 ounces =  [tex]\frac{12}{16} = \frac{3}{4} = \$0.75[/tex]

Therefore, the price, in dollars per ounce of confetti is, $0.75  per ounce.

Answer:

6.25

Step-by-step explanation:

Because to know the answer we have to divide 75 by 12 which is 6.25

Answer: x = 6

==============================================

Explanation:

The medians of a triangle meet up at the centroid in such a way that they cut each other at a ratio of 2:1, meaning that one part of the median is twice as long as the other. In this case, MO is two times longer than OP, so,

OP = 2*MO

and

MP = MO + OP

MP = MO + 2*MO .... replace OP with 2*MO

MP = 3*MO

9x-24 = 3*(x+4) ... plug in the given expressions

9x-24 = 3x+12

9x-3x = 12+24

6x = 36

x = 36/6

x = 6

Answer:

c (0,-4)

Step-by-step explanation:

-5x+y = -4

4x - 4y =16

Solve the first equation for y since we are using substitution.

-5x+y = -4

Add 5x to each side

-5x+5x+y = -4+5x

y = 5x-4

Substitute this equation y = 5x-4 into the second equation.

4x -4(5x-4) = 16

Distribute the -4

4x - 4(5x) -4(-4) = 16

4x-20x +16 = 16

Combine like terms

-16x +16 =16

Subtract 16 from each side

-16x+16-16 = 16-16

-16x =0

Divide by -16

x=0

But we still need to find y

y = 5x-4

y = 5(0) -4

y = -4

[tex]\mathsf{Given : \dfrac{(3x^2y^-^3)^3}{27(xy)^-^9}}[/tex]

[tex]\mathsf{\implies \dfrac{(3)^3(x^2)^3(y^-^3)^3}{27(x)^-^9(y)^-^9}}[/tex]

[tex]\mathsf{\implies \dfrac{27(x)^6(y)^-^9}{27(x)^-^9(y)^-^9}}[/tex]

[tex]\mathsf{\implies \dfrac{(x)^6}{(x)^-^9}}[/tex]

[tex]\mathsf{\implies x^6^+^9}[/tex]

[tex]\mathsf{\implies x^1^5}[/tex]

1. The slope of the line is 3.

2. The direct variation equation is y = 3x

3. The equation in slope-intercept form is:y = 4

4. The equation in slope-intercept form is y = 2/3x + 1.

5. The equation = −2/3 − 1

6. The equation of the parallel line is y = 5x - 11.

1. Slope of the line:

The slope (m) of the line passing through (-1, 2) and (0, 5) can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

m = (5 - 2) / (0 - (-1))

m = 3 / 1

m = 3

Therefore, the slope of the line is 3.

2. Direct variation equation:

Since y varies directly with x, we can write their relationship as y = kx, where k is the constant of proportionality. We can find k using the given information:

y = 15 when x = 5

15 = k * 5

k = 3

Therefore, the direct variation equation is y = 3x

When x = 9, y = 3 * 9 = 27.

3. Equation in slope-intercept form: First, calculate the slope using the same formula as in question 1:

m = (4 - 4) / (1 - (-3))

m = 0 / 4

m = 0

Since the slope is 0, the line is horizontal. The equation in slope-intercept form is:

y = 4 (constant y-intercept because it passes through (1, 4))

4. Equation in slope-intercept form using point-slope form:

The point-slope form equation is:

y - y1 = m(x - x1)

Plug in the given values:

y - (-1) = 2/3(x - (-3))

y + 1 = 2/3(x + 3)

3y + 3 = 2x + 6

3y = 2x + 3 (subtract 3 from both sides)

y = 2/3x + 1 (divide both sides by 3)

Therefore, the equation in slope-intercept form is y = 2/3x + 1.

5. Writing the equation in standard form:

The equation = −2/3 − 1 is already in standard form (ax + by = c), where a = -2/3, b = 0, and c = -1.

6. Equation of the parallel line:

Since the parallel line has the same slope (5) as the given line, its equation will be of the form y = 5x + b. To find b, plug the point (2, -1) into this equation:

-1 = 5(2) + b

-1 = 10 + b

b = -11

Therefore, the equation of the parallel line is y = 5x - 11.

Answer:

(A)This set of data is a function because every input has an output.

(B) This set of data would not be a function if two inputs had the same output, for example, if the inputs were 3,4,4,11 and the outputs were 5,7,11,21 then the data set would not be a function because for input 4 it has two different outputs.

Step-by-step explanation:

The solution to the inequality is [tex]\(x > -17\).[/tex]

To solve the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex], let's first find a common denominator and then combine the fractions:

[tex]\(\frac{5-2x}{-3} - 4 < -x\)[/tex]

Multiply each term by -3 to clear the fraction:

[tex]\(5 - 2x + 12 < -3x\)[/tex]

Combine like terms:

[tex]\(-2x + 17 < -3x\)[/tex]

Add [tex]\(2x\)[/tex] to each side:

[tex]\(17 < -x\)[/tex]

Multiply each side by -1 (remember to reverse the inequality when multiplying by a negative number):

[tex]\(-17 > x\)[/tex]

So, [tex]\(x > -17\).[/tex]

The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]

Step 1: Start with the given inequality:

[tex]\[\frac{5-2x}{-3} - 4 < -x\][/tex]

Step 2: Multiply both sides of the inequality by -3 to clear the fraction:

[tex]\[5-2x + (-3) \cdot 4 > -3 \cdot (-x)\][/tex]

[tex]\[5-2x -12 > 3x\][/tex]

Step 3: Combine like terms:

[tex]\[-7-2x > 3x\][/tex]

Step 4: Add 2x to both sides:

[tex]\[-7 > 5x\][/tex]

Step 5: Divide both sides by 5 (remembering to reverse the inequality when dividing by a negative number):

[tex]\[\frac{-7}{5} < x\][/tex]

So, the solution to the inequality is:

[tex]\[x \in \left(-\infty, -\frac{7}{5}\right)\][/tex]

The value of x in the inequality [tex]\(\frac{5-2x}{-3} - 4 < -x\) is \(x \in \left(-\infty, -\frac{7}{5}\right)\).[/tex]

Answer:

16 cans of corn

Step-by-step explanation:

Answer:

11x+8  cm = Perimeter

Step-by-step explanation:

A triangle has 3 sides.  We add up all three sides to get the perimeter.

s1+s2+s3 = Perimeter

(x+4) +( 3x+1) + (7x+3) = Perimeter

Combine like terms

11x+8 = Perimeter

Answer:

1. The correct answer is D) 1/36

Step-by-step explanation:

WE can tell this because the chance of rolling either is 1/6. To find the total probability we multiply those together.

1/6 * 1/6 = 1/36

Answer:  Since 1/3 can't be turned into a decimal, change .5 into 1/2. In order to subtract, the fractions need a common denominator. The least common denominator is 6. So 1/3 turns into 2/6, and 1/2 turns into 3/6. Now you need to take 9 3/6 minus 6 2/6. The answer is 3 1/6 gallons of water.

Step-by-step explanation:

Final answer:

To find the remaining water in Tank A after pouring out 6 1/3 gallons, subtract 6.333 from the tank's total capacity of 9.5 gallons, which leaves 3.167 gallons remaining in the tank.

Explanation:

The question involves determining the remaining quantity of water in a tank after a certain volume has been removed, which is a basic subtraction problem in mathematics. To solve it, subtract the volume of water that was poured out from the total capacity of the tank.

Tank A capacity: 9.5 gallons

Volume of water poured out: 6 1/3 gallons

To perform the subtraction, we first need to convert 1/3 of a gallon into a decimal. A third of a gallon is approximately 0.333 gallons. Adding this to 6 gallons gives us 6.333 gallons.

Now, subtract the volume poured out from the tank's capacity:

9.5 gallons (capacity) - 6.333 gallons (poured out) = 3.167 gallons (remaining in the tank)

Therefore, 3.167 gallons of water are left in the tank.

Answer:

5 hours

Step-by-step explanation:

given :

Distance between the cities = 540 miles

Speed of motorcycle =48 mph

TO CALCULATE THE TIME TAKEN BY MOTORCYCLE TO COVER THE TOTAL DISTANCE WE USE THE FORMULA :

[tex]\frac{DISTANCE}{SPEED}[/tex]

By putting given values in the formula we get :

[tex]\frac{540}{48}[/tex]

= 11.25 hours

Now, We are given that for a car to cover the same distance it takes 2.25 hours less than the time taken by motorcycle

⇒ 11.25 hours - 2.25 hours

⇒ 9 hours

Thus , Time taken by car to cover the same distance is 9 hours .

Now to calculate speed of car by using formula:

[tex]\frac{distance}{time}[/tex]

[tex]\frac{540}{9}[/tex]

= 60 mph

Let t be the time taken to meet if they start moving towards each other.

So distance covered by motorcycle in t hours is

speed\times time

= 48t miles

Distance covered by car in t hours is

speed\times time

= 60t miles

⇒ 60t + 48t =540

⇒ 108t = 540

⇒ t= 5 hours

Therefore, time taken to meet if they start moving towards each other is 5 hours.

Answer:

The correct answer is 86.

Step-by-step explanation:

Because 82 is only one standard deviation below the mean, then to find the mean, only add 82 + 4 = 86

The mean score for the test is 86.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We are given that;

Score=82

Number of tests=4

Now,

We can substitute σ=4 and xi​=82 into the formula. We also know that there is only one data point that satisfies this condition, so we can use N=1.

[tex]\mu = \frac{\sum_{i=1}^{N}(x_i - \mu)^2}{N\sigma^2} + \mu[/tex]

We get:

μ=(82−μ)^2/4^2 ​+μ

Simplifying and solving for μ, we get:

μ=86

Therefore, by standard deviation the answer will be 86.

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Answer:

Seven

Step-by-step explanation:

We have the following list of people coming to the reunion,

A grandmother  = 1

A grandfather = 2

Two mothers = 1 and 3

Two fathers = 2 and 4

i.e. Up until here there are total 4 people - Grandmother, Grandfather, Mother, Father ( 1, 2, 3, 4)

Four children = 4, 6, 7, 8

Three grandchildren = 6, 7, 8

One brother = 6

Two sisters = 7, 8

Two sons = 4, 6

Two daughters = 7, 8

Therefore, in addition to the four people above, one of the child will be the father and so there are 3 grandchildren.

So, number of people added in this step is 3 and total number of people up until here becomes 7.

A mother-in-law = 1

A father-in-law = 2

A daughter-in-law = 3

So, no new family member is added in this step.

Hence, total  number of family members coming to reunion are 7 namely Grandmother, Grandfather, Mother, Father, Three children.

Answer:

16 correct.

Step-by-step explanation:

We need to change 80% to a decimal

80 % = .8

If there are 20 questions

20 * .80 = 16

He got 16 questions correct

Answer: 2500 meters²

Step-by-step explanation:

Perimeter: 200 = 4w  

             ⇒    50 = w

Area = w²

        = (50)²

        = 2500

The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The perimeter of the rectangle = 2( length + Width)

                                             200 = 2( length + Width)

                                         100 - w = L

The area of the rectangle = length × Width

                                            = w(100 - w)

                                            = (-w)²+ 100w

So,  (-w)²+ 100w where, a = -1 and b = 100

w = -100/2(-1)

w = 50

The area of the rectangle = (-w)²+ 100w

                                            = (-50)²+ 100(50)

                                           = 2500

Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

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Answer:

hello : here is a solution

Answer:

m<Q = 92 degrees

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary.

Angles O and Q are opposite angles, so they are supplementary, so their measures add up to 180 degrees.

m<O + m<Q = 180

2x + 2x + 4 = 180

4x + 4 = 180

4x = 176

x = 44

m<Q = 2x + 4 = 2(44) + 4 = 92

Answer:

Q =92

Step-by-step explanation:

Since the quadrilateral is inscribed in a circle, the opposite angles add to 180 degrees.

<O + <Q = 180

2x+ 2x+4 = 180

4x+4 =180

Subtract 4 from each side

4x= 180-4

4x= 176

Divide by 4

x = 44

Q = 2x+4

Q = 2(44)+4

Q = 88+4

Q = 92

The solution is Option B.

The recursive formula to calculate Marta's salary is given by the equation

f ( n ) = f ( n - 1 ) + 2700

The salary of Marta after 4 years will be $ 33,000

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the initial salary of Marta be f ( 0 ) = $ 24,900

The increment in Marta's salary every year = $ 2700

So , the equation will be

f ( n ) = f ( n - 1 ) + 2700

when n = 1

Substitute the value of n = 1 in the equation , we get

f ( 1 ) = f ( 1 - 1 ) + 2700

f ( 1 ) = f ( 0 ) + 2700

f ( 1 ) =  24,900 + 2700

f ( 1 ) = $ 27,600

when n = 2

Substitute the value of n = 2 in the equation , we get

f ( 2 ) = f ( 2 - 1 ) + 2700

f ( 2 ) = f ( 1 ) + 2700

f ( 2 ) =  27,600 + 2700

f ( 2 ) = $ 30,300

when n = 3

Substitute the value of n = 3 in the equation , we get

f ( 3 ) = f ( 3 - 1 ) + 2700

f ( 3 ) = f ( 2 ) + 2700

f ( 3 ) =  30,300 + 2700

f ( 3 ) = $ 33,000

Hence , after 4 years the salary of Marta will be $ 33,000

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Marta's annual salary increases by $2700 each year. Applying the recursive formula: f(n) = f(n-1) + 2700; f(4)=f(3)+2700=f(2)+2700+2700=f(1)+2700+2700+2700=f(0)+2700+2700+2700+2700=24900+4*2700=35500, we determine that Marta's salary in 4 years would be $35,500.

The subject of the question involves recursion, or constructing a sequence of numbers in a specific way. In Marta's case, her salary can be calculated using a recursive formula that builds upon her previous salary. This formula relies on the concept of numerical patterns and can be represented as follows: f(n) = f(n-1) + 2700; where f(n) is Marta's salary after n years and f(n-1) is her salary the previous year.

At the start, Marta's salary is 24,900, which serves as the base case for our recursive function. Therefore, her income increases by $2700 each year. To get Marta's salary in 4 years, we would use the recursive formula: f(4) = f(3) + 2700 = f(2) + 2700 + 2700 = f(1) + 2700 + 2700 + 2700 = f(0) + 2700 + 2700 + 2700 + 2700 = 24,900 + 4*2700 = 35,500. So, Marta's salary is $35,500 after 4 years.

Therefore, the correct option among choices provided is none from the given options.

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Answer:

(x+1) is a factor with remainder 0.

Step-by-step explanation:

We divide (x+1) into the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x+1) to make the polynomial [tex]-3x^4+2x^3-x^2+6[/tex] .

[tex](x+1)(-3x^3)=-3x^4-3x^3[/tex]

We subtract this from the original [tex]-3x^4-(-3x^4)+2x^3-(-3x^3)-x^2+6[/tex].

This leaves [tex]5x^3-x^2+6[/tex]. We repeat the step above.

[tex](x+1)(5x^2)=5x^3+5x^2[/tex].

We subtract this from [tex]5x^3-(5x^3)-x^2-(5x^2)+6=-6x^2+6[/tex]. We repeat the step above.

[tex](x+1)(-6x)=-6x^2-6x[/tex].

We subtract this from [tex]-6x^2-(-6x^2)+0x-(-6x)+6=6x+6[/tex]. We repeat the step above.

[tex](x+1)(6)=-6x+1[/tex].

We subtract this from [tex]6x-(6x)+6-(6)=0[/tex]. There is no remainder. This means (x+1) is a factor.

94.46%  Is the amount of water in a tomato  

16/20 = 80/100

multiply both top and bottom by 5 to go from 16/20 to 80/100

80/100 = 80% by definition of what "percent" means, which is "per 100" or "for every 100"

So 16/20 = 80% meaning 80% of the tomato is water

Note on a calculator, 16/20 = 0.80 which converts to 80% if you move the decimal point 2 spots to the right.

Answer:

16m

Step-by-step explanation:

Since the length of the park is 7m, then the other side is also 7m so 46-14 is 32. So 32/2 is 16.

Answer:

Option C is correct.

The answer for the given expression is 0.

Step-by-step explanation:

Given the statement: Two times the difference of one-third of a number and three. and also variable given is 9.

Let x be the variable or number.

"One-third of a number"  means [tex]\frac{1}{3}x[/tex]

Also, "difference of one third of a number and three " means [tex]\frac{1}{3}x-3[/tex]

Now, "Two times the difference of one-third of a number and three" means   [tex]2 \times (\frac{1}{3} x -3)[/tex]

Then, the expression for the given statement : [tex]2 \times (\frac{1}{3} x -3)[/tex]

Substitute the value of x =9 in above expression we have;

[tex]2 \times (\frac{1}{3}(9) -3)[/tex] = [tex]2 \times (3 -3)[/tex] = [tex]2 \times (0)[/tex] = 0

therefore, the answer for the given expression is, 0