Simplify.
-6√7.4√5
-2√35
24√√35
-24 √√35

Answer:

14300

Step-by-step explanation:

this is the answer that I got I hope it works

Saving of Martina in taxes = $675

A flexible spending account (FSA) is a type of savings account, usually for healthcare expenses, that sets aside funds for later use. It is also known as a flexible spending arrangement, is one of a number of tax-advantaged financial accounts, resulting in payroll tax savings.

Given,

Wages of Martina = $68000

Tax rate = 25%

Amount to flexible savings = $2700

Then saving in taxes = $2700 × 25/100

                                   = $675

Hence, Martina saved $675 in taxes using FSA.

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Answer:

[tex]\sqrt{6}, -\sqrt{6}[/tex]

Step-by-step explanation:

[tex]f(x)=x^3+3x^2-6x-18 \\ \\ =x^2(x+3)-6(x+3) \\ \\ =(x^2-6)(x+3) \\ \\ \implies (x^2-6)(x+3)=0 \\ \\ x=\pm \sqrt{6}, -3[/tex]

Answer: 18 square unit

Step-by-step explanation:

We can divide the shape into two pieces.

a triangle and a square.

The square is 2*6=12 square unit

and the triangle is 1/2*6*2=6 square unit

So if we sum this up we get the answer

answer = 6+12 = 18 square unit

Answer:

You can pour nine 7-ounce cups of tea (63 ounces) and be left with one ounce of tea.

Step-by-step explanation:

Dividing 64 by 7 and finding the remainder.

The coordinates of N are (5,-6)  so that segment MN is 3/7 of MP.

Given the coordinates of M is (-4,6) and the coordinates of P is (17,-22).

now we have to find the coordinates of N such that the MN : NP is 3:4 .

We will use the section formula:

The section formula states that:

[tex]{\displaystyle N=\left({\frac {mx_{2}+nx_{1}}{m+n}},{\frac {my_{2}+ny_{1}}{m+n}}\right)}[/tex]

Where the coordinates of the points are given and the ratio in which the points are divided is given.

Now we will substitute the values:

[tex]{\displaystyle N=\left({\frac {17\times 3+4\times -4}{3+4}},{\frac {3\times-22+4\times 6}{3+4}}\right)}[/tex]

Solving we get:

N=(5,-6)

The Section formula is used to determine the coordinates of things like the point that separates a line segment (internally or externally) into a particular ratio.

Both physics and mathematics regularly employ this formula. In mathematics, it is used to find the centroid and incenters of a triangle, but in physics, it is used to find the center of mass, equilibrium points, etc. The section formula is often used to find the midpoint of a line segment.

Therefore coordinates of N are (5,-6) so that MN is 3/7 of MP.

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Answer:

I'm assuming that you want to find x and y.

x = 18

y = 42

Step-by-step explanation:

Angle ACD = 138°

(5x + 2) + (2x + 10) = 138

7x + 12 = 138

7x = 126

x = 18

y + (5x + 2) + (2x + 10) = 180 (sum of adjacent angles on a straight line)

Substitute x = 18 into the equation.

y + 5(18) + 2 + 2(18) + 10 = 180

y + 90 + 2 + 36 + 10 = 180

y = 42

The probability that are a normally distributed variable is less than 23 is 0.3216

The most significant probability distribution in statistics for independent, random variables is the normal distribution, sometimes referred to as the Gaussian distribution.

In statistical reports, its well-known bell-shaped curve is generally recognized.

While calculating for probability for normally distributed variables the relationship the relationship is written in the form

P > 23 = 1 - P < 23

0.6784 = 1 - P < 23

P < 23 = 1 - 0.6784

P < 23 = 0.3216

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The solution of the given inequality is y ≤ -3.

The given inequality is -

3y ≤ −9

We have to solve this given inequality.

Now, we have the inequality as -

3y ≤ −9

=> y ≤ -3

Thus, the solution of the given inequality is y ≤ -3.

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The Jeweler makes the number of Pendants  from the total weight of gold alloy = 12

The Jeweler has the total weight of gold alloy = 5 [tex]\frac{5}{8}[/tex] = 45/8  troy ounces.

Weight of a single gold alloy pendant = 15/32 troy ounces.

Jeweler makes the number of Pendants  from the total weight of gold alloy = 45/8 ÷ 15/32.

Dividing Fractions by Fractions

We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,

x/y ÷ a/b

⇒ x/y × b/a (reciprocal of a/b is b/a)

⇒ xb/ya

Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.

45/8 ÷ 15/32 = 45/8 × 32/15 = 12

∴ The value of 45/8 ÷ 15/32 = 12.

Hence the Jeweler makes the number of Pendants  from the total weight of gold alloy = 12

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The cost to rent each chair and each table is $2.75 and $6.50 respectively.

The total cost to rent 2 chairs and 3 tables is $25. This will be:

2c + 3t = 25

The total cost to rent 6 chairs and 5 tables is $49. This will be:

6c + 5t = 49

2c + 3t = 25

6c + 5t = 49

6 × (2c + 3t = 25)

2 × (6c + 5t = 49)

12c + 18t = 150

12c + 10t = 98

Subtract

8t = 52

Divide

t = 52/8

t = 6.5

Cost to rent table = $6.50

Since 2c + 3t = 25

2c + 3(6.5) = 25

2c + 19.5 = 25

Collect like terms

2c = 25 - 19.5

2c = 5.5

c = 5.5/2

c = 2.75

Cost to rent chair = $2.75.

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Answer:

skewed  to the right

Step-by-step explanation:

look at the graph

divide it in half

if both the sides are not equal then it is skewed

then to find out which way it is skewed look which side has more.

The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute, using the normal distribution and the central limit theorem, is of:

0.663 = 66.3%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

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

The parameters for the problem are given as follows:

[tex]\mu = 75, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]

The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute is the p-value of Z when X = 81 subtracted by the p-value of Z when X = 69, hence:

X = 81:

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (81 - 75)/6.25

Z = 0.96

Z = 0.96 has a p-value of 0.8315.

X = 69:

Z = (69 - 75)/6.25

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.8315 - 0.1685 = 0.663 = 66.3%.

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Answer:

y = A cos B(x - C) + D

Step-by-step explanation:

The equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -

y = √180 sin (π/12.5)(t - 25) + 12  

The sinusoidal wave is of the form -

y{x} = A sin (ωt - kx + Ф)

Given is that during a certain time of year, the daily temperature in a certain city (in degrees Celsius) follows a periodic pattern.

We can write the amplitude as -

A = √(18 - 12)² + (13 - 1)²

A = √(36 + 144)

A = √180                            ... { 1 }

{K} = 12                                       ... { 2 }

The time taken to complete one complete wave is 25 hours. So, we can write -

{T} = 25                                     ... { 3 }

ω = 2π/T = 2π/25 = π/12.5

{ω} = π/12.5                                  ... { 4 }

So, we can write the equation as -

y = √180 sin (π/12.5)(t - 25) + 12    

Therefore, the equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -

y = √180 sin (π/12.5)(t - 25) + 12    

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The subtotal before the surcharge and sales tax is $12.2

In this question, we have the following parameters

Total = $13.73

Sales tax = 4%

Surcharge = $1

The above parameters imply that:

Total = Subtotal * (1 + sales tax) + Surcharge

Substitute the known values in the above equation, so, we have the following representation

13.73 = Subtotal * (1 + 4%) + 1

This gives

Subtotal * (1 + 4%) = 12.73

Divide both sides by 1.04

Subtotal = 12.2

Hence, the subtotal is $12.2

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The measure of angle Y, m ∠Y, is 52.58°. The correct option is the last option 52.58°

From the question, we are to determine the measure of angle Y.

From the given information,

Angles X and Y are supplementary angles.

NOTE: Supplementary angles are angles that sum up to 180°

Thus,

m ∠X + m ∠Y = 180°

Also,

From the given information,

Angle X measures 127.42°

That is,

m ∠X = 127.42°

Therefore,

127.42° + m ∠Y = 180°

m ∠Y = 180° - 127.42°

m ∠Y = 52.58°

Hence, the measure of the angle is 52.58°

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Using the pattern, n can represent the the increase of dots according to step.

In the given question we have to find what values make sense for n in this situation.

n is representing the number.

As we can see that there is a pattern given.

In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.

So if we see the pattern then according to number of step the dots increasing accordingly.

As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.

So, n can represent the the increase of dots according to step.

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The properties of operations to multiply the expression are commutative property,  associative property, and distributive property.

Let us understand the properties of operations to multiplication:

The foundation of arithmetic is the Properties of Operations; we use them when performing computations and recalling basic facts.

There are basically three properties of operations to multiplication which are:

Thus, the properties of operations to multiply the expression are commutative property,  associative property, and distributive property.

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The function values;

Given,

The function; f(x) = 9 × 4ˣ

The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. coordinate's

Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.

We have to find the following function values;

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Answer:

21.17

Step-by-step explanation:

If you were to round each number to the nearest whole number you would get :

21.17 ⇒ 21

2.117 ⇒ 2

Now the question is , which is bigger 21 or 2?

Now that is a very straightforward answer (21 in case your still lost)

Hope this helped and have a good day

Jillian made the exact amount was $1598 in 3 weeks.

Each t-shirt costs $15.

Each Large purse goes for $59

And the cost of small purses is $32 each.

In the first week, she sold 4 t-shirts and 3 large purses, and 9 small ones.

Her earning in the first week = 4 × $15 + 3 × $59 + 9 × $32 = $525

In the second week, she sold another 5 t-shirts, 7 large bags, and 4 small ones.

Her earning in the second week = 5 × $15 + 7 × $59 + 4 × $32 = $616

Last week she sold 8 t-Shirts and also sold 3 large purses and 5 small purses.

Her earning in the Last week = 8 × $15 + 3 × $59 + 5 × $32 = $457

The exact amount she made in 3 weeks = $525 + $616 + $457 = $1598

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The number of students that chose band as an elective is 50

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic

let the total number of seats for choir be x and that for band be y

if there are 4 times as many seats as there in band then mathematically,

x = 4y.--------------------1

If there are 250 students, then, there would be 250 seats for the combined class.

so,

x + y = 250--------------2

substitute x = 4y in equation 2

4y + y = 250

5y = 250

y = 250/5

y = 50

In conclusion, 50 students can choose band.

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Answer:

35 cm

Step-by-step explanation:

The value the function A(12) is 2960.94

From the question, we have the following function definition that can be used in our computation:

A(t) = 710e⁰°¹¹⁹⁺

To calculate the function A(12), we set t to 12

i.e. calculate A(t) when t = 12

This equation becomes

A(12) = 710e⁰°¹¹⁹ˣ¹²

Evaluate the products

A(12) = 710e¹°⁴²⁸

Evaluate the exponents

A(12) = 2960.94

Hence, the solution is 2960.94

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The vertex of the graph of the parabola is at the point (-1, -6)

We know that for any parabola with a vertex at the point (h, k) and a leading coefficient a, can be written in vertex form as:

y = a*(x - h)^2 + k

In this case the parabola is:

f(x) = (-1)*(x + 1)^2 - 6

Comparing this with the general form, we can see that:

h = -1

k = -6

Then the vertex of the parabola is (-1, -6)

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X is a positive rational number greater than 1. If the two integers that make up the ratio are both positive, then the numerator must be greater than the denominator for the value of the ratio to be greater than 1.

So now let's look at subtracting the numerator and the denominator. We know that p > q and they are both positive integers.

So, p - q must be a positive integer greater than 1 because it is a positive integer subtracted by a smaller positive integer.

Simplified form is the -(1+sinα).

Given in question,

[tex]cos^{2}[/tex]α/sinα-1

[tex]sin^{2}[/tex]α + [tex]cos^{2}[/tex]α = 1

           [tex]cos^{2}[/tex]α = 1 - [tex]sin^{2}[/tex]α

[tex]cos^{2}[/tex]α/sinα-1 = (1 - [tex]sin^{2}[/tex]α ) / (sinα-1)

                    = (1-sinα)(1+sinα)/(sinα-1)

                    = (1-sinα)(1+sinα)/-(1-sinα)      

                    = (1+sinα)/-1

                    =  -(1+sinα)

Hence, in simplified form [tex]cos^{2}[/tex]α/sinα-1 = -(1+sinα)

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Answer:

=30

Step-by-step explanation:

The amount  that he invested in Fund B if the total profit from the two funds together was $2200 is $8,800.

Let x represent the amount invested in Fund B

Let 3x represent the  amount  invested in Fund A

Hence,

.07x + .05(3x) = 2200

.07x + .15x = 2200

.25x = 2200

Divide both side by .25x

x = 2200/.25

x = $8,800  (invested in Fund B)

Fund A:

3x = 3(8,800)

3x = $26,400 (Invested in Fund A)

Therefore $8800 was invested in Fund B.

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