Express the angle in radian measure.
-22½°
a. -π/8
b. -π/4
c. -π/16

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:

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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Answer:

create a line between (0,0) and (1,3)
the unit rate is 3/2 or 1.5

Step-by-step explanation:

pls mark

The required speed is 45 mph in each direction.

What is speed?

The definition of speed is a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

We know that distance=rate*time

d=rt

45=rt

45=(r+30)(t-2)

rt=(r+30)(t-2)    

This shows,

rt=rt+30t-2r-60

0=30t-2r-60

if 45=rt, then r=45/t

substitute in the equation

0=30t-2(45/t)-60

multiply both sides by t

0=30t²-90-60t

on solving this quadratic equation, we get  t= 3 s, t=-1 s

consider positive value

t=3 hours

45=rt

45=r*3

r=45/3 =15 mph to new site

r+30=15+30=45 mph returning

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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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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.

Answer:

m = 37

Step-by-step explanation:

The interior and corresponding exterior angle of a triangle are always supplementary.

Therefore, we can set the sum of the two given angle measures to 180°:

[tex](2m-12) \textdegree + (3m+7) \textdegree = 180 \textdegree[/tex]

and solve algebraically for m.

[tex]2m-12 + 3m+7 = 180[/tex]

[tex](2m + 3m) + (-12+7) = 180[/tex]

[tex]5m-12+7 = 180[/tex]

[tex]5m - 5 = 180[/tex]

[tex]5m = 185[/tex]

[tex]m=37[/tex]

The value of m is 37.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Given:

m ∠Z = (2m − 12)° and exterior angle ∠Z =(3m + 7)°.

int. m <Z + ext. <Z= 180

2m - 12 + 3m + 7 = 180

5m - 5 = 180

5m = 185

m = 185/ 5

m = 37

Hence, the value of m is 37.

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Answer:

=30

Step-by-step explanation:

The answer is -9.

-2 -(+7) = -2 -7

-2 -7 = -9

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 mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.

Given that,

The list of numbers are 3,6,9,7,4,6,7,0,7

The mean, median, mode, and range must be determined.

The "mean" is the standard "average," which is calculated by adding up all the numbers and dividing the result by the total number of numbers.

The value that sits in the middle of a set of numbers is known as the "median." Before you can find the median, your numbers must be listed in numerical order from smallest to greatest. This means that you might need to redo your list.

The "mode" value is the one that shows up the most often. There is no mode for the list if no number on the list is repeated.

A list of numbers' "range" is just the range between the largest and lowest values. It conveys "spread," which is the degree to which the values are scattered (or how concentrated they are).

Mean=(3+6+9+7+4+6+7+0+7)/9

Mean = 49/9

Mean = 5.4

Median is 0,3,4,6,6,7,7,7,9

The median is 6

Mode is 7

Range is

Greater number is 9 and the smallest number is 0

Difference is 9-0=9

Range is 9.

Therefore, The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.

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The library’s December record is 29442  

Mathematical operations are Operators which emphasize particular actions like adding, subtracting, adding multiple times, dividing, etc.

There are 4 basic operations in mathematics as given below.  

1. Addition  =>  (+)

2. Subtraction  => (-)

3. Division  => (÷)

4. Multiplication  =>  (x)  

Here we have

In 2017 the library was able to record 4907 borrowed books  

By December of the same year, the library has 6 times its January record.  

[ Here we use Multiplication to find the December record ]

The December record = 6 times of January record

⇒ 6 × January record

⇒ 6 × 4907    

⇒ 29442

Therefore,

The library’s December record is 29442

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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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Banerjee Company is  liable for FUTA tax this year and the net FUTA tax for the year is $528.60.

a. Yes. Banerjee Company liable for FUTA tax this year.

b. FUTA tax

FUTA tax =0.6%

Hence,

Net FUTA tax = (Wages paid  × tax rate ) +(Taxable wages × Tax rate)

Net FUTA tax = ($23,400 × 0.6%) + ($64,700 ×0.6%)

Net FUTA tax = $140.40 + $388.30

Net FUTA tax =$528.60

Therefore $528.60 is the Net FUTA tax.

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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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The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.

What is transformation of function?

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f (x) = x 2 + 3 is obtained by just moving the graph of g (x) = x 2 by 3 units up.

Given,

function g(x) = (x − 4)3 + 5 and compares to function f(x) = x3,

The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.

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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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as x -> -infinity, y -> -infinity and as x-> infinity, y-> infinity

So, last option is correct

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:

m∠1 = 126°

m∠2 = 154°

Step-by-step explanation:

First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)

We know that the measures of the interior angles of a triangle add to 180°.

Therefore,

m∠A + 96° + 30° = 180°

m∠A + 96° = 150°

m∠A = 54°

From this value, we can solve for m∠1, since it is supplementary to ∠A:

m∠A + m∠1 = 180°

54° + m∠1 = 180°

m∠1 = 126°

To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.

First, the measures of the interior angles of a triangle add to 180°:

28° + m∠1 + m∠B = 180°

28° + 126° + m∠B = 180°

m∠B = 26°

Finally, we can solve for m∠2 because it is supplementary to ∠B.

m∠B + m∠2 = 180°

26° + m∠2 = 180°

m∠2 = 154°

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 group that travels faster when groups of hikers left camp at the same time and each traveled at a constant rate is group B.

From the information, two groups of hikers left camp at the same time. each traveled at a constant rate.

Since group A covered 3/4 mile in 1/2 hour, the speed will be:

= Distance / Time

= 3/4 ÷ 1/2

= 1.5 miles per hour.

It took Group B 3/4 hour to travel 1/3 mile. The speed will be:

= Distance / Time

= 3/4 ÷ 1/3

= 2.25 miles per hour.

Group B had a faster speed.

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Complete question

Two groups of hikers left camp at the same time. each traveled at a constant rate

group A covered 3/4 mile in 1/2 hour

It took Group B 3/4 hour to travel 1/3 mile

Which group so travelling at a faster rate?

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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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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Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem

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.

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

The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .

In the question,

it is given that ,

the sum of speed of two trains = 723.5 miles per hour

let the speed of the first train = x miles per hour

let the speed of the second train = y miles per hour ,

also given that , the speed of the first train is 4.5 mph faster than that of the second train , which means

x = y + 4.5 .

the sum is 723.5 ,

so , the equation is

x + y = 723.5

y + 4.5 + y = 723.5

2y + 4.5 = 723.5

2y = 719

y = 719/2

y = 359.5

So , x = 359.5 + 4.5 = 364 .

Therefore , The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .

The given question is incomplete , the complete question is

The sum of the speed of the two trains is 723.5 miles per hour. if the speed of the first train is 4.5 mph faster than that of the second train, find the speeds of each train ?

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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