Find sin D, sin E, cos D, and cos E. Write each answer as a fraction in simplest form.

Answer:

Option C

The first two hours cost $4. Between two hours and six hours cost $2 per hour, and all hours after that cost $1.

Step-by-step explanation:

From the first part of the graph we can see that there is a flat rate of $4 for the first two hours. So the first two hours cost $4.

We can eliminate options A and B leaving C and D as only possible options.

Look at the second part of the graph

Between 2 hours and 6 hours(difference of 4 hours), the cost increases from $4 to $8 or an increase of $8

So rate per hour is $8/4 = $ 2 per hour between 2 hours and 6 hours

This information alone is enough to eliminate D but let's go to the rate beyond 6 hours just to make sure. This is the third part of the graph

Between 6 and 7 hours (1 hour) we can see the cost goes from $12 to $13 or a difference of $1. This means for every hour after 6 hours, the rate is $1 per hour.

So option C is the correct choice

The solution to the system substitution is (x , y) = (-3,3).

Here it is given that,

y=-2 x -3 and y= 3 x + 12

Take y=-2 x -3 as equation 1,

y= 3 x + 12  as equation 2'

by equating both equations,

-2x-3=3x+12

-3-12=3x+2x

5x=-15

x=-15/5

 =-3

substituting the value of x in the equation1

y=-2x-3

y=-2(-3)-3

 =3

Hence, The solution to the system substitution is (x , y) = (-3,3).

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The solution to the inequality 6x > 72 is option B x > 12

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

A is not equivalent to b in any scenario. Since a is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

There are two forms of inequality relations that are not strict, in contrast to strict inequalities:

The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).

The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).

Given, the inequality is 6x>72

6x > 72

Dividing by 6 on both sides of inequality, we get,

6x/6 > 72/6

⇒ x > 12

Hence, option B is correct.

The solution to the inequality 6x > 72 is option B, x > 12

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The system of linear inequalities is graphed is  x < -2; y ≤ -x+2. Hence option c is the correct.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The graph consists of two inequalities.

Since the one graph line is solid, thus the inequality sign either "less than or equal" or "greater than or equal". The other one is dotted, thus it will be less than or greater than

First find the equation of line.

One line passes through the points (-2,0) and (0,-2).

The equation of line that passes through the point (a,0) and (0,b) is

x/a + y/b = 1

The equation of the line is x/(-2) + y/(-2) =1

x + y = -2

y = -x - 2

The equation of the inequality will be either y ≤ -x - 2 or y ≥  -x - 2.

Putting x =0  and y = 0 in y ≤ -x - 2

0  ≤ - 0 -2

0≤ -2 (false)

In the graph (0,0) does not include in the shaded region. Therefore the inequality is   y ≤ -x - 2.

The second line is parallel to y-axis.

The equation of line will be x = a

The line passes through the point (-2,0)

Putting x = -2 and y =0  in x = a

-2 = a

Therefore the equation of the dotted line will be x = -2

The equation of the inequality will be either x > -2 and  x < -2:

Putting x =0  and y = 0 in x < -2

0 < -2

0 < -2 (false)

In the graph (0,0) does not include in the shaded region. Therefore the inequality is  x < -2.

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a. The table for the given data is as follows :

Year                  2014       2015        2016       2017

Value (in $) 254000 293000 338000 372000

b. Domain and Range for the given relation is:

Domain : {2014, 2015, 2016, 2017}

Range : {254000, 293000, 338000, 372000}

c. From the table we observe that for each year it is having a unique value so it is related to the function.

What is Domain?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

What is Range?

The range of a function is the set of values that the function assumes.

What is Relation?

A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the items x and y come from different sets, then the objects are said to be connected

a. The table for the given data is as follows :

Year                  2014       2015        2016       2017

Value (in $) 254000 293000 338000 372000

b. Domain and Range for the given relation is:

Domain : {2014, 2015, 2016, 2017}

Range : {254000, 293000, 338000, 372000}

c. From the table we observe that for each year it is having a unique value so it is related to the function.

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Answer: B. ( - ∞ , 1 ) U ( 1, 2]

Step-by-step explanation:

The equation of H(x) is [tex]\frac{\sqrt{2-x} }{x-1}[/tex]

For the bottom denominator, x-1 cannot equal zero

x-1=0

x=1

For the numerator, 2-x square root has to be greater or equal to zero.

[tex]2-x\geq 0[/tex]

[tex]x\leq 2[/tex]

so the domain is

( - ∞ , 1 ) U ( 1, 2]

Answer:

I'll help

Step-by-step explanation:

the entrance fee to the skating rink=$5

each minute the skater uses the rink costs=$0.25

Answer:

x ≤ 10

Step-by-step explanation:

3/2 x - 1 ≤ x +4

3/2 x - x ≤ 1 + 4

(3-2)/2 x ≤ 5

1/2 x ≤ 5

2 * 1/2 x ≤  2 * 5

x ≤ 10

Answer:

g(3) is 24

Step-by-step explanation:

To find the value of g(3), we need to plug 3 into the function g(x) and evaluate the resulting expression. The function g(x) is defined as g(x) = 3(2)^x. When we plug 3 into this function, we get g(3) = 3(2)^3. To evaluate this expression, we need to calculate 2^3, which is 8. Therefore, g(3) = 3 * 8 = 24.

In summary, the value of g(3) is 24.

Answer:

g(3) = 24

Step-by-step explanation:

Given information,

→ g(x) = 3(2)^x

Then the value of g(3) will be,

→ g(x) = 3(2)^x

→ g(3) = 3(2)³

→ g(3) = 3(8)

→ [ g(3) = 24 ]

Hence, the value of g(3) is 24.

Answer:

a=-2400

Step-by-step explanation:

We have -x*y*z = 150. We want to find the value of -2x*2y*-4z. Let's set this to a variable, a. We have now that [tex]2x*2y*4z = a[/tex] (because the negatives combine to a positive), where we want to solve for a. This is equal to [tex]16xyz = a[/tex], and dividing by 16 on both sides results in [tex]xyz = a/16[/tex]. Recall that we know [tex]-xyz = 150.[/tex] Negating each side gives us [tex]xyz = -150.[/tex]

Now we have two equations that are equal to the same thing(xyz), so we can set them equal to each other. This gives us [tex]-150 = a/16[/tex]. To solve for a, we multiply both sides by 16, giving us a = -2400. This is our answer!

Hope this helps!

Answer:

x = 7

Step-by-step explanation:

x(XY) = 6(WX)

x(x + 11) = 6(6 + 15)

x² + 11x = 126

x² + 11x - 126 = 0

126 = 7 × 18

(x + 18)(x - 7) = 0

x + 18 = 0   or   x - 7 = 0

x = -18   or   x = 7

We discard the negative answer.

x = 7

Answer:12

Step-by-step explanation:

The answer to this Question based on Linear Relation is given below

What is Linear Relation?

It is a relation between two variables in which one variable has linear behaviour as other

means if one variable increases or decreases then other variables does same behaviour linearly

Solution:

let us denote the battery by b and time by t

b = 54 - t/2

this relation satisfies all the conditions that are given in Question and gives variation of battery with time and this if plotted on graph will give a linear straight line

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Answer: a=33

Step-by-step explanation:

Answer:

a=33

Step-by-step explanation:

1. Multiply both sides of the equation by 11

231=6a+33

2. Move 6a to the left side by subtracting

231-6a=33

3. Move 231 to the right side by subtracting

-6a=33-231

4. Find the difference

-6a=-198

5. Divide -6 on both sides to get "a" by itself

a=33

The number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.

A system having more than two equations is known as a system of equations.

Given that, the can of soup contains 350 mg of sodium and the frozen dinner contain 650 mg of sodium.

Let the numbers of cans of soups and frozen dinners purchased be s and f, then,

s + f = 11

s = 11-f       (1)

The total sodium in all 11 cans is 4750 mg which can be expressed as:
350s + 650f = 4750

Substitute s = (11-f) into the above equation:

350(11 - f) + 650f = 4750

3850 - 350f + 650f = 4750

300f = 4750 -3850

300f = 900

f = 3

Substitute f = 3 into equation (1):

s = 11-3

s = 8

Hence, the number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.

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Different arrangements of the display are possible is 2520.

Given:

the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row.

Permutation :

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

= [tex]7_P_5[/tex]

we know that,

[tex]n_P_r[/tex] = n! / ( n - r ) !

[tex]7_P_5[/tex] = 7! / ( 7 - 5 ) !

= 7! / ( 2 ) !

= 7! / 2!

= 7 * 6 * 5 * 4 * 3 * 2! / 2!

= 42 * 20 * 3

= 840 * 3

= 2520

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A 95% two-sided confidence interval is 0.46 < a <0.31 .

The formula for confidence interval for population standard deviation is,

[tex]s\sqrt{\frac{n-1}{X^{2} _{1-a/2,n-1} } }[/tex]  < a < [tex]s\sqrt{\frac{n-1}{X^{2} _{a/2,n-1} } }[/tex]

Given in question,

Significance level, a = 1 - 0.95

                                 = 0.05

Sample size, n = 51

Sample standard deviation, s = 0.37

By using chi-square distribution table, we get

[tex]X^{2} _{1-a/2,n-1}[/tex] = [tex]X^{2} _{0.975,50}[/tex]

                  = 32.36

[tex]X^{2} _{a/2,n-1}[/tex] = [tex]X^{2} _{0.025,50}[/tex]

              = 71.42

Confidence interval for population standard deviation is :

[tex]0.37\sqrt{\frac{50}{32.36} }[/tex]  < a  < [tex]0.37\sqrt{\frac{50}{71.42} }[/tex]

0.45992018426 < a < 0.30958278534

Hence, a 95% two-sided confidence interval is 0.46 < a <0.31 .

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The disparity -9x/11 - 7 < -5 is x > -22/9

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality.

-9x/11 < 2 (add 7 to both sides) (add 7 to both sides)

-9x < 22 (multiply both sides by 11) (multiply both sides by 11)

x > 22/-9 Because you are dividing by a negative integer, change the sign.

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Answer: x > [tex]\frac{-22}{9}[/tex]

Step-by-step explanation:

     To solve this inequality, we will isolate the variable, x, with inverse operations.

   Given:

[tex]\frac{-9x}{11}[/tex]- 7 < -5

   Add 7 to both sides of the inequality:

[tex]\frac{-9x}{11}[/tex] < 2

   Multiply both sides of the inequality by 11:

-9x < 22

   Divide both sides of the inequality by -9:

* note, we must "flip" the sign since we are dividing by a negative integer

x > [tex]\frac{-22}{9}[/tex]

Refer to the attachment for graph.

What are vector equations ?

Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.

Given  vector equation:

r(t) = < t², t, 2 >

When t= -2,

r(-2) = < (-2)², -2, 2 >

      =  < 4, -2, 2 >

This means. when t= -2, the curve touches the point   ( 4, -2, 2 )

Similarly, when t= -1, the curve touches the point   ( 1, -1, 2 )

Table is attached.

graph is attached.

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To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:

12 meters.

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements in this triangle are given as follows:

If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.

Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.

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Answer:

Step-by-step explanation:

To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:

12 meters.

When does a set of three measurements can represent a triangle?

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements in this triangle are given as follows:

Smallest: 12 meters.

Largest: 22.8 meters.

If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.

Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.

Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.

Step-by-step explanation:

The term that makes NO distinction between an explanatory variable X and a response variable Y is Correlation , the correct option is (a) .

In the question ,

four options are given ,

we have to select the option that makes no distinction between explanatory variable X and a response variable Y .

Response Variable is the (dependent variable) measures the outcome of the study.

Explanatory Variable is the (independent variable) helps to explain or influence changes in a response variable.

So , Correlation makes no distinction between explanatory and response variables.

So , it makes no difference in calculating the correlation , which variable you call x and which you call y  .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e., you can interchange the roles of X and Y and get the same result) ?

(a) Correlation

(b) Regression

(c) Both correlation and regression make no distinction between X and Y.

(d) Both correlation and regression make distinction between X and Y.

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From the expression, when simplified, (1)   16a+b  (2) 17b+11a (3) 17b.

An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

The given algebraic terms are

3a+b+13a

Collect the like terms

3a+13a+b

Add the like terms

16a+b

Therefore, 3a+b+13a matches 16a+b

20b+11a-3b

Collect like terms

20b-3b+11a

=17b+11a

Therefore, 20b+11a-3b matches 17b+11a

20b-5b+2b

All the terms are alike, therefore do the arithmetic operation

15b+2b

=17b

Therefore, 20b-5b+2b matches 17b

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Answer:

b) 2/9

c) 1/3

Step-by-step explanation:

The probability of a desired event happening is the number of ways the desired event can happen divided by the total number of possible outcomes.

a) Correct

b)

There are 9 possible outcomes.

2 outcomes are negative.

p(negative) = 2/9

c)

There are 3 outcomes that are more then 3.

p(more than 3) = 3/9 = 1/3

Answer:

0.95-1.05 (please give brainliest)

Step-by-step explanation

1x.95=.95

1x1.05=1.05

The probablity that the two balls are orange and blue is 1/8

Describe Probability:

This is the chance or likelihood that an event will take place.

One orange ball, one yellow ball, and two blue balls are there in a bag.

The total number of sample space  or outcome can be given as

Total outcome = 1 + 1 + 2=4

Probablity of occouring an orange ball  can be given as, 1/4

Probablity of occouring a blue ball  can be given as, 2/4

Probablity of an orange ball and a blue ball = 1/4 * 2/4

Probablity of an orange ball and a blue ball = 1/8

Consequently, there is a 1/8 chance that the two chosen balls are orange and blue

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The first six terms of the given sequence are given as  3, -7, -17, -27, -37 and -47.

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

The given problem can be solved as follows,

The first term of the sequence is a₁ = 3

And, the common difference is d = -10.

Now, the first six terms can be written as,

a₁ = 3

a₂ = 3 - 10

   = -7

a₃ = -7 - 10

    = -17

a₄ = -17 - 10

    = -27

a₅ = -27 - 10

    = -37

a₆ = -37 - 10

    = -47

They can be graphed on the number line as follows,

Hence, the first six terms are given as 3, -7, -17, -27, -37 and -47.

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Answer:

exponential

Step-by-step explanation:

the 14% of a number will be always greater because the numbers themselves will be greater

For an average intake of 2200 calories per day, the number of acres of land is approximately 2.

A function having the formula f(x) = ax' + b is said to be linear.

It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).

You would be given the value of f(x) and asked to locate x when solving a linear function.

C(x) is a variable that tells the number of calories consumed daily by a person

x is the number of acres that person own.

C(x) = 270ln(x+1)+1900

In the given question number of acres ask a person have who consumed 2200 calories in a day.

Therefore,

C(x)=2200

2200=270ln(x+1)+1900

2200-1900=270ln(x+1)

300=270ln(x+1)

300/270 = ㏑(x+1)

10/9 = ㏑(x+1)

x+1 = e^(10/9)

x+1 = 3.037

x= 3.037-1

x=2.037

x=2(round off)

Therefore, 2 acres of land a person can consume 2200 calories in a day.

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