find the values of the trigonometric functions of t from the given information. cos(t) = − 11 61 , terminal point of t is in quadrant iii sin(t) = tan(t) = csc(t) = sec(t) = cot(t) =

[tex]f(x) = (x + 3)(x + 6) \\ f(x) = x {}^{2} + 6x + 3x + 18 \\ f(x) = x {}^{2} + 9x + 18[/tex]

Answer:

C.) y = x² + 9x + 18

Step-by-step explanation:

C.) is correct because the function has the accurate x-intercepts. X-intercepts are the x-values in which the line passes through the x-axis. We can prove this by setting the function equal to 0, factoring, then solving for "x". You can factor the function by asking yourself the question, "which two numbers multiply to 18 and add to 9?"

y = x² + 9x + 18                             <----- Original function

0 =  x² + 9x + 18                           <----- Set the function equal to 0

0 = (x + 6)(x + 3)                           <----- Factor

0 = x + 6             0 = x + 3

-6 = x                  -3 = x

So, at (-3, 0) and (-6, 0), the function crosses the x-axis. This matches the given graph.

Answer:

we have

6x+2y > -106x+2y>−10

Isolate the variable y

Subtract 6x6x both sides

2y > -6x-102y>−6x−10

Divide by 22 both sides

y > -3x-5y>−3x−5

The equation of the line of this inequality is

y=-3x-5y=−3x−5

The slope is negative and is equal to m=-3m=−3

The y-intercept is the point (0,-5)(0,−5) ----> value of y when the value of x is equal to zero

The x-intercept is the point (-5/3,0)(−5/3,0) ----> value of x when the value of y is equal to zero

The solution of the inequality is the shaded area above the dotted line

Using a graphing tool

see the attached figure

Solving a system of equations we can see that:

First, let's define the variables:

With the given information we can write 3 equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

Then we need to solve a system of equations:

A = (3/4)*V

V = K - $18

A + V + K = $386.4

We can first replace the first equation into the third to get:

(3/4)*V + V + K = $386.4

And rewrite the second to get:

k = V + $18

And replace that in the other equation:

(3/4)*V + V + V + $18 = $386.4

Now we can solve this for V:

V*(1 + 1 + 3/4) = $386.4 - $18

V*(11/4) = $368.40

V = (4/11)*$368.40 = $133.96

Now that we know the value of V, we can replace it in:

K = V + $18 = $133.96 + $18 = $151.96

A = (3/4)*V = (3/4)*$133.96 = $100.47

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Answer:

41 yards by 118 yards

Step-by-step explanation:

Let W and L be the Width and Length of the playing field:

The perimeter, P, would be P = 2W + 2L

We are told that P = 318 yards.

We learn that L = 3W - 5

Combining this information, we can say:

P = 2W + 2L                         [Oriinal equation]

318 = 2W + 2L                      [P is 318]

318 = 2W + 2(3W-5)             [ Use the definition of L = 3W - 5]

318 = 2W + 6W - 10

328 = 8W

W = 41 yards

Use this value of W to find L:

L = 3W - 5

L = 3(41) - 5

L = 123 - 5

L = 118

CHECK

Does 2*(118) + 2*(41) = 318?  YES

Is the length 5 yards less than triple the width?

3*(41) - 5 = 118  YES

The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

According to the statement

we have a given that the Among the 1000 respondents,

12​% chose chocolate​ pie, and the margin of error was given as

±5 percentage points.

and we have to explain the statement that the margin of error was given as ±5 percentage​ points.

We know that the interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

And this statements also indicates the interval between the like and unlike respondents of chocolate pie.

So, this statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

So, The statement indicates that the interval 12​%±5​% is likely to contain the true population percentage of people that prefer chocolate pie.

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The polynomial expression that represents the profit of selling x tablets is 10x - 100

profit = revenue – cost

= (100 + 30x) - (20x + 200)

= 100 + 30x - 20x - 200

Profit = 10x - 100

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2 items should be placed on the ballot to maximize the total number of votes cast on all items.

According to the statement

items on which people vote = 30

people who will vote = 240

batch containing items = 3

number of batches formed = 10

now we find the number of items placed on ballot to maximize the number of votes.

we find the average number by each items got the vote.

Average = items in batch / total votes

Average = 3/240

but if we add 2 items in the ballot then average become half.

So, 2 items should be placed on the ballot to maximize the total number of votes cast on all items.

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Total number of five letter strings formed by A,B,C and D with repetitions allowed

={4x4x4x4x4 = 4 power 5 = 1024

Now, fix BAD in a string at one place then we have 2 more places to be filled with 4 letters, total number of such strings

=4x4=16

Here, BAD can be at any of the 3 positions,

Hence the total number of strings with BAD in it

= 3 x 16=48

Now, The total number of strings not containing BAD

=1024-48

=976

Using 26 letters, the number of 5-letter words that can be formed when the letters are different is determined as follows: 26P5 = 26 × 25 × 24 × 23 × 22 = 7883600 different words.

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Jamie purchases 4 chocolate (3.57), 7 strawberry/vanilla, and 7 peanut butter cupcakes for an office party.

The steps involved are:

Given that,

Jamie is ordering cupcakes for an office party.

There are three flavors - Chocolate, Strawberry/vanilla, and peanut flavors.

Jamie purchased a total of 18 cupcakes for $55.75

The cost for a single cupcake of each flavor is as follows:

Chocolate - $3

Strawberry  - $2.75

Peanut - $3.50

Consider the number of cupcakes of each flavor as x, y, and z respectively.

So, the equations we can write from this data are,

x + y + z = 18 and

3x + 2.75y + 3. 50z = 55.75

But it is given that,

There are twice as many chocolate cupcakes purchased as peanut butter cupcakes.

So, z = 2x

Then the above two equations become,

3x + y = 18 and

10x + 2.75y = 55.75

By solving these two equations we get,

x = 3.57 ≅ 4

y = 7.28 ≅ 7

Since we know that z = 2x,

⇒ z = 2 × 3.57 = 7.14 ≅ 7

So,

There are 4 chocolate, 7 strawberry, and 7 peanut cupcakes.

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The solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

Linear inequalities are inequalities that have constant average rates of change, slope or gradient

A system of linear inequalities is a collection of at least two linear inequalities.

In this case, the system of linear inequalities is given as

7x+2y > 3

x-2y < 2

Rewrite the inequalities as equations

7x+2y = 3

x-2y = 2

Make x the subject in the second equation, by adding 2y to both sides of the equation

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

This gives

x = 2 + 2y

Substitute x = 2 + 2y in 7x+2y = 3

7(2 + 2y) +2y = 3

Expand the brackets

14 + 14y + 2y = 3

Evaluate the like terms

16y = -11

Divide both sides by 16

y = -11/16

Substitute y = -11/16 in x = 2 + 2y

x = 2 - 2 * 11/16

Evaluate the product

x = 2 - 11/8

Evaluate the difference

x = 5/8

Hence, the solution for the system of linear inequalities 7x+2y > 3 and x-2y < 2 are x = 5/8 and y = -11/16

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The data-set that places 22.6 as an outlier is given as follows:

2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9

A measure is considered an outlier in a data-set if it is very far from other measures, especially in these two cases:

In this problem, he data-set that places 22.6 as an outlier is given as follows:

2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9.

The second highest value is 5.3, which is considerably less than 22.6, hence 22.6 is an outlier in the data-set.

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The total area of the regular pentagon prism is 485 square units

The given parameters are:

Base area = 50

Height = 11

Base = 7

Start by calculating the total area of the 5 sides using

Sides = n * Height * Base

Sides = 5 * 11 * 7

Sides = 385

The total surface area is

Total = 2 * Base area + Sides

This gives

Total = 2 * 50 + 385

Evaluate

Total = 485

Hence, the total area of the regular pentagon prism is 485 square units

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Q1

Nominal - D

Ordinal-  B, G

Ratio - A, C, E, F

Q2

Quantitative- A, C, D, G

Qualitative -B, E, F, G

Q3

Simple Random - A, C

Systematic Sample - B

Nominal measures are the most accurate and meaningless, as they only show the "characteristics" or "identities" that we are interested in. In other words, in a nominal variable, a number just gives the attribute a unique "name". In this case, the number is just a label.

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The solution to the given expression [98/(82 + 283)] * (69 - 29) is; 784/73

We want to solve the expression;

[98/(82 + 283)] * (69 - 29)

Let us first simplify the first part which is;

98/(82 + 283) = 98/365

Then let us simplify the second part which is;

69 - 29 = 40

Thus, we have the expression;

(98/365) * 40

This can be simplified further to get;

(98/73) * 8 = 784/73

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Considering the definition of an equation and the way to solve it, there are 10 apples in the bag.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "or" the number of oranges in the bag, and knowing that:

the equation in this case is:

or + apples= 15

or + 2or= 15

Solving:

3or= 15

or= 15 ÷ 3

or= 5

As a bag of apples and oranges contains twice as many apples as oranges, then 2or= 2×5= 10 apples

Finally, there are 10 apples in the bag.

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The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Constant = k

= 2.1³

= 9.261

Volume of large : volume of small = k

Vl / Vs = k

Vl = Vs × k

= 24 × 9.261

= 222.264 cubic inches

Therefore,

Volume of tissue paper = volume of large - volume of small

= 222.264 cubic inches - 24 cubic inches

= 198.261 cubic inches

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Answer:

Triangle DEF is a right, scalene triangle. It is not isosceles, obtuse, acute, or equilateral

Step-by-step explanation:

All we know about m and n are that they are not equal to each other and they are positive. This was given in the problem. See image. Once it is graphed you can see on the graph the lengths of DE and EF. Use Pythagorean theorem to calculate DF. see image.

DE is horizontal and EF is vertical, so you can see their slopes or calculate using a formula. Calculate the slope of DF. Slope is y-y on top of a fraction and x-x on the bottom of the fraction.

Lastly, use midpoint formula to find the midpoints. Average the x's and average the y's to find the x- and y-coordinates of the midpoints. See image.

Finally, DEF is a right triangle. The graph as well as the slopes show us that DE and EF form a right angle. So DEF must be a right triangle (and not obtuse nor acute) We were told that m doesNOT equal n, so the triangle cannot have two equal sides, so it cannot be isosceles (2 equal sides) nor equilateral (3 equal sides) It has 3 different lengths of sides; that is called scalene.

Answer:-----------

Step-by-step explanation:------------------

Answer:

???????

Step-by-step explanation:

Please tell the question so i can answer it

Using proportions to find the radius of figure 2, we have that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The rule of three to find the radius of figure 2 is given as follows:

[tex]\frac{5}{9} = \frac{r}{4.5}[/tex]

Applying cross multiplication:

9r = 4 x 4.5

r = 4 x 4.5/9

r = 2 in

The circumference of a circle of radius r is given by:

[tex]C = 2\pi r[/tex]

In this problem, we have that r = 2 inches, hence:

[tex]C = 2\pi \times 2 = 4\pi[/tex]

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

[tex]A = \pi r^2[/tex]

Hence:

[tex]A = 4\pi[/tex]

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Answer: First one is 5, Second is 6.25

Step-by-step explanation: Correct on Edmentum/Plato

Answer:

Step-by-step explanation:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion.

imagine the cd/cd as 1 which is a whole number. then, add the denominators (d+c-cd)/cd

The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]

Distance between two points exists the length of the line segment that joins the two given points. Distance between two points in coordinate geometry can be estimated by finding the length of the line segment merging the provided coordinates.

Let the points be (4,-2) and (-6,4).

The distance between two points [tex](x_{1} ,y_{1})[/tex] and [tex](x_{2} , y_{2} )[/tex] exists provided by the distance between the two points

[tex]= $\sqrt\\(x_{2} -x_{1} )^{2} +(y_{2} -y_{1})^{2}[/tex]

substituting the points in the equation, we get

[tex]$=\sqrt\\(-6-(4)^{2} +(4-(-2)^{2}[/tex]

simplifying the equation, we get

[tex]$=\sqrt{136}[/tex]

[tex]$=2\sqrt{34}[/tex]

The distance between two points (4,-2) and (-6,4) exists [tex]2\sqrt{34}.[/tex]

Therefore, the correct answer is option c. [tex]$2\sqrt{34}.[/tex]

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The 95% confidence interval of the statistics is (7.795, 8.243).

Based on the information given, the 95% confidence interval will be:

= 8.019 + (1.962 × 3.183/✓1114)

= 8.243 and

= 8.019 - (1.962 × 3.183/✓1114)

= 7.795

In conclusion, the 95% confidence interval of the statistics is (7.795, 8.243).

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Answer:

9cm

Step-by-step explanation:

If the triangles are similar then their lengths are in a ratio to each other, Ex: PR is 3 times LN, 2*3 = 6cm

This gives us a ratio of 1:3

PQ = LM*3 = 3cm*3 = 9cm

Parallel cousins are found in the iroquois system of kinship and are defined as bifurcate merging.

Parallel cousins, or the offspring of one's mother's or father's brothers or sisters, were frequently referred to and regarded in the same way as one's siblings. Contrarily, cross-cousins, or the offspring of one's mother's brothers or father's sisters, were frequently regarded as the best source of children.

Bifurcate merging is the underlying idea of the Iroquois system. The ego divides his family into those on his mother's side and those on his father's side (bifurcation) and combines his father with his brother (A) and his mother with her sister (B) .

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The order of the numbers which satisfies commutative property exists 1/7 + (-1)+ 2/7.

The commutative property exists a math rule that states that the order in which we multiply numbers does not change the product. The commutative property uses for addition and multiplication. The property states that phrases can “commute,” or transfer locations, and the outcome will not be affected. This exists described as a + b = b + a for addition, and a × b = b × a for multiplication.

Arranging the order of the numbers the fractions

[tex]$& \frac{1}{7}+(-1)+\frac{2}{7} \\[/tex]

[tex]$=& \frac{1}{7}+\frac{2}{7}+(-1) \\[/tex]

Simplifying the equation, we get

[tex]$= \frac{1}{7}+(-1) \\[/tex]

[tex]$&=\frac{4}{7}[/tex]

Therefore, the correct answer is option A. 1/7 + (-1)+ 2/7

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The x-values are the heartbeat(s) and the y-values are the time(s)

The variables are given as:

Time(s) and Heartbeat(s)

As a general rule, the action that is being done is the independent variable.

The action here is the heartbeat.

So, the x-values are the heartbeat(s) and the y-values are the time(s)

A possible value of this is;

x = 100, y = 60 seconds

So, the ordered pair is (100,60)

When represented as ratio, we have;

Ratio = 60/100

Simplify

Ratio = 0.6 heartbeat per second

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One sample Z Test is used by cate.

According to the statement

The average tuition in Illinois is $28,950 with a standard deviation of $3,470.

Assuming we have a large enough sample, since we are testing one group's mean relative to a hypothesized value, this would be a one-sample z-test.

So, One sample Z Test is used by cate.

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Answer:

Step-by-step explanation:

The height of the pyramid (h) = 3.6m

The perimeter of the base = 4.1m

Volume of a pyramid = ?

Formula:-

[tex]\boxed{\sf Volume =\cfrac{1}{3} \: a^2h}[/tex]

So,

Perimeter = 4a

[tex]\sf 4.1=4a[/tex]

[tex]\sf a=1.025[/tex]

Now, let's put the value of a in the formula:-

[tex]\sf V=\cfrac{1}{3} \:(1.025)^{2} (3.6)[/tex]

[tex]\sf 1.26075m^2[/tex]

[tex]\sf \thickapprox 1.3m^3[/tex]

Therefore, the volume of the pyramid is 1.3m³.