What is the total perimeter of this figure?

The sum of interior angles of a tray that is of pentagon shape is 540°

Given,

There is a tray which is of pentagon shape.

We have to find the sum of interior angles of the tray.

We have to find the sum of interior angles of pentagon.

That is,

Sum of interior angle of polygon formula = (n - 2) × 180°

Where, n is the number of sides in a polygon.

Here,

Pentagon has 5 sides.

Then,

Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°

That is,

The sum of interior angles of a tray that is of pentagon shape is 540°

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The question is incomplete. Completed question is given below;

Suppose is Jeanine is building a tray for a floral table centerpiece in the shape of a pentagon. The sum of the interior angles of the tray will be

Answer: 31.5

Step-by-step explanation:

Answer:

31.5

Step-by-step explanation:

[tex]45 \times .7 = 31.5[/tex]

The time taken for the rocket to reach its maximum height is; 2.25 seconds.

The maximum height reached by the toy rocket by evaluation is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Ultimately, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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The cost of each binder is $3.

Given,

In the question:

Angel spends $29 to order binders online.

They buy 8 binders and pay a flat fee of $5 for shipping.

To find the what is x, the cost of each binder?

Now, According to the question;

Based on the given conditions:

Formulate:

Angel spends = $29 to order binders online.

Buy the = 8 binders

Paying = $5 for shipping .

5 + 8 × x = 29

Solve the equation:

5 + 8x = 29

Rearrange the terms;

8x = 29 - 5

8x = 24

x = 24/8

x = 3

Hence, The cost of each binder is $3.

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Equation of line will be y = x/3 - 2

A line's equation can be written in many forms in which one is slope-intercept form.

Equation in slope-intercept form is written as y = mx + c where

m = slope

c = y intercept

Slope shows the steepness of the line. It can be given by change in y axis by change in x axis.

y intercept is the point where the line cuts the y axis that is x = 0 at this point.

Points given to us are (6 , 0) and (9 , 1)

slope = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

m = (1 - 0) / (9-6)

m = 1/3

For c put values of either point in the equation as they both are on the line so they both will satisfy the equation.

y = mx + c

0 = (1/3)*6 + c

0 = 2 + c

c = -2

now put values of m and c in the equation and get a general equation.

Therefore of equation of line will be y = x/3 - 2

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(C) represents a function with the same rate of change at the function       [tex]y = \frac{7}{4}x+3[/tex].

Given equation,

[tex]y = \frac{7}{4}x+3[/tex]

Slope = m = 7/4

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

Now we will check every option and find slope which we be 7/4.

(A) A(1,0) and B(5,-4)

    Slope = (-4-0)/(5-1)

               = -4/4

               = -1

               ≠ m

(B) A(-1,1) and B(0,4)

     Slope = (4-1)/(0+1)

                = 3/1

                = 3

                ≠ m

(C) A(-4,-6) and (0,1)

    Slope = (1+6)/(0+4)

               = 7/4

               = m

(D) A(0,-2) and B(-4,5)

    Slope = (5+2)/(-4-0)

               = 7/-4

               = -7/4

               ≠ m

Hence, only (C) satisfies the situation.

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Answer:

38 people

Step-by-step explanation:

In this case, we can see that, being two people, the cost is 14 and when it is double, that is, 4 people, the value is not 28 but 20.

Which means that there is an additional value that is being charged for the vehicle, that is:

let "c" be the value of the vehicle and "x" be the value per person

c + 2 * x = 14

c + 4 * x = 20 => c = 20 - 4 * x

replacing:

20 - 4 * x + 2 * x = 14

-2 * x = 14-20

-2 * x = -6

x = 6/2

x = 3

for C:

c = 20 - 4 * 3

c = 8

Which means that the formula for the value of the input would then be:

e = 8 + 3 * n

where "n" is the number of people.

Now, we are told that for e = 122

122 = 8 * + 3 * n

3 * n = 122 -8

n = 114/3

n = 38

which means that for that bus there are a total of 38 people

Answer:

X = 67, Y = 113

Step-by-step explanation:

To find y: 180-62-51=67

To find x: 180-67 = 113

Total angle in a triangle sums to 180 degrees

Total angle in a straight line is also 180 degrees

Answer: $194.25

Step-by-step explanation:

Given data

Principal=  $7400

Rate=  10.5%

time= 1/4 years

The simple interest formula is given as

SI= PRT/100

substitute

SI= 7400*10.5* 0.25/100

SI= 19425/100

SI= $194.25

Hence Mark will pay  $194.25

Answer: 3: 4^21/5^6

Step-by-step explanation:

Remember when you are raising you need to multiple the powers.

Answer: honestly the only thing i know is that mean is another way of saying expected value

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

3x + 5= 2x + 7

Subtract 2x from both sides

3x + 5 −2x = 7

Combine 3x and −2x to get x

x + 5 = 7

Subtract 5 from both sides

x = 7 − 5

Subtract 5 from 7 to get 2

x = 2

The values -3 , -6 , 3 , 8 are in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3

Given, a compound inequality

4(x + 3) ≤ 0 and x + 1 > 3

Now, on solving the first inequality, we get

4(x + 3) ≤ 0

4x + 12 ≤ 0

On subtracting both the sides by 12, we get

4x + 12 - 12 ≤ 0 - 12

4x  ≤ -12

On dividing both the sides by 4, we get

4x/4  ≤ -12/4

x ≤ -3

So, the solution set of the 4(x + 3) ≤ 0 inequality be, x ≤ -3 i.e. all the real numbers less than -3.

Now, on solving the second inequality, we get

x + 1 > 3

On subtracting both the sides by 1, we get

x + 1 - 1 > 3 - 1

x > 2

So, the solution set of the x + 1 > 3 inequality be, x > 2 i.e. all the real number greater than 2.

Now, the values in the solution set of the compound inequality

4(x + 3) ≤ 0 and x + 1 > 3 be,

x ≤ -3 and  x > 2.

As, we can see -3 , -6 , 3 , 8 are satisfying the condition.

Hence, -3 , -6 , 3 , 8 are the values in the solution set of the compound inequality 4(x + 3) ≤ 0 and x + 1 > 3.

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Answer:

x = 3

Step-by-step explanation:

15x + 8 and 9x + 26 are corresponding angles and are congruent , then

15x + 8 = 9x + 26 ( subtract 9x from both sides )

6x + 8 = 26 ( subtract 8 from both sides )

6x = 18 ( divide both sides by 6 )

x = 3

By using the definitions of combinations and permutations:

a) The first permutation is not defined.

b) N =  (³C₂) / (⁴C₂) = 1/2.

A permutation:

ⁿPk is written as:

ⁿPk= n!/(n - k)!  

(the denominator only appears if nk)

And a combination is written as:

ⁿCk = n!/(n - k)ka)

We have the product of two permutations, but there is a problem:3P4 The first number is the size of the set, and the second is the number of elements we take from that set.

In that permutation we have a set of 3 elements and we need to select 4, so that permutation is not defined.

b) (³C₂) = 3!/(3 - 2)!*2! = (3*2*1)/(2*1) = 3  

(⁴C₂) = 4!/(4 - 2)!*2! = (4*3*2*1)/[(2*1)*(2*1)]

= 3*2 = 6

Then the quotient can be written as:

(³C₂) (⁴C₂)  = 3/6 = 1/2.

Note that A quotient is seen as the outcome of dividing two numbers by each other.

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The probability that exactly 3 automobiles fail the test is 0.01733.

The probability that fewer than 3 of the automobiles fail the test is

0.9803.

Complete question:

Car inspection of all the registered automobiles in Colorado, 5% fail the state emissions test. Twelve Automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places

(a) Find the probability that exactly three of them fail the test.

(b) Find the probability that fewer than three of them fail the test.

What is Binomial Distribution?

The probability of success is said to follow a binomial distribution when many similar and independent Bernoulli trials are conducted. The likelihood of success and the quantity of tries are its dimensions. For every trial, the chance of success is the same.

State emission test failure probability is 0.05.

12 vehicles total are present.

Let's look at failing the test as a victory. If success is represented by p, then p = 0.05.

Considering that n represents the number of cars, n equals 12.

Let X represent how many vehicles fail the test.

So, X ∼ Bin (8,0.05)

P(X=x)= [tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

         = [tex]^{12}C_{x}0.05^{x}(0.95)^{12-x}[/tex]

a) Probability that exactly 3 automobiles fail the test is given by,

  P(X=3)= [tex]^{12}C_{3}0.05^{3}(0.95)^{12-3}[/tex]

             =0.01733

So, the probability that exactly 3 automobiles fail the test is 0.01733.

b) Probability that fewer of them than 3 fail the test is given by,

P(X<3)= P(X≤2)

         = P(X=0)+P(X=1)+P(X=2)

         =  [tex]^{12}C_{0}(0.05)^{0}(0.95)^{12}[/tex] + [tex]^{12}C_{1}(0.05)^{1}(0.95)^{11}[/tex]+[tex]^{12}C_{2}(0.05)^{2}(0.95)^{10}[/tex]

         = 0.9803

Hence, the probability that fewer than 3 of the automobiles fail the test is

0.9803.

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The equation to line is x-y+7=0.

What is a line?

A line is an indefinitely long, straight object that, despite being drawn with a minimum width, is considered to have no particular width in mathematics.

Main Body:

We know that equation of line in two point form =

y-y₁ =( y₂-y₁)/(x₂-x₁)(x-x₁)

points given are (-5,2) and (-4,3).

Therefore

y-2 =( 3-2)/(-4+5) *( x+5)

y-2 = x+5

x-y+7=0

Hence the equation is x-y+7=0.

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1133.98 grams of rice is required for the preparation of the recipe which calls for 40 ounces of rice.

Given that:

A recipe requires 40 ounces of rice for its preparation.

We know that,

1 ounce = 28.3495 grams

We also know that,

1 gram = .035274 ounces.

To find the value of 40 ounces multiplies both sides by 40.

40 ounce = 28.3495 grams x 40

40 ounce = 1133.98 grams

Hence, for the preparation of the recipe which calls for 40 ounces of rice, 1133.98 grams of rice is required.

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Answer: its D

Step-by-step explanation

Long Term Capital Gains Taxes tend to be lower than short term

Answer: D by providing a lower tax rate for long-term gains

Answer:

y = (-1/2)x - 4

Step-by-step explanation:

y = 2x + 6

Perpendicular: y = (-1/2)x + 6

m = (-1/2); (2, -5)

                 (x₁, y₁)

y - y₁ = m(x - x₁)

y - (-5) = (-1/2)(x - 2)

y + 5 = (-1/2)x + 1

    -5               -5

----------------------------

y = (-1/2)x - 4

I hope this helps!

Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y- value when x = 0).

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

a perpendicular slope simply turns the original slope upside-down with x and y, and it flips the sign.

the slope of the origins line is 2 = 2/1.

the perpendicular slope is -1/2.

so, the equation looks like

y = -1/2 x + b

to get b we use the point coordinates :

-5 = -1/2 × 2 + b = -1 + b

-4 = b

so, the full equation is

y = -1/2 x - 4

Answer:

x = 27

Step-by-step explanation:

Cross-multiply. Wrap some parenthesis around the x+6 to keep it together. Use distributive property. See image.

Answer: x=2πn (n=0, 1, 2, 3,...)

Step-by-step explanation:

2sin²x-cosx+1=0

2(1-cos²x)-cosx+1=0

2(1)-2(cos²x)-cosx+1=0

2-2cos²x-cosx+1=0

-2cos²x-cosx+3=0

Multiply both parts of the equation by -1:

2cos²x+cosx-3=0

Let cosx=t

Domain:

-1≤cosx≤1

Hence, -1≤t≤1

2t²+t-3=0

D=b²-4ac

a=2    b=1    c=-3

D=1²-4(2)(-3)

D=1+24

D=25

√D=√25

√D=5

[tex]\displaystyle\\t=\frac{-bб\sqrt{D} }{2a} \\\\t=\frac{-1б5}{2(2)}\\\\t=\frac{-1б5}{4}\\\\t=-1.5\notin domain\\\\t=1\in domain\\\\cosx=1\\\\x=2\pi n\ where\ n=0, \ 1,\ 2,\ 3,\ ...[/tex]

The domain of the given relation is: {2, 3, 4].

A relation has ordered pairs of values that are given as x and y coordinates, (x, y) In a relation, the values of the x coordinates are the domain of the relation while the values of the y coordinates are the range of the relation.

Given the relation, {(3,4),(2,3),(2,0),(4,2),(3,6)}, the set of x-values is: {2,3,4}. the set of y-values is: {0, 2, 3, 4, 6}.

{2,3,4} represents the domain while {0, 2, 3, 4, 6}. represents the range.

Therefore, the domain of {(3,4),(2,3),(2,0),(4,2),(3,6)} is given as: {2, 3, 4].

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Answer:5 35/36

Step-by-step explanation:

63 13/18 − 57 3/4 =?

Solving the whole number parts

63−57=6

Solving the fraction parts

13/18−3/4 is equal to 26/36 − 27/36

Combining the whole and fraction parts

6−1/36 = 5 35/36

Answer:

its the third one

oh this is easy

The transformation of the graphs is

1st graph is (x,y)→(x-4,y+2)

2nd graph is (x,y)→(x+6,y+0)

Given that,

There are two graphs with 2 triangles in each graph.

We have to find the transformation of the graphs.

Take the 1st graph,

We have 2 triangles ABC and A'B'C'.

The points are,

A=(0,0), B=(3,-4) and C=(-1,-2)

A'=(-4,2), B'=(1,-2) and C'=(-5,0)

We get the transformation as

(x,y)→(x-4,y+2)

Check the A and A' points

The A terms goes left for 4 times to A' so we take x-4 and the A terms goes up for 2 times to A' so we take y+2.

Similarly,

The B terms goes left for 4 times to B' so we take x-4 and the B terms goes up for 2 times to B' so we take y+2.

Similarly,

The C terms goes left for 4 times to C' so we take x-4 and the C terms goes up for 2 times to C' so we take y+2.

Now the 2nd graph,

We have triangle FCP and F'C'P'

The points are,

F=(-5,5), C=(-2,5) and P=(-3,0)

F'=(1,5), C'=(4,5) and P'=(3,0)

We get the transformation as

(x,y)→(x+6,y+0)

Check the F and F' points

The F terms goes right for 6 times to F' so we take x+6 and the F terms remain same so we take y+0

Similarly,

The C terms goes right for 6 times to C' so we take x+6 and the C terms remain same so we take y+0

Similarly,

The P terms goes right for 6 times to P' so we take x+6 and the P terms remain same so we take y+0

Therefore, The transformation of the graphs is

1st graph is (x,y)→(x-4,y+2)

2nd graph is (x,y)→(x+6,y+0)

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Answer:1 is (x,y)>(x-4,y+2)

2nd is (x,y)>(x+6,y+0)

Step-by-step explanation:

(> = an arrow)

I talked to my professional tutor about this, she didn’t happen to explain the answer though. She’s been working as a teacher for 20 years.

The slope of equation is 3x + y = 3 is -3

The standard from of Slope - intercept form of equation is y = mx +b

where , m is slope of line

b is y-intercept

and x and y are the variables

Slope of line represents steepness of a line and also termed as gradient .

Y- intercept represents the y- coordinate of the point where the line intersect the y-axis.

In the given question ,

The equation of the line is given as : 3x + 1y = 3

bring 3x to right side,

y = -3x + 3

comparing the equation to standard from

slope of line : m = -3

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