Find the measure of exterior angle 1

Considering the given probabilities, it is found that the correct option about whether the events are independent is given as follows:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Researching this problem on the internet, the probabilities are given as follows:

[tex]P(X) = \frac{4}{5}, P(Y) = \frac{1}{4}, P(X \cap Y) = \frac{1}{5}[/tex]

Hence:

[tex]P(X)P(Y) = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} = P(X \cap Y)[/tex]

Hence the events are independent and the correct option is given by:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

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Answer:

15 lbs of onions.

Step-by-step explanation:

23 lbs divided by $46 = 0.5 lbs per $1

0.5 lbs times $30

15 lbs

=============================================================

Work Shown:

(23 pounds)/(46 dollars) = (x pounds)/(30 dollars)

23/46 = x/30

1/2 = x/30

1*30 = 2*x

30 = 2x

2x = 30

x = 30/2

x = 15

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

Another approach:

Divide the cost over the number of pounds to find the unit price

46/23 = 2

The onions cost $2 per pound.

If x is the number of pounds, and we pay $30, then

2x = 30

x = 30/2

x = 15

Meaning 15 pounds of onions cost $30.

well, the markup or the bumped up amount is 3560 - 2450 = 1110.

if we take 2450 to be the 100%, what is 1110 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 2450 & 100\\ 1110& x \end{array} \implies \cfrac{2450}{1110}~~=~~\cfrac{100}{x}\implies \cfrac{245}{111}~~=~~\cfrac{100}{x} \\\\\\ 245x=11100\implies x=\cfrac{11100}{245}\implies x\approx 45.3[/tex]

point-slope form

y - y₁ = m(x - x₁)

[tex]y-1=-\frac{1}{2}(x-8)\\\\y-1=-\frac{1}{2}x+4\\\\y=-\frac{1}{2}x+5[/tex]

The answer is A) Choice A.

Answer:

720

Step-by-step explanation:

A polygon with 6 angles is called a hexagon

To find the sum of interior angles, we use the following formula:

(n-2)*180 (n is the number of angles)

4*180 = 720

The probability that exactly four of the students were been born on a weekday (i.e. Monday through Friday) is 0.2125.

To determine the probability, we need to first find the probability of having a student being born on a weekday.

[tex]=\mathbf{\dfrac{5}{7}}[/tex]

The probability of having 4 students born on a weekday is:

[tex]=\mathbf{(\dfrac{5}{7})^4}[/tex]

Since we have 4 students, we also need to find the probability of the students that are not being born, which is:

[tex]=\mathbf{(\dfrac{2}{7})^3}[/tex]

Also, there are [tex](^7_4)[/tex] = 35 ways to get four students out of seven students.

Therefore, we have the probability as:

[tex]\mathbf{P = 35 \times (\dfrac{5}{7})^4 \times (\dfrac{2}{7})^3}[/tex]

P = 0.2125  

Therefore, we can conclude that the probability that exactly four of the students were born on a weekday is 0.2125.

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The systems of the equations for the word problem can be expressed as:

The system of equations is a set of simultaneous equations that comprises two or more equations expressed in algebraic terms.

From the given information, we are to determine two quantities

i.e.

So, 100% and 20% of saline solution produce 160 millimeters.

x + y = 160

Also, the combination of 100% and 20% of saline solution give an average of 25%.

The average now = sum of numbers/ the total numbers

25% = sum of numbers/160

sum of numbers = 25% (160)

Therefore, we can equate it to the mixture carried out by the nurse.

i.e.

25% (160) = 100%(x) + 20%(y)

100x + 20y = 4000

Therefore, the systems of the equations are:

x + y = 500              --- (1)

100x + 20y = 4000  --- (2)

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An equation is formed of two equal expressions. The equation that can be used to represent the graph is y=50x+300.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) The rate of change, in this case, signifies the number of followers Zora is gaining per hour. It can be found using any two coordinates of the line.

(x₁ , y₁) = (0,300) = coordinate of point 1,

(x₂ , y₂) = (2,400) = coordinate of point 2,

Now, the rate of change or the slope will be equal to,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{400-300}{2-0} = 50[/tex]

Hence, the rate at which Zora will gain followers is 50 followers/hour.

B.) The y-intercept is the value of y when the value of x is 0. Therefore, the y-intercept of the function is 300.

The y-intercept of the graph is 300, which means at the very initial stage Zora will have 300 followers.

C.) The graph is represented by a line, and the general equation of a line is represented by y=mx+c. To know the value of the constant c, substitute the value of the slope and any coordinate in the equation.

[tex]y=mx+c\\300=50(0)+c\\c=300[/tex]

Hence, the equation that can be used to represent the graph is y=50x+300.

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Answer:

Types of Equations and Examples

Types of Equations and Examples

There are various types of equations, such as,

Linear equation

Equation with  one variable

Equation with two variables

Equation with three variables

Polynomial equation

Monomial Equations

Binomial Equation

Trinomial Equation

Quadratic equation

Trigonometric equation

Radical equation

Exponential equation

Rational equation

types of equations

types of equations

1. Linear Equation:

A linear equation is an algebraic equation. In linear equation, each term is either a constant or the product of a constant and a single variable. If there are two variables, the graph of linear equation is a straight line.

General form of the linear equation with two variables is given below:-

y = mx + c, m ≠ 0.

Equation with one Variable: An equation who have only one variable, e.g.

12x – 10 = 0

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

Probability = number of favorable outcomes/total number of possible outcomes

We know the total number of possible outcomes is 14 since there are 14 sides to the dice.

Let's find how many of those numbers are prime numbers.

2, 3, 5, 7, 11, and 13 are all the prime numbers between 1 and 14, so there are 6 favorable outcomes.

Now create the fraction then reduce.

6/14 reduce by 2/2

3/7

Answer:

Step-by-step explanation:

There is an estimated rise of 3.58 hatched eggs for every one degree Fahrenheit increment every day. Then the correct option is B.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A scientist is interested in the relationship between the number of eggs hatched per day for frogs (y) and temperature.

Based on the collected data, the least-squares regression line is y = 15.66 +3.58x, where x is the number of degrees by which temperature exceeds 60 degrees Fahrenheit.

For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs.

Thus, the correct option is B.

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Answer: For each increase of one degree Fahrenheit per day, there is an estimated increase of 3.58 hatched eggs

Step-by-step explanation:

took the test :)

Answer:

11,880.

Step-by-step explanation:

This is given by the number of permutations of 4 from 12

= 12P4

= 12!/(12-4)!

= 12!/8!

=  (12*11*10*9*8*7*6*5*4*4*2*1) / (8*7*6*5*4*4*2*1)

= 12^11*10*9

= 11,880.

Answer:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (3, 5) and r = , hence

(x - 3)² + (y - 5)² = (  )², that is

(x - 3)² + (y - 5)² =  ← equation of circle

Step-by-step explanation:

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =36 \end{cases}\implies s=\cfrac{(36)\pi (2)}{180}\implies s=\cfrac{2\pi }{5}\implies s\approx 1.26~in[/tex]

The volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet

The formula for calculating the volume of a pyramid is expressed as:

V = Base area. * height/3

Since it is a cube with a volume of  9 cubic feet, the length of the cube will be:

l = ∛9
l = 2.08

Determine the volume of the pyramid

V = 9/3

V = 3 cubic feet

Hence the volume of a pyramid that fits exactly inside a cube is 9 cubic feet is 3 cubic feet

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[tex]\frac{10^8}{10^6} = 10^{8-6} = 10^2 = 100[/tex]

The rule used is

[tex]\frac{a^b}{a^c} = a^{b-c}[/tex]

Subtract the exponents when dividing exponentials like this of the same base.

The number of gigabytes of data can she use while staying within her budget should be less than 4.3 gigabytes.

Linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Under her cell phone plan, Ella pays a flat cost of $37.50 per month and $5 per gigabyte.

She wants to keep her bill at $59 per month.

Then the number of the gigabytes of data can she use while staying within her budget will be

Let x be the number of the gigabytes. Then the equation will be

5x + 37.5 < 59

          5x < 21.5

            x < 4.3

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The points on the function g(x) are  (–7, –10.206) (–2.5, –4.474), (0.5, –0.221) (4, –0.017) (9, –0.003)

The function f(x) is given as:

[tex]f(x) = -\frac 27(\frac 53)^x[/tex]

The rule of reflection across the y-axis is:

g(x) = f(-x)

So, we have:

[tex]g(x) = -\frac 27(\frac 53)^{-x[/tex]

All the points in the options are on the curve of the function g(x) except (0, -1.773)

Hence, the points on the function g(x) are  (–7, –10.206) (–2.5, –4.474), (0.5, –0.221) (4, –0.017) (9, –0.003)

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Answer: 1  4  6

Step-by-step explanation: its right bro.

If the dimension of the rectangular prism will be (4, 8, 16), (2, 8, 32), and (2, 4, 64). Then the surface area will be 448, 672, and 784 square units respectively.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

You work for a cereal company that is looking to design some new boxes for their cereal.

The cereal is sold in the size of 512 cubic units.

You will be designing three rectangular prisms with unique dimensions.

The possible dimension of the rectangular prism will be

Volume = 512

Volume = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Then we have

{(4, 8, 16), (2, 8, 32), (2, 4, 64)}

Then the surface area will be

If the dimension is (4, 8, 16). Then the surface area will be

Surface area = 2(4x8 + 8x16 + 16x4)

Surface area = 448 square units

If the dimension is (2, 8, 32). Then the surface area will be

Surface area = 2(2x8 + 8x32 + 32x2)

Surface area = 672 square units

If the dimension is (2, 4, 64). Then the surface area will be

Surface area = 2(2x4 + 4x64 + 64x2)

Surface area = 784 square units

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Answer:

28.27

Step-by-step explanation: used to do acellus too

Answer:

all of those answers are rational numbers

Step-by-step explanation:

Answer:

Step-by-step explanation:

Refer the attachment

Answer:

752.5 in³

Step-by-step explanation:

  Rectangular prism:

            l = 10 in ; w = 7 in ; h = 8 in

   [tex]\boxed{\text{Volume of rectangular prism=l*w*h}}[/tex]

                                                = 10 * 7 * 8

                                                = 560 in³

Half cylinder:

Diameter of the cylinder will be equal to the width of the rectangular prism.

       r = 7/2 = 3.5 inches ; h = 10 in

[tex]\boxed{\text{Volume of half cylinder =$\dfrac{1}{2}\pi r^2h$}}[/tex]

                                       [tex]\sf =\dfrac{1}{2}*3.14*3.5*3.510\\\\ = 192.5 \ in^3[/tex]

Volume of composite figure = 560 - 192.5

                                               = 752.5 in³

Answer:

A) (n+5)^2

Step-by-step explanation:

(n+5)^2

(n+5)(n+5)

n*n = n^2

(n*5)+(n*5) = 10n

5*5 = 25

Answer:

46 hours do the students play video games per week

Answer:

Area = 213.52 sq.ft

Step-by-step explanation:

[tex]A_{s} =\pi (18)^{2} -\pi (16)^{2} =324\pi -256\pi =68\pi[/tex]

[tex]\pi =3.14[/tex]

[tex]A_{s} =68(3.14)=213.52sq.ft[/tex]

Hope this helps

Answer:

  113.04 ft²

Step-by-step explanation:

The area of the ring can be found by multiplying its center-line length by its width.

__

The diameter of the circle that is the center-line of the ring is ...

  16 ft + 2 ft = 18 ft . . . . center-line diameter

The length of the center-line is then ...

  C = πd

  C = 3.14(18 ft) = 56.52 ft

And the area of the ring is ...

  A = LW = (56.52 ft)(2 ft) = 113.04 ft²

The shaded area is 113.04 square feet.

Answer:

  (d)  $36.69

Step-by-step explanation:

The total cost of the order is the sum of the costs of the items and the tax on that subtotal.

__

The price after tax can be found using the multiplier (1 +tax rate) applied to the subtotal.

  total cost = ($14.65 +8.49 +10.99)×(1 +0.075) = $34.13×1.075

  total cost = $36.69

Answer: $36.69

Step-by-step explanation: K12 Test 8.02 Grade 7 Semester B Test - Part 1

The range, standard deviation, and variance say about gas prices in 2018 discussed below

Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.

As the variance in 2018 is 0.0121.

A model with low variance means sampled data is close to where the model predicted it would be.

As the standard deviation in 2018 is 0.1098.

Low standard deviation means data are clustered around the mean

A small range means low variability in a distribution.

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Answer:

LCM of 8, 9, and 12 is 72.

Step-by-step explanation:

The LCM of three non-zero integers, a(8), b(9), and c(12), is the smallest positive integer m(72) that is divisible by a(8), b(9), and c(12) without any remainder.

appreciate it if someone will follow me.

Answer:

72

Step-by-step explanation:

To find the Lowest Common Multiple (LCM), prime factorize the included terms, and multiply the factors of each number of the highest power together.

Prime factorizing

LCM (8, 12, 9)

= 2³ x 3²

= 8 x 9

= 72