the standard deviation is used in conjunction with the

In linear equation, the unit rate of tickets at the skating rink is; 11.95 per ticket.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                  The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

We have been given Adela paid $71.70 for 6 tickets at the skating rink.

We need to find the unit rate per ticket.

Total amount = 71.70

Number of tickets = 6

Unit rate = Total amount/ Number of tickets

Unit rate =  70.70/ 6

Unit rate = 11.95/1

Therefore, the unit rate of tickets at the skating rink is; 11.95 per ticket.

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Answer:B

Step-by-step explanation:

The original price of the PlayStation 5 is $500 and there is a 30% discount, calculated as $500 x 30/100 = $150. The sale price is $500 - $150 = $350.

The calculation of the sale price of the PlayStation 5 involves finding the amount of the discount first. The original price of the PlayStation 5 is $500. The discount is 30%, which means that 30% of the original price will be taken off. To find the amount of the discount, we multiply the original price by the discount rate (30% or 0.30).

$500 x 0.30 = $150

Next, we subtract the discount from the original price to get the sale price:

$500 - $150 = $350

So, the sale price of the PlayStation 5 is $350.

The sale price of the PlayStation 5 is an important aspect for customers who are looking for a good deal. By knowing the original price and the discount, one can easily find the sale price. This type of calculation is common in retail and commerce, and is used to determine the savings that a customer can make on a particular item during a sale. Understanding these concepts is crucial for consumers to make informed decisions about their purchases, and for businesses to effectively promote their products and attract customers.

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Answer: 1,403

Step-by-step explanation: None

Answer:

1403

Step-by-step explanation:

First you find out how many minutes is each episodes at that is 23

Then you multiple 23 by 61 and you get 1403

Answer:

the probability becomes less

Step-by-step explanation:

The required equivalent expression to the given expression is Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
An expression is given in the question that is,
[tex]Z(t) = 4000(12^{2t +2})[/tex]

We have to form a problem that represents the format of a function same as shown above.

Expression and problem is given as, Lima invests $1000 in a mutual fund which gives her a return of 12% per year this situation can be modeled as y = 1000(1.2)ⁿ.

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The number of students will be equal to LCM which is 24.

Given:- A certain number of students can be arranged in groups of 3,4,6or 8 with no student left behind.

To find:- The number of students.

Solution:- To find minimum number of students need to find LCM (3,4,6,8).

[tex]3=3^{1}[/tex]

[tex]4=2*2=2^{2}[/tex]

[tex]6=2*3=2^{1} *3^{1}[/tex]

[tex]8=2*2*2=2^{3}[/tex]

LCM: Least common multiplier of given numbers is the Leastmultiplier number which is given perfectly divisible by the given numbers.

LCM= product of eac factor of highest power.

LCM=[tex]2^{3} *3^{1} =8*3=24[/tex]

Hence, minimum number of students= 24 or students are multiple of 24.  

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PART A) Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

PART B) One cup of sugar will be left over after making three batches of cookies.

What is the unit price?

A unit price is the cost of a single object or unit of measurement, such as a pound, a kilogram, or a pint, and it is used to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.

Given that Janet needs One cup of sugar to make one batch of chocolate chip cookies.

Part A:

Let The number of cups of sugar Janet needs to make three batches of cookies be 'x'.

Now,

1 batch/ 1 cup = 3 batch/ x cups

x= 3

Therefore, Janet needs only three cups of sugar to make three batches of chocolate chip cookies.

Part B:

Given that Janet has four cups of sugar.

From part A, we found that she only need three cups of sugar.

Available - Needed = Excess

4-3=1

So, one cup of sugar will be left over after making three batches of cookies.

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The pressure in the tyre when the volume is 140 cubic inches will be 30 pounds.

Boyle's law states that at a constant temperature, the pressure is inversely proportional to the volume. It means that the product of the pressure and the volume will remain constant for the given system.

Given that when air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches.

The pressure will be calculated as:-

P₁V₁ = P₂V₂

( 35 x 120 ) = 140 x P₂

P₂ = ( 35 x 120 ) / 140

P₂ = 30 pounds

Therefore, when the volume is 140 cubic inches, the tire's pressure will be 30 pounds.

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The probability that a man will test positive on two successive tests if he has the disease 81%.

In mathematical terms, probability can be represented as the ratio of the number of favorable outcomes to the number of possible outcomes. The formula for probability is as follows:

P(E) = n(E) / n(S)

Where:

P(E) is the probability of event E occurring

n(E) is the number of favorable outcomes for event E

n(S) is the number of possible outcomes in the sample space S

Let's assume the probability of a man testing positive for a disease if he has it is represented by the symbol "P".

If the tests are independent, meaning that the outcome of one test does not affect the outcome of the other, then the probability of a man testing positive on two successive tests can be calculated as the product of the probabilities of each individual test.

Therefore, the probability of a man testing positive on two successive tests if he has the disease is P * P, or P².

If the probability of a man testing positive for a disease if he has it is 90%, represented by P = 0.9, then the probability of him testing positive on two successive tests is 0.9 * 0.9 = 0.81, or 81%.

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Answer:

D

Step-by-step explanation:

7 x 1,000,000,000 + 5 x 1,000,000 + 9 x 10,000+ 9 x 100 + 7 x 1

=7,000,000,000

+        5,000,000

+              90,000

+                    900

+                         7

answer is D

If Mei has earned 30 points, the multiplication equation to find how many books she needs to read is 30=5x.

Let x represent the number of books she needs to read.

So,

The equation to find the number of books she need to read is:

30=5x

Let solve for x

30 =5x

Divide both side by 5x

x = 30/5

x = 6 books

Therefore the number of books is 6 books.

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A mathematical description of hexagon is given above.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is hexagon.

In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

Therefore, a mathematical description of hexagon is given above.

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The probability that at most one car has any surface flaws is 0.0067.

The formula to calculate the surface flaws will be -

P(X = 0) = [tex] {e}^{- lambda} {lambda}^{X} [/tex]/X!, where lambda is the mean of Poisson random variable with mean. It is 5 according to the question. Now keeping the values in formula to find the probability.

P = [tex] {e}^{- 5} {5}^{0} [/tex]/0!

As exponent 0 will be considered 1 and factor of the 0 is 0. So, rewriting the equation -

P = [tex] {e}^{- 5} [/tex]

Finding the value now

P = 0.0067

Thus, the probability is 0.0067.

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The complete question is -

The number of surface flaws in plastic panels used in the interior of automobile has a Poisson distribution with a man of 0.05 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

if 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?

After 27 years, you would have $4800 in the account.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Given:

Investment double every 9 years,

and you start with $600 investment.

So, by the exponential growth function,

y = 600(1+r)ˣ,

To find the growth rate:

1200 = 600(1 + r)⁹

r = 1.08006

So, the equation is,

y = 600(1+0.8006)ˣ

After 27 years,

y = 600 x 8

y = $4800

Therefore, $4800 is the required amount.

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Answer:

x = 56

Step-by-step explanation:

64 + x + 60 = 180

124 + x = 180

x = 56

The missing angle x of the diagram is; x = 56°

In geometry, we know that the sum of angles on a straight line sums up to 180 degrees.

Now, in the given image we see that the three angles we are concerned with all form a straight line and as such they will all add up to 180 degrees. Thus;

64 + x + 60 = 180

124 + x = 180

x = 180 - 124

x = 56°

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Answer:

Step-by-step explanation:

=22.068

Answer:

5

Step-by-step explanation:

actual answer 4.69766713281

The equation of the line parallel to 8x+5y=1 passing through the point (1,−3)

is y = (-8/5)x - (7/5).

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line is y = m(1)x + c

Now,

The equation of the line parallel to 8x+5y=1 passes through the point (1, -3).

This means,

8x + 5y = 1

5y = - 8x + 1

y = (-8/5)x + 1/5

This is in the form of y = m(2)x + c

m(2) = (-8/5)

Now,

Since the line is parallel.

m(1) = m(2) = (-8/5)

So,

y = (-8/5)x + c

Now,

(1, -3) = (x, y)

-3 = (-8/5) x 1 + c

c = -3 + 8/5

c = (-15 + 8) / 5

c = -7/5

So,

y = (-8/5)x - (7/5)

Thus,

The equation of the line is y = (-8/5)x - (7/5).

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The length of the similar polygon is as follows:

GK = 30 units

TU = 24 Units

Two polygons are similar if their corresponding angles are congruent and their corresponding sides are in proportion.

Therefore, the corresponding angles of the polygons are congruent and the sides are in ratio of each other.

Hence, let's find the side GK and TU as follows:

QRSTU ~ IJKGH

Therefore,

24 / GK = 16  /20

cross multiply

16GK = 480

GK = 480 / 16

GK = 30 Units

Hence,

TU  / 30 = 16 / 20

cross multiply

20 TU = 480

TU = 480 / 20

TU = 24 Units

Therefore,

GK = 30 units

TU = 24 units

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The perimeter of this triangular park is equal to: 3x² 37x - 4 feet.

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

P = a + b + c

Where:

P represents the perimeter of a triangle.

a, b, and c represents the length of sides of a triangle.

Substituting the given parameters into the perimeter of a triangle  formula, we have the following;

Perimeter of triangle, P = 12x + (15x + 4) + (10x + 3x² - 8)

Perimeter of triangle, P = 12x + 15x + 4 + 10x + 3x² - 8

Perimeter of triangle, P = 3x² 37x - 4 feet.

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The complex number z = 4√3 - i 4 has a norm 8 and a direction 330°. Its representation is in the image shown below.

In this question we find the definition of complex number in rectangular form, whose definition is shown below:

z = a + i b, where a, b are real numbers.

Where:

Graphically speaking, the real component is associated to the horizontal axis of Cartesian plane and the imaginary component is associated to the vertical axis of that plane. The norm (r) and direction (θ) of the complex number are, respectively:

Norm

r = √(a² + b²)

Direction

θ = tan⁻¹ (b / a)

The norm and the direction of the complex number are, respectively:

r = √[(4√3)² + (- 4)²]

r = 8

θ = tan⁻¹ [(- 4) / (4√3)]

θ ≈ 330°

Lastly, we represent the complex number with the help of a graphing tool.

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Answer:

(6, -2)

Step-by-step explanation:

The only option that satisfies both equations is (6, -2).

The volume of a cuboid will be, V =  2x² If it has one side of 2 meters and the other two sides are of equal length.

A cuboid is a three-dimensional closed figure which has volume along with surface area.

The volume of a cuboid is the product of its length, width, and height.

The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.

We know, The volume of a cuboid is (length×width×height).

Assuming the height of the cuboid to be 2 meters and it has a square base of 'x' meters.

Therefore, The volume of the cuboid V = 2×x×x.

V = 2x².

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Step-by-step explanation:

First find 1/4 of 72 runners. To do this divide by 4.

So

72/4=18

Now take 72 and subtract 18 to get 54

Next find 1/3 of 54 runners

54/3=18

Because it is 2/3 you need to multiply 18 by 2

So

18 x 2 = 36

So

54-36=18 runners that finished the race

If needed in fraction form

18/72

Now simplify

9/16 of the runners finished

Answer:

What are we looking to solve for?

How much each shirt she bought for the fundraiser costs, each.

What variable can be used to represent the unknown?

The variable "t".

What is the equation to solve the variable?

You can use the following equation as a framework for solving:

t * 22 = 231 solve for t.

Now lets solve:

I am going to use inverse operations: Divide instead of multiply.

231/22 = 10.05

Each shirt is worth $10.50.

Step-by-step explanation:

Hope it helps! =D

Answer:

We want to know how much each t-shirt costs.

t = 10.50

Step-by-step explanation:

We want to know how much each t-shirt costs.

Let the cost of each t-shirt  = t

22 * t = 231

Divide each side by 22

22t/2 = 231/22

t = 10.50

The cost of each t-shirt is 10.50

Answer: The last option would be correct p=  75 + 5a. The reason being the last option is the right one is because the expression represents the additional points plus her original 75 she had on her homework assignments.  

The distance from Antrim to Randalstown is 6 5/6 miles.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Martin is walking from Antrim to Randalstown.

Randalstown 3 1/3 miles, Toome is 9 1/4 miles Antrim 3 1/2 miles.

Therefore, the distance from Antrim to Randalstown is the sum of their distances which is,

= 3 1/3 + 3 1/2 miles.

= 10/3 + 7/2 miles.

= (20 + 21)/6 miles.

= 41/6 miles.

= 6 5/6 miles.

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Answer: is A

Step-by-step explanation: if you do the problem youd get 2 root 3x^2