two cards are drawn without replacement from a standard deck of playing cards. what is the probability that at least one of them is spades?

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:

Answer: (-3, -1/2)

Step-by-step explanation: Search math w ay on the internet for any further math questions :)

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:

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:

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

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: is A

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

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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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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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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Answer:

Step-by-step explanation:

=22.068

Answer:

5

Step-by-step explanation:

actual answer 4.69766713281

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

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

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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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 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 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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The inverse of the functions y = x + 3 and y = 2x - 4 are y = x - 3 and

y = (x + 4)/2 respectively.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A function y = x + 3 or f(x) = x + 3.

Now, To find the inverse of f(x) we'll solve for 'x' in terms of 'y'.

y = x + 3.

x = y - 3.

y = x - 3.

f⁻¹(x) = x - 3.

Again,

y = 2x - 4.

2x = y + 4.

x = (y + 4)/2.

y = (x + 4)/2.

f⁻¹(x) = (x + 4)/2.

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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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By thoroughly reacting a 2.2g zinc nail with an excess of hydrochloric acid, 0.0075 L of hydrogen gas is created.

The force per unit area on an item in the fluid or on the surface of a closed container is measured as fluid pressure. Gravity, acceleration, or forces outside a closed container can all create this pressure. Because a fluid has no fixed structure, its pressure is applied in all directions.

Here,

The reaction between zinc and hydrochloric acid produces hydrogen gas according to the following equation:

Zn + 2HCl -> ZnCl2 + H2

From the equation, we can see that 1 mole of zinc reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas. The volume of a gas is proportional to the number of moles at constant temperature and pressure, so if we can determine the number of moles of zinc that were reacted, we can calculate the volume of hydrogen produced.

The moles of zinc can be calculated using the molar mass of zinc:

moles = mass / molar mass

moles = 2.2 g / 65.38 g/mol = 0.0337 mol

Since 1 mole of zinc reacts with 2 moles of hydrochloric acid, the number of moles of hydrogen produced is 0.0337 mol * 1 mol H2/1 mol Zn = 0.0337 mol H2.

Finally, the volume of hydrogen produced at standard temperature and pressure (STP) is calculated using the Ideal Gas Law:

PV = nRT

V = nRT / P

V = (0.0337 mol) * (0.08206 L atm / K mol) * (273.15 K) / (1 atm)

V = 0.0075 L

0.0075 L of hydrogen gas are produced by completely reacting a zinc nail with a mass of 2.2g with an excess of hydrochloric acid.

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Complete question:

What volume of hydrogen gas are produced by completely reacting a zinc nail with a mass of 2.2g with an excess of hydrochloric acid?

The required angle is 26.5°, line y=1/2x + 1 made with an x-axis.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Given the equation of the line,
y = 1/2x + 1

Compare the above equation with equation y = max +c
m = 1/2

tanФ = 1/2   [since m = tanФ]
Ф = tan⁻¹[1/2]
Ф = 26.5°

Thus, the required angle is 26.5°.

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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

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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When the sample size is decreased from 39 to 29 , the impact on confidence interval will be (c) It would become wider due to using the t distribution.

we know that , in general, as the sample size decreases, the variability of the estimate increases and the width of the confidence interval becomes larger.

The t distribution is used when the sample size is small, which increases the width of the confidence interval to account for the greater uncertainty in the estimate.

When the sample size is large, the t distribution approaches the standard normal (z) distribution, which results in a narrower confidence interval.

Therefore, a decrease in sample size would result in a larger t distribution and a wider confidence interval.

The given question is incomplete , the complete question is

In a situation where the sample size was decreased from 39 to 29, what would be the impact on the confidence interval ?

(a) It would become narrower with fewer values.

(b) It would remain the same as sample size does not impact confidence intervals.

(c) It would become wider due to using the t distribution.

(d) It would become narrower due to using the z distribution.

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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?

Answer:

the probability becomes less

Step-by-step explanation:

The lateral surface area of the rectangular prism given in the picture is 36 cm ²

The lateral surface area of a rectangular prism can be found by the formula :

= 2 x height x ( Length + Breadth )

Height = 2 cm

Length = 3 cm

Breadth = 6 cm

The lateral surface area is therefore:

= 2 x 2  x ( 3 + 6 )

= 4 x 9

= 36 cm ²

In conclusion, the lateral surface area is 36 cm ².

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