1) A system of equations is shown. What is the solution to the system of equations? Show all work. (3 points) 2 + 2 = 17 {4 − = 25

The probability that all the guinea pigs selected randomly are pregnant is 1/30 or 0.033

Given, we have 10 guinea pigs out of which 4 are pregnant. We know that probability of an event ⇒ P(E) = (No of favorable outcomes)/(No of all outcomes) . So, The probability of selecting pigs that are pregnant is :

⇒ 4/10

Now, 3 selections are made randomly. The probability that the 1st selected guinea pig will be pregnant = 4/10

The probability that the 2nd selected guinea pig will be pregnant = 3/9

The probability that the 3rd selected guinea pig will be pregnant = 2/8

Therefore, the probability of all the 3 selected guinea pigs being pregnant will be :

⇒  (4/10) x (3/9) x (2/8)

⇒ 1/30

Therefore, The probability of all the selections of pigs being pregnant without replacement rounded to 3 decimal places is 0.033 or 1/30

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The complete question will be :

In a scientific study there are 10 guinea pigs,4 of which are pregnant. if 3are selected at random without replacement, find the probability that all are pregnant. enter your answer as a fraction or a decimal rounded to 3 decimal places.

An equation of the line in fully simplified slope-intercept form is y = -13x - 22.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data points (-2, 4), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 4 = (10 - (-3))/(-3 - (-2))(x - (-2))

y - 4 = -13(x + 2)

y = -13x - 26 + 4

y = -13x - 22

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The probability of being dealt a five-card poker hand that contains all hearts is approximately 0.000495, or 0.0495%.

Probability is the measure of the likelihood of an event happening, and it is expressed as a number between 0 and 1. The closer the number is to 0, the less likely the event is to occur, and the closer it is to 1, the more likely it is to occur.

Now, let's look at the first question: what is the probability of drawing six cards from a standard deck of cards and getting four aces and two kings?

So, the number of combinations of six cards from a deck of 52 cards is:

52C6 = 52!/6!(52-6)! = 20,358,520

Next, we need to find out how many ways we can draw four aces and two kings from the deck. There are 4 aces and 4 kings in a standard deck of cards, so the number of ways to draw four aces and two kings is:

4C4 x 4C2 = 1 x 6 = 6

The first factor, 4C4, represents the number of ways to draw all 4 aces, and the second factor, 4C2, represents the number of ways to draw 2 kings from the remaining 4 kings.

Finally, we can calculate the probability of getting four aces and two kings by dividing the number of ways to draw four aces and two kings by the number of combinations of six cards from the deck:

P(four aces and two kings) = 6/20,358,520 = 0.000000294

So, the probability of randomly drawing six cards from a standard deck of cards and getting four aces and two kings is approximately 0.00000029, or 0.0000294%.

Now, let's move on to the second question: what is the probability that a five-card poker hand is dealt to you that contains all hearts?

In a standard deck of cards, there are 13 hearts and 52 cards in total, so the probability of drawing one heart from the deck is 13/52, or 1/4. The probability of drawing five hearts in a row is the product of the probabilities of drawing each heart, since each card is drawn without replacement:

P(five hearts) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.000495

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The value of the equation is 4.19p = -6.1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

2.3p - 10.1 = 6.5p - 4 - 0.01p

On simplifying , we get

Adding 4 on both sides , we get

2.3p - 6.1p = 6.49p

Subtracting 2.3p on both sides , we get

4.19p = -6.1

Now , the value of the equation similar to 4.19p = -6.1 is 2.3p - 6.1p = 6.49p

Hence , the equation is 4.19p = -6.1

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She invest money at each rate

First = 1000

Second = 10,000

Simple interest is a method of calculating the interest charge. The interest can be calculated as the product of principal amount, rate and time peroid.

We are given that Phyllis invested $11,000, a portion earning a simple interest rate of 2 1/2% per year and the rest earning a rate of 2% per year.

Given the following :

Amount invested = $11,000

A portion earns 2 and 1/2 % interest per year

The rest earns a rate of 2% per year

The Total Interst earned after a year = $255

Amount invested at each rate;

Let amount invested at 2 1/2% = a

Amount invested at 2% is; 11,000 - a

Simple interest = principal x rate x time

First investment :

a x 5/2% x  1

Second :

(11000 - a) x 2%

Firat investment + second = $225

a x 0.025 + (11000 - a) x 0.02 = 225

0.025a + 220 - 0.02a = 225

0.005a = 225 - 220

0.005a = 5

a = 5 / 0.005

a = 1000

Amount in first investment = 1000

Second investment = 11000 - 1000 = 10,000

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The graph shown is the graph of the cotangent function.

The graph of the cotangent function, cot(x), is a periodic function that has a period of 2π. The cotangent function is the reciprocal of the tangent function, so its graph is related to the graph of the tangent function.

Like the tangent function, the cotangent function has singularities at x = (n + 1/2)π where n is an integer. At these points, the function has a vertical asymptote, meaning it approaches positive and negative infinity as x approaches (n + 1/2)π from either side.

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In  linear equation, √2a² is the value of a .

What are examples of linear equations?

Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).

                                    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.

      k = √f + f

       f = a²

      k = √a² + a²

         = √2a²

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Answer:

its only -11x^2

Step-by-step explanation:

2x^2 and -11x^2 have the same variable.

The given decimal in fraction as 1181/20.

Steps for conversion:

The given decimal number is 59.05

Here, multiply 100 to both the numerator and denominator of the decimal, that is

59.05/1 ×100/100

= 5905/100

= 1181/20

Therefore, the fraction is 1181/20.

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Government saving equals: a. taxes less government expenditures.

Government expenditure  can be defined as those expenses that government has incurred and this occur when government spent on goods and services.

Government saving tend to  equals taxes less government expenditure which is option A was the correct option.

Therefore we can conclude that the correct option is A.

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Answer:

m ≥ 6

Step-by-step explanation:

The question asks us to solve the following inequality:

[tex]8m - 8 \geq 40[/tex].

To solve it, we need to make m the subject of the inequality:

[tex]8m - 8 \geq 40[/tex]

⇒ [tex]8m - 8 + 8 \geq 40 + 8[/tex]          [Adding 8 to both sides of inequality]

⇒ [tex]8m \geq 48[/tex]

⇒ [tex]\frac{8}{8}m \geq \frac{48}{8}[/tex]              [Dividing both sides of inequality by 8]

⇒ [tex]m \geq \bf 6[/tex]

Therefore, the solution to the inequality is m ≥ 6.

The equation to find the total distance would be 60t.

What is total distance?

Whole distance refers to the actual distance between the origin and destination locations of the substance.

The distance traveled is equal to the speed multiplied by the time traveled, which gives the formula:

d = 60t

where d is the total distance traveled in miles, and t is the time traveled in hours.

Therefore, The equation to find the total distance would be 60t.

The table is below:

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Markup on cost price is 75%

Percent markup on selling price: 25%

Percent markup on cost: ?

Markup is the total profit on a particular commodity or service. It is represented as a percentage over a cost price.

Percent markup on selling price is 25% which means that a product is sold out with 25% profit,

Percent markup on cost price =100-markup on selling price

                                                  = 100-25

                                                  =75

Hence, markup on cost price is 75%

The value of Percent markup on cost nearest to the whole number is,

⇒ 75%.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The value of Percent markup on selling price is,

⇒ 25%

Hence, The value of Percent markup on cost is,

⇒ 100% - selling price

⇒ 100% - 25%

⇒ 75%

Thus, We get;

The value of Percent markup on cost is,

⇒ 75%

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The angular speed in radians per minute of the cyclist riding a bike with wheels of diameter 26 inches at a speed of 22 miles per hour is approximately 1124.65 radians per minute.

The formula for the angular speed is:

angular speed = linear speed / radius

where the radius is half the diameter of the wheel. We need to convert the units to be consistent, so let's convert the speed from miles per hour to inches per minute and the diameter from inches to feet:

22 miles per hour = 22 * 5280 feet per hour / 60 minutes per hour

                              ≈ 2437.3 inches per minute

26 inches = 26/12 feet = 2.1667 feet

Now we can calculate the angular speed:

angular speed = 2437.3 / 2.1667 ≈ 1124.65 radians per minute

Your question is incomplete, most likely it was:

A cyclist is riding their bicycle on flat terrain at a speed of 22 miles per hour. the wheels on the bike have a diameter of 26 inches.

Find the angular speed in radians per minute.

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The value of the function is -19.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -3x + 2

Substitute x = 7.

f(7) = -3 x 7 + 2

f(7) = -21 + 2

f(-7) = -19

Thus,

-19 is the value.

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To find the percentile of a normal distribution, first determine the mean, then convert the interested value to a standard score, look-up the normal distribution table to find the area to the left of the normal score. Finally, multiply the area by 100.

             z = (x - μ) / σ

        where x is the value of interest.

For example, suppose you want to find the percentile of a test score of 85, which comes from a normal distribution with a mean of 75 and a standard deviation of 10.

            z = (85 - 75) / 10 = 1

           0.8413 * 100 = 84.13

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Answer:

K. none of these (36 wins needed)

Step-by-step explanation:

1st way

80 + 40 = 120

80% of 120 = 96

96 - 60 = 36

2nd way

80 played + 40 left = 120 total

80% season record times 120 total =

12 times 8 is 96 = 80% win record

60 won 20 lost out of 80 total

120 total - 96 wins = 24 losses

96 wins 24 losses 120 total

96 wins - 60 wins = 36 wins out of 40 total

The equation of the graphed line can be found to be 2x + 2 y = 4

To find the equation of the line, you first need to find the slope which requires picking two points on the line. ( 4, 0 ) and ( 0, 2 )

The slope is:

= Change in y / Change in x

= ( 0 - 2 ) / ( 4 - 0 )

= - 2 / 4

= - 1 / 2

The equation form is:

y = mx + b

m = slope

b = y - intercept which is shown on the line as 2

The equation is:

y = - 1 / 2 x + 2

To put it in the form on the question,

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

2 y = - 2 x + 4

2x + 2 y = 4

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Answer:

311 fl oz only were used, that is what I got for your answer..

The answer is 49 fl oz

Answer:

Step-by-step explanation:

To find the price of the NBA ticket in 2017, we need to add 20% to the 2016 price:

Price in 2017 = $1444 + 0.20 x $1444 = $1732.80

To find the price of the NBA ticket in 2020, we need to increase the 2017 price by 20%:

Price in 2020 = $1732.80 + 0.20 x $1732.80 = $2079.36

Rounding this to the nearest dollar, we get:

Price in 2020 = $2079

The like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x

Terms whose variables (such as x or y) with any exponents (such as the 2 in x²) are the same are called like terms,

Examples: 7x and 2x are like terms because they are both "x".

Given are some pairs of expressions, we are asked to identify which are like terms,

We know that, according to the definition of the like terms,

Like terms are those terms which contain the same variable which is raised to the same power,

Therefore, the expressions showing the like terms are,

3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x

Because, they have same variable with same powers.

Hence, the like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x

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The set S spans R₃ if and only if for any vector (a, b, c) in R₃, there exist scalars x, y, and z such that z is not zero and z/2 is nonzero. This is true for all vectors in R₃, so we conclude that S spans R₃.

To determine if the set S spans R₃, we need to see if any vector in R₃ can be written as a linear combination of the vectors in S.

Let (a, b, c) be an arbitrary vector in R₃. Then we want to see if there exist scalars x, y, and z such that:

x(1, -2, 0) + y(0, 0, 1) + z(-1, 2, 0) = (a, b, c)

This is equivalent to the system of equations:

x - z = a

-2x + 2z = b

y = c

Solving for x, y, and z, we get:

x = (a - z)/2

y = c

z = (b + 2x)/2 = (b + a - z)/2

Substituting these values into the equation for the linear combination, we get:

[(a - z)/2](1, -2, 0) + c(0, 0, 1) + [(b + a - z)/2](-1, 2, 0)

= ((a - z)/2 - (b + a - z)/2, -2(a - z)/2 + 2(b + a - z)/2, 0)

= (-b/2, (3a - b)/2, z/2)

Geometrically, the set S consists of two nonparallel vectors and a vector orthogonal to the xy-plane. Thus, the subspace spanned by S is a plane in R₃ passing through the origin.

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The graph is plotted and attached

The oxygen level will be increasing as time goes on

In 0.5 weeks the oxygen level will return to 75% of its normal level

This is the end behavior of the graph, of the function f(t) = t^2 − t + 1, the graph shows that as t tends to infinity. the oxygen level will continue to increase.

The graph is plotted and attached

From the problem. the normal level of oxygen is at f(0) = 1

75% of 1 = 0.75

From the graph, the oxygen level will return to normal level in 1 week(1, 1) and at 0.5 the oxygen level is 0.75, (0.5,0.75). This is the vertex of the graph.

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The total dinner cost, including the tip, comes at $92.40.

A lunch for a few friends will set you back $82.95

They want to leave a 15% tip.

So,

Amount of tip:

15 % of 82.95 = 15*82.95 / 100

15 % of 82.95 = 12.4425

Total cost =  82.95 + 12.4425

Total cost =  95.3925

Total cost =  $92.40

Thus, the total dinner cost, including the tip, comes at $92.40.

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Answer:

b

Step-by-step explanation:

b seeds snd fertilizer

Stacy's statement is incorrect because Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.

Reflexive Property of Congruence:

Stacey did not consider the side common side to both triangles such that by Reflexive Property of Congruence.

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The volume of the right cone is (c) 400π cm cube

From the question, we have the following parameters that can be used in our computation:

Radius = 10 cm

Height = 12 cm

The volume of the cone is calculated as

Volume = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3π * 10² * 12

Evaluate

Volume = 400π

Hence, the volume is 400π cm cube

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Answer: Let's call the amount of the check Craig wrote to the hardware store "x".

According to the problem, the statement from Craig's bank shows an ending balance of $521.60. This means that his balance before writing the check was $521.60 + x.

So, we can write the equation:

$521.60 + x = $521.60

Subtracting $521.60 from both sides:

x = 0

This means that Craig's check was for $0.

Step-by-step explanation:

Answer:

= 3x² + 7 +2x³.

Step-by-step explanation:

Here is my solution to my answer.

Answer: Benjamin would save $11,720.48 over 6 years if he purchases the car instead of leasing it.

Step-by-step explanation:

To calculate the cost of the car if Benjamin purchases it, we can use the loan amortization formula. The formula for calculating the monthly payment of a loan is:

P = (r * A) / (1 - (1 + r)^(-n))

Where:

P = the monthly payment

r = the monthly interest rate (which is the annual interest rate divided by 12)

A = the loan amount

n = the total number of payments

For Benjamin's loan, the loan amount is $30,000, the interest rate is 5.25%, and the loan is for 6 years, or 72 months. Plugging these values into the formula, we get:

r = 0.0525 / 12 = 0.004375

A = $30,000

n = 72

P = (0.004375 * $30,000) / (1 - (1 + 0.004375)^(-72)) = $484.64

Therefore, Benjamin's monthly payment for the car loan is $484.64.

If Benjamin chooses to lease the car instead, he will pay $600 per month for 72 months, plus a $2,500 down payment. Therefore, the total cost of leasing the car is:

Total cost = ($600 * 72) + $2,500 = $45,700

To calculate how much money Benjamin saves by purchasing the car instead of leasing it, we can subtract the total cost of the car loan from the total cost of the lease:

Savings = Total cost of lease - Total cost of car loan

Savings = $45,700 - ($484.64 * 72)

Savings = $11,720.48