Define a variable and write an inequality to model each situation. a. To earn a profit, we must sell at least $1800 worth of inventory. b. On Sundays, you must staff a store with at most 8 employees: c. The price of a stock today is greater than yesterday's price at $625

Answer:

30

Step-by-step explanation:

Use part/whole proportions. 10/25 (15 + 10) = 12/x. Multiply 12 times 25 (300) = 10x (10 times x). 300 = 10x, isolate x by dividing both sides by 10 and you get 30 = x.

Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations.

When the equations are solved simultaneously, they are known as simultaneous equations.

Jogging be considered as x

Cycling be considered as y

Shelly spent 40 minutes jogging and 22 minutes cycling, and burned 620 calories to write this in equation we get,

40x + 22y = 620

Shelly swapped times,

22 minutes of jogging and 40 minutes of cycling and burned the same number of calories,

22x + 40y = 620

By multiplying two equation we get,

multiply equation 1 by 22 and equation 2 by 40 we get,

880x + 484y = 13640

880x + 1600y = 24800

Now subtracting equation 1 from 2 we get,

1116y = 11160

y = 11160/1116

y = 10

Therefore, putting value of y in equation 1 we get,

880x + 484(10) = 13640

880x = 13640 - 4840

x = 8800/880

x = 10

Therefore, calories were burned for each minute of jogging is 10 calories and for each minute of cycling is 10 calories.

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The solution to the given system of equations [x+3y=5, x+4y=6] using a matrix equation is x = 2 and y = 1.

To solve the system of equations using a matrix equation, we can write the augmented matrix [1 3 5; 1 4 6] where the coefficients of x and y are represented by the matrix elements. We can then perform row operations to transform the matrix into row-echelon form or reduced row-echelon form. Applying row operations, we can subtract the first row from the second row to eliminate x, resulting in the row [1 3 5; 0 1 1]. This represents the system x + 3y = 5 and y = 1. By substituting y = 1 into the first equation, we find x = 2. Therefore, the solution to the system is x = 2 and y = 1. To check the solution, we substitute these values back into the original equations and verify that both equations hold true.

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Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Answer:

12.5%

Step-by-step explanation:

The price for the ski = $2000

The payments made each = $250

percentage of the total cost that the payment is = ?

The percentage will be calculated as

the ratio of the payments made to the price of ski times 100%

250/2000 x 100%

==> 0.125 x 100% = 12.5%

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:  

m<1 = 51

m<2 = 34

m<3 = 95

m<4 = 38

m<5 = 47

m<6 = 74

m<7 = 59

Step-by-step explanation: because to get angle 1 you take 180 (because its is a straight line) and subtract the angle 129 giving you m<1 witch is 51. the second one is 180 - (m<1 + 95) =m<2 witch is 34 so m<2 = 34. third is the angle 95 because the lines that intersect give equal opposite angles so m<3 = 95. Four is 180 - (m<3 + 47) =m<4 witch is 38. fifth is opposite angle so it is 47. sixth is m<5 +m<6 + m<7 = 180 so m<5 is 47 and we can find m>7 by subtracting from 180 the angle 121 giving us m<7 = 59 so we will add m<5 and m<7 and subtract from 180 giving us m<6 witch is 74.    

Answer:

(g ∘ f)(6) = 216

Step-by-step explanation:

We are given the functions f(x) = 2x - 6 and g(x)=x³

We want to find the value of (g∘f)(6), where we first find the value of f(6), and then substitute that value into g(x).

Substitute 6 as x in f(x)=2x-6.

f(6)=2(6)-6

Multiply

f(6)=12-6

Subtract

f(6)=6

Now substitute 6, which is the value of f(6) as x in g(x) = x³.

g(6)=6³ = 6 * 6 * 6 = 36 * 6 = 216

The value of g(6) is the same as the value of (g ∘ f)(6), as the 6 that we plugged into g(x) is the value of f(6).

Therefore, (g ∘ f)(6) = 216.

Answer:

6

Step-by-step explanation:

The number completes the sequence is 6

Answer:

4 x - 1\/x + 2 - 2 = 2 x - 1\/x + 2

Step-by-step explanation:

x = 1

Answer:

2.08 or 2

Step-by-step explanation:

26 = 12.5x

y=mx+b

it will approximately take  2 hours, but to be exact, 2.08

The even integers are 10,12 and 14.

Concept:  An integer is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Let x,x+2,x+4 be the least, middle and greatest integer respectively.

According to the question,

15< x+x+2+x+4< 21

(3x+6)/2> 15      and    (3x+6)/2< 21

30< 3x+6                      3x+6> 42

24<3x                            3x<36

8<x                                x>12

x=10

x+2=12

x+4=14

Hence, The even integers are 10,12 and 14.

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Answer:

56.70

Step-by-step explanation:

Answer:

x= 42

Step-by-step explanation:

(2x +1)°= 85° (vert. opp. ∠s)

2x +1= 85

2x= 85 -1 (bring constant to 1 side)

2x= 84 (simplify)

x= 84 ÷2

x= 42

Answer:

Step-by-step explanation:

The root which is 2 is the fractional portion of your exponent

\(\sqrt{x^{7} y^{12} }\)

=\((x^{7} y^{12} )^{\frac{1}{2} }\)              >You can distribute 1/2 to each term by multiplying

\(=x^{\frac{7}{2} } y^{6\)

To solve this problem, we can use the binomial probability distribution. Let's define a "success" as scoring a goal and a "failure" as missing a goal.

Then, each attempt by Sky can be considered a Bernoulli trial with probability of success p = 1/2.

Let X be the number of goals that Sky scores in five attempts. Then, X follows a binomial distribution with parameters n = 5 and p = 1/2.

To find the probability that Sky scores at least two goals, we need to calculate the probability of the following events:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

We can use the binomial probability formula to calculate these probabilities:

P(X = k) = (n choose k) * \(p^k\) *\((1-p)^(n-k)\)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we get:

P(X = 2) = (5 choose 2) * \((1/2)^2\) * \((1/2)^3\) = 10/32

P(X = 3) = (5 choose 3) * \((1/2)^3\) * \((1/2)^2\) = 10/32

P(X = 4) = (5 choose 4) * \((1/2)^4\) *\((1/2)^1\) = 5/32

P(X = 5) = (5 choose 5) * \((1/2)^5\) * \((1/2)^0\) = 1/32

Therefore, the probability that Sky scores at least two goals is:

P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = (10 + 10 + 5 + 1)/32 = 26/32 = 13/16

So the probability that Sky scored at least two goals is 13/16.

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The total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

Sky attempted to score a goal five times. For each attempt, she was equally likely to make a goal or miss. So the probability that Sky scored at least two goals is 13/16.

To find the probability that Sky scored at least two goals, we can use complementary probability, which means finding the probability that she scored fewer than two goals (either 0 or 1 goal) and subtracting that from 1.1.

Probability of scoring 0 goals: Since there are 5 attempts and she is equally likely to make a goal or miss (1/2 chance for each), the probability of missing all 5 is (1/2)^5 = 1/32.2.

Probability of scoring 1 goal: Sky could score in any of the 5 attempts, so we need to consider all possible ways of scoring one goal.

There are 5 ways (score in the 1st, 2nd, 3rd, 4th, or 5th attempt). The probability for each of these scenarios is (1/2)^5 = 1/32.

Therefore, the total probability of scoring 1 goal is 5 * (1/32) = 5/32.Now we find the complementary probability:1 - (Probability of 0 goals + Probability of 1 goal) = 1 - (1/32 + 5/32) = 1 - 6/32 = 26/32.

To express this as a common fraction, we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:26/32 = (26/2) / (32/2) = 13/16So the probability that Sky scored at least two goals is 13/16.

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15: The confidence interval is associated with a degree of confidence that includes the population parameter of interest.

16: The process in inferential statistics consists of using various statistical techniques to draw conclusions and make inferences about a population based on sample data.

15: A confidence interval is a range of values within which the true population parameter is likely to fall. It is associated with a degree of confidence, typically expressed as a percentage (e.g., 95% confidence interval), which represents the likelihood that the interval captures the true parameter. The confidence interval provides a measure of uncertainty and allows researchers to estimate the range within which the population parameter is likely to be.

16: The process in inferential statistics involves using statistical techniques to make inferences and draw conclusions about a population based on sample data. This process typically includes steps such as formulating a research question, collecting a representative sample, analyzing the sample data, and drawing conclusions or making predictions about the population. Inferential statistics allows researchers to generalize findings from a sample to a larger population and make evidence-based decisions.

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Answer:

B

Step-by-step explanation:

jimmy woo

Cot θ is equal to 1/2.

To find cot θ, we need to use the given information:

csc θ = √(5/2)

tan θ = 0

We can use the reciprocal identities and the Pythagorean identity to find cot θ.

Reciprocal Identity:

csc θ = 1/sin θ

Pythagorean Identity:

\(sin^2\) θ + \(cos^2\)θ = 1

Given that csc θ = √(5/2), we can find sin θ:

1/sin θ = √(5/2)

sin θ = 2/√5

Using the Pythagorean identity, we can find cos θ:

\(sin^2\) θ + \(cos^2\) θ = 1

\((2/√5)^2\)+ \(cos^2\) θ = 1

4/5 + \(cos^2\) θ = 1

\(cos^2\) θ = 1 - 4/5

\(cos^2\)θ = 1/5

cos θ = ±√(1/5)

Now, we can find cot θ:

cot θ = cos θ / sin θ

Since tan θ = 0, it means that sin θ is not equal to 0, as tan θ = sin θ / cos θ. Therefore, we can use the positive value of cos θ.

cot θ = (√(1/5)) / (2/√5)

cot θ = (√5/√5) / (2/√5)

cot θ = 1/2

Therefore, cot θ is equal to 1/2.

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Solution

A standard deck of cards has 4 suits: Hearts, Clubs, Spades, and Diamonds

Each suite contains an ace, 2, 3, 4,5,6,7,8,9,10, jack, queen, and king, a total of 13 cards

Therefore a standard pack of cards has 4 x13 cards = 52 cards/elements

An expression for probability is

The question requires us to find the probability of picking an Ace or a Club

No of Aces = 4 across all the suits

No of Clubs = 4 across all suits

Total number of cards = 52

The probability of picking an Ace or a Club is

Answer = 2/13

C)

1) Examining those sentences we have:

A) Integers and fractions are rational numbers. True

Since any integer is a Rational number and fractions are ratios.

B) Whole numbers are rational numbers. True

The whole Number Set is within at Rational Set

C) π is a rational number. False

π is an Irrational number for can't be written as a ratio a/b.

D) square root of 25 is a rational number.​ True

Since √25 = 5 and 5 is a rational number.

Answer: 1182

Step-by-step explanation:

Using substitution method, the solution to the linear equations is (2, -1) which is option e

To solve this system of linear equations, we will use substitution method

Equation 1: x - 2y = 4

Equation 2: 4x + 2y = 6

By adding Equation 1 and Equation 2, we eliminate the y variable:

Equation 1 + Equation 2:

(x - 2y) + (4x + 2y) = 4 + 6

5x = 10

x = 2

Substitute the value of x back into Equation 1 to solve for y:

x - 2y = 4

2 - 2y = 4

-2y = 2

y = -1

Therefore, the solution to the linear system is x = 2 and y = -1.

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Answer:

\(18\sqrt{3} + 55\sqrt{3} = 73\sqrt{3}\)

Step-by-step explanation:

27= 3 * 3 * 3

75 = 3 * 5*5

18 sqr 3 + 55 sqr 3 = 73 sqr 3

Answer:

644

Step-by-step explanation:

SA=[2×(5×20 + 5×6 + 20×6)] +

[2×(4×12 + 4×6 + 12×6)] -

[ 2× 12×6]

= [2×(250)]+[2×(144)] - [144]

= 500+288-144

= 644 cm²

Answer:

C. because it does not contain a equal sign. please matk me as the brainliest. Please...

How you actually measure the variable is called the Operational definition of the variable .

The Operational Definition of a variable is how you actually measure it.

It specifies the methods, techniques, and procedures used to measure a particular variable. It is the concrete, specific, and practical definition of the variable in a way that makes it possible to be observed, measured, and recorded.

The operational definition is also used to ensure that all researchers are measuring the variable in the same way and to reduce the potential for measurement error. It is an important step in the scientific process as it allows for replication of results and makes the variable more concrete and tangible.

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Population standard deviation, level of significance are same.

Margin of error increased.

With increase in margin of error sample size decreases.

By dividing the population's standard deviation by the sample size and then multiplying the resulting number by the crucial factor, the margin of error—a statistical expression used to estimate how much a result will deviate from the value of the full population—can be determined.

The standard deviation of the sample statistics, if we could take several samples of the same size, is the standard error.

Population standard deviation, level of significance are same.

Margin of error increased.

Margin of error increases leads to decrease in the sample size

as the margin of error is in denominator position in sample size formula. Hence with increase in margin of error sample size decreases.

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