4x+3 to find the value of ST

If Zoe the goat is tied to a corner of a rectangular barn measuring 15m by 25m in the middle of a field, Zoe can graze within an area of 2660.5 sqm.

The area of the field that Zoe can graze depends on the length of the rope, which is not given in the problem. However, we can use the Pythagorean theorem to find the length of the diagonal of the barn, which represents the maximum length of the rope.

The diagonal of a rectangle with sides of length 15 meters and 25 meters can be found using the Pythagorean theorem:

diagonal² = 15² + 25²

diagonal² = 225 + 625

diagonal² = 850

diagonal =[tex]\sqrt{850}[/tex] ≈ 29.15 meters

This means that the maximum length of the rope is about 29.15 meters. The area that Zoe can graze is a circle with radius equal to the length of the rope. We can use the formula for the area of a circle to find this area:

Area = π(radius)²

Area = π(29.15)²

Area ≈ 2660.5 square meters

Therefore, the correct answer is approximately 2660.5 square meters

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The null hypothesis was rejected as the mean of the sweetness losses was greater than the critical value. Thus, the cola did lose sweetness.

1. State the null hypothesis: The null hypothesis is that the cola did not lose sweetness.

2. Determine the level of significance: The level of significance is 5%.

3. Calculate the test statistic and The test statistic is calculated by subtracting the mean of the sweetness losses from zero.

4. Make a decision: If the test statistic is greater than the a critical value, then the null hypothesis should be rejected and the cola did lose sweetness. which is greater than the a critical value of 0.05. Therefore, the null hypothesis should be rejected and the cola did indeed lose sweetness.

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If a student looks out of a third story window and sees the top of the school flagpole at an angle of elevation of 22°. the height of the flagpole to the nearest foot is approximately 52 ft.

Let's call the height of the flagpole "h". We can use the tangent function to set up an equation based on the angle of elevation:

tan(22°) = h / 60

Solving for h, we get:

h = 60 tan(22°)

h ≈ 23.7 ft

However, this value is the distance from the base of the flagpole to the top of the flagpole, and we need to find the actual height of the flagpole.

h_actual = h + 28

h_actual  =23.7 + 28

h_actual  = 51.7 ft

h_actual  =  52 ft (Approximately)

Therefore, the height of the flagpole to the nearest foot is approximately 52 ft.

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The answer fοr this is Substitutiοn Prοperty

What is Substitutiοn Prοperty?  

The substitutiοn prοperty is a cοncept in algebra that is used tο substitute the value οf a given variable οr a quantity intο an expressiοn tο find the value οf the unknοwn. In simple wοrds, we can say that the substitutiοn prοperty is used tο replace the value οf a quantity in an equatiοn οr an expressiοn tο sοlve a mathematical prοblem. We will discuss the meaning οf the substitutiοn prοperty οf equality, the substitutiοn prοperty in geοmetry, and the direct substitutiοn prοperty in limits in the fοllοwing sectiοns.

Substitutiοn Prοperty is cοnsidered as οne οf the mοst intuitive οf the mathematical prοperties that yοu'll prοbably encοunter. Yοu may have been using substitutiοn withοut even knοwing it. This prοperty says that if x=y, then in any true equatiοn invοlving y, yοu can replace y with x, and yet yοu'll still have a true equatiοn.

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Take a loοk at the attached example shοwn below.

The probability that the third card will be an ace is 0.0045, probability of all cards to be of same suit is 0.000495, and the probability of two or more aces is 0.004.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

(a) The probability that the third card is an ace:

We can approach this problem by using the conditional probability formula, which states that the probability of an event A given that event B has occurred is:

P(A|B) = P(A and B) / P(B)

Let A be the event that the third card is an ace, and let B be the event that the first two cards are not aces. The probability of the first card being an ace is 4/52 (since there are four aces in a standard deck of 52 cards). The probability of the second card being an ace given that the first card was not an ace is 3/51 (since there are three aces left in the deck of 51 cards). The probability of the third card being an ace given that the first two cards were not aces is 2/50 (since there are two aces left in the deck of 50 cards).

Therefore, using the conditional probability formula, we have:

P(A|B) = P(A and B) / P(B)

P(A|B) = (4/52) * (3/51) * (2/50) / (1 - (4/52) * (3/51))

P(A|B) ≈ 0.0045

So the probability that the third card is an ace is approximately 0.0045.

(b) The probability that all cards are of the same suit:

There are four suits in a standard deck of cards: clubs, diamonds, hearts, and spades. We can compute the probability that all five cards are of the same suit as follows:

P(all cards are of the same suit) = P(first card is a particular suit) * P(second card is the same suit) * P(third card is the same suit) * P(fourth card is the same suit) * P(fifth card is the same suit)

P(all cards are of the same suit) = (13/52) * (12/51) * (11/50) * (10/49) * (9/48)

P(all cards are of the same suit) ≈ 0.000495

So the probability that all cards are of the same suit is approximately 0.000495.

(c) The probability of two or more aces:

We can compute the probability of two or more aces by considering the complementary event: the probability that there are zero or one aces in the five cards dealt. The probability of getting zero aces is:

P(zero aces) = (48/52) * (47/51) * (46/50) * (45/49) * (44/48)

P(zero aces) ≈ 0.617

The probability of getting one ace is:

P(one ace) = (4/52) * (48/51) * (47/50) * (46/49) * (45/48) * 5

P(one ace) ≈ 0.379

Therefore, the probability of two or more aces is:

P(two or more aces) = 1 - P(zero aces) - P(one ace)

P(two or more aces) ≈ 0.004

So the probability of two or more aces is approximately 0.004.

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The probability of y that when a point is randomly selected on the surface of a lake that has a maximum depth of 100 feet are all real numbers from 0 to 100.

A lake is a body of freshwater that is surrounded by land. The water in a lake is still, unlike a river or a stream, which flows from one place to another. Lakes are a vital component of the water cycle and play an important role in the ecosystem.

Since the maximum depth of the lake is 100 feet, the depth of the lake at the randomly chosen point cannot be greater than 100 feet. Therefore, y can have any value between 0 and 100. As a result, all real numbers from 0 to 100 are possible values of y.

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Answer:

4

Step-by-step explanation:

Let x be the number of shirts that Rachel can buy, and y be the number of pants she can buy. Then the cost equation would be:

Cost = 25x + 20y

Since Rachel has a total budget of $200, we can write:

25x + 20y ≤ 200

To find the maximum number of shirts that Rachel can buy if she buys 5 pants, we can substitute y = 5 into the inequality and solve for x:

25x + 20(5) ≤ 200

25x ≤ 100

x ≤ 4

Therefore, Rachel can buy a maximum of 4 shirts if she buys 5 pants.

The expression (6.25x + 12) - (4.25x - 7) / (6.25 + 12) - (4.25 - 7) to its simplest form, which is (2x + 19) / 21.

To simplify the given expression, we need to apply the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we will simplify the expression inside the parentheses using the distributive property.

(6.25x + 12) - (4.25x - 7) = 6.25x + 12 - 4.25x + 7

Next, we will combine like terms, which are the terms with the same variable and exponent.

6.25x - 4.25x = 2x

12 + 7 = 19

Therefore, the simplified expression becomes:

2x + 19

Now, we will simplify the expression in the denominator.

(6.25 + 12) - (4.25 - 7) = 18.25 - (-2.75)

Remember that subtracting a negative number is the same as adding a positive number.

18.25 + 2.75 = 21

Finally, we can write the simplified expression as:

(2x + 19) / 21

This is the simplest form of the given expression, and it cannot be further simplified.

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Complete Question:

Simplify the expression: ( 6. 25 x + 12 ) − ( 4. 25 x − 7 ) ( 6. 2 5 + 1 2 ) − ( 4. 2 5 − 7 )

6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.

To calculate the original length given that 6% of it is 570m, we can use the following formula: Original length = (570 ÷ 0.06) Original length = 9500mTo solve this problem, firstly the percentage of 6% needs to be converted into a decimal by dividing 6 by 100. This will give us 0.06. Then, the original length is found by dividing the given value of 6% (570m) by the decimal equivalent (0.06). Therefore, the original length is 9500m. To summarise, 6% of a length is 570m and the original length can be calculated by dividing 570m by 0.06, resulting in 9500m.

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Father : 50 years old

Son : 10 years old

Answer:

B

Step-by-step explanation:

the answer is B please see on the attached.

Scale ratio is 9 cm which can be calculated by comparing lengths and using division.

The scale ratio between two rectangles is a way to compare the size of their corresponding sides. It is calculated by dividing the length of one side of the first rectangle by the length of the corresponding side of the second rectangle.

In this case, let's compare the length of the longer side of the first rectangle (72 cm) with the length of the longer side of the second rectangle (8 cm):

scale ratio = 72 cm ÷ 8 cm = 9

This means that the longer side of the first rectangle is 9 times as long as the longer side of the second rectangle. We could also calculate the scale ratio using the shorter sides:

scale ratio = 36 cm ÷ 4 cm = 9

In either case, the scale ratio is 9, which tells us that the first rectangle is 9 times as large as the second rectangle. This can be useful for creating accurate scale drawings or models of objects.

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Thus, out of 40 problems, 6 problems will have two parts problems which is 15% of the 40.

The phrase "percent" refers to a number out of 100 or per 100. The term is derived from the Roman expression per centum, which means "by the hundred." Hence, a single percent would be one of those hundred units, and one percent, for every one hundred of anything.

Given data:

Out of 100 problems -  15% have two parts.

Out of 100 problems -  85% will not have two parts.

Thus, out of 40 problems, also 15% will contain two parts.

Then,

Number of two-part problem = 15% of 40

Number of two-part problem = 15 * 40 / 100

Number of two-part problem =  600 / 100

Number of two-part problem = 6

Thus, out of 40 problems, 6 problems will have two parts which is 15% of the 40.

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the answer will be -137

After calculating the future value of the current balance, You will still owe $72.97 after one year.

Calculate the future value of the current balance: FV = PV x (1 + r)
Where, FV = Future Value, PV = Present Value (the current balance of $1,000), and r = interest rate of 2% per month.
Thus, FV = 1,000 x (1 + 0.02) = 1,020

Calculate the future value of the annuity payments of $100 per month:
FV = c x ı((1 + y)+ - 1)
Where, c = $100, y = interest rate of 2% per month.
Thus, FV = 100 x ı((1 + 0.02)12 - 1) = 1,246.24

Calculate the future value of the account balance: FV = 1,020 + 1,246.24 = 2,266.24
Finally, calculate the balance at the end of one year:
Balance at the end of one year = Future Value - Annuity Payments

Thus, Balance at the end of one year = 2,266.24 - (12 x 100) = 72.97.

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Answer:

To find out which cake is the most expensive per serving, we need to calculate the cost per serving for each cake.

The first cake serves 2 people and costs $4.50. So the cost per serving is:

$4.50 ÷ 2 = $2.25 per serving

The second cake serves 8 people and costs $10.00. So the cost per serving is:

$10.00 ÷ 8 = $1.25 per serving

The third cake serves 10 people and costs $20.00. So the cost per serving is:

$20.00 ÷ 10 = $2.00 per serving

Therefore, the first cake is the most expensive per serving, at $2.25 per serving.

Answer:

We can see that each term in the sequence is 3 more than the previous term. So we can find the 5th term by adding 3 to the fourth term, the 6th term by adding 3 to the 5th term, and so on.

5th term = 11 + 3 = 14

6th term = 14 + 3 = 17

7th term = 17 + 3 = 20

...

We can see that each term can be written as:

term = 2 + 3n

where n is the position of the term in the sequence starting from 0 (i.e. the first term is at position 0, the second term is at position 1, etc.)

To find the 19th term, we can substitute n = 17 into the formula:

19th term = 2 + 3(17) = 53

However, the problem states that the 19th term is actually 56. This means that we need to adjust our formula to account for any initial shift in the sequence. We can do this by subtracting a certain value from n, so that the first term in the sequence corresponds to n = 0.

Let's call this adjustment value "a". We know that when n = 0, the first term in the sequence is 2. So we can set up an equation:

2 + 3a = 2

Solving for a, we get a = 0.

Therefore, the adjusted formula for the nth term is:

term = 2 + 3(n-1)

where n is the position of the term in the sequence starting from 1.

Substituting n = 19, we get:

19th term = 2 + 3(18) = 56

So our adjusted formula is correct, and the answer is 56.

(Please could you kindly mark my answer as brainliest)

Answer:

48,232.8

Step-by-step explanation:

4,823.28 x 0.01

Answer:

$6.48

Step-by-step explanation:

First, let's find the discount.

1.60 * 0.1 = $0.16 (the discount)

Second, subtract the discount to the original price.

1.60 - 0.16 = $1.44 (price after discount was applied)

Third, multiply to 4 1/2 to find how much it will cost.

1.44 * 4.5 = $6.48 (price of 4 1/2 pounds of apples with discount applied)

Answer:

its c

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be $25,548.87 is the expected consumption when the available income is $33,000.

The mathematics lesson covers a wide range of topics, including math, numbers, and one's subsets, as well as building, construction, and both real and fictitious geographic places. The relationships between various components that all cooperate to create the same outcome are covered by a work. A utility is composed of an assortment of unique parts that work together to produce unique outcomes for each input.

Here,

Utilizing Excel or statistical software, we can discover a sample linear regression equation. Using the regression analysis function in Excel, we obtain:

=> Consumption = -5117.41 + 0.9694 * Discretionary Income Marginal Propensity to Consume

=> (MPC): 0.9694 Regression equation

MPC interpretation: The MPC shows the percentage of extra disposable income that is spent on consumption.

The MPC in this instance is 0.9694, indicating that on average 0.9694 cents are spent on consumption for every extra dollar of disposable income.

When the available income is $33,000, we can enter the number as follows into the regression equation to determine the predicted consumption:

=> Usage = -5117.41 plus 0.9694 times 33,000.

=>Usage =  $25,548,87

Therefore, $25,548.87 is the expected consumption when the available income is $33,000.

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For the latte, the values are obtained as -

Absolute change - $0.48

Relative change - 13.7%

What is absolute change?

Absolute change tells us the magnitude of the difference or change between two values, regardless of whether the change was an increase or a decrease. It is often used in economics, finance, and other fields to measure changes in variables such as prices, income, sales, or quantities.

The absolute change in the price of a latte is the difference between the original price and the new price, without regard to the direction of the change.

Absolute change = | New price - Original price |

Absolute change = | $3.02 - $3.50 |

Absolute change = $0.48

The relative change in the price of a latte is the absolute change expressed as a percentage of the original price.

Relative change = (Absolute change / Original price) x 100%

Relative change = ($0.48 / $3.50) x 100%

Relative change = 13.7%

Therefore, the absolute change in the price of a latte is $0.48, and the relative change is 13.7%.

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The mean of the data is 8.1 cm, which is the most appropriate measure of central tendency to use in this situation.

The most appropriate measure of central tendency to use in this situation is the mean. The mean is the sum of all of the values divided by the number of values. In this case, this would be 8.1 cm (the sum of 8.3 cm, 8.4 cm, 8.8 cm, 8.2 cm, 8.3 cm, 8.0 cm, 8.1 cm, and 8.5 cm divided by 8).

The formula for mean is as follows:

Mean = Sum of values / Number of values

In this situation, the sum of values is 8.3 cm + 8.4 cm + 8.8 cm + 8.2 cm + 8.3 cm + 8.0 cm + 8.1 cm + 8.5 cm = 67.7 cm

Number of values = 8

Mean = 67.7 cm / 8 = 8.1 cm

The mean is the best measure of central tendency to use in this situation because it is the most accurate representation of the data, as it takes into account all of the values in the dataset.

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Answer:

To write an expression for the total cost of both memberships after m months, we can use the following vocabulary words:

- Startup fee: a one-time fee charged at the beginning of a service or membership

- Monthly fee: a recurring fee charged every month for a service or membership

Using this information, we can write the expression as:

Total cost = (Startup fee for digital library) + (Monthly fee for digital library x number of months) + (Monthly fee for video streaming service x number of months)

Substituting the given values, we get:

Total cost = (5) + (9.95 x m) + (7.99 x m)

Simplifying the expression, we get:

Total cost = 5 + 17.94m

Therefore, the total cost of both memberships after m months can be expressed as 5 + 17.94m.

Combining events A and B results in the entire event, with a probability of 1 for the entire event. The probability P(EC)= 1-P(E) OR P(EC)= 1-0.42= 0.58 is the result.

When conducting an experiment, the probability of an event serves as a gauge for the likelihood that the event will actually occur. When there are only two possible outcomes, such as passing an exam or failing it, complementary events take place. The opposite of an event is represented by the complement.
When one event only happens if and when the other one doesn't, two events are said to be complementary. For instance, it rains or it doesn't.
The probability of an event occurring when added to the probability of the complement of that event occurring is always 1. Considering A to be an event, P(A) + P(A') = 1.
Associated events are exhausting.
Events that complement one another can never coexist.

P(EC)+P(E)=1

P(EC)= 1-P(E)

P(EC)= 1-0.42

P(EC)= 0.58.

Hence, the probability P(EC)= 0.58.

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Answer:

green is x ≥ -3

blue is y < -2x - 4

Step-by-step explanation:

The values of 'x' that solve for given conditions are (a) 11.349  (b) 13.29  (c) 7.44 and 12.56  (d) 6.08 and 13.92  (e) 5.84 and 14.16.

The z-score, also known as the standard score, is a measure of how many standard deviations a data point is away from the mean of its distribution.

The formula for calculating the z-score of a data point x, with mean μ and standard deviation σ, is:

where z is the z-score.

Here we have

X is normally distributed with a mean of 10 and a standard deviation of 2

As we know z score, z = (x - μ) / σ.

=> x =  μ + zσ  

Hence, to find the 'x' value we need to know the value of the z score in each situation

(a) P(X > x) = 0.5

The z-score corresponding to a right-tail probability of 0.5 is 0.6745.

=> x = 10 + 0.6745 * 2

=> x = 11.349  

(b) P(X > x) = 0.95

The z-score corresponding to a right-tail probability of 0.05 is 1.645.

Substituting the given values into the formula, we get:

x = 10 + 1.645 * 2

x = 13.29

(c) P(x < X < 10) = 0.2

The z-score corresponding to a left-tail probability of 0.1 is -1.28 and the z-score corresponding to a right-tail probability of 0.1 is 1.28.

From formula, z = (x - μ) / σ

=> -1.28 = (x - 10) / 2

=> x = 7.44

and

=> 1.28 = (x - 10) / 2

=> x = 12.56

Therefore,

The values of x that solve P(x < X < 10) = 0.2 are 7.44 and 12.56.

(d) P(-x < X - 10 < x) = 0.95

The z-score corresponding to a right-tail probability of 0.025 is 1.96.

=> -1.96 = (-x - 10) / 2

=> x = 6.08

and

=> 1.96 = (x - 10) / 2

=> x = 13.92

Therefore,

The values of x that solve P(-x < X - 10 < x) = 0.95 are 6.08 and 13.92.

(e) P(-x < X - 10 < x) = 0.99

The z-score corresponding to a right-tail probability of 0.005 is 2.58.

=> -2.58 = (-x - 10) / 2

=> x = 5.84

and

=> 2.58 = (x - 10) / 2

=> x = 14.16

Therefore,

The values of x that solve P(-x < X - 10 < x) = 0.99 are 5.84 and 14.16.

Therefore,

The values of 'x' that solve for given conditions are (a) 11.349  (b) 13.29  (c) 7.44 and 12.56  (d) 6.08 and 13.92  (e) 5.84 and 14.16.

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Answer:

x= 3

Step-by-step explanation:

Since triangle is equilateral...

2y = 25x - 15

And....

Here,

2y + 2y + 2y = 180

6y = 180

y = 180/6

= 30

Again,

2y = 25x -15

2*30 + 15 = 25 x

x = 75/25

= 3

As x approaches to infinity y  also approaches to infinity.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. Formally, a function f from a set A to a set B is defined as a subset of the Cartesian product A × B such that for every element a in A, there is a unique element b in B such that (a, b) belongs to the subset.

A function can be represented using the function notation f(x) = y, where x is the input (or independent variable), y is the output (or dependent variable), and f is the name of the function. The value of f(x) depends on the value of x and the rules of the function.

From the graph

x approaches to infinity

y  also approaches to infinity.

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