Solve the equation: 7x = 42
A. x = 7
B. x = 6
C. x = -7
D. x = -6

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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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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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 )

The location of A using graphs, is at (4, -1).

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.

Here in the question,

Coordinates of A= (8,2)

Now it is dilated by a scale factor of 1/2. So,

New coordinates, A' = (8/2,2/2)

= (4,1)

Now the triangle is reflected over the x-axis.

A' now becomes A" which is (4, -1).

Therefore, the new coordinate of A is (4, -1).

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The complete question is:

Triangle ABC is shown on the coordinate plane. Triangle on coordinate plane with vertices A at 8 comma 2, B at 10 comma 6, and C at 4 comma 4. Triangle ABC is dilated by a scale factor of one half about the origin and then reflected over the x-axis. What is the location of A″ after the sequence of transformations? (8, −2) (4, 1) (4, −1) (−4, 1)

The factors of 16 are 1, 2, 4, 8, and 16, so we have:

P = {1, 2, 4, 8, 16}

Divisors are another name for factors. As a result, they can equally split into the number of which they are a factor. In other words, they do not even leave a remnant when you divide with them. For instance, 36 has a factor of 4 in it.

We can write the sets P, Q, and R using set-builder notation as follows:

P = {1, 2, 4, 8, 16} (the factors of 16)

Q = {0, 4, 8, 12, 16} (the multiples of 4 less than 17)

R = {12, 13, 14, 15, 16} (the whole numbers from 12 to 16)

The multiples of 4 less than 17 are 4, 8, 12, and 16. However, Q is defined as the complement of this set, so we have:

Q = {-3, -2, -1, 0, 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15}

The whole numbers from 12 to 16 are 12, 13, 14, 15, and 16, so we have:

R = {12, 13, 14, 15, 16}

Due to the fact that it is a combination of 4 and less than 17, we have included 0 in set Q.

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Answer:

green is x ≥ -3

blue is y < -2x - 4

Step-by-step explanation:

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.

Answer:

8

Step-by-step explanation:

Use PEDMAS

P - Parenthesis

E - Exponents

D -Division

M - Multiplication

A & S - Addition and subtraction.      [tex]\bf 7 + (2 +6)^2 \div 4 * (\dfrac{1}{2})^2 = 7 + 8^2 \div 4 * \dfrac{1}{16}\\\\\\\text{\bf First perform the operation inside the parenthesis and then the exponents}[/tex]

                                [tex]= 7 + 64 \div 4 * \dfrac{1}{16}[/tex]

Here, exponents 8² = 64 is done

                                [tex]\bf = 7 + 16 * \dfrac{1}{16} \ {(\bf Division \ is \ done)}[/tex]

                                 = 7 + 1

                                 = 8

Answer:

wait I big speak. it's important for learn how.

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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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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The weight of the first basket full of apples is 8.66 kilograms more as compare to weight of the second basket.

Number of full of apples basket with Tommy = 2

Weight of first basket full of apples = 18.63 kilograms

Weight of second basket full of apples = 9.97 kilograms

Weight of first basket is greater than the weight of the second basket.

More weight in first basket

= Subtract the weight of the second basket from the weight of the first basket

⇒ More weight in first basket  = Weight of first basket - Weight of second basket

⇒ More weight in first basket = ( 18.63 - 9.97 ) kilograms

⇒ More weight in first basket = 8.66 kilograms

Therefore, the first basket weighed 8.66 kilograms more than the second basket.

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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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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

To find the total area of the pool and the walkway, we can add the areas of the pool and the walkway together.

Let's assume that the pool has dimensions of length L and width W, and that the walkway has a uniform width of 2 feet all around the pool. This means that the dimensions of the pool plus the walkway will be (L + 4) feet by (W + 4) feet, since we add 2 feet on each side.

The area of the pool alone is given by L x W. The area of the pool plus the walkway is then given by (L + 4) x (W + 4). To simplify, we can use FOIL (First, Outer, Inner, Last) method to expand the expression:

(L + 4) x (W + 4) = LW + 4L + 4W + 16

Therefore, the polynomial expression that represents the total area of the pool and the walkway is:

A(L,W) = LW + 4L + 4W + 16

where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.

1.Start by assuming that the pool has dimensions of length L and width W, in feet.

2.Since Mrs. Smith wants to add a 2-foot walkway around the edge of the pool, we need to add 2 feet to both the length and width of the pool to get the dimensions of the pool plus the walkway. This means that the dimensions of the pool plus the walkway are (L + 2) feet by (W + 2) feet.

3.To find the area of the pool alone, we can simply multiply the length by the width: A_pool = L x W.

4.To find the area of the pool plus the walkway, we need to multiply the length and width of the larger rectangle that includes both the pool and the walkway. This rectangle has dimensions of (L + 2) feet by (W + 2) feet. Therefore, the area of the pool plus the walkway is:

A_total = (L + 2) x (W + 2)

5.We can simplify this expression by using the distributive property of multiplication. We first multiply L by W to get LW. Then, we multiply L by 2 and W by 2 to get 2L and 2W, respectively. Finally, we add 2 x 2 = 4 to account for the extra area added by the walkway. Therefore, the total area of the pool plus the walkway can be written as:

A_total = LW + 2L + 2W + 4

6.Finally, we can rewrite this expression as a polynomial in standard form, by rearranging the terms in descending order of degree:

A_total = LW + 2L + 2W + 4

    = LW + 2L + 2W + 0x² + 4

    = 0x² + LW + 2L + 2W + 4

So the polynomial expression that represents the total area of the pool and the walkway is:

A(L,W) = LW + 2L + 2W + 4

where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.

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the answer will be -137

Father : 50 years old

Son : 10 years old

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.

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.

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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The activity involved multiplying two polynomials using the distributive property to find the product, which has a degree equal to the sum of the degrees of the terms being multiplied together.

The activity involved multiplying two polynomials. This involves using the distributive property to multiply each term of one of the polynomials with each term of the other polynomial.

For example, when multiplying [tex]2x2+10x-36[/tex] with 3 we use the distributive property to get [tex]6x2+30x-108[/tex].

To find the product of two polynomials, each term of one polynomial must be multiplied with each term of the other polynomial. The terms of the product of two polynomials will have the same degree as the sum of the degrees of the terms being multiplied together.

For example, when multiplying [tex]2x2-32[/tex] with 4 we use the distributive property to get [tex]8x2-128[/tex]. Here the degree of the product is 2, which is the sum of the degrees of the terms being multiplied together [tex](2+0=2)[/tex].

To multiply two polynomials, we use the distributive property to multiply each term of one polynomial with each term of the other polynomial. The degree of the product will be the sum of the degrees of the terms being multiplied together.

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Complete question:

What is the product of [tex]2x^2+10x-36[/tex] and [tex]3x-4[/tex]?

Answer:

$6.49

Step-by-step explanation:

The original admission price was $5.50, and it increased by 18%. Let's find 18% of 5.50 and then add it to $5.50, meaning $5.50 would increase by 18% (of itself.)

So 18% of 5.50 = 0.99 ( thats 0.18 x 5.50)

Add the 99 cents (0.99) to $5.50

and then you get $6.49

here is the equation I used:

(5.50 x 0.18) + 5.50

hope this helped :)

The combined area of all the circles is 907.46 sq. cm.

The area of a given circle is the amount of space that the circle would cover in a 2 dimensional plane. The area of a circle can be determined by;

area of a circle = π r^2

In the given question, the diameters of the circles form a segment that is 68 cm. Thus;

diameter of one circle = 68/ 4

                       = 17 cm

So that,

radius of each circle = diameter/ 2

                                  = 17/ 2

                                  = 8.5 cm

area of each circle = 3.14 *(8.5)^2

                               = 226.865

The area of the circles combined = 4*226.865

                                   = 907.46

The combined area of all the circles is 907.46 sq. cm.

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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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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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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:

B

Step-by-step explanation:

the answer is B please see on the attached.

Knowing that the drum is a cylinder, we will get that:

Here we can see that the drum is a cylinder, remember that the circular areas of a cylinder of radius R and height H are:

A = 2*3.14*R^2

And the curved surface is:

S = 2*3.14*R*H

Here we can see that:

R = 21cm

H = 9.5cm

a) The area of leather needed is:

A = 2*3.14*(21cm)^2 = 2,769.48 cm^2

b) The area of wood needed is:

S = 2*3.14*21cm*9.5cm = 1,378.42 cm^2

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