Can someone help me with these 3 problems?

In the aerobics classes of 8 will the cost for members and nonmember be the same.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

At a local fitness center, members pay an $8 membership fee and $5 for each aerobic class.

And, Nonmembers pay $6 for each aerobic class.

Now,

We can formulate;

For members, the cost = $8 + 5x

Where, x is the aerobic class.

For nonmembers;

The cost = 6x

We can equate both the equation, we get;

6x = 8 + 5x

Solve for x as;

6x - 5x = 8

1x = 8

x = 8

Thus, In the aerobics classes of 8 will the cost for members and nonmember be the same.

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Danika walks 50 blocks in one week.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

As per the data given,

We have,

Danika lives at 5 blocks from her school.

As Danika walks 5 blocks to and from school, making her round trip

So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.

As Danika walks to and from school 5 days a week,

Hence, she walks 10 blocks * 5 days = 50 blocks in one week.

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a. The equation of the perimeter is x + x + x + 2x + 2x = 42. Option A

b. x = 6 centimeters

c. The lengths are 6 centimeters , 6 centimeters , 6 centimeters  , 12 centimeters  and 12 centimeters respectively.

It is important to note that the formula for calculating the perimeter of a pentagon is expressed as;

Perimeter = 5a

Where: 'a' represents the length of one of its side

From the information given, we have that the perimeter of the geometrical figure is the sum of its sides.

Given the sides;

x , x , x, 2x , 2x

Now, substitute the values into the formula for perimeter

x + x + x + 2x + 2x = 42

collect like terms and add them

7x = 42

Now, make 'x' the subject of formula by dividing both sides by the coefficient of the variable 'x'

We have;

7x/7 == 42/7

x = 6 centimeters

But the length of the sides is determined by substituting the value of x as 6

x = 6 centimeters

x = 6 centimeters

x = 6 centimeters

2x = 2(6) = 12 centimeters

2x = 2(6) = 12 centimeters

Hence, the lengths are 6, 6, 6 , 12 and 12 centimeters respectively.

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The probability that the web site has fewer than 5 million visitors in a single day is 0.7293.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 5 million

μ = mean = 4.56 million

σ = standard deviation = 720,000

z-score = (5 million - 4.56 million) / 720,000

z-score = 440,000 / 720,000

z-score = 0.6111

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score =  0.6111

Using interpolation of values,

probability = 0.7293

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Let's assume the original length of the rectangle is 'l' cm and the original width is 'w' cm. The area of the original rectangle is given as 48 cm^2. It seems there might be an error or inconsistency in the problem statement or calculation.

1. When both the length and width are increased by 4 cm, the area of the larger rectangle is increased by 12 cm^2. To find the length and width of the original rectangle, we can set up an equation and solve for the unknowns.

2. Let's start by considering the original rectangle with length 'l' cm and width 'w' cm. The area of a rectangle is calculated by multiplying its length and width, so the area of the original rectangle is given by A = l * w.

3. According to the problem, the area of the original rectangle is 48 cm^2. Therefore, we have the equation:

l * w = 48   ----(1)

4. Now, let's consider the larger rectangle, where both the length and width are increased by 4 cm. The new length would be 'l + 4' cm, and the new width would be 'w + 4' cm. The area of the larger rectangle is given by A' = (l + 4)(w + 4).

5. The problem states that the area of the larger rectangle is increased by 12 cm^2 compared to the original rectangle. Therefore, we can set up another equation:

(l + 4)(w + 4) = 48 + 12   ----(2)

6. We now have a system of two equations (equations 1 and 2) with two unknowns (l and w). To solve this system, we can substitute equation 1 into equation 2 and simplify:

(l + 4)(w + 4) = 48 + 12

lw + 4l + 4w + 16 = 60

lw + 4l + 4w = 44

7. Using equation 1, we can substitute lw with 48:

48 + 4l + 4w = 44

4l + 4w = 44 - 48

4l + 4w = -4

Dividing both sides by 4, we get:

l + w = -1

8. Since we are dealing with dimensions, the length and width cannot be negative. Therefore, it seems there might be an error or inconsistency in the problem statement or calculation. Please verify the given information to find a solution.

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Answer:

See below, please.

Step-by-step explanation:

\(45 \div ( \frac{3}{4} ) = 60\)

Hence, the number is 60.

Answer:

60

Step-by-step explanation:

¾ of X is 45

what is X!???

Answer:

C

Step-by-step explanation:

m∠7=m∠3

3x-10=2x+5

x=15

m∠3=2(15)+5

      =35

m∠1=m∠3 (vert. opp. ∠)

       = 35

Answer:

72 × 3 = 216m

216 m is the combined length

Note that based on probabilities,

The expected number of Democrats on the committee is 5.

The expected number of states represented on the committee is 26.

The expected number of states such that both of the state's senators are on the committee is 9.09.

a)  The probability that a randomly chosen senator is a Democrat is 50/100 = 1/2.

So, the expected number of Democrats on a committee of size 10 is

1/2 * 10 = 5.

b) The minimum number of   states that can be represented on a committee of size 10 is 2, and the maximum numberis 50.

The expected number of states representedon the committee is the average of these two values, which is (2 + 50)/  2 = 26.

c)  There are 50 states, and each state has 2 senators. So, there are a total of 100 pairs of senators.

The probability that a randomly chosen pair of senators both belong to the same state is 50/100 * 49/99

= 1/11.

The expected number of states such that both of the state's senators are on the committee is 100 * 1/11 = 9.09.

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W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

To show that W=Rn, we need to show that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W.

Let v be any vector in Rn. Since the n non-zero orthogonal vectors span W, we can write v as a linear combination of them:

v = c1v1 + c2v2 + ... + cnvn

where c1, c2, ..., cn are scalars, and v1, v2, ..., vn are the n non-zero orthogonal vectors that span W.

To show that v is in W, we need to show that v is orthogonal to all vectors in W except itself. Since the n non-zero orthogonal vectors are linearly independent, any linear combination of them that is orthogonal to v must be the zero vector.

Therefore, if w is any vector in W that is not equal to v, we have:

=  = c1 + c2 + ... + cn = 0

since v is orthogonal to all the non-zero orthogonal vectors. This means that v is orthogonal to all vectors in W except itself.

Therefore, since v is in W and is orthogonal to all vectors in W except itself, we have shown that any vector in Rn can be written as a linear combination of the n non-zero orthogonal vectors that span W, and hence W=Rn.

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In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given few inequalities and some operations are performed on them

For first inequality:

=> 4 < 7

Multiply both sides by 3, then by 2, then by 4, then by 9

=> 4 *3 * 2 * 4 * 9 < 7  *3 * 2 * 4 * 9

=> 864 < 1512

there is no change in the inequality sign and it is still true.

For the second inequality:

=>11 > -2

Add 3 to both sides, then add 3, then add (-4)

=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)

=> 13 > 0

there is no change in the inequality sign and it is still true.

For the third inequality:

=> -2 ≤ -2

Subtract 6 from both sides, then 8, and then 2

=> -2 -6 -8 -2 ≤  -2 -6 -8 -2

=>  -18 ≤ -18

there is no change in the inequality sign and it is still true.

For the fourth inequality:

=> -4 < 8

Divide both sides by -4

=> -4 / -4 < 8 / -4

Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign

=> 1 > -2

Divide both sides by -2

=> -1/2 < 1

there are two times a change in the inequality sign and it is still true.

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Answer:

48

Step-by-step explanation:

you first have to take the 3 and 5 and multiply them by 6 individually which will give you 18 and 30 respectively, which so happens to be 12 less than the other, then you add them together and you have your answer

The derivative of f(x) = √(x) at the number a is 1/12. The given limit, lim_(h->0) (√(36+h) - 6)/h, represents the derivative of the function f(x) = √(x) at a particular number a.

To find the derivative of f(x) using the limit, we can rewrite the expression as: lim_(h->0) (√(36+h) - 6)/h = lim_(h->0) (√(36+h) - √36)/(h). Now, let's simplify the expression further by rationalizing the numerator: lim_(h->0) [(√(36+h) - √36)/(h)] * [(√(36+h) + √36)/(√(36+h) + √36)]. This simplifies to: lim_(h->0) [(36+h - 36)/(h * (√(36+h) + √36))]. The numerator simplifies to h, and the denominator remains the same. lim_(h->0) [h/(h * (√(36+h) + √36))].

Now, cancel out the h in the numerator and denominator: lim_(h->0) [1/(√(36+h) + √36)]. Taking the limit as h approaches 0, we obtain: 1/(√(36+0) + √36) = 1/(6 + 6) = 1/12. Therefore, the derivative of f(x) = √(x) at the number a is 1/12.

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Step-by-step explanation:

here you go also I like your profile picture classroom of elite !

Answer: the first one

Step-by-step explanation:

No constant rate of change

Answer:

#1 - 11

#2 - 5

Step-by-step explanation:

#1 - This is really simple, as long as you don't think of it as numbers. The numbers 5 and 3 are being added to a number to make 19, so all you have to do is 19 - 5 - 3 or 19 - 8, which equals 11. So the certain number is 11.

#2 - The equation for this problem is (3 x ?) - 5 = 10. This equation is formed because you are subtracting 5 from 3 times a number, and to do all of this first, you need to figure out what 3 times a number equals (so it goes into the parentheses). From there, all you need to do is give a value that would substitute the question mark (normally you use a variable like n, x, y, etc.). This value would be 5, because 3 x 5 = 15 and 15 - 5 = 10.

:DDDDDDDDD

The value of x is 10.

Triangle is a plane figure with three angles and three straight sides.

Given information: In ΔABC, AD is the angle bisector, AB = 8, BD =( x+4),

DC = (2x+1), and AC = 12

The angle bisector theorem states that an angle bisector divides the opposing side of the triangle into two segments that are proportional to the other two sides.

In ΔABC, AD is an angle bisector, By using the angle bisector theorem, we get

BD/DC = AB/BC

(x+4) / (2x+1) = 8/12

By Cross Multiplying, we get

12(x+4) = 8(2x+1)

12x + 48 = 16 x + 8

After solving the above equation we get,

4x = 40

x = 10 (By Dividing 40 by 4 )

Therefore the value of x is 10.

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The average time Americans spend watching TV per day is reported to be approximately 300 minutes, following a normal distribution with a standard deviation of 26 minutes.

To address this question, we can use the provided information to describe the distribution of minutes per day spent watching TV by Americans.

Given that the distribution follows a normal distribution, we can assume that the data is symmetrically distributed around the mean. The mean of the distribution is given as 300 minutes.

The standard deviation, which measures the spread of the data, is stated as 26 minutes. This indicates that most people fall within one standard deviation of the mean.

Using the properties of a normal distribution, we can make various probabilistic statements. For example, approximately 68% of Americans would spend between 274 minutes (mean - 1 standard deviation) and 326 minutes (mean + 1 standard deviation) watching TV per day.

By understanding the characteristics of the normal distribution and the provided parameters (mean and standard deviation), we can analyze and make predictions about the amount of time Americans spend watching TV on a daily basis.

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Answer:

a

Step-by-step explanation:

y=4x+6 is the equation simplified and that is what the graph is showing.

Answer:

A  y-2=4(x+1)

Step-by-step explanation:

y-2=4(x+1)

Statement a is true; if b and d are odd, then f is odd. Statement b is false; if b and d are even, f can be even or odd.


a. To prove that if b and d are odd, then f is odd, we analyze the addition of two rational numbers with odd denominators. Let's rewrite s:
s = q + r = a/b + c/d = (ad + bc) / (bd)

Since b and d are odd, their product (bd) is also odd. Now, to have a fraction in the lowest terms, the numerator and denominator must be coprime (i.e., their greatest common divisor is 1). If (ad + bc) were even, then (ad + bc) and (bd) would share a common factor of 2, contradicting the lowest terms requirement.

Therefore, (ad + bc) must be odd. An odd numerator and an odd denominator result in an odd f.

b. If b and d are even, we cannot guarantee that f is even. For example, consider q = 1/2 and r = 1/4:
s = 1/2 + 1/4 = 3/4

Here, both b and d are even, but f is odd. So, statement b is false.

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Graph 4 would be the correct answer because the line appears to be three spaces above coordinate (0, 0).

Answer:

k = i√ 5 , -i√ 5

Step-by-step explanation:

3 + kx^2 + 2 = ?

3 + k(1)^2 + 2 = ?

5 + k(1)^2 = ?

5 + k^2 = ?

k^2 = -5

k = i√ 5 , -i√ 5

Answer:

8

Step-by-step explanation:

This is because the expression is already in decimal form

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope / gradient

c is the y intercept

y = 3x + 7

Comparing this equation with the general form above

Gradient of the line = 3

2y - 6x = 8

Divide both sides by 2

We have

y - 3x = 8

To make y the subject move 3x to the right side of the equation

That's

y = 3x + 8

Comparing with the general form above that's y = mx + c

The gradient = 3

y = 3x + 7

A(2 , y ) , B( x , 4)

Since they lie on the line we can substitute their values into the equation to find the missing points

For A(2 ,y)

We have

y = 3(2) + 7

y = 6 + 7

For B( x , 4)

4 = 3x + 7

3x = 4 - 7

3x = - 3

Divide both sides by 3

Hope this helps you

Use pythagoras theorem, a²+b²=c², where c is the hypotenuse, and a and b are the smaller sides.

Therefore, (2√2)²-(√6)²=x²

therefore, square rooting both sides, noting that the square root, which is usually ±, is only positive since it's a length, x = √2

and (√10)²+(√17)²=x²

x=√27

Answer: 9x-15

Step-by-step explanation:

Given

34x-(25x-3)-18

Expand parenthesis

34x-25x+3-18

Put like terms together

(34x-25x)+(3-18)

Combine like terms

9x-15

Hope this helps!! :)

Please let me know if you have any questions

Answer:

  y ≤ \(\frac{1}{2} x + 2\)

Step-by-step explanation:

≤ because the area below the line is shaded.

Answer: 6.78%

Step-by-step explanation:

You just add the 1.50% to the 5.28% to get 6.78%.

Phil gets paid 10 hours and Mary gets paied $300 a week, then the ratio of Phil to Mary is...

I wrote the ratio, but I dont really know the answer...