Evaluate 24-(7-2+x) when x=4
(show work) ​

The sum of Peter, Richard, and John's ages is 191.

We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)

The ratio of John's age to Peter's age is = 7/12 --(ii)

Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)

Using the value of (i),(ii),(iii), we get -

Age of Peter = (5*12)/(8*12) = 60/96

= 60 years of age

Age of John = (7*5)/(12*5) = 35/60

=35 years of age

From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age

Hence the sum of their ages is = 96+35+60

= 191

Therefore, we know that the sum of their ages is 191.

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Answer:

2 hours

Hope its right

Randomly selecting a white golf ball first and then a white golf ball second are independent events.

What do you mean by dependent events?

Events that are dependent upon prior events are called dependent events. The results of earlier events have an impact on these current ones. For example, two or more events that are interdependent are referred to as dependent events.

It is given that in the beginning we have 3 white balss and 2 yellow balls

Total number of balls = 3 + 2 = 5

Probability of first selecting a white ball = 3/5

Now remaining white balls = 3 - 2 = 1

Remaining total balls = 5 - 1 = 4

Probability of selecting second white ball = 2/4

Probability of selecting a white golf ball first and then a white golf ball second = 3/5 × 2/4 = 3/10

Both the events are dependent as if we select first white ball, then it will change the number of white balls for selecting second time.

Therefore,  randomly selecting a white golf ball first and then a white golf ball second are independent events.

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Answer:

Step-by-step explanation:

Even functions are symmetrical about the y-axis: f (x)=f (-x). Odd functions are symmetrical about the x- and y-axis: f (x)=-f (-x)

Let's test it:

Even:  f(x)=f(-x)   =>     f(3)=f(-3)     =>    -8≠-4    not even

Odd:  f(x)=f(-x)     =>      f(3)= -f(-3)    =>    -8≠ -(-4)   not odd

neither

Answer:

B) \(q=\pm\frac{5\sqrt{p}}{4p}\)

Step-by-step explanation:

\(16pq^2=25\\pq^2=\frac{25}{16}\\q^2=\frac{25}{16p}\\q=\pm\frac{5}{4\sqrt{p}}\\q=\pm\frac{5\sqrt{p}}{4p}\)

Make sure to rationalize the denominator in the last few steps

The inequality for finding the values of x for which the area of the rectangle is greater than the area of the triangle is 2x + 6 < x².

The area of the rectangle is given by the formula A = l × w, where l is the length and w is the width of the rectangle. Therefore, for the rectangle in question, the area is given by A = (x + 3)(x - 1) = x² + 2x - 3. On the other hand, the area of the triangle is given by the formula A = 1/2bh, where b is the base and h is the height of the triangle. Therefore, for the triangle in question, the area is given by A = 1/2(x - 3)4 = 2x - 6. To find the values of x for which the area of the rectangle is greater than the area of the triangle, we set the inequality A(rectangle) > A(triangle). Thus,x² + 2x - 3 > 2x - 6x² > 6x - 3x² > 9x - 3(x - 3)(x + 1) < 0Therefore, the inequality for finding the values of x for which the area of the rectangle is greater than the area of the triangle is 2x + 6 < x².

The Latin word rectus, which means "right" or "straight," is the source of the rect in the rectangle. A rectangle has straight sides because of its right angles. Rectitude, which refers to moral uprightness, is an additional word with the same root.

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Answer:

d. 0.85m + 2.50

Step-by-step explanation:

In the figure attached, the complete question is shown.

We can see in the table that $2.50 is a fixed charge, that is, it is not modified by any variable. On the other hand, for each travelled mile, the cost of the travel increases $0.85 ($0.75 by mileage charge + $0.1 by city gas tax). Then, if m miles are travelled, the cost of the travel increases 0.85*m

Answer:

We conclude that the gradient of the line is: 2/3

Step-by-step explanation:

It is clear that the given graph represents a line or linear function.

From the graph, taking two points

Finding the gradient or slope of the line

Using the formula

Gradient = m =  [y₂ - y₁] /  [x₂ - x₁]

                      =  [-2 - 0] / [0 - 3]

                      = -2 / -3

                       = 2/3

Thus, the slope of the line = m = 2/3

Therefore, we conclude that the gradient of the line is: 2/3

Answer:

w = -7z/2

Step-by-step explanation:

We need to solve for w in terms of z.

The equation given is:

5w + 9z = 2z + 3w

Collect like terms:

5w - 3w = 2z - 9z

2w = -7z

w = -7z/2

Answer:

option A (-7/2z)

Step-by-step explanation:

The mix fraction as an improper fraction is 11/7.

We have,

Mix fraction:

1(4/7)

This can be simplified as an improper fraction:

= {(7 x 1) + 4} / 7

= (7+ 4) / 7

= 11/7

Thus,

The mix fraction as an improper fraction is 11/7.

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In 10,000 independent tosses of a coin and the coin landed on heads 5800 times, is it reasonable to assume that the coin is not fair and may be biased towards heads.

In order to determine if the coin is fair or not, we need to calculate the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair.

The probability of getting a head on any one toss of a fair coin is 0.5. The number of heads in 10,000 tosses is a binomial random variable with parameters n=10,000 and p=0.5. We can use the normal approximation to the binomial distribution to calculate the probability of getting 5800 or more heads.

The mean of the binomial distribution is np = 5000 and the standard deviation is sqrt(np(1-p)) = 50.

We can standardize the variable X = number of heads in 10,000 tosses by subtracting the mean and dividing by the standard deviation:

Z = (X - 5000) / 50

The probability of getting 5800 or more heads can be calculated as:

P(X >= 5800) = P(Z >= (5800-5000)/50)

Using a standard normal table or calculator, we find that P(Z >= 1.6) = 0.0548.

This means that the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair is only 0.0548, which is quite low.

Therefore, it is reasonable to conclude that the coin is not fair and may be biased towards heads.

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The paper clip costs $0.05 and the folder Costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

Let's solve this problem step by step:

Let's assume the cost of the paper clip is x dollars.

According to the information given, the folder costs $1.00 more than the paper clip, so the cost of the folder would be (x + $1.00).

The total cost of the folder and the paper clip is $1.10, so we can write the equation:

x + (x + $1.00) = $1.10

Combining like terms, we have:

2x + $1.00 = $1.10

Subtracting $1.00 from both sides of the equation, we get:

2x = $0.10

Dividing both sides by 2, we find the value of x:

x = $0.10 / 2

x = $0.05

Therefore, the paper clip costs $0.05.

In summary, the paper clip costs $0.05 and the folder costs $1.00 more, which is $1.05. Together, they add up to the total of $1.10.

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first we miltiply by the number of seconds on a hour(3600) to change the unitis to hours

so the velocity is 199882.8 meters/hour

now transform the meters on kilometers dividing between 1000

the new velocity is 199.8828 kilometers/hour

The correct interpretation of this p-value with an alpha level of 0.05 is explain below.

P-value is the margin of error importance inside a factual speculation test, addressing the likelihood of the event of a given occasion.

We have, P-value =0.07

Level of significance = 0.05

We know that,

P-value is less than level of significance, then H® is rejected,smaller the p-value longer the evidence that you should reject the null hypothesis.

Now P-value is greater than 0.05.

With a p-value greater than 0.05, fail to reject the H®.Look at multiple comparison of each Level of significance.

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Answer:

The method of substitution involves three steps:

Solve one equation for one of the variables.

Substitute (plug-in) this expression into the other equation and solve.

Resubstitute the value into the original equation to find the corresponding variable.

Step-by-step explanation:

Answer:

14 minuts.

Step-by-step explanation:

350 divided by 25 is 14.

Please mark brainiest tysm

Answer:

77

Step-by-step explanation:

(6 + 3)² is same as (a +  b)²

Since (a +  b)² = a² + 2ab + b²

Therefore,

(6 + 3)² - 4

= (36 + 36 + 9) - 4

= 81 - 4

= 77  

Hi there! Hopefully this helps!

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Since PEMDAS exists, we will do parentheses "(6+3)" first to get 9.

Then we do the exponent which is:

\(9^{2}\) = 81.

Then we subtract.

81 - 4 = 77.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More broken down explanation:

\((6+3)^{2} -4\)

Add 6 and 3 to get 9.

\(9^{2} - 4\) ≈ \(77\)

Calculate 9 to the power of 2 and get 81.

\(81-4\) = \(77\)

The ratio of the volume of sphere B to the volume of sphere A is (C) 125 if the radius of sphere B is five times that of sphere A.

The correct option is (C)

A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.

The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.

Let's take the 2 radii:

x where x is 5.

5x where 5x is 25.

Now, calculate the volume of the sphere in both cases.

We know,

Formula of volume of sphere :

V = 4/3πr²

Where r = 5.

V = 4/3πr²

V = 523.59878

Round off: 524 units²

Where r = 25.

V = 4/3πr²

V = 65449.84695

Rounding off: 65450 units²

Now, divide to find the ratio:

65450/524 = 124.90

Rounding off: 125

Therefore, the ratio of the volume of sphere B to the volume of sphere A is (C) 125 if the radius of sphere B is five times that of sphere A.

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Correct option for sets of numbers with sufficient for the calculation is;

(3) p(A = 1), p(B = 1 | A = 1), p(C = 1 | A = 1)

A more detailed explanation of the answer.

(a) In order to calculate p(A = 1 | B = 1, C = 1), we need to find the joint probability p(A = 1, B = 1, C = 1) and divide it by p(B = 1, C = 1). To find the joint probability, we can use the following formula:

p(A = 1, B = 1, C = 1) = p(A = 1) * p(B = 1 | A = 1) * p(C = 1 | A = 1, B = 1)

Based on this formula, we can see that none of the given sets are sufficient for the calculation.

(b) Now that we know p(B | A, C) = p(B | A), the joint probability formula becomes:

p(A = 1, B = 1, C = 1) = p(A = 1) * p(B = 1 | A = 1) * p(C = 1 | A = 1)

In this case, set (3) is sufficient for the calculation:

(3) p(A = 1), p(B = 1 | A = 1), p(C = 1 | A = 1)

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Answer:

Screenshot 1 = Option B (5x-1)²

Screenshot 2 = (x+9)(x+9)

Screenshot 3 = Option 3 100x²-20x+1

Step-by-step explanation:

Screenshot 1 -

(5x-1)² = (5x-1)(5x-1)

5x · 5x = 25x²

5x · -1 = -5x

5x · -1 = -5x

(-1) · (-1) = 1

25x²- 5x- 5x + 1 = 25x² - 10x + 1

Screenshot 2 -

(x+9)(x+9)

x · x = x²

x · 9 = 9x

x · 9 = 9x

9 · 9 = 81

x² + 9x + 9x + 81 = x² + 18x + 81

Screenshot 3 -

100x²-20x+1

(10x-1)(10x-1)

10x · 10x = 100x²

10x · (-1) = -10x

10x · (-1) = -10x

(-1) · (-1) = 1

100x² - 10x - 10x + 1 = 100x² - 20x +1

The solution for A'0 is as follows:

A'0 = (βR^(-1/γ) / (1 - R^(-1/γ)))^(1/γ)

We start with the equation (A0 - A0')^(-γ) = βR(RA0')^(-γ). To solve for A'0, we isolate it on one side of the equation.

First, we raise both sides to the power of -1/γ, which gives us (A0 - A0') = (βR(RA0'))^(1/γ).

Next, we rearrange the equation to isolate A'0 by subtracting A0 from both sides, resulting in -A0' = (βR(RA0'))^(1/γ) - A0.

Finally, we multiply both sides by -1, giving us A'0 = -((βR(RA0'))^(1/γ) - A0).

Simplifying further, we get A'0 = (βR^(-1/γ) / (1 - R^(-1/γ)))^(1/γ).

Complete question - Solve for A'0, given the equation (A0 - A0')^(-γ) = βR(RA0')^(-γ),

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Answer:

Their coefficient have the same number but with opposite sign

Step-by-step explanation:

We can tell that the two coefficient will add to zero because they have the same value but opposite signs.

  When two numbers are of the same value but with opposite sign, they add up to zero.

  The given numbers are;

             -2x²   and  2x²

Coefficient is the number before the variable. Here, the variable is x,

            -2x² = -2

               2x² = 2

    -2 + 2  = 0

the 60th percentile of breaking strength for this type of fishing line is

k= 6.64

assume that k pounds is the both percentile of breaking strength for this type of finishing line

p( x<k) = 0.60

p( x- 6.44/0.75 < k- 6.44/0.75)= 0.60

then k-6.44 /0.75 = 0.26

thus k= 6.64

Hence , the 60th percentile of breaking strength for this type of fishing line is 6.64

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Without spectacles, Witney Pete has a 5/10 chance of hitting the bullseye. Witney Pete could strike the bullseye with his spectacles 0.7 of the time. This likelihood is far higher than hitting the bullseye without glasses. the probability that Pete hits five or fewer of his next ten shots is approximately 2.487.

Generally, To find the probability that Pete hits five or fewer of his next ten shots, we need to find the probability that he hits exactly 0, 1, 2, 3, 4, or 5 bull's eyes.

The probability that Pete hits exactly k bull's eyes in n throws is given by the binomial distribution:

P(k bull's eyes in n throws) = (n choose k) * p^k * (1-p)^(n-k)

where p is the probability of hitting a bull's eye on a single throw and n choose k is the binomial coefficient, which is equal to n!/(k!(n-k)!).

Substituting the given values, we get:

P(0 bull's eyes in 10 throws) = (10 choose 0) * (0.7)^0 * (0.3)^10 = 0.028 P(1 bull's eyes in 10 throws) = (10 choose 1) * (0.7)^1 * (0.3)^9 = 0.189 P(2 bull's eyes in 10 throws) = (10 choose 2) * (0.7)^2 * (0.3)^8 = 0.462 P(3 bull's eyes in 10 throws) = (10 choose 3) * (0.7)^3 * (0.3)^7 = 0.605 P(4 bull's eyes in 10 throws) = (10 choose 4) * (0.7)^4 * (0.3)^6 = 0.501 P(5 bull's eyes in 10 throws) = (10 choose 5) * (0.7)^5 * (0.3)^5 = 0.302

The probability that Pete hits five or fewer bull's eyes in his next ten shots is the sum of the probabilities of hitting exactly 0, 1, 2, 3, 4, or 5 bull's eyes:

P(hitting 5 or fewer bull's eyes in 10 shots) = 0.028 + 0.189 + 0.462 + 0.605 + 0.501 + 0.302 = 2.487

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The admissions office wishes to estimate the average cost of textbooks for all students, represented by the parameter μ (the population mean).

There are steps followed to determine the parameter the admissions office wishes to estimate:

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Recall that 60 minutes makes 1 hour

Hence 4 hours will be

= 60 * 4

= 240 minutes

If in 15 minutes, she can pick 1/3 pounds of berries

then 240 minutes

= 240/15 * 1/3

= 16/3 pounds

= 5 1/3 pounds

The possible roots of the given polynomial function are 5, -2 and -1/2 which are obtained by using the Rational Root Theorem.

To determine the possible rational roots of the polynomial function F(x) = 4\(x^3\) - 6\(x^2\) + 9x + 10, we can apply the Rational Root Theorem. The possible rational roots are all the factors of the constant term (10) divided by all the factors of the leading coefficient (4).

For the given polynomial function F(x) = 4\(x^3\) - 6\(x^2\) + 9x + 10, the constant term is 10 and the leading coefficient is 4.

The factors of 10 are ±1, ±2, ±5, and ±10. The factors of 4 are ±1 and ±2.

Therefore, the possible rational roots of the polynomial function are all the combinations of the factors of 10 divided by the factors of 4. These include ±1/1, ±2/1, ±5/1, ±10/1, ±1/2, ±2/2, ±5/2, and ±10/2.

Simplifying these fractions, we find that the possible rational roots of the polynomial function are ±1, ±2, ±5, ±10, ±1/2, ±5/2, and ±10/2.

Hence, these are the possible rational roots of the given polynomial function.

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The complete question is:

According to the rational root theorem, which of the following are possible roots of the polynomial function below?

F(x) = 4\(x^3\) - 6\(x^2\) + 9x + 10

A. 6

B. 5

C. -1/2

D. 5/4

E. 1/3

F. -2