estimate the area of the circle to the nearest unit.

Answer:

x < 3

Step-by-step explanation:

4x -7 < 5

4x < 12

x < 3

Answer:x < 3

Step-by-step explanation:4x -7 < 5

4x < 12

x < 3

The solution to the equation is x = 4 when the given equation in the question is 24 + 0.44x = 19 + 1.69x.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by collecting the x terms on one side and the constant terms on the other side, as follows:

24 + 0.44x = 19 + 1.69x

Subtract 0.44x from both sides:

24 = 19 + 1.25x

Subtract 19 from both sides:

5 = 1.25x

Divide both sides by 1.25:

4 = x

Therefore, the solution to the equation is x = 4. To check our answer, we can substitute x = 4 back into the original equation and verify that both sides are equal:

24 + 0.44(4) = 19 + 1.69(4)

26.76 = 26.76

This confirms that x = 4 is indeed the solution to the equation.

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The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.

Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.

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Answer:

x = -10/3

Step-by-step explanation:

6(2x – 1) – 12 = 3(7x + 4)

12x - 6 - 12 = 21x + 12

12x - 18 = 21x + 12

-9x - 18 = 12

-9x = 30

x = -30/9

x = -10/3

Answer:

Step-by-step explanation:

[tex]6(2x -1) - 12 = 3(7x + 4)[/tex]

   [tex]12x-6-12=21x+12[/tex]         (multiplied to remove brackets)

         [tex]12x-18=21x+12[/tex]        

                 [tex]12x=21x+30[/tex]          (+18 to both sides of the equation)

                 [tex]-9x=30[/tex]                   (-21x both sides)

                      [tex]x=-\frac{30}{9}=-\frac{10}{3}[/tex]    (÷-9 both sides and then simplified the

                                                    fraction)

None of the answers are correct

The coordinates of Point V, given the base of the triangle and the coordinates of the triangle is  (4, 3).

To find the coordinates of point V, which is the intersection of the height YV and the base XZ, we first need to find the equation of the line XZ and then the equation of the perpendicular line YV.

First, find the slope of XZ:

m_XZ = (y2 - y1) / (x2 - x1) = (1 - 5) / (6 - 2) = (-4) / (4) = -1

We can plug in the coordinates of point X (2, 5) to find b:

5 = -1 x 2 + b

5 = -2 + b

b = 7

So the equation of line XZ is:

y = -x + 7

The equation of line YV is:

y = x - 1

To find the intersection point V, we need to solve the system of equations:

y = -x + 7

y = x - 1

-x + 7 = x - 1

7 = 2x - 1

x = 4

Now plug x back into either equation to find y. We'll use the second equation:

y = 4 - 1

y = 3

So the coordinates of point V are (4, 3).

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Answer:

x = y = 5

Step-by-step explanation:

This triangle and its markings show that the acute angles are equal. Given that it is a right triangle, this is a 45-45-90 triangle. This also means that the values of x and y are equal. Note that for any triangle, if two angles are equal, then their corresponding side lengths are also equal. The side lengths for this type of triangle follow the pattern s - s - s√2 where the first two are side lengths and last value is the length of the hypotenuse. (s represents the length of a side)

We want to find x and y, so we need the value of s.

s√2 = 5√2
s = 5

Therefore, x = 5, y = 5.

The probability that the child must wait at least 9 minutes on a given morning is approximately 0.2231.

Let X be the waiting time at the bus stop. We know that X is exponentially distributed with mean 6 minutes. Therefore, the probability density function (PDF) of X is given by:

f(x) = 1/6 * e^(-x/6) for x >= 0

To find the probability that the child must wait at least 9 minutes, we need to calculate the following probability:

P(X >= 9) = integral of f(x) from 9 to infinity

= integral from 9 to infinity of (1/6 * e^(-x/6)) dx

Using integration by substitution, let u = x/6, du = 1/6 dx, so that:

P(X >= 9) = integral from 3/2 to infinity of e^(-u) du

= [e^(-u)] evaluated from 3/2 to infinity

= e^(-3/2)

≈ 0.2231

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Answer:

the answer will be: C. 1/25

Step-by-step explanation:

There are five possible values for each coupon, so there are 5 x 5 = 25 possible combinations of food and pharmacy coupons. Each combination is equally likely, so the probability of getting any particular combination is 1/25.

There is only one combination that gives a $0.25 food coupon and a $0.40 pharmacy coupon, so the probability of getting this combination is 1/25.

Therefore, the probability that a customer receives a $0.25 food coupon and a $0.40 pharmacy coupon at the checkout is 1/25 or 0.04 (4%).

In this case, we are given a coupon-printing machine at the checkout of a grocery store prints one food coupon and one pharmacy coupon for each customer: $0.25, $0.30, $0.40, $0.45, or $0.50. It is asked in the problem to give the probability that a customer receives a $0.25 food coupon and a $0.40 pharmacy coupon at the checkout. Since the customer chose the $0.25 food coupon and a $0.40 pharmacy coupon,

Then the probability is 2/5. this is equal to 40%.

Answer:

The correct answer is Option A, (x | 57 < x < 67}. This means that Darnell could spend any amount of time between 57 and 67 minutes on homework one day, give or take 5 minutes.

Step-by-step explanation:

The x-intercepts of the quadratic function shown is (−2, 0) and (2, 0). Hence, option D is correct.

A quadratic equation is a second-degree polynomial equation of the form [tex]\rm ax^{2} + bx + c = 0[/tex], where x is the variable and a, b, and c are constants, with a ≠ 0.

Quadratic equations can have one, two, or no real solutions depending on the values of the constants a, b, and c. The solutions of a quadratic equation can be found by using the quadratic formula.

None of the given options are correct as they all describe x-intercepts that lie on either the x-axis or y-axis.

For a quadratic function in standard form, [tex]\rm y = ax^{2} + bx + c[/tex], the x-intercepts can be found by setting y = 0 and solving for x using the quadratic formula.

a. (0, −2) and (0, 1),

Here x - intercepts is 0 as x vale in both points are 0

b. (0, −2) and (0, 2)

Here x - intercepts is 0 as x value in both points are 0

c. (−2, 0) and (2, 0)

x - intercepts are -2 and 2 and is the correct answer.

d.  (−2, 0) and (1, 0)

x - intercepts are -2 and 1 and is the incorrect answer.

Thus, the x-intercepts of the quadratic function shown is (−2, 0) and (2, 0). Hence, option D is correct.

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What are the x-intercepts of the quadratic function?

(graph in attachment)

a. (0, −2) and (0, 1)

b. (0, −2) and (0, 2)

c. (−2, 0) and (2, 0)

d. (−2, 0) and (1, 0)

Answer:

Step-by-step explanation:

Mason subtracted 5 from each side instead of adding 5.

x - 5 < 11

x - 5 + 5 < 11 + 5

x < 16

The number line will have an open circle at 16 since it does not include

16.  It will be shaded to the left from that open circle as it includes

all values less than 16.  

The amount of radioactive goo that will remain after 29 minutes is approximately 58.862 grams.

To solve this problem, we need to use the formula for radioactive decay

N(t) = N0 × e^(-λt)

Where

N(t) is the amount of radioactive material at time t

N0 is the initial amount of radioactive material

λ is the decay constant

t is the time elapsed

We can find λ using the half-life of the substance. Let's assume that the half-life of the radioactive goo is 25 minutes. This means that after 25 minutes, half of the initial amount will remain, and after another 25 minutes, half of that remaining amount will remain, and so on.

To find λ, we can use the formula

λ = ln(2) / half-life

λ = ln(2) / 25

λ = 0.0278 (rounded to four decimal places)

Now we can use the formula for N(t) to find the amount of radioactive material after 29 minutes

N(29) = 132 × e^(-0.0278 × 29)

N(29) = 132 × e^(-0.8072)

N(29) = 132 × 0.4465

N(29) = 58.862 grams (rounded to three decimal places)

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The given question is incomplete, the complete question is:

At the beginning of an experiment, a scientist has 132 grams of radioactive goo. After 75 minutes, her sample has decayed to 2.0625 grams . How many grams of goo will remain after 29 minutes?

Answer:

Step-by-step explana add

The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.85, 0.976).

Rhythm is the pattern of regular or irregular pulses or beats in music or poetry. It is the underlying structure in music, the beat or pulse that provides the framework for a musical composition. It is also the sense of movement created by the alternation of different sounds and silences.  Rhythm can be described as a fundamental element of all forms of music and art, as it is the primary way in which music is perceived and experienced.

This can be calculated using the following formula:
p ± (Z *√( p * (1- p ) ) /√n )
Where:
p = sample proportion = 85/125 = 0.68
Z = z-score for 99% confidence interval = 2.575
n = sample size = 125
The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.85, 0.976).

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The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.783, 0.577).

A confidence interval is the mean of an estimate minus the variability of that estimate. This is the range of values ​​within which the estimate will fall within a certain level of confidence when the test is repeated. Confidence is an alternative way of expressing probability in statistics.

This can be calculated using the following formula:

p ± (Z ×√( p × (1- p ) ) /√n )

Where:

p = sample proportion

p = 85/125

p = 0.68

Z = z-score for 99% confidence interval

Z = 2.575

n = sample size

n = 125

Now, substitute the values:

0.68 ± (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )

For 0.68 + (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )

= 0.783

For 0.68 - (2.575 ×√( 0.68 × (1- 0.68 ) ) /√125 )

= 0.577

The 99% confidence interval for the proportion of people who cannot repeat the rhythm after one minute is (0.783, 0.577).

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Step-by-step explanation:

Based on the information you provided, an actuary earns $94,740 per year while a nurse practitioner earns $89,960 per year. The difference in their annual salaries is $4,780. Over 20 years, an actuary would earn $95,600 more than a nurse practitioner (20 years * $4,780/year = $95,600).

The sum of 1/6 and 1/4 is greater than 1/2.

The sum of 1/6 and 1/4 is greater than 1/2. This can be demonstrated with a simple formula and calculation.

To begin, the fraction 1/6 can be written as the decimal 0.1667, and the fraction 1/4 can be written as the decimal 0.25. When these two decimals are added together, the sum is 0.4167. This number can then be converted back into a fraction. 0.4167 can be written as 41/99. When simplified, this fraction is 41/99, which is greater than 1/2 when written as a fraction.

This can be demonstrated with a formula as well. The sum of 1/6 and 1/4 can be written as the equation 1/6 + 1/4 = x. When this equation is solved, the sum is x = 5/12. This fraction can be simplified to 41/99, which is greater than 1/2.

In conclusion, the sum of 1/6 and 1/4 is greater than 1/2. This can be shown with a simple calculation and formula.

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Answer: Geometric and common difference is 1/3

Step-by-step explanation:

a. The minimum number of dogs which could have a mass of more than 26 kg is of: 5.

b. The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table shows the number of times that each value, or values in each range, appears in the data-set.

A number of 11 weights are between 20 and 30, hence:

Full words "The table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than 26 kg

b) Work out the maximum number of dogs that could have a mass of more than 26 kg

Mass, x (kg)  Frequency

0≤x≤10    4

10≤x≤20    8

20≤x≤30   11

30≤x≤40   5

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Answer:

x=0,[tex]\frac{9}{2}[/tex]   Decimal Form: 0, 4.5

Step-by-step explanation:

1 )Move all terms to one side.

56[tex]x^{2}[/tex]-252x=0

2 )Factor out the common term 28x.

28x(2x−9)=0

3 )Solve for x

x=0,[tex]\frac{9}{2}[/tex]   Decimal Form: 0, 4.5

Answer:

A

Step-by-step explanation:

Proofs attached to answer

Answer: y=mx+c

m is the gradient, and c is the y-intercept.

lmk if u want me to try to solve it::} (try)

Step-by-step explanation:

hope you understood the answer

Answer: 243.617

Step-by-step explanation:

300 = [tex]x[/tex] x (1 + 7/100/4)^(4 x 3)

300 = [tex]x[/tex] x (1.0175)^12

300 = [tex]x[/tex] x 1.231

[tex]x[/tex] = 300/1.231

[tex]x[/tex] = 243.617

The distance between her house and her mother's house =135 miles

Let the entire distance be 3x

Normally that takes 180 minutes

speed would be  (3x)/180  =  x/60   miles per minute

It would take 60 minutes to go the first distance of x and 276-60 = 216 minutes to the next 2x miles

She hits a bad snowstorm and reduces her speed by 20 miles per hour.

So her speed would be, (x - 20)/60 miles

for given situation we formulate an equation,

(x - 20)/60 = 2x/216

(x - 20)/10 = x/18

18x - 360 = 10x

8x = 360

x = 45 miles

So, the total distance would be:

3x = 3 × 45

    = 135 miles

Therefore, the required distance is 135 miles

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This means that there is a 25% chance that the salesperson will make no more than 3 sales in an hour.

A salesperson is a professional who works to solicit and close sales with customers. They typically work in retail stores, warehouses, or other businesses where customers come to purchase goods or services. Salespeople focus on providing excellent customer service and developing relationships with potential and existing customers. They must be able to build trust with their customers and understand their needs in order to make successful sales. They must also be able to use different techniques to present products, services, and solutions to customers.

The probability of making no more than 3 sales in an hour is calculated by dividing the total number of possible outcomes with 3 or fewer sales (in this case, 4) by the total number of possible outcomes (16). This gives us a probability of 4/16, or 25%. This means that there is a 25% chance that the salesperson will make no more than 3 sales in an hour.

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By the end of the hour he will have made no more than 3 sales and the probability is  25%  or 1/4.

What is probability?

Probability means possibility of something or some incident. In this part of mathematics we deals with the occurrence of a random event. The value is in between zero and one.

The probability of making no more than 3 sales in an hour is calculated by dividing the total number of possible outcomes with 3 or fewer sales.

twenty minutes into the hour, the salesperson has made his first sale.

here the occurrence of 3 or fewer sales is 4

and the total number of possible outcomes is 16

so the probability is 4/16= 1/4

that is 25%.

Hence, there is a 25% chance that the salesperson will make no more than 3 sales in an hour also the probability is 1/4.

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The expected grade for a student working six hours on the project is given as follows:

b) 90.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function that predicts the grade of a student working x hours in the project is given as follows:

y = 5x + 60.

Hence, for a student working six hours, the expected grade is given as follows:

y = 5(6) + 60

y = 90.

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Step-by-step explanation:

To find the vertices of triangle ABC after the translation T = (2/3), we can use the following formula:

(x', y') = (x + 2/3, y + 2/3)

where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the translated point.

Using this formula, we can translate each vertex of triangle A'B'C' back to its original position:

Vertex A:

x = 3 - 2/3 = 7/3

y = 1 - 2/3 = 1/3

Therefore, the coordinates of vertex A in triangle ABC are (7/3, 1/3).

Vertex B:

x = 1 - 2/3 = 1/3

y = -2 - 2/3 = -8/3

Therefore, the coordinates of vertex B in triangle ABC are (1/3, -8/3).

Vertex C:

x = 1 - 2/3 = 1/3

y = 2 - 2/3 = 4/3

Therefore, the coordinates of vertex C in triangle ABC are (1/3, 4/3).

Therefore, the vertices of triangle ABC are (7/3, 1/3), (1/3, -8/3), and (1/3, 4/3).

Answer:

Let A(x1, y1), B(x2, y2), and C(x3, y3) be the vertices of triangle ABC.

Under the translation T, each point (x, y) is mapped to the point (x + 2/3, y), which means that the new coordinates of A, B, and C will be:

A' = (x1 + 2/3, y1)

B' = (x2 + 2/3, y2)

C' = (x3 + 2/3, y3)

We are given the coordinates of A' (3, 1), B' (1, -2), and C' (1, 2), so we can set up a system of equations to solve for the coordinates of A, B, and C:

x1 + 2/3 = 3 => x1 = 2 1/3

y1 = 1

x2 + 2/3 = 1 => x2 = 1/3

y2 = -2

x3 + 2/3 = 1 => x3 = 1/3

y3 = 2

Therefore, the vertices of triangle ABC are A(2 1/3, 1), B(1/3, -2), and C(1/3, 2).

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We can be reasonably confident that our estimate adequate sample size of 67% is within 2.5% of the true proportion.

To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.

We can use the following formula to calculate the margin of error:

[tex]E = z \sqrt{\frac{(p (1-p)}{n} )[/tex]

where:

Plugging in the values, we get:

[tex]E = 1.96 \sqrt{(0.67 (1-0.67)/1400)[/tex]

≈ 0.025

Thus, the error margin is around 0.025. This indicates that there is a 95% chance that the real percentage will be within 0.025 of the estimated proportion.

We may infer that a sample size of 1,400 is sufficient for predicting a proportion of 67% with the provided degree of confidence and tolerance as the computed margin of error is equal to the required tolerance level. As a result, we can say with some degree of assurance that our estimate of 67% is within 2.5% of the actual proportion.

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