HELPPP
Timmy and Sam ran in a marathon. Timmy ran at a constant speed of 5 miles per hour. Sam ran at a
constant speed of 4 miles per hour and had a head start of 2 miles. Determine where Timmy and Sam will
meet.

Answer:

50

Step-by-step explanation:

\(\sqrt{-64}\) and \(\sqrt{-16}\) can be expressed in complex form, with \(\sqrt{-1}\) = i

\(\sqrt{-64}\) = \(\sqrt{64(-1)}\) = \(\sqrt{64}\) × \(\sqrt{-1}\) = 8i

\(\sqrt{-16}\) = \(\sqrt{16(-1)}\) = \(\sqrt{16}\) × \(\sqrt{-1}\) = 4i

the factors can then be expressed as

(6 + 8i)(3 - 4i) ← expand using FOIL

= 18 - 24i + 24i - 32i² [ i² = (\(\sqrt{-1}\) )² = - 1 ]

= 18 - 24i + 24i + 32 ← collect like terms

= 18 + 32 + 0

= 50

Estimates suggest that up to 90% of children with disabilities have some type of nutritional problem.

These children often face unique challenges that can contribute to a higher risk of nutritional deficiencies or imbalances.

Disabilities can affect various aspects of a child's health, including their ability to eat, digest, absorb nutrients, and maintain a healthy weight.

Additionally, certain disabilities may require specific dietary restrictions or specialized nutritional interventions, which can further complicate their nutritional status.

It is crucial to address these nutritional issues and provide appropriate support to ensure the optimal growth and development of children with disabilities.

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Answer:

60

Step-by-step explanation:

100%/5%=20

20*3=60

The measure of angle A in a right triangle with base 5 cm and hypotenuse 10 cm is approximately 38.21 degrees.

We can use the inverse cosine function (cos⁻¹) to find the measure of angle A, using the cosine rule for triangles.

According to the cosine rule, we have:

cos(A) = (b² + c² - a²) / (2bc)

where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively. In this case, we have b = 5 cm and c = 10 cm (the hypotenuse), and we need to find A.

Applying the cosine rule, we get:

cos(A) = (5² + 10² - a²) / (2 * 5 * 10)

cos(A) = (25 + 100 - a²) / 100

cos(A) = (125 - a²) / 100

To solve for A, we need to take the inverse cosine of both sides:

A = cos⁻¹((125 - a²) / 100)

Since this is a right triangle, we know that A must be acute, meaning it is less than 90 degrees. Therefore, we can conclude that A is the smaller of the two acute angles opposite the shorter leg of the triangle.

Using the Pythagorean theorem, we can find the length of the missing side at

a² = c² - b² = 10² - 5² = 75

a = √75 = 5√3

Substituting this into the formula for A, we get:

A = cos⁻¹((125 - (5√3)²) / 100) ≈ 38.21 degrees

Therefore, the measure of angle A is approximately 38.21 degrees.

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The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

x³ + 6x² + 11x + 6 = 0

Factorize the equation, then we have

x³ + 6x² + 11x + 6 = 0

x³ + x² + 5x² + 5x + 6x + 6 = 0

x²(x + 1) + 5x(x + 1) + 6(x + 1) = 0

(x + 1)(x² + 5x + 6) = 0

(x + 1)[x² + 3x + 2x + 6] = 0

(x + 1)(x + 3)(x + 2) = 0

x = -1, -2, -3

The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.

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Answer:

C

Step-by-step explanation:

x²-10x+(-10×0.5)²=4+(-10×0.5)²

x²-10x+25=29

Answer:

A

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

613.87 dollars

Step-by-step explanation:

Times 400 by 1.055 and you'll get 422 dollars. Keep doing this with the product (Result of you multiplying the previous answer by 1.055) eight times and you'll get 613.87 dollars

Answer:

A = $400e^(0.055·8) ≈ $621.08

Step-by-step explanation:

hope this helps

Step-by-step explanation:

x = number of years after 2007.

x = 0 for 2007.

PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).

PC(x) = 0.8x + 52

0 <= x <= 5

in 2007 (x = 0) the average adult ate 52 pounds.

in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.

so, in 2012 (x = 5) the average adult will eat

PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.

Answer:

64800

Step-by-step explanation:

you will multiply 60 by 18m to get how much you go in a minute. and then you multiply that by 60 again to get how much you go in an hour.

Answer:

64800

Step-by-step explanation:

18x60= 1080

1080x60= 64800

a. The standard error of the mean can be calculated using the formula:

Standard Error of the Mean = standard deviation / square root of sample size.

In this example, the standard deviation is given as 80 minutes and the sample size is 40. Plugging these values into the formula:

Standard Error of the Mean = 80 / √40 ≈ 12.727

Therefore, the standard error of the mean in this example is approximately 12.727 minutes.

b. To find the likelihood that the sample mean is greater than 320 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table.

The formula for z-score is:

z = (x - μ) / (σ / √n)

In this case, x is the sample mean of 320 minutes, μ is the population mean (330 minutes), σ is the standard deviation (80 minutes), and n is the sample size (40).

Plugging in these values:

z = (320 - 330) / (80 / √40) ≈ -0.447

Now, referring to Appendix B1 for the z-values, we can find the corresponding probability. The z-value of -0.447 corresponds to a probability of approximately 0.3264.

Therefore, the likelihood that the sample mean is greater than 320 minutes is approximately 0.3264.

c. To find the likelihood that the sample mean is between 320 and 350 minutes, we need to calculate the z-scores for these values and then find the corresponding probabilities from the z-table.

Using the same formula as in part b, we can calculate the z-scores:

For 320 minutes:
z = (320 - 330) / (80 / √40) ≈ -0.447

For 350 minutes:
z = (350 - 330) / (80 / √40) ≈ 1.118

Referring to Appendix B1, the z-value of -0.447 corresponds to a probability of approximately 0.3264, and the z-value of 1.118 corresponds to a probability of approximately 0.8686.

To find the likelihood between these two values, we subtract the probability corresponding to the lower z-value from the probability corresponding to the higher z-value:

0.8686 - 0.3264 ≈ 0.5422

Therefore, the likelihood that the sample mean is between 320 and 350 minutes is approximately 0.5422.

d. To find the likelihood that the sample mean is greater than 350 minutes, we can use the z-score formula:

z = (x - μ) / (σ / √n)

Plugging in the values:
z = (350 - 330) / (80 / √40) ≈ 1.118

Referring to Appendix B1, the z-value of 1.118 corresponds to a probability of approximately 0.8686.

Therefore, the likelihood that the sample mean is greater than 350 minutes is approximately 0.8686.

e. In this example, we assume that the distribution of times for taxpayers to prepare, copy, and electronically file an income tax return follows a normal distribution. This assumption is based on the given statement that the distribution of times follows the normal distribution.

By assuming a normal distribution, we can use z-scores and the z-table to calculate probabilities and make inferences about the sample mean. However, it is important to note that this assumption may not hold true in all cases, and other statistical methods may need to be used if the data does not follow a normal distribution.

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We have to solve this equation by completing the square.

We have two terms from the quadratic equation: x² + 14x, so we can add the third term as:

We add the same term to both sides of the equation to preserve the equality.

We now can continue solving the equation as:

This equation does not have solutions for x for the set of real values, as we have a square root of a negative number.

We can express the solution as complex numbers as:

Answer: the solutions for the equation are x = -7 - 2(√5)i and x = -7 + 2(√5)i.

Answer:

one solution

Step-by-step explanation:

3x + 3 = -3x + 3

6x + 3 = 3

6x = 0

x = 0

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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There can be 90% confident that the population mean salary of college graduates who took a statistics course is between $60,947.78 and $66,652.22.

To construct a 90% confidence interval for estimating the population means μ of salaries for college graduates who took a statistics course, we can use the formula:

Confidence interval = sample mean ± (critical value) x (standard error)

First, we need to find the critical value from the t-distribution table with a degree of freedom of n-1. Since we have 49 college graduates, our degrees of freedom are 48. Looking at the table, the critical value for a 90% confidence level is 1.677.

Next, we need to find the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error is $11,936/sqrt(49) = $1703.05.

Substituting these values into the formula, we get:

Confidence interval = $63,800 ± 1.677 x $1703.05
Confidence interval = $63,800 ± $2852.22

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Answer:

$2715

Step-by-step explanation:

Given that 15 food booths were rented out for ‘d’ days at $100 plus $5 per day. On the food booths only, the company will earn 15($100+$5d) = $1500 + $75d Given that 20 game booths were rented out for ‘d’ days at $50 plus $7 per day. On the game booths only, the company will earn 20($50 + $7d) = $1000 + $140d

The total amount that the company is paid is therefore, $1500 + $75d + $1000 + $140d = $2500 + $215d

(a) 0.034 L, (b) 27,000 mg, (c) 310 L

To express each value with two significant figures, we follow these rules:

If the first non-zero digit is before the decimal point, count all the digits starting from the first non-zero digit.

If the first non-zero digit is after the decimal point, count all the digits starting from the first non-zero digit until the second significant figure.

Round the last digit if it is greater than or equal to 5.

(a) 0.03405 L:

The first non-zero digit is 3. Since it is before the decimal point, we count all the digits starting from 3. The second significant figure is 4. Therefore, rounding to two significant figures gives us 0.034 L.

(b) 26,978 mg:

The first non-zero digit is 2. Since it is before the decimal point, we count all the digits starting from 2. The second significant figure is 6. Therefore, rounding to two significant figures gives us 27,000 mg.

(c) 310.490 L:

The first non-zero digit is 3. Since it is before the decimal point, we count all the digits starting from 3. The second significant figure is 1. Therefore, rounding to two significant figures gives us 310 L.

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Answer:

undefined

Step-by-step explanation:

The line on the graph is completely vertical, which is characteristic of an undefined graph.

Answer:

Step-by-step explanation:

You are right it is 8!

\(4x+22~ > ~-2(14+3x)\implies 4x+22~ > ~-28-6x\implies 10x+22 > -28 \\\\\\ 10x > -50\implies x > \cfrac{-50}{10}\implies x > -5\)

Check the picture below.

Answer:

Step-by-step explanation:

2x-25,6=90

2x=90+25,6

2x=115,6

x=57,8

Answer:

The number is 57.8

Step-by-step explanation:

Let x = number

2x -25.6 = 90

Add 25.6 to each side

2x-25.6 +25.6 = 90+25.6

2x=115.6

Divide by 2

2x/2 =115.6/2

x =57.8

Answer:

1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

perimeter of first square = 4 × side = 60 m

∴ side = 60/4 = 15 m

so area = s × s = 15 × 15 = 225 m^2

perimeter of second square = 4 × side = 144 m

∴ side = 144/4 = 36 m

so area = s × s = 36 × 36 = 1296 m^2

Perimeter of the third square = sum of areas of the first and second triangle

= 225 + 1296

= 1521 m

hope this helps

plz mark as brainliest!!!!!

Answer:

Perimeter of new square =  156 m

Step-by-step explanation:

First square:

 Perimeter = 60 m

 4 * side = 60 m

side = 60/4

side = 15 m

Area of first square = side * side = 15 * 15 = 225 m²

Second square:

 Perimeter = 144 m

 4 * side = 144 m

side = 144/4

side = 36 m

Area of second square = side * side = 36 * 36 = 1296 m²

New square:

Area of new square = area of first square + area of second square

                                  = 225 + 129

Area of new square = 1521 m²

   side * side = 1521

    side = √1521 = √39*39

     side = 39 m

Perimeter of new square = 4 * 39 = 156 m

Given a Math exam with 7 short answer questions and Peter intending to answer three of them, there are a total of 35 different combinations of short answer questions he can choose.

To determine the number of combinations, we can use the concept of combinations in combinatorics. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:

C(n, r) represents the number of combinations of choosing r items from a set of n items.

n! denotes the factorial of n, which is the product of all positive integers up to n.

In this case, Peter wants to answer three out of the seven questions, so we can calculate it as:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!)

Simplifying further:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1

3! = 3 * 2 * 1

4! = 4 * 3 * 2 * 1

C(7, 3) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / [(3 * 2 * 1) * (4 * 3 * 2 * 1)]

After canceling out common terms, we get:

C(7, 3) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different combinations of short answer questions Peter can choose to answer.

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Answer:

31.2

Step-by-step explanation:

it should be the answer

Answer:

31.2

Step-by-step explanation:

First, subtract 15. This makes 62.4. Then divide by 2, which gets 31.2

Step-by-step explanation:

-3x+7y = -18 ...1

4x-4y = 8 ...2

...1 × 4

-12x + 28y = -72 ...3

...2 × 3

12x - 12y = 24 ...4

...3 + ...4

28y - 12y = -72 + 24

16y = -48

y = -3

Replace y = -3 in ...2

4x - 4(-3) = 8

4x + 12 = 8

4x = 8 - 12

4x = -4

x = -1

Answer:

\(\huge\boxed{\boxed{(x,y)=(-1,-3)}}\)

Step-by-step explanation:

multiply first equation by 4 and second by 3 respectively:

\( \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}\)

combine the equations:

\( \underline{ \begin{cases} \displaystyle - 12x + 28y = - 72 \\ \: \: \displaystyle \: 12x - 12y = 24 \end{cases}} \\ \displaystyle16y = - 48\)

divide both sides by -48:

\( \displaystyle \: \frac{16y}{16} = \frac{ - 48}{16} \\ y = - 3\)

substitute the value of y to the second equation

\( \displaystyle \: 4x - 4. - 3 = 8\)

simplify multiplication:

\( \displaystyle \: 4x + 12 = 8\)

cancel 12 from both sides:

\( \displaystyle \: 4x = - 4\)

divide both sides by 4

\( \displaystyle \: \frac{4x}{4} = \frac{ - 4}{4} \\ x = - 1\)

therefore our solution is

\(\displaystyle (x,y)=(-1,-3)\)

Complete Question

Which division problem does the model show? 3 fraction bars. The bars are labeled 1 and each has 3 boxes underneath labeled one-third.

a) 3 divided by one-third = 9

b)3 divided by two-thirds = 9

c) 9 divided by one-third = 3

d) 9 divided by two-thirds = 3

Answer:

a) 3 divided by one-third = 9

Step-by-step explanation:

We are told in the question that:

3 fraction bars. The bars are labeled 1 and each has 3 boxes underneath labeled one-third.

The division problem does the model shows from the description above is calculated as:

3 fraction bars ÷ 1/3

= 3 ÷ 1/3

= 3 × 3

= 9

Hence:

Option a) 3 divided by one-third = 9 is the correct option.

Answer:

3rd one is correct

Step-by-step explanation:

A string is wrapped around the edge of a uniform cylinder with a radius of 42 cm and a mass of 5 kg. The cylinder is initially at rest on a frictionless table.

In this scenario, the string wrapped around the cylinder can be used to apply a force and set the cylinder into motion. The tension in the string creates a torque that causes the cylinder to rotate. The key parameters of the cylinder are its radius (r = 42 cm) and mass (m = 5 kg).

To analyze the motion of the cylinder, we can consider the principles of rotational dynamics. The torque exerted on the cylinder is equal to the product of the tension in the string and the radius of the cylinder (τ = T * r). According to Newton's second law for rotation, the torque is also equal to the moment of inertia (I) multiplied by the angular acceleration (α) of the cylinder (τ = I * α).

Since the cylinder is initially at rest, the angular acceleration is zero. Therefore, the torque applied by the tension in the string is also zero. This implies that the tension in the string is zero, and there is no force acting on the cylinder to set it into motion.

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