Sandra can run 5 miles per hour. Write an equation to show the relationship between the amount of hours, h, and the total distance, d. Explain how you got your answer.

On solving the provided question, we cans ay that inches will evaporate, the equation will be = 12x = 1/2y + 7.43

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

he water evaporates at the rate in a, for 12 hours.

inches will evaporate,

the equation will be = 12x = 1/2y + 7.43

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The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.

What is synthetic division?

Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."

We are given the expression as (n^3+3n^2-15n+19)

The expression is to be divided by (n-2)

So, by using the synthetic division, we get

2 |  1     3     -15      19    

     -     2      10     -10        

     1     5      -5       9    

Quotient =  n^2+5n-5

Remainder = 9

Hence, the quotient is n^2+5n-5 and the remainder is 9.

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If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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Answer:

n = 7 1/3 weeks

Step-by-step explanation:

Amount Jabari wants to save = $66

Amount he earns per week = $9

Hours worked per week = 2 hours

How many weeks will it take him to save $66?

Let

n = number of weeks will it take him to save $66

66 = 9n

n = 66/9

n = 7 3/9

n = 7 1/3 weeks

Or

n = 7.33 weeks

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

The equation of motion of the spring-mass-damper system is given by2x'' + 8x' + 26x = 0

            where x is the displacement of the mass from its equilibrium position, x' is the velocity of the mass, and x'' is the acceleration of the mass.

The characteristic equation for this differential equation is:

                          2r² + 8r + 26 = 0

Dividing by 2 gives:r² + 4r + 13 = 0

Solving this quadratic equation, we get the roots: r = -2 ± 3i

The general solution of the differential equation is:

                    x = e^-2t (c₁ cos(3t) + c₂ sin(3t))

where c₁ and c₂ are constants determined by the initial conditions.

Using the initial conditions x(0) = -1 m and x'(0) = 2 m/s,

we get:-1 = c₁cos(0) + c₂

              sin(0) = c₁c₁ + 3c₂ = -2c₁

              sin(0) + 3c₂cos(0) = 2c₂

Solving these equations for c₁ and c₂, we get: c₁ = -1/2c₂ = 1

Substituting these values into the general solution, we get:x = e^-2t (-1/2 cos(3t) + sin(3t))

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

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The equilibrium point is the point of intersection of the supply and demand curve.

To calculate the equilibrium point, you need to find out the value of x where both the demand and supply are equal. This will be the equilibrium quantity. After this, substitute the equilibrium quantity back into either the demand or supply function to get the equilibrium price.To find the equilibrium quantity, you need to set the two demand and supply equations equal to each other and solve for x as follows:

57x² = 5x² + 18x - 11152x² - 18x + 111 = 0

Use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac))/(2a)

where a = 52, b = -18, and c = 111

x = (-(-18) ± sqrt((-18)² - 4(52)(111)))/(2(52))≈ 1.734

So the equilibrium quantity is approximately 1.734 hundreds of jerseys.

To find the equilibrium price, substitute this value back into either the demand or supply equation. For example, using the demand equation:

p = d(x) = 57x²p = 57(1.734)²≈ $174.31

So the equilibrium price is approximately $174.31.

The equilibrium point is the point of intersection of the demand and supply curve. The equilibrium quantity is the amount of goods or services that will be produced and sold in the market when the demand and supply are equal. This is where the buyers and sellers agree on the market price. The equilibrium price is the price at which the demand and supply curves intersect. The equilibrium quantity and price can be calculated by finding the value of x where both the demand and supply equations are equal and substituting this value back into either the demand or supply equation. For Penn State ice hockey jerseys, the equilibrium quantity is approximately 1.734 hundreds of jerseys, and the equilibrium price is approximately $174.31.

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The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.

we know that

In the right triangle XYZ

\(tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}\)

In this problem,

Opposite side angle YZX= XY = 12.4cm

Adjacent side angle YZX= YZ = 15.1cm

substitute the values,

\(tan ( Y Z X) = \frac{12.4}{15.1}\)

\(Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )\)

Angle ( Y Z X) = 39.4°

So,  the approximate measure of angle YZX is 39.4°.

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The complete question is:

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

A .34.8°

B .39.4°

C .50.6°

D. 55.2°

Answer:

Solution:

(1/12)^(-2b) * 12^(-2b+2) = 12

(12^-1)^(-2b) (12)^(-2b+2) = 12

(12^2b)(12)^(-2b+2) = 12

12^(2b-2b+2) = 12

12^2 = 12

144 does not equal 12

No solution.

Step-by-step explanation:

The measure of angle PNL will be equivalent to 69 degrees.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle KLM such that N is a midpoint of KL and P is a midpoint of LM.

Triangles LMP and LKM are similar to each other. Therefore, PN will be parallel to MK. So angle PNL will be equal to angle MKN. Therefore -

2x + 61 = 97 - 7x

9x = 97 - 61

9x = 36

x = 4

So, angle PNL will be equal to -

2 x 4 + 61

69 degrees

Therefore, the measure of angle PNL will be equivalent to 69 degrees.

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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To find the probability that the mean salary of a person selected at random from Acme Corporation is less than 61,000, we can use the Z-score formula.

First, we need to calculate the Z-score, which measures the number of standard deviations a value is away from the mean. The formula for the Z-score is:

Z = (X - μ) / (σ / √n)

Where:
- X is the value we are interested in (in this case, $61,000)
- μ is the population mean annual salary for Acme Corporation ($63,500)
- σ is the population standard deviation (unknown in this case)
- n is the sample size (unknown in this case)

Since we don't have the population standard deviation or sample size, we cannot calculate the exact Z-score. Therefore, we cannot find the exact probability.

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Based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

The probability of a person selected at random having a salary less than $61,000 can be determined using the z-score and the standard normal distribution.

To calculate the z-score, we need to know the population standard deviation. Since it is not provided, we cannot calculate the exact probability. However, we can use the assumption that the population standard deviation is the same as the sample standard deviation.

Let's assume the sample standard deviation is $5,000.

First, we calculate the z-score:
    \(z = (x - \mu) / (\sigma / \sqrt n)\)
=> z = (61000 - 63500) / (5000 / √1)
=> z = -2500 / 5000
=> z = -0.5

Next, we find the corresponding area under the standard normal curve using a z-table or a calculator. The area to the left of -0.5 is approximately 0.3085.

Therefore, the probability that a person selected at random will have a salary less than $61,000 is approximately 0.3085 or 30.85%.

In conclusion, based on the assumption of a sample standard deviation of $5,000, the probability that the mean salary of a person selected at random will be less than $61,000 is approximately 30.85%.

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Answer:

The correct answer is h(t) = 14.25 + 0.25 * sin((π/26) * t)

To model the hours of daylight in a year using a sinusoidal equation, we can consider the average length of daylight, the amplitude of the variation, and the period of the function.

Given:

Summer solstice (longest day) is 14.5 hours

Winter solstice (longest night) is 14 hours

Let's analyze the information:

Average daylight: The average daylight throughout the year would be the average of the summer and winter solstices. It can be calculated as:

Average daylight = (14.5 + 14) / 2 = 14.25 hours

Amplitude: The difference between the average daylight and the longest day or night is the amplitude. In this case, the amplitude is half the difference between the summer and winter solstices. It can be calculated as:

Amplitude = (14.5 - 14) / 2 = 0.25 hours

Period: We are modeling the function over a year, which we'll consider as 52 weeks. Since we want to measure time in weeks (t), the period of the function is 52 weeks.

Putting all the information together, we can write the sinusoidal equation:

h(t) = Average daylight + Amplitude * sin((2π / Period) * t)

Substituting the values we calculated:

h(t) = 14.25 + 0.25 * sin((2π / 52) * t)

Simplifying further, the sinusoidal equation modeling the hours of daylight in a year is:

h(t) = 14.25 + 0.25 * sin(π/26 * t)

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The answer is 1/8.

If you count all the spaces you get 8 and you can also see that the dot is on the first line. Hence the answer being 1/8.

Answer:

1/8

Step-by-step explanation:

There are 8 "slices" between the 0 and the 1 in this graph, so it is safe to assume that the fraction you'll end up with will be something out of 8. The dot on the graph given is resting on the firts line on the graph, or the first portion of eight, so you have 1 out of eight pieces.

The scale factor of the given parameters will be 1.75 and the length of qy is 2.37.

We have,

Point q as the center of dilation,

And,

Line wy is dilated to created line w'y',

And,

Length of yw' = 3.5,

And,

Length of qw = 2,

Also,

Length of qy' = 4.125,

Now,

First we will find out the length of qy,

i.e.

The lines are similar so in equal ratio,

i.e.,

qw : qy = qw' : qy'

Now,

Putting values,

i.e.

2 : qy = 3.5 : 4.15

on solving we get,

qy = 1.5

So,

The length of qy is 2.37.

Now,

Scale factor : Scale Factor is the ratio of size of new image formed to the size of old image.

i.e.,

Scale factor = \(\frac{Change\ in\ size}{Original\ size}\)

So,

Scale factor = \(\frac{3.5}{2}\) = 1.75

Hence, we can say that the scale factor of the given parameters will be 1.75 and the length of qy is 2.37.

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Answer:

it is 2.75. and 1.5

Step-by-step explanation:

right on edge

Answer:

4 pizzas are needed.

Step-by-step explanation:

See image. You could totally think this through and use mental math to figure out how many pizzas are needed. See first image. Picture a pizza, cut it into 6 slices. It feeds 6 people. 2 pizzas feed 12 people. 3 pizzas feed 18 people. 4 pizzas feed 24 people.

If you have to write equations and show math work, you can write a single-variable equation or use a proportion. See image.

6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

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Answer:

(4, 0)

Explanation:

The difference between -5 and -1 is 4 and the difference between-3 and -3 is 0.

Answer:

A sixth grade silence club needs 180$ to pay for the tickets to a science museum.

1. Suppose there 15 students in the club, then each of them needs to pay

\dfrac{\$180}{15}=\$12

15

$180

=$12

This means each ticket costs $12.

2. Suppose each ticket cost $15, then there are

\dfrac{\$180}{\$15}=12

$15

$180

=12 students in the club.

Answer:

17

Step-by-step explanation:

Use the perimeter formula, P = 2l + 2w, where l is the length and w is width

Since the length of the rectangle is 3 less than twice the width, it can be represented by 2w - 3

Plug in the perimeter, w for the width, and 2w - 3 for the length in the equation:

P = 2l + 2w

54 = 2(2w - 3) + 2w

Distribute the 2 to the parentheses:

54 = 4w - 6 + 2w

Add like terms:

54 = 6w - 6

Solve for w:

60 = 6w

10 = w

So, the width is 10. To find the length, plug in 10 as w into 2w - 3

2w - 3

2(10) - 3

= 17

So, the length is 17.

Answer:

\(p\geq 1.15(4,500)\)

Step-by-step explanation:

If she makes a minimum profit, we need to use the symbol \(\geq\), which indicates minimum quality.

Let's call \(p\) profit, so the inequality which represent this problem would be

\(p\geq 1.15(4,500)\)

The price of the car is multiplied by 1.15, because she must add her profit comission which is 0.15 or 15%.

Therefore, the right answer is the last choice.

Answer:

D

Step-by-step explanation:

i did the same thing

Answer:

To calculate the probability that neither of your two groupmates has studied any statistics, we need to make certain assumptions about the probability of an individual studying statistics. Let's assume that the probability of an individual studying statistics is denoted by P(statistics).

Since we have two groupmates, let's represent them as A and B. The probability that neither of them has studied statistics can be calculated as the product of the probabilities that each of them has not studied statistics.

So, the probability that groupmate A has not studied statistics is given by P(not A) = 1 - P(statistics), and the probability that groupmate B has not studied statistics is given by P(not B) = 1 - P(statistics).

Assuming the events of groupmate A and groupmate B not studying statistics are independent, we can multiply these probabilities together:

P(neither has studied statistics) = P(not A) * P(not B) = (1 - P(statistics)) * (1 - P(statistics)).

This is the probability that neither of your two groupmates has studied any statistics.

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Answer:

-------------------

If we add heights from both top vertices, we'll get two isosceles right triangles on sides and a rectangle in the middle.

The triangles are isosceles because of a 45° angle.

Let's call the legs h. Then we have three segments on the bottom base, 2 of a length h and 12 in, but we know it is 20 inches.

Set up an equation:

Find the area:

The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

\(\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}\)

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

\(\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}\)

\(\frac{BC}{sinA}=\frac{AB}{sinC}\)

\(\frac{2}{sin25}=\frac{3}{sinC}\)

\(\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )\)

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

\(\frac{BC}{sinA}=\frac{AC}{SinB}\)

\(\frac{2}{sin25}=\frac{l}{sin(115.66)}\)

\(l=\frac{2\times sin(115.66)}{sin25}\)

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

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Answer:

f>1/2

Step-by-step explanation:

 8 + 10ƒ > 14 – 2ƒ.

-8                   +2f

12f > 6

/12      /12

f>1/2

Answer:

Step-by-step explanation:

That last number there, the constant, represents the height from which the projectile was launched. So the platform is 108 m high.

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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The statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:

A. measure of angle FEB + measure of angle HGD = 180°

By definition, supplementary angles are two angles that have a sum of 180 degrees when added together, that is, one is a supplement of the other.

Given the image below, we know the following:

Since angle FEA is supplementary to angle FEA would be congruent to angle HGC, and angle HGD is congruent to angle FEB. This is because, the supplement of angle

angle FEA + angle FEB - angle FEA + angle HGD = 180° - 180°. Therefore,

angle FEB = angle HGD.

In summary, from the options given, the statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:

A. measure of angle FEB + measure of angle HGD = 180°

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Answer:

equal to

Step-by-step explanation:

5/42       10/84

5/42, if you times the faction by 2 it’ll equal to 10/42

Answer:

5/42 is equal to 10/84.

Step-by-step explanation:

To compare the fractions 5/42 and 10/84, we can simplify them to have a common denominator and then compare the numerators.

To find a common denominator, we need to determine the least common multiple (LCM) of 42 and 84, which is 84.

Now let's convert the fractions to have a denominator of 84:

5/42 = (5/42) * (2/2) = 10/84

10/84 = (10/84) * (1/1) = 10/84

Since both fractions have the same numerator and denominator, 5/42 is equal to 10/84.

Therefore, 5/42 is equal to 10/84.