Find the length x of RS.

Answer:

The answer is x=1 and y=1

Step-by-step explanation:

Multiply the second equation by -1, then add the equations together.

(2x+3y=5)

−1(2x+7y=9)

Becomes:

2x+3y=5

−2x−7y=−9

Add these equations to eliminate x:

−4y=−4

Then solve−4y=−4for y:

−4y=−4 Divide -4

\(\frac{-4y}{-4}= \frac{-4}{-4}\)

y=1

Now that we've found y let's plug it back in to solve for x.

Here's was the original equation:

2x+3y=5

Substitute 1 for y in 2x+3y=5:

2x+(3)(1)=5

2x+3=5

2x+3+−3=5+−3 ( Add -3 on both sides)

2x=2 Divide by 2

\(\frac{2x}{2} =\frac{2}{2}\)

x=1

Answer:

Zayn= $928.72

Angelo= $880.64

Zayn has 48.08 more than Angelo.

Step-by-step explanation:

Answer:

zayn- 934.58

angelo- 880.64

Step-by-step explanation:

The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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The value of the expressions (3.683 × 10⁴) and (7.51 × 10¹²) in scientific notation is 4.9041 × 10⁻⁹. Then the correct option is B.

The division means the separation of something into different parts, sharing of something among different people, places, etc.

The expressions are (3.683 × 10⁴) and (7.51 × 10¹²).

We have to divide (3.683 × 10⁴) from (7.51 × 10¹²).

\(\dfrac{3.683 * 10^4}{7.51*10^{12}}\\\\0.4904*10^{-8}\\\\4.9041*10^{-9}\)

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Answer:

12345

Step-by-step explanation:

A higher level of confidence results in a wider confidence interval, which means that there is a greater chance that the true value lies within the confidence interval.

The role of the following factors can be determined using the formula for a confidence interval percentage:

a) Sample size (percentage): The sample size (percentage) determines the size of the standard error in the estimate. The formula for calculating a confidence interval percentage takes into account the sample size and the variability of the data.

b) Variability: The variability is a measure of how much the data deviates from the mean or expected value. The variability is represented by the standard deviation of the data.

A higher variability results in a larger confidence interval, which means that there is a greater chance that the true value lies outside the confidence interval.

c) Level of confidence: The level of confidence determines the size of the confidence interval. The level of confidence is typically set to 95%, which means that there is a 95% chance that the true value lies within the confidence interval.

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The number of pieces of fish that would be there if Jorge divided each fish into tenths is 1730.

It is given that Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces.

We need to calculate the number of pieces of fish that would be there if Jorge divided each fish into tenths.

We know that each of the fish is divided into 10 parts.

The total number of fish available for the dog is 173.

The total number of pieces of fish is equal to the product of the number of available fish and the number of parts each fish is divided into.

The total number of pieces of fish is equal to 173*10.

The total number of pieces of fish is equal to 1730.

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The graph of the inequality y^2 > 0 represents all real numbers except y = 0.

The graph of the inequality y < 30 represents all real numbers less than 30.

The inequality y^2 > 0 represents all values of y where y squared is greater than 0. Since the square of any nonzero number is always positive, the solution is all real numbers except y = 0, which can be graphed as a number line with an open circle at y = 0.

The inequality y < 30 represents all values of y that are less than 30. This can be graphed as a horizontal line on the y-axis with an open circle at y = 30, indicating that 30 is not included in the solution set.

For the real-world applications, let's solve them step-by-step:

Two numbers add up to 144. One number is half the square of the other number.

Let's assume the two numbers are x and y. We have the following system of equations:

x + y = 144 (Equation 1)

x = (1/2)y^2 (Equation 2)

From Equation 1, we can solve for x in terms of y: x = 144 - y.

Substituting this into Equation 2, we get 144 - y = (1/2)y^2.

Rearranging the equation, we have: (1/2)y^2 + y - 144 = 0.

Now we can solve this quadratic equation for y. Once we find the value(s) of y, we can substitute them back into Equation 1 to find the corresponding values of x.

The squares of two numbers add to 1,156. The second number is the square root of three times the square of the first number.

Let's assume the two numbers are x and y. We have the following system of equations:

x^2 + y^2 = 1156 (Equation 1)

y = √(3x^2) (Equation 2)

Substituting Equation 2 into Equation 1, we get: x^2 + (√(3x^2))^2 = 1156.

Simplifying, we have x^2 + 3x^2 = 1156.

Combining like terms, we get 4x^2 = 1156.

Now we can solve this quadratic equation for x. Once we find the value(s) of x, we can substitute them back into Equation 2 to find the corresponding values of y.

Remember to leave a 1 line space between paragraphs in your answer.

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Given :

The amount with Rahul is $720.

The cost of new bicycle is $378.51.

The cost of 2 bicycle reflectors is

The cost of pair of bike gloves is $29.74.

The cost of new biking outfit is $55.16.

Explanation :

Let the number of outfits be x.

Then the inequality formed is

Answer:

Hence the greatest number of outfits Rahul can buy with the money that's left over is 5.

The domain of f is the range of f^-1, and the domain of f^ −1 is the range of f.

The domain of a function f consists of all possible input values that can be used as arguments for f to generate output values.

If we consider the inverse function of f, denoted as f^−1, it will swap the roles of the input and output values of f. In other words, if f(x) = y, then f^−1(y) = x.

Therefore, the domain of f^−1 is equal to the range of f, which consists of all possible output values generated by f for any valid input value. This is because any output value of f can be used as an input value for f^−1.

Similarly, the range of f^−1 is equal to the domain of f, which consists of all possible input values that can be used as arguments for f to generate output values. This is because any valid input value of f can be used as an output value for f^−1.

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Answer:

Step-by-step explanation:

x^2+7=16

  -7      -7

x^2=9

x=\(\sqrt{9\)

x=3

A Helmholtz coil is designed to create a relatively uniform magnetic field between the two coils. To find the magnetic field at the midpoint between the coils, we can use the Biot-Savart law, which calculates the magnetic field produced by a current-carrying wire.

Step 1: Define the position of the coils
Let's define the positions of the coils as y1 = -r/2 and y2 = r/2. This places the midpoint between the coils at the origin (0, 0).

Step 2: Use the Biot-Savart law
The Biot-Savart law states that the magnetic field dB produced by a small segment of wire is given by:

dB = (μ₀ * i * dl × r') / (4π * |r'|³)

where μ₀ is the permeability of free space, i is the current in the wire, dl is the length of the wire segment, and r' is the vector from the wire segment to the point where we want to calculate the magnetic field.

Step 3: Calculate the magnetic field for each coil
Integrate the magnetic field dB along the entire circumference of each coil to find the total magnetic field B produced by each coil.

Step 4: Add the magnetic fields from both coils
Since the two coils have the same current and are symmetric about the y-axis, their magnetic fields at the midpoint will add up. Add the magnetic fields from both coils to find the total magnetic field B_total at the midpoint:

B_total = B1 + B2

By following these steps, you can calculate the magnetic field at the midpoint between the two Helmholtz coils along the y-axis.

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The model used by Victor in the linear equation is incorrect,

The parameters are that;

Victor saved: $89.25

Cost of the bicycle = $129.85

Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;

$89.25 + x = $129.85

This can be expressed in words as;

The amount of money he already has saved + the amount of money he still requires = the total price of the bike.

An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle

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Complete question is;

Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.

89.25 + 129.85 = x

Does Victor's equation correctly model the problem?

Answer:

I think it could be 13 percent srry if am wong.

Step-by-step explanation:

Each mile has 1760 yards, so to convert we can divide 46112 by 1760:

So, 46,112 yards is the same as 26.2 miles.

If 0.4 Customers arrives after 1 minute-

0.4*5 = 2.0 cm

From 1947 to 1987, Willowbrook State School served Staten Island's Willowbrook neighborhood as a state-funded facility for youngsters with intellectual disabilities. The school had 6,000 students enrolled by 1965 despite being intended for 4,000.

Aerts entered through the doors of Willowbrook State School in 1971 with former Staten Island Advance writer Jane Kurtin, and took disturbing photos of children and adults with special problems who were confined in cages, hungry, and used as research experiments.

Geraldo Rivera, who was working as an investigative reporter for WABC-TV in New York at the time, began an investigation into Willowbrook soon after and found a number of appalling circumstances there, including overcrowding and subpar sanitary facilities.

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Answer:

slope = 9 , y- intercept = - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 9x - 3 ← is in slope- intercept form

with slope m = 9 and y- intercept c = - 3

The value of the expression below when x=5x=5?

8x+9 is equal to \(7^{2}\) (or) 49.

Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)

The expression,

y = 8x + 9

If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:

So, we can substitute x = 5,

Then, y = 8 * 5 + 9

Calculate the product or quotient,

y = 40 + 9

Calculate the sum or difference,

y = 49

We can write alternative form,

y = \(7^{2}\)

Therefore,

Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.

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The value of the variable and the measure of each labeled angle is 13.

According to the theory of vertical angle, it states that any angle that are opposite to one another is congruent and equal.

The angles are:

(x + 15)°

(5x - 37)°

Equate both angles

(x + 15)° = (5x - 37)°

open parenthesis

x + 15 = 5x - 37

collect like terms

x - 5x = -37 - 15

- 4x = - 52

divide both sides by -4

x = -52/-4

x = 13

Hence,

(x + 15)°

= (13 + 15)°

= 28°

(5x - 37)°

= 5(13) - 37

= 65 - 37

= 28°

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Answer:

\(11 \frac{3}{7}\)

Step-by-step explanation:

80 divided by 7 is 11 with a remainder of 3.

Answer:

11 3/7

Step-by-step explanation:

How you get this is you divide 80 from 7. Since it is 11.(So many numbers), you are going to take that number you just got, and multiply it from 7- the number you were dividing. You will get 77. Then you minus it. 80-77 is 3, so your answer would be 11 3/7. Since this can't be reduced more, this is your answer.

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

Answer:

The slope is 1/3 and the y intercept is 6

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

3y -x =18

Add x to each side

3y = x+18

Divide each side by 3

3y/3 = x/3 +18/3

y = 1/3x +6

The slope is 1/3 and the y intercept is 6

We need to solve for y (y = mx + b):

3y - x = 18

~Add x to both sides

3y = 18 + x

~Divide 3 to everything

y = 6 + x/3 or y = 6 + 1/3/x

So... 1/3 is the slope and 6 is the y-intercept.

Best of Luck!

The difference between strength and fit when interpreting regression equations is that strength refers to the relationship between two variables, while fit refers to how well a regression line fits the data.

When interpreting regression equations, strength and fit are two different concepts.

Here is a detailed explanation of both concepts:

Strength: In regression analysis, the strength of the relationship between two variables is measured by the correlation coefficient.

The correlation coefficient measures the degree of association between two variables.

It ranges between -1 and +1.

A correlation coefficient of -1 indicates a perfect negative relationship, whereas a correlation coefficient of +1 indicates a perfect positive relationship.

When the correlation coefficient is close to 0, it indicates that there is no relationship between the two variables.

Fit: Fit refers to how well a regression line fits the data.

The goodness of fit of a regression line is measured by the coefficient of determination, also known as R-squared.

The R-squared value ranges between 0 and 1. A high R-squared value indicates a good fit, while a low R-squared value indicates a poor fit.

In general, an R-squared value greater than 0.5 is considered acceptable.

The R-squared value tells us the proportion of the variation in the dependent variable that can be explained by the independent variable(s).

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According to the information, to estimate the total cost for a 50-kilometer taxi ride by extending the line to a distance of 50 kilometers and reading off the corresponding y-value, which is approximately $105.00.

Distance (km) Total Cost ($)

0 5.00

1 7.00

2 9.00

3 11.00

4 13.00

5 15.00

b. The graph of the total cost C as a function of the distance d up to 10 kilometers is a linear function with a slope of $2.00/km and a y-intercept of $5.00.

The start value of the total cost is $5.00, which is the initial fee charged by the taxi service. The rate of change is $2.00/km, which is the cost per kilometer travelled.

The equation that models the total cost C of using the taxi service for a distance of d kilometers is:

Using the equation from part d, we can calculate the total cost of a 50-kilometer taxi ride:

Alternatively, we could use the graph to estimate the total cost for a 50-kilometer taxi ride by extending the line to a distance of 50 kilometers and reading off the corresponding y-value, which is approximately $105.00.

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A two point charges are held in place along with equation of the x-axis:

1.E1x = (k × (-27Q0)) / (-5a)²

2.E1y = 0

3.E2x = (k ×(55Q0)) / (9a)²

4.E2y = 0

5.E= √((E1x + E2x)²)

6.F3x = (k ×(-27Q0) × (+115Q0)) / (-5a)²

7.F3x = (k × (-27Q0) × (-115Q0)) / (-5a)²

To determine the electric field at point P, we need to consider the contributions from both point charges Q1 and Q2.

The x-component of the electric field from Q1 at point P can be calculated using Coulomb's law:

E1x = (k × Q1) / r1²

Here, k represents the electrostatic constant, Q1 is the charge of Q1, and r1 is the distance between Q1 and point P along the x-axis.

Given that Q1 = -27Q0 and the distance between Q1 and point P is x1 = -5a, we can substitute these values into the formula:

E1x = (k × (-27Q0)) / (-5a)²

The y-component of the electric field from Q1 at point P is zero since Q1 is located on the x-axis.

E1y = 0

The x-component of the electric field from Q2 at point P can also be calculated using Coulomb's law:

E2x = (k × Q2) / r2²

Here, Q2 = +55Q0 and the distance between Q2 and point P is x2 = 9a:

E2x = (k × (55Q0)) / (9a)²

The y-component of the electric field from Q2 at point P is also zero since Q2 is located on the x-axis.

E2y = 0

To calculate the magnitude of the net electric field at point P, we can use the Pythagorean theorem:

E = √((E1x + E2x)² + (E1y + E2y)²)

Since E1y and E2y are both zero, the equation simplifies to:

E = √((E1x + E2x)²)

If we place another point charge q3 = +115Q0 at point P, the x-component of the net force on it can be calculated using Coulomb's law:

F3x = (k × Q1 × q3) / r1

Here, Q1 = -27Q0 and q3 = +115Q0, and the distance between Q1 and point P is x1 = -5a:

F3x = (k × (-27Q0) × (+115Q0)) / (-5a)²

If the sign of q3 is changed to q3 = -115Q0, the x-component of the net force on it can be calculated as:

F3x = (k × Q1 ×q3) / r1²

Here, Q1 = -27Q0 and q3 = -115Q0, and the distance between Q1 and point P is x1 = -5a:

F3x = (k ×(-27Q0) ×(-115Q0)) / (-5a)²

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Answer:

5d+4

Step-by-step explanation:

Number of ticket sold by Daniel = d .... 1

If Sara sold 4 more tickets to the school play than the number Danielle sold, the total number sold by Sarah is expressed as d+4 .... 2

If Brett sold 3 times as many as Danielle sold, the amount sold by Brett is 3×d = 3d ..... 3

The number of tickets that the 3 students sold altogether can be gotten by adding equation 1, 2 and 3 together as shown;

d+(d+4)+3d

Collect like terms

= d+d+3d+4

= 2d+3d+4

= 5d+4

Hence the number of tickets that the 3 students sold altogether is represented as 5d+4

Answer:

5d+4

Step-by-step explanation:

Have a good day