The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?

ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE

When George Washington became president in 1789, the army he had

commanded in the American Revolution had disbanded. This means that

the soldiers were released from service and the military units were

dissolved after the end of the war.He pursued two intertwined interests:

military arts and western expansion. At 16 he helped survey Shenandoah

lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,

he fought the first skirmishes of what grew into the French and Indian War.

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The lowest score a student could have received and still have passed the quiz with a normally distributed class is 55.

This is because the upper 35% of a normally distributed class corresponds to a score of 1.5 standard deviations above the mean. Since the mean was 70 and the standard deviation was 10, that would mean the lowest score a student could have received and still have passed the quiz is 70 + (1.5 * 10) = 70 + 15 = 55.

In summary,
1. Start with the mean of the quiz which is 70.
2. Add 1.5 standard deviations which is 1.5 * 10 = 15.
3. The result is the lowest score a student could have received and still have passed the quiz which is 70 + 15 = 55.

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Answer:

Step-by-step explanation:

820-380=440

440:44=10

10!

Answer:

10 months

Step-by-step explanation:

820-380=440then divuse the cost 44 so 440/44 to get 10 months

Answer:

[tex]2 \sqrt{61} \: in[/tex]

Step-by-step explanation:

Use the Pythagorean theorem (assume, that the length of hypotenuse is x):

[tex] {x}^{2} = {10}^{2} + {12}^{2} = 100 + 144 = 244[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{244} = 2 \sqrt{61} [/tex]

The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]

The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.

Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:

P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)

[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]

[tex]= 1/144[/tex]

Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately  [tex]0.0069[/tex] (rounded to four decimal places).

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The  least common denominator of 7/9 and 2/3 is 9

To find the least common denominator of 7/9 and 2/3, we need to find the smallest multiple that both denominators share.

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, ...

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

We can see that the smallest multiple that both denominators share is 9.

To convert 7/9 and 2/3 to have a denominator of 9, we need to multiply the numerator and denominator of 7/9 by 1 (which is equivalent to 9/9), and the numerator and denominator of 2/3 by 3:

7/9 * 1 = 7/9

2/3 * 3/3 = 6/9

Now both fractions have a denominator of 9, so we can compare them easily:

7/9 and 6/9

Therefore, the least common denominator of 7/9 and 2/3 is 9.

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The expression √36x^6 z² can be simplified. The expression is equivalent to 6x³z.

A simplified expression is an algebraic expression that has been reduced or simplified as much as possible using various mathematical operations, such as combining like terms, factoring, or cancelling common factors.

The expression √36x^6 z² can be simplified using the properties of square roots as follows:

√36x^6 z² = √(36) √(x^6) √(z²)

Since 36 is a perfect square and x^6 and z² are perfect squares (since x and z are both greater than 0), we can simplify further as:

√36x^6 z² = 6x³ z

So the expression is equivalent to 6x³z.

Therefore, the correct answer is option B: 6x³z.

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Considering they left at precise noon, at 12:45 they will be 9 miles apart after they leave the intersection.

Let's call the time it takes for them to be 9 miles apart "t". During this time, the truck will have traveled a distance of 30t, and the car will have traveled a distance of 42t. Since they are traveling in the same direction, we can subtract the distances to find the distance between them:

42t - 30t = 12t

So they are separating at a rate of 12 miles per hour.

To find when they will be 9 miles apart, we can set up the equation:

12t = 9

Solving for t:

t = 9/12

t = 0.75 hours,

To convert 0.75 hours into minutes, we have to multiply it by 60.

= 0.75 × 60

= 45 minutes

So they will be 9 miles apart 45 minutes after they leave the intersection, or at 12:45pm.

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The capacity of Supercut in customers per hour is 18.

The capacity of Supercut is the total number of customers served by three stylists in an hour, considering the average time it takes each stylist to serve one customer. This capacity calculation helps Supercut in keeping up with demand and avoiding long waiting periods, which could discourage clients.

The given data: Supercut salon has three stylists. The average time each stylist takes to serve one customer is 10 minutes. According to the data provided, it takes 10 minutes for each stylist to serve one customer, and there are three stylists. So, in 1 hour (60 minutes), each stylist will have the capacity to serve six clients.

Supercut's total capacity in an hour is calculated by adding up the capacity of each stylist. Therefore, the capacity of Supercut is: Capacity of Supercut = Capacity of each stylist * Number of Stylists= 6 customers * 3 stylists= 18 customers. Therefore, the capacity of the Supercut salon in customers per hour is 18.

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According to the question, "Suppose we randomly select 5 cell-phone owners. What is the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating?"The formula for finding the probability of an event is:P(E) = number of favorable outcomes/number of total possible outcomes.The given data in the question states that 67% of cell-phone owners find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating.

Therefore, the probability of any cell-phone owner checking their phone when it is not ringing or vibrating is:P(E) = 67/100 = 0.67To find the probability of 5 cell-phone owners checking their phones when they are not ringing or vibrating, we have to use the multiplication rule of probability. [tex]P(E₁∩E₂∩E₃∩E₄∩E₅) = P(E₁) × P(E₂) × P(E₃) × P(E₄) × P(E₅)P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.67 × 0.67 × 0.67 × 0.67 × 0.67P(E₁∩E₂∩E₃∩E₄∩E₅) = 0.2197[/tex]

Therefore, the probability that all 5 of them find themselves checking their phone for messages, alerts, or calls even when they don't notice their phone ringing or vibrating is approximately 0.2197 or 22%.

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Answer: There is one unique solution: (-3,1)

The gradient is equal to the rise in elevation/distance.

The correct answer is "rise." What is the gradient? The term "gradient" refers to the amount of steepness or slope in a surface, represented by a number or percentage. The gradient is calculated as the change in elevation divided by the change in distance.

As a result, the gradient is measured in units of elevation per distance, such as feet per mile or meters per kilometer. The formula for the gradient is given by:Gradient = Rise / RunWhere rise is the change in elevation and run is the change in distance.

The gradient, on the other hand, indicates the steepness or slope of a surface. It represents the angle of the slope and the direction of flow of a stream, among other things. It's also used to figure out the water flow rate in a pipeline or open channel.

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The area of this polygon is equal to 428 ft².

In order to calculate the area of this polygon, we would have to determine the total area of the two different parts of the given composite figure.

Therefore, the total area of this polygon is the sum of the area of the each geometric figure (rectangle):

Area of rectangle A = Length × Width

Area of rectangle A = 13 × 26

Area of rectangle A = 338 ft²

Area of rectangle B = 9 × (23 - 13)

Area of rectangle B = 9 × 10

Area of rectangle B = 90 ft²

Therefore, total area is given by:

Total area = 90 + 338

Total area = 428 ft²

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Answer:

We can use the slope-intercept form of a linear equation to model the balance y after t months, where the slope represents the rate of change of the balance and the y-intercept represents the initial balance.

The initial balance (y-intercept) is the amount Tina borrowed to buy the refrigerator, which we don't know. But we can find the slope using the two data points provided:

Four months: balance = $630

Six months: balance = $520

The change in the balance over the two-month period is:

$520 - $630 = -$110

The slope of the line is the rate of change of the balance per month, which is:

slope = Δy/Δt = (-$110)/(6-4) = -$55/month

Using the point-slope form of a linear equation, we can plug in one of the data points to find the y-intercept:

y - 630 = -$55(t - 4)

y - 630 = -$55t + 220

y = -$55t + 850

Therefore, the equation that models the balance y after t months is:

y = -$55t + 850.

The water surface in the conical tank is rising at a rate of approximately 0.16 feet per minute when the water depth is 5 feet.

To solve for this, we can use related rates. Since the tank is being filled with water at a constant rate of 2 ft³/min , we know that the rate of change of the volume of water in the tank is constant. We can use the formula for the volume of a cone to relate the volume of water in the tank to the height of the water in the tank:

V = (1/3) * pi * r² * h

Taking the derivative of both sides with respect to time gives:

dV/dt = (1/3) * pi * r² * dh/dt

We know that dV/dt = 2 ft³/min, r = 2 ft, and h = 5 ft. Solving for dh/dt:

dh/dt = (3 / pi * r²) * dV/dt

dh/dt = (3 / 4 * pi) * 2

dh/dt = 0.16 ft/min

Therefore, the water surface is rising at a rate of approximately 0.16 feet per minute when the water depth is 5 feet.

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Jennifer needs to sample at least 151 vets to achieve a standard error of the mean of 3.42 years or less.

The variability or uncertainty of a sample statistic, like the mean or proportion, is measured by standard error. It represents the sample distribution's standard deviation for that statistic. In other words, it calculates the amount by which chance is likely to cause the sample statistic to deviate from the actual population parameter.

The calculation of the standard error is based on the particular statistic being produced as well as the characteristics of the sampled population. For instance, the population's standard deviation is divided by the square root of the sample size to determine the standard error of the mean. If p is the estimated proportion based on the sample, then the standard error of a proportion is determined as (p * (1 - p)) divided by the square root of the sample size.

A population parameter estimate that has a lower standard error is more accurate. Inferential statistics frequently employ the standard error to compute confidence intervals and test population parameter-related hypotheses.

The formula for the standard error of the mean can be used to get the approximate number of veterans Jennifer needs to sample:

[tex]SE = / \sqrt{n}[/tex]

where n: sample size, delta: age standard deviation, and SE: standard error of the mean.

In this instance, we are aware that = 22 years and SE = 3.42 years. As we solve for n, we obtain:

[tex]n = (delta / SE)^2 n = (22 / 3.42)^2 \sn = 150.39[/tex]

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Answer:

18.29 x 10^12

Step-by-step explanation:

you can simplify the answer as needed

The coordinates of the image after rotating the figure 180 degrees about the origin are T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Given that

T'(-4, 3). V'(-5, 5), W'(-2, 5). X(-1, 3)

Rotating a figure by 180 degrees is equivalent to flipping it over the horizontal and vertical axes simultaneously.

This means that the x-coordinate of each point will be negated, and the y-coordinate will be negated as well.

Therefore, to find the coordinates of the image of a point after rotating it by 180 degrees, you can use the following formula:

(x', y') = (-x, -y)

Using the above, the image is

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

Hence, the image is T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

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Complete question

Rotate the figure 180 degrees about the origin

T'(4. -3). V'(5, -5), W'(2, -5). X.(1, -3)

T'(3, 4). V'(5, 5), W'(5, 2), X '(3. 1) (Th

T'(-3, 4) V(-5. 5), W'(-5, 2). X'(-3, 1)

T'(-3, -4), V'(-5, -5). W(-5, -2), X '(-3, -1)

The graph of g can be obtained using a horizontal stretch by a factor of 4 and a vertical translation 3 units up of the graph of f.

In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented by this mathematical expression g(x) = f(x) + N.

Where:

Based on the information provided about the parent function f, a function that represents g(x) is given by:

g(x) = 4f + N

g(x) = 4x + 3

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In the present scenario, the angle of Θ= π terminates in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.

the terminal point (x, y) of Θ= π on the unit circle can be calculated with the help of the following steps:

Step 1: Firstly, let’s recall the unit circle, which is a circle having a radius of 1 unit, and it is centered at the origin of a coordinate plane.

Step 2: Draw the angle of Θ= π on the unit circle. We can see that this angle has been formed by rotating in the clockwise direction along the unit circle from its initial position on the positive x-axis.

Step 3: As we know that the terminal point (x, y) of an angle in standard position is given by (cos Θ, sin Θ). Therefore, we can apply this formula to calculate the coordinates of the terminal point for the given angle of Θ= π on the unit circle.

Here, cos π= -1 and sin π= 0. Thus, the coordinates of the terminal point are (-1, 0). Hence, the correct answer is (-1, 0).Note: The coordinates of the terminal point for an angle in standard position can be negative, positive, or zero, based on the quadrant in which the angle terminates.

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Answer:

3

Step-by-step explanation:

Number of people in the choir = 80

Number of women = half of 80 = 40

Number of men in the choir is ¼ of the women = 40/4 = 10

Number of men plus women = 10 +40 = 50

Number of children = 80 - 50 = 30

Ratio of children to men = n:1 = 30:10

Divide both sides by 10

30:10 = 3:1

n = 3

Plug the corresponding R(s) for each input type and the transfer functions of the given systems into the equations above to find yss and ess for each case. Keep in mind that some systems might not have a finite steady-state response or error for specific input types, depending on the system's type (order and poles).

To determine the steady-state response (yss) and steady-state error (ess) values for the given systems, we need to use their transfer functions and input types (unit step, unit ramp, and unit parabolic). Unfortunately, without information about the specific transfer functions for figures 5.74 a, b, 5.75, and 5.76, it is not possible to provide a definitive answer.

In general, for a system with transfer function G(s), you can calculate the steady-state response and error using the Final Value Theorem:

yss = lim (s -> 0) s * Y(s), where Y(s) = G(s) * R(s) is the system's output.
ess = lim (s -> 0) s * E(s), where E(s) = R(s) - Y(s) is the system's error.

For different input types:
- Unit step input: R(s) = 1/s
- Unit ramp input: R(s) = 1/s^2
- Unit parabolic input: R(s) = 1/s^3

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Answer:

Step-by-step explanation:

To find the volume of a pyramid, we can use the formula:

V = (1/3) * base area * height

First, we need to find the height of the pyramid. To do this, we can draw a diagram of the pyramid and create a right triangle using half a side of the base, the height of the pyramid, and one of the segments connecting the apex to a midpoint of a side of the base.

Using the Pythagorean theorem, we can solve for the height:

h^2 + (14/2)^2 = 25^2

h^2 + 49 = 625

h^2 = 576

h = 24

Now we can find the base area:

Base area = 14^2

Base area = 196

And finally, we can use the formula to find the volume:

V = (1/3) * 196 * 24

V = 1568 cubic units

Therefore, the volume of the pyramid is 1568 cubic units.

Answer:

C is the correct function.

The answer is 'The indicator variable and square footage would be combined to get the interaction term'

In an equation or formula, a variable is a symbol or letter that stands in for an unknowable or varying quantity or value.

To create an interaction term in this regression model, we would multiply the indicator variable (1 if the house is within 3 miles of campus, 0 if not) by the square footage. This would allow us to examine whether the effect of square footage on house price is different for houses that are within 3 miles of campus compared to those that are not.

So, the answer is: The indicator variable and square footage would be combined to get the interaction term.

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The area of the figure composing of a rectangle and a semi-circle is 105.12 ft².

The figure in the image composes of a rectangle and a semi-circle.

The area of a rectangle is expressed as;

Area = Length × Width

The area of a semi-circle is expressed as;

Area = 1/2 × πr²

First, we find the area of the rectangle.

Area = Length × Width

Plug in Length = 10ft and Width = 8ft

Area = 10ft × 8ft

Area = 80ft²

Next, find the area of the semi-circle.

Area = 1/2 × πr²

Since diameter = 8ft, radius r = diameter/2 = 8ft/2 = 4ft

Area = 1/2 × 3.14 × (4ft)²

Area = 1/2 × 3.14 × 16 ft²

Area = 25.12 ft²

Now, area of the composite figure will be:

Area of the rectangle + Area of the semi-circle.

Area = 80ft² + 25.12 ft²

Area = 105.12 ft²

Therefore, the area of the figure is 105.12 ft².

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Since the value of a is less than 0, the graph of the parabola would be opening downwards. Because of this we can rule out option C. In a quadratic equation, c represents the y-intercept, and, in this case c is negative, meaning the y-intercept is less than 0. Only option B has a downward-opening curve and a y-intercept less than 0, so it is the answer.

Answer: p= 2+c

Step-by-step explanation:

Answer:

I attached your answer along with an explanation

Step-by-step explanation:

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A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex]  .

The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that  [tex]ZF = ZD + DF = 24 + 28 = 52[/tex]  and [tex]FH = ZG = 30 and ZH = 36.[/tex]

As a result, Fard ZH's perimeter is as follows:

perimeter = [tex]= ZF + FH + ZH + ZG[/tex]

perimeter  [tex]= 52 + 30 + 36 + 30[/tex]

perimeter  [tex]= 148[/tex]

So the perimeter of Fard ZH is [tex]148[/tex]  .

(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:

[tex]V = (xB - xA, yB - yA)[/tex]

Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.

Plugging in the given values, we get:

[tex]V = (5 - 10, 2 - 14)[/tex]

[tex]V = (-5, -12)[/tex]

Therefore, The V's direction is [tex](-5, -12)[/tex] .

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