Give your vector u = (-1,3) and v = (2,-2), find a linear combination of the vectors u and v of the form au+bv that would result in the vector (5,-3)

The percentage change in production is 20%.

To find the percentage change in production, we need to calculate the difference between the old production and the new production, divide it by the old production, and then multiply by 100 to get the percentage change.

Old production:

Number of boxes produced in two 10-hour shifts = 500 boxes

New production:

Number of boxes produced in three 8-hour shifts = 600 boxes

Difference in production:

600 boxes - 500 boxes = 100 boxes

Percentage change in production:

(100 boxes / 500 boxes) × 100 = 20%

Therefore, the percentage change in production is 20%.

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Answer:

5

Step-by-step explanation:

U means union which is the collection or combination of two or more sets. So (AUB)= {1,2,3,5}

n means intersection which is the set of element common in two or more set. So (AUB)'n c ={5}

Answer:

-2 3/4 < -1 1/2

Step-by-step explanation:

Positives are always greater than negatives (Example: 2 is greater than -2).

This eliminates the first and last inequalities.

Smaller negative numbers are always greater than larger negative numbers (Example: -2 is greater than -4).

This eliminates the third unequality.

For the second given inequality, convert the fractions to share the same denominator.

-2 3/4 < -1 2/4

They are both negative numbers.

We know smaller negative are always greater than larger negative numbers.

This inequality aligns with this statement.

Therefore, only the second inequlity is true.

The series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other is a combination of translation and rotation that involves 150 degrees. A transformation refers to the process of changing an object's position, size, or shape.

Translation, reflection, rotation, dilation, and skew are the five basic transformation types that modify an object.In geometry, congruent shapes have the same shape and size. To superimpose one shape onto another means to make them coincide with each other.

The following series of transformations would show that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other: Step 1: Translation. Translate the parallelogram ABCD by 5 units to the right and 6 units down to obtain parallelogram A1B1C1D1.Step 2: Rotation. Rotate parallelogram A1B1C1D1 by 150 degrees counterclockwise around point A1 to obtain parallelogram A2B2C2D2.Step 3: Translation. Translate parallelogram A2B2C2D2 by 8 units to the right and 3 units up to obtain parallelogram A'B'C'D'.Thus, the series of transformations that shows that parallelogram ABCD is congruent to parallelogram A'B'C'D' by superimposing one onto the other involves translation and rotation, with a rotation of 150 degrees.

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Answer:

It should be 17, hope this helps!

Answer:

2804

Step-by-step explanation:

2504 + 140 + 160 = 2804   (hint: add the 140 + 160 first. It sums up to 300 which is easy to add to 2504)

Answer:

sorry I don't understand it

Answer:

just guess

Step-by-step explanation:

ion know its better den nothing

To calculate inflation, the following equation is given

where i represents the inflation rate(in decimals), p1 the starting value of the house, p2 the value of the house after a amount of n years.

If we use this equation for a house with a current cost of $224,200 and an inflation of 2.37%, we're going to have

To calculate the how much the house will be worth in 2 years, we substitute n for 2 and solve for p2.

Answer:

-6

Step-by-step explanation:

14 - 8 = 6

Answer:

-6

Step-by-step explanation:

u subtracted right but its a negative and a positive and the -14 is bigger than the 8 so it would be a negative answer which is -6

The percent decrease is 10.16%

Percent decrease can be calculated by dividing the decrease by the original value and multiplying by 100

The first step is to calculate the decrease

= 4.33 - 3.89

= 0.44

The percent decrease can be calculated as follows

= 0.44/4.33 × 100

= 0.1016 × 100

= 10.16

Hence the percent decrease is 10.16 %

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Answer:

(B)  10.16%

Step-by-step explanation:

Correct on my quiz.

Answer:

for the first line let (-4,-3) be (x1,y1) and (8,0) be x2,y2.

now,

slope (m1) = (y2-y1)/ (x2-x1)

or, m1= 0-(-3)/ 8-(-4)

or, m1=3/12=1/4

again, for line two consider (0,2) as x1,y1 and (-1,6) be (x2,y2)

apply the same formula and find the slope(m2)

m2=6-2/-1-0

or, m2=4/-1

for b) m1 multiply m2

or 1/4 x 4/-1

=-1 so it is perpendicular

Step-by-step explanation:

for a we simply apply the formula of slope considering the given points as x1,y1 and x2,y2 respectively.

while for the b number if m1 x m2 =-1 the line is considered to be perpendicular.

similarly, if m1=m2 then it is considered to be parallel.

here m1 is slope of the first line, m2 is slope of second line and m3 is the slope of the third line

To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.

To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.

After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.

Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.

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Answer:

24

Step-by-step explanation:

You have to distribute the parenthesis. 7 x 2 is 14 and 7 x 1 is 7.

Add those and you get 21.

21 + 3 = 24

Answer:

24

Step-by-step explanation:

7 (2 + 3) + 3

7 (3) + 3

21 + 3

24

hope this helps

Answer:

6 feet

Step-by-step explanation:

C. 6 feet

Length of Side g is 6 feet

Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.

Given,

∠F = 49°

Length of side f = 7 feet

∠G = 40°

length of side g = ?

According Sine rule,

\(\frac{\sin E}{e}=\frac{\sin F}{f}=\frac{\sin G}{g}\)

\(\frac{\sin 49}{7}=\frac{\sin 40}{g}\)

\({g}=7(\frac{\sin 40}{sin 49})\)

g = 5.96 ≈ 6

Hence, length of side g is 6 feet.

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Answer:

Step-by-step explanation:

You want to know how to determine the y-intercepts of a rational function, and their possible number.

A rational function f(x) is the ratio of two polynomial functions p(x) and q(x):

  f(x) = p(x)/q(x)

As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...

  f(0) = p(0)/q(0)

The values of p(0) and q(0) are simply the constant terms in those respective functions.

The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.

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An equation and graph that represents the total cost (in dollars) of ordering the shirts is c = 20t + 10.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, a linear equation that models the situation with respect to the number of T-shirts is given by;

y = mx + b

c = 20t + 10

Where:

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

\(\textsf{A)} \quad \cos 2 \theta=\dfrac{9}{25}\)

\(\textsf{B)} \quad \sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}\)

Step-by-step explanation:

Given:

\(\sin \theta=\dfrac{2\sqrt{2}}{5},\quad \dfrac{\pi}{2} < \theta < \pi\)

\(\hrulefill\)

To determine the exact value of cos 2θ, we can use the Cosine Double-Angle formula:

\(\large\boxed{\cos^2\theta = 1 - 2 \sin^2 \theta}\)

Substitute the given value of sin θ into the formula:

\(\begin{aligned}\cos 2 \theta&=1-2\left(\dfrac{2\sqrt{2}}{5}\right)^2\\\\\cos 2 \theta&=1-2\left(\dfrac{8}{25}\right)\\\\\cos 2 \theta&=\dfrac{25}{25}-\dfrac{16}{25}\\\\\cos 2 \theta&=\dfrac{9}{25}\end{aligned}\)

\(\hrulefill\)

To determine the exact value of sin (θ/2), we can use the half-angle formula for sine:

\(\large\boxed{\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\cos \theta}{2}}}\)

First, find the value of cos θ by substituting the given value of sin θ into the trigonometric identity sin²θ + cos²θ = 1:

\(\begin{aligned}\left(\dfrac{2\sqrt{2}}{5}\right)^2+\cos^2\theta&=1\\\\\dfrac{8}{25}+\cos^2\theta&=1\\\\\cos^2\theta&=1-\dfrac{8}{25}\\\\\cos^2\theta&=\dfrac{17}{25}\\\\\cos\theta&=\pm \sqrt{\dfrac{17}{25}}\\\\\cos\theta&=\pm \dfrac{\sqrt{17}}{5}\end{aligned}\)

As cos θ is negative on the interval π/2 < θ < π, we take the negative square root. Therefore:

\(\cos\theta&=-\dfrac{\sqrt{17}}{5}\)

Now, substitute the found value of cos θ into the half-angle formula:

\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\left(-\dfrac{\sqrt{17}}{5}\right)}{2}}\)

Therefore:

\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5}{5}+\dfrac{\sqrt{17}}{5}}{2}}\)

\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5+\sqrt{17}}{5}}{2}}\)

​​

​\(\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{5+\sqrt{17}}{10}}\)

As sin θ is positive on the interval π/2 < θ < π, we take the positive square root. Therefore:

\(\sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}\)

The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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Answer:

C. y = -1/5x

Step-by-step explanation:

y = -1/5 exhibits direct proportionality.  This means that y varies directly as x (for every change in x, y also experiences change), while the "-1/5" represents the constant of proportionality.  Because -1/5 is negative, every increase in x will result in a decrease in y.

Answer:

y= -12x - 77

Step-by-step explanation:

HOPE THIS HELPS

Answer:

I think 15%

Step-by-step explanation:

sorry if wrong Hope you do good !

                 -Ash

Answer:

102%

Step-by-step explanation:

a model can help you solve surface area and volume problems. a diagram shows faces and helps you find; a diagram helps you choose a base and height when finding Surface area.

A model can help you solve surface area and volume problems by providing visual representations and aiding in the determination of relevant measurements. Specifically, a "diagram" shows faces and helps you find the different sides or surfaces involved in the problem. It visually presents the shape and its various components, allowing you to identify and analyze the relevant areas or volumes.

A model can be in the form of a physical object or a digital representation. It shows faces and helps you find the different surfaces or sides of the object that contribute to its surface area. By visually observing the model, you can count the number of faces and determine their shapes and sizes, enabling you to calculate the total surface area accurately.

Furthermore, a model helps you choose a base and height when finding the volume of a three-dimensional object. It allows you to visualize the dimensions that define the object's shape and select appropriate measurements for the base and height. By manipulating the model or observing its features, you can determine the appropriate dimensions needed to calculate the volume correctly.

In summary, a model serves as a visual aid, providing a tangible representation of the object or shape. It shows faces, helping you identify the surfaces for surface area calculations, and assists in choosing a base and height when finding the volume of three-dimensional objects.

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Multiplication: 4 significant figures

Division: 4 significant figures

Addition: 4 significant figures

To determine the number of significant figures, we need to count the non-zero digits in each number and any zeros between them.

For the number 6.429×10³, there are four significant figures: 6, 4, 2, and 9.

For the number 3.18785×10², there are six significant figures: 3, 1, 8, 7, 8, and 5.

When multiplying two numbers, the result should have the same number of significant figures as the least precise number in the calculation. In this case, the least precise number is 6.429×10³ with four significant figures. Therefore, the product will also have four significant figures.

When dividing two numbers, the result should have the same number of significant figures as the dividend (the number being divided). In this case, the dividend is 6.429×10³ with four significant figures. Therefore, the quotient will also have four significant figures.

When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places. However, since we are adding whole numbers here, the decimal places are not relevant. We only need to consider the significant figures. In this case, both numbers have four significant figures, so the sum will also have four significant figures.

In summary:

Multiplication: 4 significant figures

Division: 4 significant figures

Addition: 4 significant figures

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A player has played 15 games at a local arcade and 10 games at an amusement park, with the belief that her mean score at the arcade is greater than her mean score at the amusement park.

To determine whether the player's belief is supported by the data, we need to compare the mean scores at the arcade and the amusement park. Let's assume the scores for the arcade games are: 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28. And the scores for the amusement park games are: 8, 9, 10, 12, 14, 15, 16, 18, 19, 20.

To find the mean score for each set of games, we sum up the scores and divide by the number of games. For the arcade games, the sum is 334, and the mean score is 334 / 15 = 22.27. For the amusement park games, the sum is 141, and the mean score is 141 / 10 = 14.1.

Comparing the mean scores, we see that the mean score at the arcade (22.27) is indeed greater than the mean score at the amusement park (14.1). Therefore, the player's belief that her mean score at the arcade is greater than her mean score at the amusement park is supported by the given data.

By calculating the mean scores for the games played at the arcade and the amusement park, we can compare the average performance at each location. The mean score is calculated by summing up the scores and dividing by the number of games played.

In this case, the mean score at the arcade (22.27) is higher than the mean score at the amusement park (14.1), suggesting that the player performs better on average at the arcade. This analysis supports the player's belief that her mean score at the arcade is greater than her mean score at the amusement park.

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Answer:

No value of x

Step-by-step explanation:

SEE the image for solution.

HOPE it helps

Have a great day

There are 4²⁴ possible ways to complete the multiple-choice test consisting of 24 questions, with each question having four possible answers.

We have 24 questions with each having 4 possible outcomes. If we had a question, then we would have 4 ways of answering question 1 and for each of the four answers in question 1, we would have four ways of answering question 2. So, we have 4² ways of answering the questions.

Like this, we have 24 questions. There are four ways to choose an answer to each question. By counting principle, we multiply the number of choices at each step and then we have -

= 4×4×4×4...= 4²⁴ ways to complete the test

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Answer:

32=X becuase you said He subtracted 7 three times or thrice so we multiply that then add 11 because it was our remaining number from subtraction. so 32

Step-by-step explanation:

The required sample size is  8.90400.

Given a student wants to make a guess within 0.03 of the true ratio with a 90% confidence level.

Margin of Error, E = 0.03

significance level α=0.10  {90% confidence}

A given estimate of the percentage of population p is p = 0.79.

The critical value for the significance level α = 0.10 is Zc = 1.645. This can be determined using either Excel or a normal probability table.

Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.

n≥p(1-p)(Zc÷E)²

n = 0.796×(1-0.796)(1.645÷0.03)²

n = 0.796 x 0.204 x 54.833

n = 8.90400

Therefore, the resample size required to meet the condition is n ≥  8.90400 and must be an integer. From this, we conclude that the minimum sample size required is n =  8.90400

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Answer:

y=4/3x+2

Step-by-step explanation:

The equation is in standard form right now, which is ax+by=c

your question is asking for slope intercept form, which is y=mx+b

so we need to isolate y onto 1 side

-4x+3y=6

add 4x to both sides

3y=4x+6

divide by 3 on both sides

y=4/3x+2

The probability of the family having at most one right-handed child is \((2/3)^3 + 3 * (2/3)^2 * (1/3) = 0.593\).

The probability of event A can be calculated using the formula P(A) = 1 - P(not A). Since the left-handed:right-handed ratio is 1:2, the probability of a child being right-handed is 2/3 and the probability of a child being left-handed is 1/3. Thus, the probability of the family having children of both handedness is\(1 - P(not A) = 1 - (2/3)^3 = 0.741\).

The probability of event B can be calculated using the formula P(B) = P(not A) + P(A and B). Since the left-handed:right-handed ratio is 1:2, the probability of a child being right-handed is 2/3 and the probability of a child being left-handed is 1/3. Thus, the probability of the family having at most one right-handed child is\((2/3)^3 + 3 * (2/3)^2 * (1/3) = 0.593.\)

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