Find the measure of ∠7.

Given:
∠1 is a right angle
∠3 = 37°
∠8 =62°

A. 53°
B. 65°
C. 105°
D. 127°
E. 245°

The range of the quadratic function is {y |0 ≤ y < 9}

The range of a function is the set of output values of the graph. This in other words mean the range of a function is the set of y values of the graph.

From the question, we have the following parameters:

Write out the vertex

So, we have

Vertex = (0, 0)

Remove the x value

y = 0

From the question, we have

The parabola opens upward

This means that the vertex is a minimum

So, the range is

y ≥ 0

Rewrite as

0 ≤ y

Recall that:

Closed circle point = (-2, 4)

Open circle point = (3, 9)

Remove the x values

Closed circle point = 4

Open circle point = 9

Remove the smaller y value

Open circle point = 9

This means that the highest value of y is at open circle point = 9

This is represented as

y < 9

So, we have

0 ≤ y and y < 9

Combine both

0 ≤ y < 9

Rewrite properly as

{y |0 ≤ y < 9}

Hence, the range of the quadratic function is {y |0 ≤ y < 9}

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{y |0 ≤ y < 9}

The person above need the shine, im just making it simple

In LR2 (two-dimensional Euclidean space), a line passing through the origin is closed under vector addition, meaning that if you take any two vectors on that line, their sum will also lie on the same line.

However, a line not passing through the origin is not closed under vector addition.

To illustrate this, let's consider a line L in LR2 that does not pass through the origin. We can represent this line as a straight line segment starting from a point A and ending at a point B. The line segment AB represents the line L.

Now, consider two vectors represented by two line segments starting from the origin O and ending at points C and D, respectively. These vectors can be represented as OC and OD. Since the line L does not pass through the origin, OC and OD will not lie on line L.

If we try to add these two vectors, we construct the parallelogram OBCD, where BC represents the vector addition OC + OD. Since OC and OD do not lie on line L, their sum BC will also not lie on line L. This violates the closure property, where the sum of two vectors on a line should also be on the same line.

the geometric figure, in this case, would consist of a line L not passing through the origin, two vectors OC and OD not lying on line L, and the resulting vector BC (sum of OC and OD) not lying on line L. This figure demonstrates that a line in LR2 not passing through the origin is not closed under vector addition.

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I'm not sure if it is dynamic or static equilibrium but if I had to choose I'd say dynamic

Answer:

It is in static equilibrium with a net force of 0 N.

Step-by-step explanation:

EDGE21

The solution to the compound inequality 5x + 7 < -3 or 3x - 4 > 11 is x < -2 or x > 5.

To solve the compound inequality, we will solve each inequality separately and then combine the solutions using "or".

For the first inequality:

5x + 7 < -3

Subtracting 7 from both sides:

5x < -10

Dividing both sides by 5 (remembering to flip the inequality when dividing by a negative number):

x < -2

For the second inequality:

3x - 4 > 11

Adding 4 to both sides:

3x > 15

Dividing both sides by 3:

x > 5

Combining the solutions:

x < -2 or x > 5

Therefore, the solution to the compound inequality is x < -2 or x > 5.

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Answer:

91.125 or 729/8

Step-by-step explanation:

take 4.5^3 to get 91.125

Answer:

7

Step-by-step explanation:

Answer:

Independent variable - type of cola drink

dependent variable - taste rating of cola drink

extraneous variable - type of cola drink

Step-by-step explanation:

The independent variable is the variable that the person carrying out an experiment changes or manipulates. the independent variable usually have a direct effect on the dependent variable

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable.

The extraneous variable is the variable  that is not been researched in the experiment but it has the potential to influence the results of the experiment.

The type of cola drink given to participants can be manipulated to derive different ratings. the ratings that participants would give the cola drink is determined by the type of cola drink served. Here, the type of drink served is the independent variable while the ratings given is the dependent variable.

the extraneous variable is the type of drink cups used. this is not relevant to the experiment but can affect the results of the experiments. for example, imagine a red cup is used for the experiment and a participant hates red cups. it is more likely that the participant would give a low rating for the cola drink even if the drink tastes good

If 10% of all resistance exceeding 10.256 ohms, and 5% have resistance less than 9.671 ohms, then the mean value is 10 ohms and standard deviation of resistance distribution is 0.2 ohms.

To determine mean-value and standard deviation of resistance distribution, we use properties of normal-distribution and given information.

We denote the mean value of resistance distribution as μ and standard deviation as σ.

We know that 10% of all resistors exceed 10.256 ohms, The z-score represents the number of standard deviations away from the mean.

We know that the z-score corresponding to the 10% percentile is approximately 1.28,

Similarly, also given that 5% of resistors have resistance smaller than 9.671 ohms, We also know that the z-score for the 5% percentile is approximately -1.64,

The z-score equation for the 10% percentile : 10.256 = μ + 1.28σ,

The z-score equation for the 5% percentile : 9.671 = μ - 1.64σ,

Now we solve these two equations to find the values of μ and σ.

From equation(1), we rewrite it as : μ = 10.256 - 1.28σ,

Substituting this expression for μ into equation(2), We get :

9.671 = (10.256 - 1.28σ) - 1.64σ

9.671 = 10.256 - 1.28σ - 1.64σ

9.671 = 10.256 - 2.92σ

2.92σ = 10.256 - 9.671

2.92σ = 0.585

σ ≈ 0.2,

Substituting this value of σ into equation(1),

We get,

μ = 10.256 - 1.28σ

μ = 10.256 - 1.28 × 0.2

μ ≈ 10.256 - 0.256

μ ≈ 10,

Therefore, the required mean is 10 ohms and standard-deviation is 0.2 ohms.

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The mean value of the resistance distribution is μ and the standard deviation is σ.

To find the mean and standard deviation of the resistance distribution, we can use the properties of a normal distribution.

Let's denote the mean as μ and the standard deviation as σ.

From the given information, we know that 10% of the resistance values exceed 10.256 ohms, and 5% have resistance smaller than 9.671 ohms.

Using the properties of a normal distribution, we can determine the z-scores corresponding to these percentages.

The z-score represents the number of standard deviations a data point is away from the mean.

For the 10% exceeding 10.256 ohms, the z-score can be calculated as:

z = (x - μ) / σ

where x is the resistance value and z is the z-score.

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to the 10% exceeding value. Let's denote this z-score as z1.

Similarly, for the 5% smaller than 9.671 ohms, we can find the z-score corresponding to this percentage and denote it as z2.

Now, we have two equations:

z1 = (10.256 - μ) / σ

z2 = (9.671 - μ) / σ

We can solve these two equations simultaneously to find the values of μ and σ.

Once we have the values of μ and σ, we can conclude that the mean value of the resistance distribution is μ and the standard deviation is σ.

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Step-by-step explanation:

To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x-value of each point by 2.

Statistical tools are used for all of the above options: A) describing numbers, B) making inferences about numbers, and C) drawing conclusions about numbers.

Statistical tools are essential for analyzing and interpreting data. They provide methods and techniques for describing, analyzing, and drawing meaningful conclusions from numerical data.

Firstly, statistical tools are used for describing numbers. Descriptive statistics summarize and present data in a meaningful way, allowing us to understand the characteristics and patterns within the data. Measures such as mean, median, mode, range, and standard deviation provide descriptive information about the data.

Secondly, statistical tools are used for making inferences about numbers. Inferential statistics involve making predictions, generalizations, or estimates about a population based on sample data.

By using statistical techniques such as hypothesis testing and confidence intervals, we can draw conclusions about a population based on a subset of data.

Lastly, statistical tools are used for drawing conclusions about numbers. By applying appropriate statistical tests and analyses,

we can draw valid conclusions and make informed decisions based on the data. Statistical tools enable us to evaluate relationships, compare groups, detect patterns, and assess the significance of findings.

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Answer:

y - 1 = -6( x - 2)

Step-by-step explanation:

(2,1)  The x is 2 and the y is 1.

Answer:

4(5x - 3y)(5x + 3y)

Step-by-step explanation:

Assuming you require the expression factored.

Given

100x² - 36y² ← factor out 4 from each term

= 4(25x² - 9y²) ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , thus

25x² - 9y²

= (5x)² - (3y)² ← with a = 5x and b = 3y

= (5x - 3y)(5x + 3y)

Thus

100x² - 36y² = 4(5x - 3y)(5x + 3y) ← in factored form

The qyaeriin has no attached diagram. A related diagram was found and used to provide the steps required to solve the problem.

Answer:

1 inch = 8.333 feets

Step-by-step explanation:

Initial dimension of rectangle :

100 feets by 10 feets

Fractional decrease in garden = 2/3

New Dimension of garden :

2/3(100 feets) by 2/3(10 feets)

66.667 feets by 6.6667 feets

Hence

From the picture attached :

8 inch = 66.667

1 inch = 8.333

The new scale of the drawing = 1 inch = 8.333 feets

Answer:

ty

Step-by-step explanation:

thanks for points have a good day sir

Answer:

ik right ughh

Step-by-step explanation:

To determine whether the expressions "(p → (q → r))", "((p & q) → r)", and "(p → (q & r))" are equivalent using the Long Truth-Table method.

We need to create a truth table and evaluate the expressions for all possible combinations of truth values for the variables p, q, and r.

Let's first create the truth table:

|   p   |   q   |   r   | p → (q → r) | (p & q) → r | p → (q & r) |

|-------|-------|-------|-------------|-------------|-------------|

| True  | True  | True  |             |             |             |

| True  | True  | False |             |             |             |

| True  | False | True  |             |             |             |

| True  | False | False |             |             |             |

| False | True  | True  |             |             |             |

| False | True  | False |             |             |             |

| False | False | True  |             |             |             |

| False | False | False |             |             |             |

Now, let's fill in the truth values for each expression step-by-step:

1.  p → (q → r):

|   p   |   q   |   r   | p → (q → r) |

|-------|-------|-------|-------------|

| True  | True  | True  |    True     |

| True  | True  | False |    False    |

| True  | False | True  |    True     |

| True  | False | False |    True     |

| False | True  | True  |    True     |

| False | True  | False |    True     |

| False | False | True  |    True     |

| False | False | False |    True     |

2.  (p & q) → r:

|   p   |   q   |   r   | p → (q → r) | (p & q) → r |

|-------|-------|-------|-------------|-------------|

| True  | True  | True  |    True     |    True     |

| True  | True  | False |    False    |    False    |

| True  | False | True  |    True     |    True     |

| True  | False | False |    True     |    True     |

| False | True  | True  |    True     |    True     |

| False | True  | False |    True     |    True     |

| False | False | True  |    True     |    True     |

| False | False | False |    True     |    True     |

3.  p → (q & r):

|   p   |   q   |   r   | p → (q → r) | (p & q) → r | p → (q & r) |

|-------|-------|-------|-------------|-------------|-------------|

| True  | True  | True  |    True     |    True     |    True     |

| True  | True  | False |    False    |    False    |    False    |

| True  | False | True  |    True     |    True     |    True     |

| True  | False | False |    True     |    True     |    True     |

| False | True  | True  |    True     |    True     |    True     |

| False | True  | False |    True     |    True     |    True     |

| False | False | True  |    True     |    True     |    True     |

| False | False | False |    True     |    True     |    True     |

By comparing the truth values of the three expressions, we can conclude that "(p → (q → r))", "((p & q) → r)", and "(p → (q & r))" are all equivalent. They have the same truth conditions for all possible combinations of truth values for p, q, and r in the truth table.

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Without specific data on the number of students who prefer each option, we cannot calculate the probability.

To determine the probability that a student prefers the zoo or the water park, we need to know the total number of students and the number of students who prefer each option. Without this information, it is not possible to calculate the probability accurately.

To calculate the probability, we would need to divide the number of students who prefer the zoo or the water park by the total number of students. For example, if there are 50 students in total and 30 prefer the zoo and 20 prefer the water park, the probability would be:

P(prefer zoo or water park) = (30 + 20) / 50 = 50 / 50 = 1

However, without specific data on the number of students who prefer each option, we cannot calculate the probability.

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The number of regions created when constructing a Venn diagram with three overlapping sets is 8.

In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.

When three sets overlap, there are different combinations of elements that can be present in each region.

For three sets, the number of regions can be calculated using the formula:

Number of Regions = 2^(Number of Sets)

In this case, since we have three sets, the formula becomes:

Number of Regions = 2^3 = 8

So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.

Each region represents a unique combination of elements belonging to different sets.

These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.

Therefore, the correct answer is 8.

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The situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

The domain is 0 <= x <= 4 and the range is 0 <= y <= 120

The statement is given as

A cell phone plan costs $30 for each line

Let the number of lines be x and the total cost be y

So, we have

y = cost per line * x

This gives

y = 30x

The above equation represents a linear function

This means that the situation is a function; the independent variable is the number of lines and the dependent variables is the total cost

From the question, we have

You can have a maximum of four lines on a plan.

This means that the possible values of x are

x = 0, 1, ... 4

When these values are substituted in y = 30x, we have

y = 30 * 0 = 0

y = 30 * 4 = 120

Hence, the domain is 0 <= x <= 4 and the range is 0 <= y <= 120

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On solving the provided question, we can say that In light of this, the lowest common denominator of the equation is (x - 4)(x + 1)(x - 2) (x - 2)

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

equation is given as:

x2 — 3x — 4 = x2 — Ox + 8

x2 — 4x + x — 4 =

x(x — 4) + I(x — 4)

Factor out x - 4

(x + I)(x — 4) = x-2(x-4)

The common factor between the two sides of the equation is x – 4.

In light of this, the lowest common denominator is (x - 4)

(x + 1)(x - 2) (x - 2)

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Option C: Less than \(\sqrt58\\\) inches but greater than 7 inches

Ramon wants to make an acute triangle with three pieces of wood. So far,

he has cut wood lengths of 7 inches and 3 inches.

What length must the longest side be in order for the triangle to be acute?

According to the property of triangle,

If the square of larger side of triangle is equating to the sum of square of smaller side.

If \(a^{2} < b^{2}+c^{2}\) the triangle is acute triangle.

where, 'a' is the larger side and 'b' ,'c' are the smaller side

According to the question, Let a =a , b = 7, c = 3

\(a^{2} < 7^{2}+3^{2}\\ a^{2} < 49+9\\ a < \sqrt58\)

Means to be acute triangle third side must be less than \(\sqrt58\) inches but greater than 7 inches.

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Answer:

less than 58 inches but greater than 7

Step-by-step explanation:

i got it right on edge

Perimeter of rectangular garden = 34 ft

Area of rectangular garden = 60 ft²

Perimeter = 2(length + width)

Area = (length)(width)

The rectangular garden has the following vertices:

Length of the rectangular garden = QR = |-5 - 7| = |-12| = 12 units

Width of the rectangular garden = RS = |3 -(-2)| = |3 + 2| = 5 units

Perimeter = 2(length + width) = 2(12 + 5) = 34 units = 34 ft

Area = (length)(width) = (12)(5) = 60 units = 60 ft²

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Answer:C

Step-by-step explanation:

288 divided by 4 equals 72

Option C is correct, y=72x is the equation which represents the number of times her heart beats per minutes.

A division is a process of splitting a specific amount into equal parts.

The equation that represents the relationship between the number of times Lupe's heart beats per minute and the time (in minutes) is:

y = 72x

where y is the number of times Lupe's heart beats per minute, and x is the time in minutes.

We can see this by dividing the total number of heart beats by the time in minutes:

y = (288 beats / 4 minutes) = 72 beats/minute

Hence, y=72x is the equation which represents the number of times her heart beats per minutes.

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Answer:

12x-13

Step-by-step explanation:

Answer:

12x-13

Step-by-step explanation:

 First using PEMDAS you would solve the parenthesis multiply 2x by 3 and -4 by 3 which would form a equation -> 6x-12, then add on the other following equation. 6x-12+6x-1 as now it's just addition and subtraction it doesn't really matter what order you go in. Add both of the 6x's to get 12x and -12 and -1 to get -13 and your answer will be 12x-13. Hope this helps!

The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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1st question (the image):

y= -5/4x + 3/2

how to solve:

y=mx+b

b: where the line meets the y axis

3/2 is 1.5 which matches up perfectly with the graph

m: the direction of the slope

If you look where the line matches with a point and you go down -5 and go right 4 it matches up and thats why m = -5/4

2nd question (the text):

C) y = 3/4 x + 1/4

how to solve

draw a graph (up above)

y:mx+b

to find m: rise/run

find the first point (1,1) you have to go 3 points up and 4 points right to get to the next point

(5,4) and thats why m=3/4

b: where the link hits the y axis compare the answers and the graph and find the most resonable one... which is 1/4

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

\(\frac{3}{22}\)

Step-by-step explanation:

To multiply fractions, just multiply the numerators (tops) times each other and the denominators (bottoms) times each other:

\(\frac{-1}{4}\) x \(\frac{-6}{11}\) = \(\frac{6}{44}\)

Now all we have to do is to simplify.  In this case, just find the largest number that goes evenly into the numerator and the denominator: it is 2.  Divide numerator and denominator by 2 to get the final answer: \(\frac{3}{22}\)

Answer:

The balance point is the,number in between your set of numbers so you need to find The middle of 3 and 7, and then when you get that answer you find the number in between 8 and the,number you just found

Step-by-step explanation:

I'm not good at figuring this out myself but, I know the steps

Answer:

Below

Step-by-step explanation:

Answer 10.1: 15

Explanation:

(-4)^2 is 16 and (-1)^3 is -1, so (-4)^2 + (-1)^3 = 16 - 1 = 15.

Answer 10.3: -23

Explanation:

(-2)^2 is 4 and -27 minus 4 is -23.

Answer 10.5: None

Explanation:

The expression is incomplete as there is no number or operation after the "^3".

Answer 10.7: 0.7

Explanation:

√0.04 is 0.2 and (0.5)^2 is 0.25, so 0.2 + 0.25 = 0.45. The square root of 0.45 is approximately 0.671.

Answer 10.9: 0.02788

Explanation:

(0.2)^3 is 0.008 and 0.027 plus 0.008 is 0.035. Raising 0.035 to the power of 1/3 gives approximately 0.315. Therefore, the final answer is approximately 0.02788.

Answer 10.2: -2018

Explanation:

Using the order of operations, we start with 62 divided by 3 which is approximately 20.67, then multiply that by -33 to get approximately -682.44.

Answer 10.4: -2

Explanation:

Empty brackets imply multiplication. Therefore, ()^2 is 0, and (-1)^3 is -1. Thus, 0 - 1 = -1.

Answer 10.6: 0.11

Explanation:

(0.1)^2 is 0.01 and (0.1)^3 is 0.001, so 0.01 + 0.001 = 0.011.

Answer 10.8: 0.38

Explanation:

0.0144 + 0.04 = 0.0544, and the square root of 0.0544 is approximately 0.2336. Subtracting (-0.2)^2 (which is 0.04) from 0.0544 gives 0.0144. Taking the square root of 0.0144 gives approximately 0.12. Finally, 0.2336 minus 0.12 is approximately 0.38.

Answer:

16/33

Step-by-step explanation:

We have a bag of :

9 red marbles

6 blue marbles

7 green marbles

11 yellow marbles

Total number of marbles = 33 marbles.

The possibility that a red or green marble will be selected from a bag

P( Red or Green) = P(Red) + P(Green)

In the question we are not told if it is with replacement or without. We do both

With replacement

P( R or G) = P(Red) + P(Green)

P(Red)= 9/33

P(Green) = 7/33

= 9/33 + 7/33

= 16/33

Therefore, the possibility that a red or green marble will be selected from a bag is 16/33