What are all of the factors of 84? A 1, 2, 4, 21, 42, 84 B 1, 2, 3, 4, 21, 28, 42, 84 C 1, 2, 3, 4, 6, 14, 21, 28, 42, 84 D 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Answer:

Vertex:

\(f(x)=-5(x-1)^2+4\)

Standard:

\(f(x)=-5x^2+10x-1\)

Factored:

This is unfactorable.

Step-by-step explanation:

The parabola has a vertex at (1, 4) and it crosses a point at (2, -1).

We will start off with the vertex form, given by:

\(f(x)=a(x-h)^2+k\)

Where (h, k) is the vertex.

Therefore:

\(f(x)=a(x-1)^2+4\)

Since the function passes through (2, -1), f(x) = -1 when x = 2:

\(-1=a(2-1)^2+4\)

Solve for a:

\(-5=a(1)\Rightarrow a =-5\)

Therefore, vertex form is:

\(f(x)=-5(x-1)^2+4\)

To find the standard form, expand:

\(f(x)=-5(x^2-2x+1)+4\)

Distribute:

\(f(x)=-5x^2+10x-5+4\)

And simplify:

\(f(x)=-5x^2+10x-1\)

We can now factor. Which two values multiply to be 5 and add up to be 10?

Since this is no possible, the equation is unfactorable.

Answer:

see explanation

Step-by-step explanation:

The area (A) of a sector is calculated as

A = area of circe × fraction of circle

   = πr² × \(\frac{0}{360}\) ← where θ is in degrees

[ note that 360° = 2π radians ], then

A = πr² × \(\frac{0}{2\pi }\) ← where θ is in radians

( Cancel π on numerator/ denominator )

A = \(\frac{1}{2}\)θr²

9514 1404 393

Answer:

  top down: 2, 4, 1, 7, 6, 5, 3, 8

Step-by-step explanation:

It appears the expected order may be ...

__

Write the formula for a sector area of a circle with central angle, θ, in degrees.

  \(\textit{Area of a Sector}=\dfrac{\theta}{360^{\circ}}\cdot\pi r^2\)

Replace 360° with 2π radians.

  \(\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}\)

Replace the angle ratio in degrees with the angle ratio in radians.

  \(\textit{Area of a Sector}=\dfrac{\theta}{2\pi}\cdot\pi r^2\)

Simplify by cancelling

  \(\textit{Area of a Sector}=\dfrac{1}{2}\theta r^2\)

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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Answer:

rhombus

Step-by-step explanation:

you can't see what shape that is but Im doing this assignment right now I know what it looks like

The equation of the line is y = x.

To find the equation of a line given its graph, you need to follow the steps below.

Step 1: Determine the slope of the line.The slope of the line can be determined using the formula: slope = rise/run or m = Δy/Δx. Rise is the change in the y-coordinates and run is the change in the x-coordinates.

Step 2: Determine the y-intercept of the line.The y-intercept is the point where the line intersects the y-axis. You can determine the y-intercept by looking at the point where the line crosses the y-axis on the graph. The y-intercept is denoted by the letter b.

Step 3: Write the equation of the lineThe equation of the line can be written in slope-intercept form, which is y = mx + b. The slope (m) and y-intercept (b) that were determined in steps 1 and 2 are used to substitute into this equation. Thus, the equation of the line becomes y = slope(x) + y-intercept.

Example:Let's say you are given the graph of a line below: .

Step 1: Determine the slope of the line.To determine the slope of the line, you need to choose two points on the line and calculate the rise and run. Let's choose the points (2, 1) and (4, 3). The rise is 2 (3 - 1) and the run is 2 (4 - 2). Therefore, the slope of the line is: m = 2/2 = 1.

Step 2: Determine the y-intercept of the lineThe line crosses the y-axis at the point (0, 0). Therefore, the y-intercept of the line is b = 0.

Step 3: Write the equation of the line.The equation of the line in slope-intercept form is y = mx + b. Substituting the slope and y-intercept into this equation gives: y = 1x + 0 or y = x.

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The vertex of the graph of this equation y = x² - x - 2 is equal to -2.25.

In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

For the given quadratic function y = x² - x - 2 in question 9, the axis of symmetry can be calculated as follows:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-1)/2(1)

Axis of symmetry, Xmax = 1/2

Axis of symmetry, Xmax = 1/2.

Next, we would determine the vertex when x = 1/2 as follows;

y = x² - x - 2

y = (1/2)² - 1/2 - 2

y = 1/4 - 1/2 - 2

y = 0.25 - 0.5 - 2

y = -2.25.

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The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.

Given:

- Each correct question is worth 10 points.

- Every student receives an additional 555 bonus points.

Let's calculate the mean and standard deviation of YY:

Mean of YY:

The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:

μY = μX * 10 + 555

Substituting the value of μX from the given information:

μY = 1.95 * 10 + 555

μY = 19.5 + 555

μY = 574.5

Therefore, the mean score of a random student (YY) is 574.5.

Standard Deviation of YY:

The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:

σY = σX * 10

Substituting the value of σX from the given information:

σY = 0.8 * 10

σY = 8

Therefore, the standard deviation of the random student's score (YY) is 8.

Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

that a randomly chosen student answered correctly. Here is the probability distribution of X along with

summary statistics:

0

1

2

2.

3

X = # correct

P(X)

0.05

0.20

0.50

0.25

Mean: Hex = 1.95

Standard deviation: Ox 0.8

Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give

every student 5 additional bonus points. Let Y represent a random student's score.

What are the mean and standard deviation of Y?

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Answer:

Step-by-step explanation:

To make sure that you are adding 2 odd numbers, the first one is 2x - 1 and 2x + 1

Their sum is 216

Equation

2x - 1 + 2x + 1 = 216

Solution

2x - 1 + 2x + 1 = 216                   Combine like terms on the left

4x = 216                                     Divide by 4

4x/4 = 216/4                               Combine

x = 54

Answer

2x - 1 = 2*54 - 1 = 108 - 1 = 107

2x + 1 = 2*54 + 1 = 108+1 = 109

The two consecutive odd numbers are 107 and 109

Answer:

Step-by-step explanation: Here if we put \(x=0\) then we will get initial temperature. That is \(T_0=70+20=90\).

The temperature will cools down \(70(0.8)^{10}+20=27.52(approx)\).

So the final temperature after 10 minutes will be :\(90-27.52=62.48(approx)\).

Final Answer: The temperature is 62.48 degree Celsius.

Answer:

Step-by-step explanation:

The correct answer is a. A larger sample size was used.As per the Law of Large Numbers, the more times an experiment is repeated, the closer the actual results will be to the expected probability. In this case, rolling the cube 100 times provides a larger sample size than rolling it only 20 times. The more rolls that are made, the greater the likelihood that the actual results will converge towards the expected probability of 1/2 for rolling an even number.Option b, The 100 tosses were controlled better, is not relevant to this scenario since the fairness of the cube is assumed.Option c, The expected probability changed when the cube was rolled 100 times, is not true. The expected probability of rolling an even number on a fair six-sided die is always 1/2, regardless of the number of times it is rolled.Option d, The thrower considered only the even rolls, and disregarded the odd rolls, is not a valid assumption. The question states that the number of even rolls was recorded, but it does not imply that odd rolls were disregarded.

Answer:

Step-by-step explanation:

How do I make my question?

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

The hypothesis :

H0 : σ²= 47.1

H1 : σ² > 47.1

α = 5% = 0.05

Population variance, σ² = 47.1

Sample variance, s² = 83.2

Sample size, n = 15

The test statistic = (n-1)*s²/σ²

Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1

Test statistic = T = [(14 * 83.2)] * 47.1

Test statistic = 1164.8 / 47.1

Test statistic = 24.73

The degree of freedom, df = n - 1 ; 10 = 9

Critical value (0.05, 9) = 16.92 (Chisquare distribution table)

Reject H0 ; If Test statistic > Critical value

Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.

Answer:

boom bam ba boom bam ba

Answer: -3/4

Step-by-step explanation:

The y value is decreasing by -0.75

-3.75 - 0.75 = -4.5

-4.5 - 0.75 = -5.25

-5.25 - 0.75 = -6

ect.

-0.75 in fraction form is -3/4

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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The measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.

The arc measure DE and the angle it subtends at the center of the circle are directly proportional.

so arc DE = m∠DQE {central angle}

Arc length of the sector = (central angle / 360) x (2 x π x radius)

8.73 in = (m∠DQE / 360) x (2 x 22/7 x 10 in)

m∠DQE = (8.13 in × 360 × 7)/(2 × 22 × 10) {cross multiplication}

m∠DQE = 46.5055° = arc DE

Therefore, the measure of the arc angle DE is derived to be 46.5055° using the arc length of the sector.

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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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Answer: 225

Step-by-step explanation:

Create a ratio part/whole for radians = part/whole for degrees

\(\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}\)      Keep change flip because you are dividing fractions for left side

\(\frac{5\pi }{4} (\frac{1}{2\pi }\)) = \(\frac{x}{360}\)

\(\frac{5}{8} (\frac{360}{1} ) =x\)

x = 225

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

60

Step-by-step explanation:

\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)

Therefore, the value of a is 60 degrees

The equation that represents the average least squared error and the regression line on the scatter plot is called a) Partial Correlation.

Partial Correlation:

In probability theory and statistics, partial correlation measures the degree of association between two random variables and removes the influence of many driving random variables. Using their correlation coefficients in determining the numerical relationship between two variables of interest can lead to misleading results when there is another confounding variable that is numerically related to both variables of interest increase. This misleading information can be avoided by controlling for confounding variables. This is done by calculating the partial correlation coefficient. This is exactly the motivation for including other right-sided variables in the multiple regression. However, while multiple regression provides unbiased results for effect sizes, it does not provide numerical values ​​as a measure of the strength of the relationship between two variables of interest.

For example:

Given economic data on consumption, income, and wealth for different people, consider the relationship between consumption and income. Not considering wealth when calculating the correlation coefficient between consumption and income can lead to misleading results. Indeed, the measured correlations between consumption and income can be tainted by these other correlations.

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Answer:

The answer is 7 : 48.

Step-by-step explanation:

First, you can to calculate how many students are there in Jill's grade by adding the number of students who have pet with the students without pets :

total = 41 + 7 = 48

Next, you have to find the ratio of students without pets to total students :

7 : 48

Answer:

Total student = Student who have pet + Student who don't have pet

Total Student = 41 + 7

Total Student = 48

Ratio

\( \tt \:7 \ratio \: 48\)

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Answer:

\(3 {x}^{2} - 15x - 18 = 0\)

\( {x}^{2} - 5x - 6 = 0\)

\((x + 1)(x - 6) = 0\)

x = -1 or x = 6

The coordinates of the zeroes are (-1, 0) and (6, 0).