Pleaseee help for robust

The vertex of the parabola is (-2, -3/2).

First, let's expand the given expression:

[tex]1/2(x-3)(x+5) = 1/2(x^2 + 2x - 15)[/tex]

Now, we can see that the coefficient of[tex]x^2[/tex] is positive, which means the parabola opens upwards.

To find the vertex, we can use the formula:

Vertex = (-b/2a, f(-b/2a))

where a = 1/2, b = 2, and f(x) =[tex]1/2(x^2 + 2x - 15).[/tex]

Substituting the values, we get:

Vertex = (-2/(21/2), f(-2/(21/2))) = (-2, f(-2))

To find f(-2), we can substitute x = -2 in the expression for f(x):

f(x) = [tex]1/2(x^2 + 2x - 15)[/tex]

f(-2) = [tex]1/2((-2)^2 + 2(-2) - 15)[/tex]

      = 1/2(-3)

      = -3/2

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Step-by-step explanation:

10 % off means you pay 90 %

the price of 50 jars times  90 % is:

50 * 1.20 * .90 = $ 54.00

The percentage of measurements in a data set that are above and below each of the following percentiles are 68%, 95% and 99.7%.

We need to calculate the percentage of the measurements contained in each of the following intervals:

According to the empirical rule, approximately 68% of the measurements in a normally distributed data set will fall within one standard deviation of the mean. Therefore, approximately 68% of the measurements will fall within the interval (mean - s, mean + s).

Similarly, approximately 95% of the measurements in a normally distributed data set will fall within two standard deviations of the mean. Therefore, approximately 95% of the measurements will fall within the interval (mean - 2s, mean + 2s).

Likewise, approximately 99.7% of the measurements in a normally distributed data set will fall within three standard deviations of the mean. Therefore, approximately 99.7% of the measurements will fall within the interval (mean - 3s, mean + 3s).

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Answer:

Step-by-step explanation:

[tex]f(x)=\frac{(x-1)(x+1)}{x-1}[/tex]

       [tex]=x+1[/tex]

Limit is found by substitution: Limit = 1+1 = 2

The output of 0.7326 represents the test statistic (Z-score) computed from the 1-sample Z-test in Excel.

It tells you how many standard deviations the sample mean is from the population mean under the null hypothesis.

A test statistic (Z-score) is a numerical value used in statistical hypothesis testing to assess the evidence against the null hypothesis.

A test statistic measures the difference between a sample statistic (eg sample mean) and the corresponding population parameter (eg population mean) assuming the null hypothesis is true.

For the Z-test, the test statistic is computed as

z = (x - μ) / (σ / √n)

where x = sample mean,

μ = population mean,

σ= population standard deviation,

and n = sample size.

The resulting Z-score indicates how many standard deviations the sample mean is from the population mean, assuming the null hypothesis is true.

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Answer: 1264.2857%

Step-by-step explanation:

Answer:

She earned 67.29% profit

Step-by-step explanation:

First let's find how much she spent on the coats.

50 x $28

$1400

So, her expense was $1400

Now, let's find how much she earned selling these coats.

We know she sold 38 of these coats at $49 each. Let's find how much she earned for these 38 coats.

38 x $49

$1862

She earned $1862 on these 38 coats.

Now, let's find how much she earned on the rest of the coats (50-38 which is 12). We know she sold the remaining for $40 each.

12 x $40

$480

She earned $480 on the rest of the coats.

The total she earned $2342

To find the profit:

Profit= $ Earned - Expenses

Profit= 2342-1400

Profit=$942

The question is asking for the percentage.

To find the percentage, we can use the percentage formula:

[tex]\frac{Profit}{Expense}[/tex] x 100

We know that the profit is $942 and the expense is $1400

(We want to find how much profit she made out of the expense)

[tex]\frac{942}{1400}[/tex] x [tex]\frac{100}{1}[/tex]

If you round your answer, you will get 67.29

Answer: She earned 67.29% profit

Answer:

Therefore, -8(2x-4) simplifies to -16x + 32.

Step-by-step explanation:

-8 * 2x - (-8 * 4)

Simplifying this expression further gives:

-16x + 32

Therefore, -8(2x-4) simplifies to -16x + 32.

Answer:

Step-by-step explanation:

There are 56 ways to select a group of five employees from the eight employees in the company for advanced training.

To select a group of five employees from a company that employs eight people, you can use the concept of combinations.
A combination is the selection of items from a larger set, where the order of items does not matter.

In this case, we want to choose 5 employees from a group of 8.

The formula for calculating combinations is:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of items, k is the number of items you want to select, and ! denotes the factorial.
So, for this problem:
n = 8 (total employees)
k = 5 (employees to be selected)
Now, we can plug these values into the formula:
C(8, 5) = 8! / (5!(8-5)!)
C(8, 5) = 8! / (5!3!)
C(8, 5) = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / ((5 × 4 × 3 × 2 × 1)(3 × 2 × 1))
C(8, 5) = (8 × 7 × 6) / (3 × 2 × 1)
C(8, 5) = (336) / (6)
C(8, 5) = 56

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Answer:

He would be 28

Step-by-step explanation:

If 7 students divided by 8 sandwiches each student gets 8 pieces of sandwich.

If 7 students are divided by 8 sandwiches, we can start by calculating the total number of pieces of sandwich available:

Total number of pieces of sandwich = 7 * 8 = 56

So there are 56 pieces of sandwich available for 7 students.

To find out how many pieces of sandwich each student gets, we divide the total number of pieces of sandwich by the number of students:

Each student gets 56 / 7 = 8 pieces of sandwich.

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In a circle dance, there are 17 dancers in the circle.

Circle dance is a type of folk dance that involves people holding hands and dancing in a circular formation. The dancers move around in a circle, following a set of steps or patterns, and the dance may include turns, hops, and other movements.

In a circle dance, the total number of dancers is equal to the sum of the dancers on opposite sides of the circle.

Let's assume there are "x" dancers in the circle.

Since dancer 15 is directly opposite dancer 3, there are (x - 1) dancers between them.

Therefore, the sum of the dancers on opposite sides of the circle is (15 + 3) + (x - 1) = (x + 17).

Since the dancers are evenly spaced around the circle, the sum of the dancers on opposite sides of the circle is equal to the total number of dancers in the circle.

So we can write:

x + 17 = x

Solving for x, we get:

x = 17

Therefore, there are 17 dancers in the circle.

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The values of x, y, and z in the given rhombus are: x = -31, y = 20, z = -87.

An equation is a mathematical statement saying that two amounts or values are the same, for example 6 x4=12x

We know that the side of a rhombus are equal in length.therefore we can solve the given equation

4y + 8 = -3x - 5 = -z + 1 = 88

Solving each equation for the variables, we get:

4y + 8 = 88

4y = 80

y = 20

-3x - 5 = 88

-3x = 93

x = -31

-z + 1 = 88

-z = 87

z = -87

Heance , the values of x, y, and z in the given rhombus are:

x = -31, y = 20, z = -87.

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By answering the presented question, we may conclude that the value of the equation is 5/x --> x/5 or (1/5)x

In mathematics, an equation is a statement that states the equivalence of two expressions. An equation is made up of two sides separated by an algebraic equation (=).

For example, the argument contends that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to identify the value or values of the variable(s) that will make the equation true.

Simple or complicated equations, regular or nonlinear, with one or more components are all possible. For example, in the equation [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are utilized in many areas of mathematics, including algebra, calculus, and geometry.

[tex](x)(2) -- > 2x[/tex]

[tex]x/2 -- > 0.5x or (1/2)x[/tex]

[tex]5+x -- > x+5[/tex]

[tex](1/5)x -- > x/5 or (x \times 0.2)[/tex]

[tex](x)/5 -- > 0.2x or (1/5)x[/tex]

2x --> same as (x)(2)

[tex](1/2)x -- > 0.5x or x/2[/tex]

Therefore,  [tex]5/x -- > x/5 or (1/5)x[/tex]

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Answer:

The statement that is FALSE is b) "The area is 26ft²".

Answer:

There are 55 boys.

Step-by-step explanation:

The ratio of

girls: boys:total

4           5     4+5

4            5      9

The total is 99

To get from 9 to 99, we multiply by 11.

girls: boys:total

4*11    5*11   9*11

44      55      99

There are 55 boys.

Answer:

5 units

Step-by-step explanation:

The distance from -3 to 1 is 4 and the distance from 3 to 0 is 3.  Use the Pythagorean Theorem.  

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]4^{2}[/tex] + [tex]3^{2}[/tex] = [tex]c^{2}[/tex]

16 + 9 = [tex]c^{2}[/tex]

25 = [tex]c^{2}[/tex]

[tex]\sqrt{25}[/tex] = [tex]\sqrt{c^{2} }[/tex]

5 = c

Helping in the name of Jesus.

The number of books that had no damage or minor damage in the sample is:

722 + 75 = 797

To estimate the number of books in the entire collection that would have no damage or minor damage, we can assume that the proportion of books with no or minor damage in the sample is approximately equal to the proportion of books with no or minor damage in the entire collection.

The proportion of books with no or minor damage in the sample is:

797 / (722 + 75 + 29) = 0.9064

So we can estimate the number of books with no damage or minor damage in the entire collection as:

0.9064 x 70,500 = 63,912.6

Rounding to the nearest whole number, we get:

63,913

Completed table is shown below. With this h number, we can calculate the cone's volume as V = (1/3)(72)h[tex]\pi[/tex] = 49/3h[tex]\pi[/tex] = 6[tex]\pi[/tex]h = 131.88.

To complete the table relating the height and volume of cones with a radius of 7 units using the equation[tex]v = 6\pi h[/tex], we need to substitute the radius value of 7 units into the formula for volume and then solve for height.

Height (h) Volume (V)

1                  131.88

2                  263.76

3                  395.64

4                  527.52

5                  659.4

To obtain volume for each height, we plug in radius value of 7 units into the formula for the volume of a cone, which is given by [tex]V = (1/3)\pi r^{2} h[/tex]. This gives us [tex]V = (1/3)\pi (7^{2} )h = 49/3\pi h[/tex],

which simplifies to V = 16.33h. Then we substitute this expression for V into given equation [tex]v = 6\pi h[/tex] to obtain [tex]16.33h = 6\pi h[/tex], and solve for h to obtain h = 6.56.

Using this value of h, we can obtain the volume of the cone as [tex]V = (1/3)\pi (7x^{2} )h = \\49/3\pi h = \\6\pi h = \\131.88[/tex]

After that, by multiplying the value of h by 16.33 and rounding to two decimal places, we can determine the volumes for the other heights in the table.

Therefore, the completed table is as shown above.

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First, we need to calculate the percentage of citizens who chose either Snakes or Dogs.

The percentage of citizens who chose Dogs is 26%, which is equivalent to 0.26 as a decimal.

The percentage of citizens who chose Snakes is 10%, which is equivalent to 0.10 as a decimal.

To find the number of citizens who chose either Snakes or Dogs, we need to multiply the total number of citizens by the combined percentage of Snakes and Dogs:

0.26 + 0.10 = 0.36

So the combined percentage of Snakes and Dogs is 36%.

To find the number of citizens who chose Snakes or Dogs, we can multiply the total number of citizens by this percentage:

0.36 x 95,000 = 34,200

The team opened 4 packs of juice.

To find out how many packs of juice the team opened, follow these steps:
1. First, find the total number of juice boxes bought by multiplying the number of packs by the number of boxes in each pack: 7 packs × 8 boxes = 56 boxes.
2. Next, subtract the remaining boxes of juice to find out how many boxes the team drank: 56 boxes - 29 boxes = 27 boxes.
3. Finally, divide the number of boxes the team drank by the number of boxes in each pack to find the number of packs they opened: 27 boxes ÷ 8 boxes = 3.375 packs.
Since they only opened each pack after they drank all the boxes from the pack before, the team opened 4 packs of juice.

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After answering the presented question, we can conclude that Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.

In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either idea can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you take length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.

First, we need to find the radius of the cone:

[tex]radius = diameter/2 = 6.4/2 = 3.2 ft[/tex]

Now we can use the Pythagorean theorem to find the height of the cone:

[tex]height^2 = slant height^2 - radius^2[/tex]

[tex]height^2 = 5.8^2 - 3.2^2[/tex]

[tex]height^2 = 20.84[/tex]

height ≈ 4.56 ft

Next, we can find the surface area of the cone by adding the area of the base to the lateral surface area. The base is a circle with radius 3.2 ft, so its area is:

base area =[tex]\pi (radius)^2[/tex]

base area =[tex]\pi (3.2)^2[/tex]

base area ≈ 32.17 sq. ft.

The lateral surface area is the curved surface area of the cone, which can be found using the slant height and the radius:

lateral surface area = [tex]\pi (radius)(slant height)[/tex]

lateral surface area = [tex]\pi (3.2)(5.8)[/tex]

lateral surface area ≈ 58.92 sq. ft.

Therefore, the total surface area is:

total surface area ≈ base area + lateral surface area

total surface area ≈ [tex]32.17 + 58.92[/tex]

total surface area ≈ 91.09 sq. ft

Rounding this to the nearest whole number, we get a surface area of 91 sq. ft.

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1. IQR, because Sunny Town is skewed 2. Both coffee shops typically sell the same amount of coffee per hour. 3. Burger Quick is able to estimate their wait time more consistently than Super Fast Food, since it has a smaller IQR.

The middle 50% of a dataset are represented by the interquartile range (IQR), a measure of variability. It is computed as IQR = Q3 - Q1, where IQR is the difference between the first and third quartiles (Q1 and Q3). The dataset is divided into four equal portions by quartiles, with Q1 standing for the 25th percentile and Q3 for the 75th percentile. The IQR is an effective tool for comparing the spread of datasets since it is a robust measure of variability that is unaffected by extreme values or skewness.

To determine the location with the most consistent temperature use IQR, since it is the best way to compare the consistency of temperature readings between the two sites.

2. The mean is:

(1.5 + 20 + 3.5 + 12 + 2 + 5 + 11 + 7 + 2.5 + 9.5 + 3 + 5) / 12 = 6.25

Arrange the values in order: 1.5, 2, 3, 3.5, 5, 7, 9.5, 11, 12, 20

The middle two values are 7 and 9.5.

The median is (7 + 9.5) / 2 = 8.25

Thus, we can conclude that both coffee shops typically sell the same amount of coffee per hour.

3. Super Fast Food:

IQR of 7.5 (15.5 - 8.5) and a range of 24 (27 - 3)

Burger Quick:

IQR of 15 (24 - 9.5) and a range of 28 (30 - 2).

Burger Quick is able to estimate their wait time more consistently

than Super Fast Food, since it has a smaller IQR.

4. Bus 47 :

IQR of 8 (16 - 8) and a range of 24 (28 - 4)

Bus 14:

IQR of 6 (18 - 12) and a range of 18 (28 - 10).

Hence, Bus 14 is the most consistent, since it has a smaller IQR.

5. For the Allstars, the mean is:

(73 + 62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15 = 67.

The Champs, with a median of about 67 inches

6. For the given data:

Median = (5 + 5) / 2 = 5

The measures of center for Bay Side School and Seaside School are both 5.

B: Range = 8 - 0 = 8.

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A and B can have values that would give a sum of 11 when they are added together, such as (2,9), (3,8), (4,7), and (5,6).

Here, it is evident that since

AB+ BA= CDC

the hundreds and ones digit of the answer are equal and since we are talking about 2 digit numbers, hundreds place C can only be 1 since it is obtained from carry of the tens place (B+A) and the maximum carry that a 2 digit number can give is 1 (99+99 gives carry 1).

Also, D must be equal to C+1 since it is obtained by B+A and carry of ones place.

C=A+B= 1

D=C+1= 2

The possible values of A and B can be the ones that result in 11 when added, i.e. (2,9),(3,8),(4,7) and (5,6).

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Complete question is attached below

the standard equation of the circle is (x + 2)² + (y + 4)²= 100 .  we can use The standard equation of a circle with center (h,k) and radius r is:

(x - h)² + (y - k)² = r²

what is standard equation of circle ?

The standard equation of a circle with center (h,k) and radius r where (x,y) are the coordinates of any point on the circle. This equation represents all the points in the plane that are a fixed distance (the radius r) from the center of the circle (h,k).

In the given question,

The standard equation of a circle with center (h,k) and radius r is:

(x - h)² + (y - k)² = r²

In this case, we know that the point (4, -12) is on a circle with center (-2, -4). We also know that the radius of the circle is the distance between the center and the point on the circle, which we can find using the distance formula:

r = √((4 - (-2))² + (-12 - (-4))²)

r = √(6² + (-8)²)

r = √(100)

r = 10

So the equation of the circle is:

(x - (-2))² + (y - (-4))² = 10²

(x + 2)² + (y + 4)² = 100

Therefore, the standard equation of the circle is:

(x + 2)² + (y + 4)²= 100

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Answer:

To multiply (3x - 4y) and (4x - 7y), we need to use the distributive property, which states that: a(b + c) = ab + ac Using this property, we can expand the given expression as: (3x - 4y)(4x - 7y) = 3x(4x) + 3x(-7y) - 4y(4x) - 4y(-7y) Simplifying each term, we get: = 12x^2 - 21xy - 16xy + 28y^2 = 12x^2 - 37xy + 28y^2 Therefore, the simplified answer is 12x^2 - 37xy + 28y^2.

Answer:

c ik this because I took the same question as you

The product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].

The given expression is [tex]\frac{8x+8}{x^2-2x+1} .\frac{x-1}{2x+2}[/tex].

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Here, [tex]\frac{4(2x+2)}{x^2-1x-1x+1} \times \frac{x-1}{2x+2}[/tex]

= [tex]\frac{4(2x+2)}{x(x-1)-1(x-1)} \times \frac{x-1}{2x+2}[/tex]

= [tex]\frac{4(2x+2)}{(x-1)(x-1)} \times \frac{x-1}{2x+2}[/tex]

Cancel the same factors, that is

= [tex]\frac{4}{(x-1)} \times \frac{1}{1}[/tex]

= [tex]\frac{4}{(x-1)}[/tex]

Therefore, the product of the given algebraic expression is [tex]\frac{4}{(x-1)}[/tex].

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The answer is C. (x,y) - (x - 6, y + 2)

The simplified expression for the given variables is -7x³y² + 3x²y³ + 6y³.

A set of principles called the algebraic order of operations specifies the order in which mathematical operations should be carried out in order to simplify equations. The following is the order of events:

Operation inside parentheses should come first. Simplify exponential formulas by using exponents.

Division and multiplication should be done from left to right.

Operationally, add and subtract should be done from left to right.

The given expression can be simplifies as follows:

(3x²y³ + x² - 7x³y²) - (4x³y² - 6y³ + 2x²)

= 3x²y³ + x² - 7x³y² - 4x³y² + 6y³ - 2x²

= -7x³y² + 3x²y³ + 6y³

Hence, the simplified expression is -7x³y² + 3x²y³ + 6y³.

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Answer:

True

Step-by-step explanation:

The following parts can be answered by the concept of  confidence interval.

a. True

b. False

c. Incomplete statement, please provide complete statement.

a. True. A 95% confidence interval includes the range of values that are consistent with the observed data at the 95% level of confidence. Since a 99% confidence interval is wider than a 95% confidence interval, it must also include the null hypothesized value within it.

b. False. Decreasing the significance level ($\alpha$) reduces the probability of making a type 1 error, as it sets a higher threshold for rejecting the null hypothesis.

c. The statement is incomplete, and therefore cannot be evaluated.

Therefore, if a given value is within a 95% confidence interval, it will also be within a 99% confidence interval. However, decreasing the significance level ($\alpha$) reduces the probability of making a type 1 error. It is important to provide a complete statement for proper evaluation

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