Write a formula for g(x) in terms of x.

Answer:

jnjgnjgn n fwdn d ndjdd

Step-by-step explanation:

Answer:

1/48

Step-by-step explanation:

1/8 divided by 6 is 1/8*1/6=1/48

Answer:  see proof below

Step-by-step explanation:

Since (a, b) is equidistant from (-a, 2) and (2, -b), then it is the midpoint of the those two points. Use Midpoint formula to find (a, b).

\(M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\a=\dfrac{-a+2}{2}\qquad \qquad \qquad \quad b=\dfrac{2-b}{2}\\\\\\2a=-a+2\qquad \qquad \qquad \quad 2b=2-b\\\\\\3a=2\qquad \qquad \qquad \qquad \qquad 3b=2\\\\\\a=\dfrac{2}{3}\qquad \qquad \qquad \qquad \qquad b=\dfrac{2}{3}\)

3(a + b) - 4 = 0

\(3\bigg(\dfrac{2}{3}+\dfrac{2}{3}\bigg)-4=0\\\\\\3\bigg(\dfrac{4}{3}\bigg)-4=0\\\\\\4-4=0\\\\0=0\qquad \text{TRUE!}\)

Notice that I changed the equation to "negative 4" because the equation you provided did not make a true statement.

Answer:

A

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ 2, 4 ], thus

f(b) = f(4) = 16 ← corresponding value of y from table

f(a) = f(2) = 4 ← corresponding value of y from table , thus

average rate of change = \(\frac{16-4}{4-2}\) = \(\frac{12}{2}\) = 6 → A

The average rate of change of function f(x) in the interval from x = 2 to x = 4 is 6.

The average rate of change of a function is defined as the average rate at which one quantity is changing with respect to something else changing.

\(A([a, b]) = \frac{f(b)-f(a)}{b-a}\)

Where,

A([a, b]) is the average rate of change of function A(x) in the closed  interval [a, b].

According to the given question

We have an interval [2, 4]

⇒ [a, b] = [2, 4]

Now,

f(b) = f(4) = 16   (corresponding value of f(4) from table)

and, f(a) = f(2) = 4  (corresponding value of f(2) from table)

Therefore  average rate of change of f(x) in the closed interval [ 2, 4 ] is

⇒ Average rate of change of f(x) = \(\frac{f(4)-f(2)}{4-2}\)

⇒ Average rate of change of f(x) = \(\frac{16-4}{2}\)

⇒ Average rate of change of f(x) = \(\frac{12}{2}\)

⇒ Average rate of change of f(x) = 6

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Answer:

a = 127° , b = 12° , c = 115°

Step-by-step explanation:

a and 53° are same- side interior angles and sum to 180° , that is

a + 53° = 180° ( subtract 53° from both sides )

a = 127°

c and 115° are alternate angles and are congruent , then

c = 115°

53° , b and c lie on a straight line and sum to 180°

53° + b + c = 180°

53° + b + 115° = 180°

b + 168° = 180° ( subtract 168° from both sides )

b = 12°

then a = 127° , b = 12° , c = 115°

Answer:

a = 127; b = 12; c = 115

Step-by-step explanation:

c =115

b = 180 - 115 - 53

b = 12

a = b + c

a = 12 + 115

a = 127

The pressure applied on the whole table top = 361.9 N/m² to 4 significant figures.

Pressure= force/area

Area of the circular table = πr²

where r = 75cm = 0.75m

Area of the circular table = 3.143 × 0.75 × 0.75

= 1.768m²

Force = 640 N

Pressure = 640/1.768

= 361.99

= 361.9 N/m² to 4 significant figures.

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9514 1404 393

Answer:

  396,040

Step-by-step explanation:

Factors of 2020 are 2, 5, 101.

There are 1,000,000 / 1010 = 990 multiples of 2 and 5 and 101.

There are 1,000,000 / 505 -990 = 990 multiples of 5 and 101 only.

There are 1,000,000 / 202 -990 = 3,960 multiples of 2 and 101 only.

There are 1,000,000 / 10 - 990 = 99,010 multiples of 2 and 5 only.

There are 1,000,000 / 101 -990 -990 -3960 = 3,960 multiples of 101 only.

There are 1,000,000 / 5 -990 -990 -99,010 = 99,010 multiples of 5 only.

There are 1,000,000 / 2 -990 -3960 -99,010 = 396,040 multiples of 2 only.

So, the total number of multiples of any factor of 2020 is ...

  990 +990 +3960 +99,010 +3960 +99010 +396040 = 603960

Then the number of integers in the first million that do not share any common factors greater than 1 with 2020 is ...

  1,000,000 -603,960 = 396,040

The analyst should include at least 60,088 gas stations in her sample to estimate the 95% confidence interval for the average price of unleaded gasoline with a maximum deviation of $0.04.

To estimate the 95% confidence interval for the average price of unleaded gasoline in California with a maximum deviation of $0.04, we need to determine the minimum number of gas stations to include in the sample. We'll use the standard deviation estimate of 50.24 and the z table.

Step 1: Determine the z-score for a 95% confidence interval. You can find this in a z table or use a calculator. The z-score is 1.96.

Step 2: Use the margin of error formula:
The margin of error = \(Z(\frac{Standard Deviation}{\sqrt{(Sample Size)}})\)

Step 3: Plug in the given values and solve for the Sample Size (n):
$0.04 = \(1.96(\frac{50.24}{\sqrt{(n)}})\)

Step 4: Rearrange the formula to solve for n:
\(n=[\frac{ (1.96)(50.24)}{ 0.04}]^2 = 60087.69\)

Round up to the nearest whole number:
n ≈ 60088

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Answer:

Step-by-step explanation:

The required exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is y = 86 * (1.20)ˣ.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Let's let the variable x represent the number of weeks after opening the shop, and let y represent the weekly sales in dollars. We know that in the first week, her sales were $86. After that, her sales increased by 20% each week. This means that her sales in the second week were,

We can see that her sales are increasing by a factor of 1.20 each week. This means that we can model her sales using an exponential equation of the form:

y = a * (1.20)ˣ

Where a is the amount of the initial sales in the first week (which we know is $86).

So the exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is:

y = 86 * (1.20)ˣ

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Answer:

Everything is x2 itself.

Step-by-step explanation:

5x2=10 10x2=20 20x2=40

Answer:

it multiples time 2 every time

Step-by-step explanation:

5 to ten 5times 2

10 to 20 10 time 2

20 to 40. 20 time 2

Answer: y = f(x-1) + 4

Step-by-step explanation:

The dotted line is the function if it was translated 4 units upwards and 1 unit to the right. Therefore, we add 4 to the end of the equation (adding 4 to y) to shift it up, and subtract 1 from the x to shift it to the right.

Answer:

++hhhhhhhhhhhhhhhhhh

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

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The ladder on pulling 6 feet father from the house now reaches 45.83 feet, which is lower than previous height.

The distance between ladder and house, the distance till ladder reaches and length of ladder given by Pythagoras theorem. The distance till ladder reaches is perpendicular, ladder is hypotenuse and the base is horizontal distance between the two. So, finding the base first.

Base² = 50² - 48²

Base² = 2500 - 2304

Base² = 196

Base = ✓196

Base or horizontal distance = 14 feet.

Now, on moving 6 feet, the horizontal distance will be 14 + 6 = 20 feet. Finding the new height or perpendicular now.

50² = 20² + Perpendicular²

Perpendicular² = 2500 - 400

Perpendicular² = 2100

Perpendicular = 45.83 feet

Hence, the ladder now reached to 45.83 feet height of the house.

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Answer:

"I think there are a whole bunch of points that are 3 units away from (-5, 0)". Lin's statement is correct.

Step-by-step explanation:

from the question, the point has a coordinate (-5, 0) which can be plotted on a Cartesian plane to show its location or position. A Cartesian coordinate is a system that consists of two perpendicularly intersecting axis used for plotting of the locations or positions of given points.

There are a whole bunch of points that are 3 units away from (-5, 0) because real numbers that are 3 units away are more than 4. Real numbers consists of all rational numbers, fractions and irrational numbers. So if all real numbers that are 3 units away from (-5, 0) are plotted, then the points would be more than 4.

Therefore, Lin's statement is correct.

Answer:

y=-2/5x

Step-by-step explanation:

y-y1=m(x-x1)

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

y+2=-2/5(x-5)

y=-2/5x+10/5-2

y=-2/5x+2-2

y=-2/5x

Answer:

5 + (.75 * x ) + y = z

Step-by-step explanation:

X = number of added ounces

Y = toppings added

Z = cost of smoothie bowl

$5 the cost of minimum bowl.

Then add that to the .75 cents  multiplied by the number added ounces.

Then add that to the .50 if you get toppings.

The .50 equals the y but it could be 0 to so that's why I added Y.

Answer: 1.88 x 10^6

Step-by-step explanation:

This is converted to scientific notation

Answer:

the last one

Step-by-step explanation:

just click the last one

Answer:

0.05x

Step-by-step explanation:

0.05x

Answer:

Step-by-step explanation:

5% as a decimal is 0.05 so:

0.05x

multiply 0.05 with that number.

5% as a fraction is:

or 1/20

multiply 1/20 with that number

Hope this helps :)

Answer:

-$500

Step-by-step explanation:

Answer:

Step-by-step explanation:

100X5=500

500 Was deducted from the account

Answer:

a)  See the attachment for the completed Venn diagram.

b)  The number of people who liked to watch television only is 20.

c)  The total number of people who took part in the survey was 200.

Step-by-step explanation:

Draw a Venn diagram with two overlapping circles.

Label one circle "Radio" and the other circle "TV".

Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.

Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:

Therefore, place the number 70 in the part where the two circles overlap.

Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:

Therefore, place the number 60 in the area outside the two circles.

Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:

Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.

Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:

Therefore, there was a total of 200 people who took part in the survey.

A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.

A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.

The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.

On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.

This approach can help to improve the accuracy of forecasts and predictions based on the time series data.

In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.

Therefore, Option C is correct answer.

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Hey there!

10 + 5 + 0 + (-5) + (-10) + (-15)

= 10 + 5 - 5 - 10 - 15

= 15 - 5 - 10 - 15

= 10 - 10 - 15

= 0 - 15

= -15

Therefore, the answer should be: -15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

270

Step-by-step explanation:

\(360 - 90 = 270\)

The correct statements are:

b. The population variances for each of the cells should be equal (i.e., there is homogeneity of variance).

c. The populations from which the samples are taken for a two-way ANOVA must be distributed normally.

In a two-way ANOVA, there are several assumptions that need to be met for valid statistical inference. Two of these assumptions are the equality of population variances and the normal distribution of populations.

b. The assumption of homogeneity of variance states that the population variances for each combination of levels of the two factors in a two-way ANOVA should be equal. Violation of this assumption can lead to biased results and affect the validity of the statistical test.

c. The assumption of normality states that the populations from which the samples are taken should follow a normal distribution. This assumption is important because the validity of the F-test used in ANOVA is based on the assumption of normality. Departures from normality can impact the accuracy and reliability of the results.

a. The statement in option (a) is not true. The two-way ANOVA is not robust to violations of the assumptions of sampling from normal distributions and homogeneity of variance, even if the samples are of equal size. Violations of these assumptions can lead to inaccurate and unreliable results.

d. The statement in option (d) is also not true. If the assumptions of a two-way ANOVA are violated, it does not necessarily mean that the researcher should conduct two separate one-way ANOVAs. There are alternative non-parametric tests or robust ANOVA methods that can be used in such cases. The choice of appropriate statistical analysis depends on the nature of the data and the specific research question.

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Answer:

Slope = \(-\frac{1}{6}\)

Step-by-step explanation:

Slope = \(\frac{Rise}{Run}\)

Slope = \(\frac{6-10}{24-0}\)

Slope = \(-\frac{1}{6}\)

Answer:

-1/6

Step-by-step explanation:

Just use the formula Y2-Y1/X2-X1.

In this case if you substitute the coordinates of those numbers, then it would be 6-10/24-0 which is 24/-4 and if you simplify it, then you get the slope -1/6.

Answer:

- 920

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

d = 22- 30 = 14 - 22 = 6 - 14 = - 8

This indicates the sequence is arithmetic with sum to n terms given by

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 30 and d = - 8 , thus

\(S_{20}\) = \(\frac{20}{2}\) [ (2 × 30) + (19 × - 8) ]

     = 10(60 - 152)

     = 10 × - 92

     = - 920

Answer:

k < -1 or k > 11

Step-by-step explanation:

Given quadratic equation:

\(3x^2-x+ k = kx-1\)

First, rearrange the given quadratic equation in standard form ax² + bx + c = 0:

\(\begin{aligned}3x^2-x+ k &= kx-1\\3x^2-x+ k-kx+1&=0-kx+1\\3x^2-x-kx+ k+1&=0\\3x^2-(1+k)x+ (k+1)&=0\end{aligned}\)

\(3x^2-(1+k)x+ (k+1)=0\)

Comparing this with the standard form, the coefficients a, b and c are:

\(\boxed{\begin{minipage}{7 cm}\underline{Discriminant}\\\\$\boxed{b^2-4ac}$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}\)

If the quadratic equation has two distinct roots, its discriminant is positive.

\(b^2-4ac > 0\)

Substitute the values of a, b and c into the discriminant:

\((-1 - k)^2-4(3)(k+1) > 0\)

Simplify:

\((-1 - k)(-1-k)-12(k+1) > 0\)

\(1+2k+k^2-12k-12 > 0\)

\(k^2+2k-12k+1-12 > 0\)

\(k^2-10k-11 > 0\)

Factor the left side of the inequality:

\(k^2+k-11k-11 > 0\)

\(k(k+1)-11(k+1) > 0\)

\((k-11)(k-1) > 0\)

If we graph the quadratic k² - 10k - 11, it is a parabola that opens upwards (since its leading coefficient is positive), and crosses the x-axis at k = -1 and k = 11. Therefore, the curve will be positive (above the x-axis) either side of the x-intercepts, so when k < -1 or k > 11.

Therefore, the range of values of k for which the given quadratic equation has two distinct roots is:

\(\boxed{k < -1 \; \textsf{or} \;k > 11}\)