which quadratic equation fits the data in the table?

The inverse of the function f(x) = 4x is inverse of f(x) = x/4.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

F(x)= 4x

Let , y=4x

Now we will switch the variables x to y,

x= 4y

Simplify the expression so that y is by itself. And divide each side by 4

x/4= y

or f(x)= x/4.

Therefore, the inverse of the function f(x) = 4x is inverse of f(x) = x/4.

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Answer:

Step-by-step explanation:

The required graph of the given function d(x)=−1/2x−3 has been shown.

Given that, to plot the graph of the linear function,  d(x)=−1/2x−3.

What is the graph?

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,

The graph of the liner function d(x)=−1/2x−3 can be plot by putting the values of the x in the equation which gives the value of y by calculating such an ordered pair we can plot the curve of the liner equation on the graph. i.e.

At x = 0

d(0) = -1/2 * (0) - 3

d(0) = -3

So, the ordered pair will be (0, -3).

Now, put x = 2

d(2) = -1/2 * 2 - 3

d(2) = -1 - 3

d(2) = - 4

So the ordered pair will be (2, -4)

joining these two points will show the graph of the given equation d(x)=−1/2x−3.

Thus, the required graph of the given function d(x)=−1/2x−3 has been shown.

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1.9 × 10³ is 2.15 times more than 4.085 × 10⁵  

To find how many times a number can be smaller than another number we need to divide the large number by the smaller number.  

Example: how many times 5 is smaller than 25

               => 25/5 = 5   [ Since 5(5) = 25 ]  

Here we have

1.9 × 10³ and 4.085 × 10⁵

Let the number 1.9 × 10³ is x times smaller than 4.085 × 10⁵

Then 1.9 × 10³ (x) must be equal to 4.085 × 10⁵  

=>  1.9 × 103 (x) = 4.085 × 105  

=>  x = [tex]\frac{4.085 \times 105 }{1.9\times 103 }[/tex]  

=>  x = [tex]\frac{428.925 }{195.7 }[/tex]  

=>  x = 2.1917475 ≅ 2.15

Therefore,

1.9 × 10³ is 2.15 times smaller than 4.085 × 10⁵  

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If there are 6 students and one is selected for best student and another is selected for runner up, then 15 different ways that we can arrange the students

Total number of students in the class = 6 students

Number of students for best student = 1 student

Number of students for runner up = 1 students

Total number of students needed = 2

Here we have to use the combination

6[tex]C_2[/tex] = 6! / 2!(6 - 2)!

= 6! / 2! × 4!

Split the terms and cancel it

= 6 × 5 / 2 × 1

Multiply the terms

= 30 / 2

Divide the numbers

= 15 combinations

Therefore, there are 15 combinations

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George Canter showed that, for any set a, we have |a|<|p(a)|. This is a well-known theorem of canter, known as the 'Canter's Theorem'.

Proving this theorem:                                              

Proof: At the first instance, we need to show that, A bar ≤P(A) bar, we will define the injection by  f:A→P(A) by: f(a)={a}. Let g be the contradiction.

We need to prove that there is no bijection  g:A→P(A).

Now, Let: S={a∈A:a∉g(a)}⊆A.}

In the present condition, there are two possibilities,  first, x∈S  and second, x∉S.

Therefore,

1. If x∈S, then x∉g(x)=S, i.e., x∉S, a contradiction.

2. If x∉S, then x∈g(x)=S, i.e., x∈S, a contradiction.

Thus, such a bijection, is not possible.

This theorem, coined by Canter, basically implies that there is no largest cardinal number present. There are 'n' number of cardinal numbers present, i.e., there are infinite number of cardinal numbers.

Now, suppose that, A is a set of all sets, this was proved by the continuum hypothesis.  But, the continuum hypothesis can't be proved. It can't be disproved also.

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The Coefficient of xⁿ In the Expansion 1 / (1 + x + x²) is 1

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.

It is typically a number, but it can also be any expression. They may also be referred to as parameters

The coefficient is usually the number in front of the variable represent by an letter.

For the given problem the given letter is x and the coefficient is 1, a coefficient of 1 is most times not written and hence we know the coefficient is 1

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Answer:

Given :

A train travels 110 miles per hour.

To Find :

How fast does the  train travel in feet per second.

Solution :

We know, 1  mile = 5280 feet .

1 hour = 3600 s.

So, speed in feet per second is :

Hence, this is the required solution.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use conversion factors to find the answer.  

By definition:

5280 feet (ft) = 1 mile

1 hour(hr) = 60 minutes (min)

1 min = 60 seconds (sec)

We are given 110 miles/hr.  We want to change the unit from miles/hr to feet/sec.

Make the definitions into conversion factors by dividing one side by the other.

5280 ft = 1 mile can be either:

 5280 ft/(1 mile)  = 1, or

 (1 mile)/(5280 ft) =1

These are conversion factos since we can multiply them times anything without making the value invalid, since they are both equal to 1, and 1 multiplied by anything will not change it's validity.  Yes the number changes, but the units also change, accordingly.

Knowing this, we can make the conversion factors we need to change miles/hr into feet/sec.  I like to line everything up and apply the factors one at a time until we get the units desired.

(miles/hr)*[(5280ft/mile)]*[(1 hr)/(60 min)][(1 min)/(60 sec)]

                miles cancel          hr cancel          min cancel

We are left with feet/sec after everything else cancels

Now just do the math on the numbers and add feet/sec afterwards.

 5289/(60)*(60) = 1.46667  feet/sec

110*(1.46667  feet/sec) = 161 feet/sec

The rectangular prism that has the dimensions of 3 inches by 4.75 inches by 20.5 inches, has a total surface area, found by adding the surface areas of the six faces of 346.25 in²

The surface area of a solid three dimensional object is the area of the boundary surface of the object and its surroundings.

The dimensions of the rectangular prism in the question can be defined as follows;

Let the length of the rectangular prism = 3 inches

Let the width of the prism = 4.75 inches

Let the height of the prism = 20.5 inches

The surface area, A, of a rectangular prism can be found using the formula

A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width

Therefore, the surface area of the rectangular prism in the question is found as follows;

Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25

The total surface area of the rectangular prism is; 346.25 in²

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6x - 11y = - 13 is the the equation of this line in standard form that is option A from the group of choices.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Coefficients, variables, operators, constants, terms, expressions, and an equal to sign are all components of an equation. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.

Here,

6x - 11y = - 13 is the the equation of this line in standard form that is option A from the set of possibilities.

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Therefore, option (c)normality assumption is checked when looking at a  Q–Q plot in one-way ANOVA model.

In statistics, a Q–Q plot is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point on the plot corresponds to one of the quantiles of the second distribution plotted against the same quantile of the first distribution

Here,

normality assumption is checked when looking at a Q–Q plot in one-way ANOVA model.

Explanation: The core tenet of the assumption of normality states that the sample mean distribution (across independent variables) is normal. Technically speaking, the Assumption of Normality asserts that the mean's sampling distribution or the distribution of means among samples is normal.

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Answer:

Move all terms not containing p to the right side of the equation.

p=5

Step-by-step explanation:

Hey there!

3 + p = 8

p + 3 = 8

SUBTRACT 3 to BOTH SIDES

p + 3 - 3 = 8 - 3

SIMPLIFY IT!
p = 8 - 3

p = 5

Therefore, your answer should be:

p = 5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The simplified expression for its perimeter and area are 8x and 4x².

What is the square's perimeter?

What is a square area?

Area of square = a²

= (2x)²

= 4x²

Area of square = 4x²

Perimeter of square = 4*a

= 4 * 2x

= 8x

Perimeter of square = 8x

Hence, the simplified expression for its perimeter and area are 8x and 4x².

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Answer:

f(x) / g(x) = x - 1   where x ≠ -1.

Step-by-step explanation:

f(x) / g(x) =   x² - 1 / x + 1

                = (x + 1)(x - 1) / (x + 1)

                = x - 1.

When testing individual cofficients of a Multiple regression model, i.e y = β + β₁x₁ + β₂x₂ + ---+βₖxₖ + ε where β , β₁ , --- , βₖ are regression cofficients

the sampling distribution is tested by hypothesis testing.

Testing the Regression Coefficients:

An individual regression coefficient, if we want to test if there is a relationship between the dependent variable and the independent variable.

for the test and identify the significance level α.

The p-value is the sum of the area in the tails of the t -distribution. The t-score and degrees of freedom are t , df = n−k−1

Compare the p-value to the significance level and state the outcome of the test:

The results of the sample data are significant. There is sufficient evidence to conclude that the null hypothesis H₀ is an incorrect belief and that the alternative hypothesis. Hₐ is most likely correct.

The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis Hₐ may be correct.

Write down a concluding sentence specific to the context of the question.

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As the standard deviation for Sample Values and Population are different. The sample Standard Deviation is 5.196

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

Formula for standard deviation calculation is:

[tex]\sigma = \sqrt {\sum \frac {(X - \mu) ^ {2}}{N}}[/tex] (Population Standard Deviation)

[tex]s = \sqrt {\sum \frac {(X - \bar x) ^ {2}}{n-1}}[/tex] (Sample Standard Deviation)

[tex]\bar x= 19.1[/tex]

[tex]\sum {(X - \bar x) ^ {2}} = 162[/tex]

[tex]n-1 = 6[/tex]

[tex]s = \sqrt {\sum \frac {(X - \bar x) ^ {2}}{n-1}} = \sqrt {\frac {162}{6}}[/tex]

[tex]s= \sqrt 27[/tex]

[tex]s= 5.196[/tex]

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The 3 combinations of coins with the value of 30% of a dollar are 2 dimes + 1 Nickel + 5 Pennies, 1 dime + 2 Nickels + 10 Pennies, 3 Nickels + 1 dime + 5 Pennies.

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Now calculate 30 percentage of a dollar.

1 dollar = 100 cents.

30% of 100 cents = (30/100) × 100 = 30 cents.

2 dimes + 1 Nickel + 5 Pennies = 20 cents + 5 cents + 5 cents = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 cents + 10 cents + 10 cents = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 cents + 10 cents + 5 cents = 30 cents

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The answer for this Simplifiction 4x3−12x24x2 7x−22x2−6x5x2 11x 2 using  BODMASS rule is -19316

=4*3-12*24*27*-22*2-6*5*211*2

=-19316

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The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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Answer:

5x

Step-by-step explanation:

when 2 terms have a the same variable you can just add the coeefiects

2x+3x

2+3=5 so 2x+3x=5x

hopes this helps please mark brainliest

Answer:

-5/4

Step-by-step explanation:

To find the slope, we have to use this formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

in this case -2 is your first x

5 would be your first y

2 would be your second x

and 0 is your second y

so:

0 - 5

-------    = -5/4

2 - (-2)

43920  is the lowest amount that a teacher needs to make and still be one of the top 7% earners with a mean of $38,000 and a standard deviation of $4,000

According to information provided to us, the pay for elementary school teachers in a certain nation is generally distributed, with a mean of $38,000 and a standard deviation of $4,000 per year.

To resolve the issue at hand, we shall make use of the normal distribution table. Finding the z-score corresponding to the top 7% or the 93% probability from the normal distribution table (0.93).

The normal distribution table provides us with the 1.48 z-score we need.

We will now solve for the sample score using the z-score formula as follows:

z = x - μ/σ

1.48 = x - 38,000/4000

1.48 × 4000 = x - 38,000

5920 = x - 38000

x = 5920+38000

x = 43920

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Answer:

To find the value of log1000, you can use the logarithmic property that states that log(a^b) = b * log(a). In this case, we can rewrite 1000 as 10^3, so log1000 = log(10^3) = 3 * log(10) = 3.

The probability that they all are women is 0.0333 and that two of them are men is 0.50

There are 6 men and 4 women in your committee, that gives you a total of 10 people to choose from.

Without restrictions, there's a total of 10C3 ways to choose a subcommittee of 3 people.

a) A subcomitte of 3 people consisting of all women can be chosen in 6C0*4C3 ways.

So, the probability for the first problem is 6C0*4C3/10C3 = 0.0333

b) A subcommittee consisting of 2 men and 1 woman can be chosen in 6C2*4C1 ways.

So, the probability for this problem is 6C2*4C1/10C3 = 0.50.

Therefore, the probability that they all are women is 0.0333 and that two of them are men is 0.50.

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Disclaimer

the question given by you is incomplete, the answer is solved as per a similar question and the question is

A committee consist of six men and four women. A subcommittee is made by randomly choosing three of the committee members. What is the probability that: a. they are all women b. two of them are men?

The proportion of the class that scored higher than the student will be 0.0912.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The class normal is 85% and the standard deviation is 3%. Then the student from the class who earned 89% higher will be given as,

z = (0.89 - 0.85) / 0.03

z = 0.04 / 0.03

z = 1.3333

Then the probability is given as,

P(x > 89%) = P(z > 1.3333)

P(x > 89%) = 0.091211

The proportion of the class that scored higher than the student will be 0.0912.

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The probability that the two pets selected are of the same species  is 0.2426   .

In the question ,

it is given that ,

the number of puppies in the pet store = 6

the number of kittens in the pet store = 9

the number of lizards in the pet store = 4

the number of snakes in the pet store = 5

total animals = 24

the probability of selecting 2 puppies = ⁶C₂/²⁴C₂

the probability of selecting 2 kittens = ⁹C₂/²⁴C₂

the probability of selecting 2 lizards = ⁴C₂/²⁴C₂

the probability of selecting 2 snakes = ⁵C₂/²⁴C₂

So , the required probability is

= ⁶C₂/²⁴C₂  + ⁹C₂/²⁴C₂ + ⁴C₂/²⁴C₂  + ⁵C₂/²⁴C₂  

Simplifying further ,

we get ,

= 5/92 + 3/23 + 1/46 + 5/138

= 0.0543 + 0.1304 + 0.0217 + 0.0362

= 0.2426

Therefore , the required probability is 0.2426   .

The given question is incomplete , the complete question is

The pet store has 6 puppies , 9 kittens , 4 lizards and 5 snakes . if you select two pets from the store randomly, what is the probability that they are both the same species ?

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The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

Given that,

We have to find the system of linear equation in which (2,-1) is a solution of the first equation but not for the second equation and (5,5) is a solution for system of equation.

We know that,

To find the system of equation we have a formula that is

y=mx-mx₁+y₂

Here m is slope

m=-1-5/2-5

m=-6/-3

m=2

The equation is

y=2x-2(5)+5

y=2x-10+5

y=2x-5

Therefore, The system of linear equation of the line are y=2x-5 when (2,-1) is a solution of the first equation but not for the second equation.

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Answer:

5.4* 10^-2

Step-by-step explanation:

The value of the exponential equation is A = 5.4 x 10⁻²

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the number be represented as n

The value of n = 0.054

On simplifying the equation , we get

A = 5.4 x 10⁻²

On further simplification , we get

A = 0.054

Hence , the exponential equation is A = 5.4 x 10⁻²

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To multiply the division expression 3/4 ÷ 1/3 is 9/4. Division expressions are mathematical expressions using division

  3/4 : 1/3

= 3/4 · 3/1

= 3·3/4.1

= 9/4

Hence this proved.

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Answer:

a. Point B

b. Point D

c. Point E

d. Point B

Step-by-step explanation:

See the attached image for a graphed solution with color-coded lines drawn.

To test the claim that meal preference and gender are not related, you can use a chi-squared test for independence.

The null hypothesis for this test is that there is no relationship between the variables, while the alternative hypothesis is that there is a relationship. To conduct the test, you will need to calculate the chi-squared statistic and compare it to the critical value from a chi-squared distribution with one degree of freedom. The degrees of freedom for this test are calculated as (number of rows - 1) * (number of columns - 1), which in this case is (2-1)*(2-1) = 1.

To calculate the chi-squared statistic, you will need to compare the observed frequencies in the table to the expected frequencies if the null hypothesis were true. The expected frequency for each cell is calculated as the row total * column total / sample size.

For example, the expected frequency for females who prefer hamburgers is (39 * 15)/59 = 12.71. The chi-squared statistic is then calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. In this case, the chi-squared statistic would be:

((15-12.71)^2/12.71) + ((23-26.29)^2/26.29) + ((24-26.29)^2/26.29) + ((16-12.71)^2/12.71) = 7.39

To determine whether this result is statistically significant, you would compare the chi-squared statistic to the critical value from a chi-squared distribution with one degree of freedom. At a significance level of 0.05, the critical value is 3.84. Since the chi-squared statistic (7.39) is greater than the critical value (3.84), you can reject the null hypothesis and conclude that there is a relationship between meal preference and gender in this sample.

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