Notice the two points in the coordinate plane. Which answer choice is closest to the distance between the two points?
(ignore my answer, I didn't mean to click on it)

Answer: 4) 3x²-14x+14

Explanation:

Use the binomial theorem (a−b)² = a² - 2ab + b² to expand (x-2)².

Use the distributive property to multiply 3 by x²-4x+4.

Use the distributive property to multiply −2 by x−1.

Combine −12x and −2x to get −14x.

Add 12 and 2 to get 14.

It is 3x²+14x+14, the trinomial equivalent to 3(x-2)²-2(x-1). OPTION 4.

Answer:

To find the sum of the two fractions, we first need to express them in a common denominator. Since the denominators of the two fractions are different, we will need to find the least common multiple (LCM) of the two denominators.

The LCM of 4 and 5 is 20, so we can express the two fractions in terms of 20 as follows:

-3 1/4 = -3 5/20

-4 2/5 = -4 8/20

Now that the two fractions have a common denominator, we can add them by adding the numerators and keeping the denominator the same:

(-3 5/20) + (-4 8/20) = (-3 + -4) 13/20 = -7 13/20

Therefore, the sum of the two fractions is -7 13/20.

The sum of −3 1/4 + (−4 2/5) is 7.65

Mixed fractions are type of a fraction which includes a whole number and a fraction.

So, any improper fraction can be written as a mixed fraction. Quotient will be the whole number and in the fractional part, numerator is the remainder and denominator will be the divisor.

[−(3 1/4)] + [−(4 2/5)] = [-(13/4)] + [-(22/5)]

When cross multiplying, we will get

-(13/4 + 22/5) = -(65 + 88)/20 = -153/20 = 7.65

Hence, the sum of −3 1/4 + (−4 2/5) is 7.65.

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There is not sufficient evidence at the 0.02 level of significance to say that the percentage is less than 59%.

The correct option is (b)

Now, According to the question:

In this problem, we have the following hypothesis:

[tex]H_0[/tex] : μ [tex]\geq[/tex] 0.59

[tex]H_\alpha[/tex] : μ < 0.59

The null hypothesis is the prevailing claim which the study is testing, and the alternative hypothesis is what the study is trying to prove. The null hypothesis can either be rejected or not rejected by a sample study. A sample study cannot say that the claim is absolutely correct. Only a count of the whole population can do that, and that could change at any time. In this study, the null was not rejected. The study did not have enough evidence to reject the null.

Hence, There is not sufficient evidence at the 0.02 level of significance to say that the percentage is less than 59%.

The correct option is (b)

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The complete question is this:

A newsletter publisher believes that less than 59% of their readers own a Rolls Royce. For marketing purposes, an advertiser wants to confirm his claim. After performing a test at the 0.02 level of significance, the advertiser failed to reject the null hypothesis.

What is the conclusion regarding the publisher's claim? Select one:

a) There is sufficient evidence at the 0.02 level of significance that the percentage is less than 59%.

b) There is not sufficient evidence at the 0.02 level of significance to say that the percentage is less than 59%.

As per the combination method, there are 120, 5 length m words can be formed from an n-letter alphabet, if no letter is used more than once.

Combination method:

in statistics, mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter is known as combination method.

Given,

Here we need to find how many length m words can be formed from an n-letter alphabet, if no letter is used more than once.

Let us consider letters (a,b,c,d,e) how many distinct n length words can be formed.

Here we note that every word can contain same letter m times at most.

So, it can be calculated as,

=> 5 x 4 x 3 x 2 x 1

=> 120

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Answer:

yellow = red - 3 and green = yellow x 2 and red = yellow + 3

or

green= (red-3) x 2

Step-by-step explanation:

Three fewer yellow than read is the same as saying red -3

twice as many green as yellow is the same as yellow x 2

if green is yellow x 2 you can substitute yellow for the equation to find yellow

you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3

The amount of fencing feet the city needs to enclose the pond is 94.29 feet.

Perimeter can be defined the total distance around an object.

To calculate the amount of fencing the city needs to enclose the pond, we use the formula for the perimeter of a circle.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the feet of fencing needed is 94.29 feet.

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Answer:

nnnn

Step-by-step explanation:

hh

Answer:

Step-by-step explanation:

6-(-2^3)+-2

Answer:

360 inches.

Step-by-step explanation:

because 1 yard is 36 inches (3 rulers) so just multiply 36 by your number of yards.

The probability that it was that of a male is 2/5 .

This problem of probability can be solved using Baye's Theorem . In simple terms , Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event. Hence , proceeding accordingly -
Given in the question is :

P(Males reacting negatively = M) = 1-40%= 60% = 60/100

P(Females reacting negatively = F) = 1-70%= 30% = 30/100

Now , P(Females' response being selected= f) = 15/20
P(Males' response being selected = m ) = 5/20
P(M/m) = P(M) P(m)/ P(M) P(m) + P(F) P(f)
⇒ 5/30 × 60/100 ÷ 5/30 × 60/100 + 15/20 × 30/100

⇒ 300/300+450
⇒ 300/750

⇒ 2/5
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The conventional form of the polynomial is f(x)=x 28x+17. If polynomial function f has rational coefficients and a leading factor of 1, then it has the lowest degree.

A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses quasi integer powers or only positive integer coefficients of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.

As conjugate pairs make up complex zeros, we can infer that 4-i4-i is also a zero from the fact that 4+i4+i is also a zero.

A polynomial function's factor x-axa is one of the factors if aa is its zero. Consequently, the polynomial function is

f(x)=a[x-(4+i)] [x-(4-i)]

f(x)=a[x−(4+i)]

[x−(4−i)]

Expand:\sf(x)=a[x^2-(4-i)

x-(4+i)x+(4+i)(4-i)]

F(x) = a [x 2 (4i)x(4+i)x+(4+i)(4i)]

f(x)=a[x^2-4x+ix-4x-ix+

(16-i^2)]

F(x) = a [x 2 4x+ix4x+ix+(16i 2)]

f(x)=a[x^2-8x +(16-(-1))]

f(x)=a[x 2 −8x+(16−(−1))]

f(x)=a(x^2-8x +17)

f(x)=a(x 2 −8x+17)

Considering that a=1a=1 is the leading coefficient, this means:

color="#c34632" f(x)="x2-8x +17"

f(x)=x 2 −8x+17

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The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The two points are (3, 5) and (6, 10).

Let 'x' be the number of yards of fabric and 'y' be the cost in dollars. Then the equation is given as,

(y - 5) = [(10 - 5) / (6 - 3)](x - 3)

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

y = (5/3)x

The cost of the 12 yards of fabric is given as,

y = (5/3) × 12

y = 5 × 4

y = $20

The equation is y = (5/3)x. Then the cost of the 12 yards of fabric will be $20. Then the correct option is B.

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The wave function that satisfies wave equation is D(x,t) = A cos(kx + ωt) that is option C is correct.

This wave function satisfies the wave equation because it can be rewritten as:

D(x,t) = A cos(kx) cos(ωt) - A sin(kx) sin(ωt)

And the left-hand side of the wave equation is simply the sum of the second derivatives of the two cosine and sine functions with respect to x, while the right-hand side is the product of the second derivative of the cosine function with respect to t and the second derivative of the sine function with respect to t.

For the transverse velocity of a particle at point x, the function is given by:

v(x,t) = -Aω sin(kx) cos(ωt) - Ak cos(kx) sin(ωt)

And for the transverse acceleration, the function is given by:

a(x,t) = -Aω^2 cos(kx) cos(ωt) + Ak^2 sin(kx) sin(ωt)

These functions can be derived by taking the first and second derivatives of the wave function with respect to time.

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The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:

m = (y2 − y1) / (x2 − x1)

If the graph of a line rises from left to right, the slope is positive.

What is slope ?

Slope is a ratio and can have a value that is positive, negative, equal to zero, or undefined. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run".

What is positive slope ?

A positive slope means that two variables are positively related—that is, when x increases, so does y, and when x decreases, y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises. We will learn in other sections that “price” and “quantity supplied” have a positive relationship; that is, firms will supply more when the price is higher.

The slope m of a line passing through two points (x1 , y1) and (x2 , y2) is:

m = (y2 − y1) / (x2 − x1)

If the graph of a line rises from left to right, the slope is positive.

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The expression is x-12.

12 less than a number means subtracting 12 from that number.

So, 12 less than 20 is 8, because is 20−12, 12 less than 12 is 0, because it's 12−12, and so on.

But since the number you need to subtract from is unknown, it's a variable, and you can call it as you like, suppose x. So, using the variable we can write an expression that holds for any number, which always means "take 12 away from my number". If your number is x, the expression would be x-12

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Meiosis causes the cell to divide instead of makeing new cells.

Cells are the fundamental building blocks of all life. Trillions of cells make up the human body. They support the body's structure, absorb nutrients from food, convert those nutrients into energy, and perform specialized functions.

Meiosis is a type of cell division that occurs in sexually reproducing organisms and results in a reduction in the number of chromosomes in gametes; he sex cells, or egg and sperm. Body or somatic cells in humans are diploid, with two sets of chromosomes one from each parent.

It should be noted that meiosis is a type of cell division of germ cells that produces gametes such as sperm or egg cells in sexually reproducing organisms. It consists of two rounds of division that result in four cells with only one copy of each chromosome.

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Answer:

[tex]y=\dfrac{\boxed{1}}{\boxed{2}}\:x+\boxed{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Therefore, the slope of the given line  y = -2x + 5  is -2.

If two lines are perpendicular to each other, their slopes are negative reciprocals.  

Therefore, the slope of a perpendicular line ¹/₂.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and point (-4, 2) into the point-slope formula:

[tex]\implies y-2=\dfrac{1}{2}(x-(-4))[/tex]

Rearrange to slope-intercept form:

[tex]\implies y-2=\dfrac{1}{2}(x+4)[/tex]

[tex]\implies y-2=\dfrac{1}{2}x+2[/tex]

[tex]\implies y=\dfrac{1}{2}x+4[/tex]

fog(x) =4x²+44x+12,

f(x) is quadratic function  whose value is x²+6x -4 at x.

so , we have asked the value of f(x) at x=g(x) , which another function whose value is 2x-8 .

so, by the concept of composition of functions we have to put the value 2x-8 in place of x in the f(x) function to get fog(x).

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The given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

We shall represent this as 1.5 pizzas in decimal form.

In this case, the dot stands in for the decimal point, the number before the dot, in this case, "1," represents one entire pizza, and the number after the decimal point, or the fractional component, represents the other half of the pizza.

So, we have the rational number:

1/4

Convert to decimal as follows:

1/4 = 0.25

Rounding off to the nearest thousandth: 0.2500 ⇒ 0.25

Therefore, the given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

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The height of the trapezoid is 5mm.

A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. It is referred to as a trapezium in British and other varieties of English.

In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases. If the remaining two sides are parallel, the trapezoid is a parallelogram and has two pairs of bases; if not, they are referred to as the legs (or lateral sides). A scalene trapezoid is a trapezoid without equal-sized sides.

Given: Area of trapezoid = [tex]35mm^{2}[/tex]

We know, area of trapezoid = [tex]\frac{(a+b)}{2} .h[/tex]

⇒ [tex]\frac{(8+6)}{2} .h=35[/tex]

⇒ [tex]7h=35[/tex]

⇒ [tex]h=5mm[/tex]

Hence, the height of the trapezoid is 5mm.

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the answer is 1

Step-by-step explanation:

The Insurance policy's anticipated value in this case is -20.

What is Insurance?

Insurance is a tool for risk management. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.

Given,

Man pays -118 for one year

coverage = 140000

probability = 0.9993

The method used to calculate the insurance policy's expected value is:

= Chance that he won't live to see the end of the year * Coverage value - The cost of the insurance

= (1 - 0.9993)*140,000 - 118

= -20.

In this situation, the man's insurance coverage is expected to be worth -20.

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In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.

In the given question, the issue of capital punishment is a hotly debated topic.

Do more republicans than democrats support capital punishment?

A researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment.

In this problem, we want to make inferences about:

A. one mean

B. comparing means from dependent samples

C. comparing means from two independent samples

D. one proportion

E. comparing proportions from two independent samples

F. comparing proportions from dependent samples

As we know that,

A hypothesis test can assist in figuring out whether a variation in the estimated proportions actually reflects a variation in the population proportions. An approximation of the normal distribution is shown by the difference between two proportions. The null hypothesis often argues that the two proportions are equal.

So, a researcher randomly selects 100 republicans and 100 democrats and asks them if they support or do not support capital punishment. In this problem, we want to make inferences about comparing proportions from dependent samples. So the option F is correct.

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Using the Pythagorean Theorem, the length of the base is: 15 units.

The Pythagorean theorem is used to find any of the length of the legs or hypotenuse of a right triangle if we know any two measures of its side. The theorem is given as: the square of the hypotenuse = sum of the squares of the legs of the right triangle.

It can be expressed as c² = a² + b², where c is the longest side of the right triangle.

Note: The hypotenuse is the longest side of the triangle.

Thus, given the triangle in the image below, where:

c = 25

a = 20

b = length of the base

The expression that would be appropriate for this situation would be written based on the Pythagorean Theorem, which is:

b = √(c² - a²)

Substitute

b = √(25² - 20²)

b = 15 units

The length of the base is: 15 units.

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(A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

A polynomial is a mathematical equation made up of coefficients and indeterminates that exclusively uses the operations of addition, subtraction, multiplication, or powers of positive numbers of the variables.

x² - 4x + 7 is an illustration of a quadratic with a solitary indeterminate x.

(A) 4x² - 3x + 7:

'x' is the only variable in the provided polynomial.

As a result, the polynomial 4x² - 3x + 7 has one variable.

(B) y² + √2:

'Y' is the only variable in the provided polynomial.

y² + √2 is a polynomial in one variable as a result.

(C) 3√t + t√2:

Since the power of the variable in the first term is 1/2, which is not a whole integer, 3√t + t√2 is not a polynomial.

(D) y + (2/y):

Because the power of the variable in the second term is -1, which is not a whole number, y + 2y⁻¹ is not a polynomial.

(E) x¹⁰ + y³ + t⁵⁰

Due to the fact that x, y, and t are all three variables, x¹⁰ + y³ + t⁵⁰ is not a polynomial in one variable.

Therefore, (A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.

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The coordinates of the y-intercept is (0, 10)

The coordinate of the x-intercept is (5 / 2, 0)

Cynthia is participating in the Spartan Super, a 10-mile obstacle course.  She completes 4 miles of the obstacle course every hour.

Cynthia’s distance from this finish line, y, after x hours is represented by the function 4x + y = 10.

Therefore, the y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x = 0.

The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.

Linear function in slope intercept form is as follows:

y = mx + b

where

Hence,

4x + y = 10

y = -4x + 10

Hence, y-intercept is 10.

y = -4x + 10

Let's find x-intercept

0 = -4x + 10

-10 = -4x

x = 10 / 4

x = 5 / 2

x-intercept is 5 / 2.

Hence the coordinate of the y-intercept is (0, 10) and the x-intercept is (5 / 2, 0)

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The possible formula for polynomial is P(x)=x⁵+3x⁴-9x³+5x²

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given,

The polynomial of degree 5.

P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=−5

Each root corresponds to a linear factor, so we can write

P(x)=x²(x-1)²(x+5)

=x²(x²+1-2x)(x+5)

=(x⁴+x²-2x³)(x+5)

=x⁵+x³-2x⁴+5x⁴+5x²-10x³

=x⁵+3x⁴-9x³+5x²

Hence, the possible formula for polynomial is P(x)=x⁵+3x⁴-9x³+5x²

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Answer:

3 years

Step-by-step explanation:

Lawson's tree starts at 14 inches and grows 3 inches every year, so we can represent that as 3x+14

Ezra's tree starts at 8 inches and grows 5 inches every year, so we can represent that as 5x+8

x=years

So, now that we have an equation for each tree, we will now set them as equal

5x+8=3x+14

Subtract 8 from each side

5x=3x+6

Subtract 3x from each side

2x=6

Divide each side by 2

x=3

It will take 3 years for the trees to reach the same height.

Answer:

y = 5

Step-by-step explanation:

The equation 5x − 2y = 30 tells us that if we take 5 times x and subtract 2 times y, the answer will be 30.  If we know either x or y, we can solve for the other.

We are given that x=8.  Use the 8 for x in the equation:

5x − 2y=30  

5*(8) − 2y=30

40 − 2y=30

-2y = -10

y = 5