For each chart below, identify the output rule and classify the function as exponential, linear or neither.

The probability that the proportion of Rolls Royce owners in a sample of 694 Americans would differ from the population proportion by less than 3% is; 0.36%

The Central Limit Theorem states that, for a normally distributed random variable X, with mean μ and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ/√n

The standard deviation for proportion is given by the formula;

s = √(p(1 - p)/n)

We are given;

p = 8% = 0.08

n = 694

Thus;

s = √(0.08(1 - 0.08)/694)

s = 0.0103

Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Due to the fact that the normal distribution is symmetric, the probabilities will be equal, and as a result, we find one of them and multiply by 2.

Probability the proportion is less than 5%:

P-value of Z when X = 0.05.

z = (X - μ)/s

z = (0.05 - 0.08)/0.0103

z = -2.91

From p-value from z-score calculator, we have;

p-value = 0.001807

We multiply it by 2 to get the probability

Probability = 2 * 0.001807 = 0.0036 = 0.36%

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Explanation:

The equation y = 3x-1 is in slope-intercept form y = mx+b

Parallel lines have equal slopes, but different y intercepts.

The answer will also have a slope of m = 3.

Plug that slope value, and the coordinates of the given point [tex](x_1,y_1) = (1,5)[/tex] , into the point-slope formula below.

Solve for y.

[tex]y - y_1 = m(x - x_1)\\\\y - 5 = 3(x - 1)\\\\y - 5 = 3x - 3\\\\y = 3x - 3+5\\\\y = 3x + 2\\\\[/tex]

That's how we arrive at the answer of y = 3x+2

As a check, plugging x = 1 into that answer should get us y = 5.

It confirms that the point (1,5) is on this line.

Equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.

Given points:

(-4, 7), (-3, 9), and (4,-5).

Let parabola equation be y = a[tex]x^{2} +bx+c[/tex].

substitute (-4,7)

7 = a(16)+b(-4)+c

16a-4b+c-7 = 0.

substitute (-3,9)

9 = a(9)+b(-3)+c

9a-3b+c-9 = 0

substitute (4,-5)

-5 = 16a+4b+c

16a+4b+c+5=0.

solving three equations we get,

a = -1/2 , b = -3/2 and c = 9

substitute a,b and c values we get,

y = (-1/2)[tex]x^{2}[/tex] + (-3/2)x + 9

y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.

Therefore the equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.

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Answer: There is no solution

Step-by-step explanation:

The formatting of the question isn't clear, but I'll still explore both possibilities. If the square root is only applied to x, we can solve for the variable by adding 4 to both sides and then squaring both sides, which would give us 4. Since that is not an answer choice, it means the square root applies to x-4. With this problem, we square both sides right away. That gives us x=0, but plug 0 back into the original equation. Doing so gives us the square root of -4, which is not possible with real numbers, only with imaginary numbers.

Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.

The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).

Given,

Factor sipping distributive property,

For the numbers 28 and 49

GCF:

28 + 49

7(4) + 7(7)

7(4+7)

7(11)

77

Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.

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Answer:

US$1.00=EC$2.70 TT$1.00=EC$0.40 calculate the value of : 1.EC$1in TT$ 2.US$80inEC$ 3.TT$648 in US$

Step-by-step explanation:

that what i've got is that I hope that helps you

For given equation, the constant of proportionality is 4

In this question, we have been given an equation m = 4b that represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).

We need to determine the constant of proportionality.

We know that the the constant of proportionality is nothing but the ratio of two proportional values.

In this case the time a chef needs to cook depend on the number of bacon cheeseburgers (b).

So, m is directly proportional to the b

Therefore, the constant of proportionality is 4

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Answer:

The answer is 4

Step-by-step explanation:

I hope this helps!!

It will take 7 days for Claire to sell as many candy bars as Ayden

Claire has sold 8 candy bars and sells 5 more each day

The first term = 8

Common difference = 5

nth term is = a+(n-1)d

= 8 +(n-1)5

= 8 + 5n - 5

= 3 +5n

Ayden has sold 20 candy bars and sells 3 more each day

The first term = 20

Common difference = 3

nth term = a+(n-1) d

= 20 +(n-1)3

= 20 + 3n -3

= 17 + 3n

Then,

3 + 5n = 17 + 3n

5n - 3n = 17 - 3

2n = 14

n = 14/2

n = 7

Hence, it will take 7 days for Claire to sell as many candy bars as Ayden

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{3}{2}}x+4 \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is -2/3 and that it passes through (-6 , 2)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -2= -\cfrac{2}{3} (x +6) \\\\\\ y-2=-\cfrac{2}{3}x-4\implies {\Large \begin{array}{llll} y=-\cfrac{2}{3}x-2 \end{array}}[/tex]

Jarrod needs to walk 1 mile to reach the swimming pool

Given that: He lives 2 3/4 miles from the swimming pool

He walked 7/8 mile to the library

Then he walked 7/8 mile to the museum

The concept we need here is the addition or subtraction of fractions

To determine the miles left, we need to subtract the miles he walked from the miles 2 3/4 miles (since that is the distance from where he lives to the swimming pool)

Thus:

Miles left = 2 3/4 - 7/8 - 7/8

              = 11/4 - 7/8 -7/8              (Note:   2 3/4 = 11/4)

              =  8/8 = 1

Therefore,  he needs to walk 1 mile to reach the swimming pool

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The system of equations has its solutions to be (0, 3)

From the question, the system of equations is represented on the graph

On the graph, we have the following representations

Say the functions are f(x) and g(x)

To determine the solution to the system of equations, we set both equations equal

i.e. f(x) = g(x)

This in other words mean that we determine the coordinates of the points where the graphs intersect

In this case, they intersect at point (0, 3)

This represents the solution

Hence, the solution to the system of equations is (0, 3)

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The area of two lawns will be 4000 square meters.

According to the question,

We have the following information:

Craig mows two lawns. The first lawn is 40 meters long and 20 meters wide. The second lawn has the same length, and a width that is 4 times as much as the first one.

So, the width of the second lawn = 4*20

Width of second lawn = 80 m

Now, formula to find area of rectangle:

Length*width

Area of first lawn:

40*20

800 square meters

Area of second lawn:

40*80

3200 square meters

Now, the area of two lawns = area of first lawn+ area of second lawn

Area = 800+3200

Area = 4000 square meters

Hence, the total area of two lawns is 4000 square meters.

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He needs to buy 7 bags of fertilizer to fertilize the garden

The radius of the garden = 10 feet

The area of the garden A = π × [tex]r^2[/tex]

Where A is the area of the garden

r is the radius of the garden

Substitute the values in the equation

A = π × [tex]10^2[/tex]

= π × 100

= 314.16 feet square

Each bag of fertilizer covers 50 square feet

Then the number of bags required to fertilize the garden = The area of the garden / 50

Substitute the values in the equation

= 314.16 / 50

= 6.28

≈ 7 bags

Hence, he need to buy 7 bags of fertilizer to fertilize the garden

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The value of y is - 0.326 when x = 7.

A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is typically expressed as x: y or x/y, although it may alternatively be read as x is to y.

Comparatively speaking, a proportional equation states that two ratios are comparable. A ratio is expressed as x: y: : z: w and is understood to mean that x is to y as z is to w. Here, w and y are not equal to 0, therefore x/y Equals z/w.

A connection between two quantities is said to be in inverse proportion if one quantity rises while the other falls, and vice versa. As a result, an inverse ratio is expressed as y ∝ 1/x.

The general equation of proportion is given by

y = k/x²

-4 = k/(-2)²

k = -4(4)=-16

y = -16/x²

When x=7, then

y= -16/49

y= - 0.326

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The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

What is the scale factor?

A scale factor is Scaling the shape of an object. it means the shape of the object remains the same but the size of the object is either increased or decreased. A scale factor greater than 1 means size is increased and less than one means size is decreased

We are given a point (0,-4)

Which is to be scaled by the factor of 2 at the center position

As the value is greater than 1 the size increase

We multiply the coordinate to find the new coordinates

We get (0,-8)

Hence, The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)

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Answer:

30

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

A = 15 x 2 = 30

a) The confidence interval is given as follows: (71.43, 77.17).

b) The manufacturer's claim is not correct, as 78 is not a part of the interval.

c) A sample of 55 employees is needed to achieve the desired margin of error.

The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are presented as follows:

The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:

t = 2.201.

The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:

[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]

(obtained using a calculator from the sample given in this problem).

The bounds of the interval are given as follows:

The interval does not contain the number 78, hence it is not a good estimate for the mean amount.

For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]

[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]

n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).

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The comparison done by Mr Jones means that Test A of standard deviation 7 is closer to the mean scores and Test B of standard deviation 12 is further apart from the mean score

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

A high standard deviation suggests that the values are dispersed throughout a wider range,

A low standard deviation suggests that the values tend to be close to the established mean.

A positive value means the standard deviation is above the mean while a negative value means the standard deviation is below the mean

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The equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.

Given function:

g(x) = 6/x-1

vertical asymptote for any function is denominator is equal to zero.

x - 1 = 0

x = 1.

Therefore the equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.

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The cost function for the Acme Corporation is -0.2x² + 100x - 300. a cost function, transfers an event or the values of one or more variables onto a real number that signifies the event's "cost" in real terms.

A loss function, also known as a cost function, is a function used in mathematical optimization and decision theory that transfers an event or the values of one or more variables onto a real number that intuitively represents some "cost" connected to the occurrence. A loss function is the goal of an optimization problem.

The event in question is some function of the difference between the estimated and true values for a particular instance of data, and in statistics, parameter estimation is typically done using a loss function.

Given that the profit function is

p(x) = 0.5x^2 + 250x+300

also given that the revenue is given as

r(x) = 0.3x^2 + 150x

we know that profit= revenue - cost

hence cost = revenue-profit

cost = r(x) -p(x)

cost=  0.3x^2 + 150x-(0.5x^2 + 250x+300)

cost=  0.3x^2 + 150x-0.5x^2 - 250x-300

collect like terms

cost=0.3x^2-0.5^2+150x-250x-300

The cost function for the Acme Corporation = -0.2x^2-100x-300

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Answer:

A

B

Step-by-step explanation:

that's it

Answer:

40

Step-by-step explanation:

2 x 10⁷/5 x 10⁵ = 2/5 x 10^5-7 = 2/5 x 10² = 2 x 100/5

There were 40 times more white-tailed deer in 2000 than in 1905

The statement that shows the correct relationship between production cost and the number of golf balls produced is that the minimum production cost of 17.5 occurs when 35 golf balls are produced.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Then the minimum is represented by the formula;

c - b² / 4a

We have given equation C(x) = 0.1x² - 7x + 140

a = 0.1

b = -7

c = 140

Now plugging in values to c - b² / 2a

= 140 - 7² / (4 * 0.1)

=  17.5

The minimum production cost will be; 17.5

Now plugging 35 into the given equation;

C(x) = 0.1x² - 7x + 140

C(x) = 0.1 ( 35)² - 7 (35) + 140

C(x) = 17.5

Therefore, 35 golf balls produce the minimum cost.

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Answer:

that the minimum production cost of 17.5 occurs when 35 golf balls are produced.

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{3}[/tex] (2x + 5) = 3 , then

2x + 5 = 3³ = 27 ( subtract 5 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11

The z-score under which 3/4 of the data lies is of:

Z = 0.675.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score under which 75% of the distribution lies is the 75th percentile, hence it is the value of Z with a p-value of 0.75.

Looking at the z-table, this value is of 0.675, as 0.675 is the mean of the p-values of Z = 0.67 and Z = 0.68.

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Answer: $38,125

Step-by-step explanation:

1/8*305000

Answer:

$1.70 per share

Step-by-step explanation:

37.90-36.20=1.70

The value of (2/3) ÷ (1/4) is 8/3 and the value of 7 ÷ (2/3) is 21/2.

This is a question from the division of fractions.

We know the property of fractions is given by:-

(m/n) ÷ (a/b) = (m/n)*(b/a) = mb/na

Hence, we can write,

(2/3) ÷ (1/4) = (2/3) * (4/1) = 2*4/3*1 = 8/3

7 ÷ (2/3) = (7/1)*(3/2) = 7*3/ 1*2 = 21/2

Fractions

A fraction represents a part of a whole or, more generally, any number of equal parts. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

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