Alex, a manager at Symbic Inc., plotted the company's total energy costs of 1 billion dollars over the past 10 years on a chart. The chart suggested that the energy costs appear to be increasing in a fairly predictable linear fashion and that the energy costs are related to time by a linear function Y t =3+5t, where Y trepresents the estimate of the energy cost in year t. Given the equation, which of the following is the value of the intercept of the straight line that best fits the time series?
A. 1
B. 3
C. 5
D. 10

Answer:

(a) 12 m

(b) 32 m/s

Step-by-step explanation:

(a) The height of the platform is h(0) i.e. the height, h, at time t = 0 secs, since the ball would not have been thrown at that time.

Therefore, h(0) is:

[tex]h(0) = -16(0^2) + 32(0) + 12\\\\\\h(0) = 0 + 0 + 12\\\\\\h(0) = 12 m[/tex]

The height of the platform is 12 m.

(b) The initial velocity when the baseball is thrown will be v(0) that is velocity when t = 0 secs.

We obtain velocity, v, by differentiating height, h, with respect to time:

[tex]v(t) = \frac{dh}{dt} = -32t + 32[/tex]

Therefore, at time t = 0 secs:

[tex]v(0) = -32(0) + 32\\\\\\v(0) = 32 m/s[/tex]

The initial velocity of the baseball when it is thrown is 32 m/s.

Answer:

0.6 feet

Step-by-step explanation:

The first rectangle to scaled down. Therefore, the scale factor will be less than 1.

[tex]\frac{4.5}{16.8}=\frac{15}{56}[/tex]

Therefore, the scale factor is  [tex]\frac{15}{56}[/tex].

[tex]\frac{15}{56}*2.3=\frac{69}{112}[/tex]

[tex]\frac{69}{112}[/tex] ≈ 0.6, so the value of x is 0.6 feet.

Answer:

The answer to your question is Apothem = 9 cm

Step-by-step explanation:

Data

Area = 216 cm²

Perimeter = 48 cm

Formula

Area = Perimeter x apothem / 2

Perimeter = length of the side x number of sides

Process

Substitute the values in the area formula and simplify it.

1.- Substitution

       216 = 48a/2

-Solve for a

      216 x 2 = 48a

      432 = 48a

      a = 432 / 48

-Result

      a = 9 cm      

Answer:

$2.07 per pound

Step-by-step explanation:

price divided by amount will get you the unit price. $123.99/60 equals 2.0665.

Answer:

2x + 3(8 - 3x) = 3

x = 3

y = -1

Step-by-step explanation:

2x + 3y = 3

y = 8 – 3x

2x + 3(8 - 3x) = 3

2x + 24 - 9x = 3

7x = 21

x = 3

y = 8 - 3(3)

y = -1

Answer:

✔ 2x + 3(8 – 3x) = 3

What is the value of x?

✔ 3

What is the value of y?

✔ –1

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Step-by-step explanation:

Answer:

[tex]x^2+8x+15[/tex]

Step-by-step explanation:

[tex]f(x)=x+4\\g(f(x))=g(x+4)\\g(x+4)=(x+4)^2-1\\(x+4)^2-1=x^2+8x+15[/tex]

The frequency of the note a perfect fifth below C4, which is F3, is calculated by multiplying the frequency of C4 (261.63 Hz) by 2/3, resulting in 174.42 Hz.

The frequency of the musical note C4 is about 261.63 Hz. A perfect fifth below a note is 7 half-steps below on the chromatic scale, which corresponds to a frequency ratio of approximately 2/3. Therefore, to find the frequency of the note that is a perfect fifth below C4, we multiply the frequency of C4 by 2/3.

Calculating this, 261.63 Hz × (2/3) = 174.42 Hz which is the note F3. Hence, the frequency of the note a perfect fifth below C4 is 174.42 Hz.

Given:

Given that the parallelogram with the lengths 5x, 3x + 1, 2y - 5 and y.

We need to determine the values of x and y.

Values of x and y:

We know the property that the opposite sides of a parallelogram are congruent.

Thus, we have;

[tex]5x=2y-5[/tex] ------- (1)

[tex]3x+1=y[/tex]  ------- (2)

The value of x and y can be determined using the substitution method.

Substituting equation (2) in equation (1), we have;

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

[tex]5x=6x+2-5[/tex]

[tex]5x=6x-3[/tex]

[tex]-x=-3[/tex]

  [tex]x=3[/tex]

Thus, the value of x is 3.

Substituting x = 3 in equation (2), we have;

[tex]3(3)+1=y[/tex]

    [tex]9+1=y[/tex]

         [tex]10=y[/tex]

Thus, the value of y is 10.

Answer:

For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for [tex]\mu[/tex] would be:

[tex]\bar X = \frac{1.2+1.8}{2}= 1.5[/tex]

And the margin of error is given by:

[tex] ME = \frac{1.8-1.2}{2}= 0.3[/tex]

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

[tex]\bar X[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for [tex]\mu[/tex] would be:

[tex]\bar X = \frac{1.2+1.8}{2}= 1.5[/tex]

And the margin of error is given by:

[tex] ME = \frac{1.8-1.2}{2}= 0.3[/tex]

Answer:

The volume of shipping container is 2880 cubic inches.

Step-by-step explanation:

We are given the following in the question:

Dimensions of tissue box =

4 inches by 6 inches by 3 inches

Volume of tissue box =

[tex]V = l \times w\times h\\V = 4\times 6\times 3\\V = 72\text{ cubic inches}[/tex]

Number of tissue box in shipping container, n = 40

Volume of shipping container =

[tex]V = n\times \text{Volume of tissue box}\\V = 40\times 72\\V = 2880\text{ cubic inches}[/tex]

Thus, the volume of shipping container is 2880 cubic inches.

This question is based on volume of cuboid. Therefore, the volume of the shipping container is 2880 cubic inches.

Given:

A shipping container holds 40 tissue boxes the dimensions of a tissue box are 4 inches by 6 inches by 3 inches.

We need to calculating the  volume of the shipping container.

According to this question,

It is given that, dimensions of tissue box =  4 inches by 6 inches by 3 inches

As we know that,

Volume of tissue box = [tex]length \times breadth \times height[/tex]

[tex]= 4 \times 6 \times 3\\= 72 \, inch^3[/tex]

As it is given that, number of tissue box in shipping container, n = 40.

[tex]Volume \,of \,40\, tissue \,box = n \times 72\\\\Volume \,of \,40 \,tissue \,box = 40 \times 72\\\\Volume \,of \,40 \,tissue \,box = 2880 \, inch^3[/tex]

Therefore, the  volume of the shipping container is 2880 cubic inches.

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To make F the subject of the formula in the Celsius to Fahrenheit conversion, multiply by 9, divide by 5, and then add 32, resulting in F = (9/5)C + 32.

To make F the subject of the formula when given the Celsius to Fahrenheit conversion formula c = 5(f - 32)/9, we start by isolating Fahrenheit on one side of the equation. Here's a step-by-step process:

Now the formula for F in terms of C is in the form aC + b with a = 9/5, b = 32, and there's no c as in the denominator since the conversion is direct.

[tex]\( F = \frac{9c + 160}{5} \).[/tex] In form [tex]\( aC + \frac{b}{c} \), \( a = 9 \), \( b = 160 \),[/tex] and [tex]\( c = 5 \).[/tex]

Let's break down the process of rearranging the formula step by step.

Given formula: [tex]\( c = \frac{5(F - 32)}{9} \)[/tex]

We want to isolate [tex]\( F \)[/tex] on one side of the equation.

1. Multiply both sides by [tex]\( \frac{9}{5} \):[/tex]

[tex]\[ \frac{9}{5} \cdot c = \frac{9}{5} \cdot \frac{5(F - 32)}{9} \][/tex]

  This cancels out the fraction on the right side.

  [tex]\[ \frac{9}{5} \cdot c = F - 32 \][/tex]

2. Add 32 to both sides to isolate [tex]\( F \):[/tex]

[tex]\[ \frac{9}{5} \cdot c + 32 = F \][/tex]

Now, [tex]\( F \)[/tex] is isolated on the right side of the equation.

3. Rewrite [tex]\( F \)[/tex] in the required form [tex]\( aC + \frac{b}{c} \):[/tex]

 [tex]\[ F = \frac{9}{5}c + 32 \][/tex]

  To express [tex]\( F \)[/tex] in the required form, we can rewrite [tex]\( \frac{9}{5}c \) as \( \frac{9c}{5} \),[/tex]so the form becomes [tex]\( aC + \frac{b}{c} \).[/tex]

  So, [tex]\( a = 9 \), \( b = 32 \), and \( c = 5 \).[/tex]

4. Final Form:

 [tex]\[ F = \frac{9c + 160}{5} \][/tex]

  So, in the form [tex]\( aC + \frac{b}{c} \),[/tex] we have [tex]\( a = 9 \), \( b = 160 \), and \( c = 5 \).[/tex]

Answer:

4.5 hundreds dulcimers should be build to achieve the minimum  average cost per dulcimer $ 1.7 hundreds.

Step-by-step explanation:

The average cost per dulcimer can be estimated by

C(x)=0.3x² -2.7x+7.775

where C(x) is hundreds of dollar, x hundred dulcimers are built.

C(x)=0.3x² -2.7x+7.775

Differentiating with respect to x

C'(x)=0.6x-2.7

Again differentiating with respect to x

C''(x)=0.6

For maximum or minimum C'(x)=0

0.6x-2.7=0

⇒0.6x=27

[tex]\Rightarrow x=\frac {2.7}{0.6}[/tex]

⇒ x= 4.5

Now [tex]C''(x)|_{x=4.5}= 0.6>0[/tex]

Since at x= 4.5 , C''(x)>0, So, the average cost per dulcimer is minimum.

C(4.5)= 0.3(4.5)²-2.7×4.5 +7.775×

        =1.7

4.5 hundreds dulcimers should be build to achieve the minimum  average cost per dulcimer $ 1.7 hundreds.

The graph of g(x) compare to the graph of the function[tex]f(x)=x^2[/tex] is; identical.

For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, the solution to a system is the intersection of all its equation at a single point.

We are given that;

[tex]g(x)=(x-3)^2+9[/tex] and [tex]f(x)=x^2[/tex]

The vertex form of a quadratic function is given by:

[tex]g(x) = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola.

Now Comparing [tex]g(x)=(x-3)^2+9[/tex] to  [tex]f(x)=x^2[/tex]we can see that g(x) is the result of translating the graph of f(x) horizontally by 3 units to the right and vertically by 9 units upward.

The vertex of g(x) is (3, 9), that is obtained by shifting the vertex of f(x) at the origin (0, 0) to the right by 3 units and up by 9 units.

Since the coefficient is positive in both functions, both parabolas open upwards.

The shape of the parabolas is the same since both have the same coefficient [tex]x^2[/tex].

Therefore, the graph of g(x) is identical to the graph of f(x), its shape, but it is shifted horizontally and vertically with respect to f(x).

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Answer:

x = +2, x = -2

Step-by-step explanation:

The equation to solve in this problem is

[tex]10x^2-5=35[/tex]

The first step we do is to subtract 35 on both sides of the equation, so we get:

[tex]10x^2-5-35=0\\10x^2-40=0[/tex]

Now we simplify the equation by dividing both terms by 10:

[tex]\frac{10x^2-40}{10}=0\\x^2-4=0[/tex]

Now we observe that the term on the left is the difference between two squares, so it can be rewritten using the property:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Where here,

a = x

b = 2

So we can rewrite the equation as:

[tex]x^2-4=0\\(x+2)(x-2)=0[/tex]

And this equation is zero when either one of the two factors is zero, so the two solutions are:

[tex]x+2=0\rightarrow x=-2\\x-2=0 \rightarrow x=+2[/tex]

Answer:

(A) The additional information that is needed to confirm about the conditions for this test have been met is ‘Population is approximately normal.

(B) The test statistic = 1.9965

(C1) P-value = 0.0556

(C2) There is no significant difference between mean VOT for children and adults.

D1) It is possible to make type II error.

(D2) There should be a difference in the VOT of adults and children.

Step-by-step explanation:

Let na be the number of adults = 20

xa mean VOT for adults = 88.17

sa standard deviatiation of VOT for adults = 24.74

Let nc be the number of children = 10

xc mean VOT for children =60.67

sc standard deviatiation of VOT for children = 39.89

(A) From the information the population variances are unknown and the two sample are assumed to be independent and the sample the sample size are smaller that is (n<30).

This indicates that the additional information that is required for the conditions of the test to be satisfied is 'distribution of the population'. the addition assumption to be made is, that the population distribution is normal.

(b) Calculating the test statistics using the formula;

t = (xa -xc)/SE - d

where SE = standard deviation , d= hypothesized difference = 0

But SE = √sa²/na +sc²/nc

           = √24.74 ²/20 + 39.89²/10

           = √189.72559

           = 13.774

Substituting into test statistics equation, we have

t = (xa -xc)/SE - d

  = (88.17 - 60.67/13.774

  = 1.9965

Therefore the test statistic is 1.9965

(c) Calculating the p-value, we have;

Degree of freedom = na + nc -2

                                 = 10+ 20 -2

                                 = 28

The p-value for t=1.9965 at 28 degrees of freedom and 0.05 level of significance is 0.0556.

The p-value 0.0556 is greater than given level of significance 0.05 hence we fail to reject the null hypothesis and conclude that there is no significant difference between mean VOT for children and adults.

(D1) From the information in part (C) the null hypothesis is not rejected.

Since the null hypothesis is not rejected, there might be a chance that not rejecting null hypothesis would be wrong. In this type of situation the error that can occur would be type II error.

(D2) The type of error describe in the context of this study is obtained by the concept of the type II error which tells that the null hypothesis is not rejected when it is actually false.

Answer: The displacement is -4 ft.

Step-by-step explanation:

The velocity is:

v(t) = 2t - 5ft/s

If we want to find the displacement between t = 0s and t = 4s, we need to find the difference between the position at t = 0s and at t= 4s

The equation for the position is obtained by integrating over time:

P(t) = (2t^2)/2 - 5*t + c

where c is the initial position, then we have:

P(t) = t^2 - 5t

P(4) - P(0) = 4*4 - 5*4 - 0 = 16 - 20 = -4

The total displacement is -4 feet

Answer:

Displacement, d = - 4ft

Step-by-step explanation:

Given,

The velocity function for a particle v(t) = 2t - 5 ft/sec.

To obtain the displacement for the particle from t = 0 to t = 4 sec

We integrate v(t) with respect to t

: Displacement, d = ∫₀⁴ ( 2t - 5) dt

= t² - 5t |₀⁴ = (4² - 5(4)) - 0² - 5(0)

=16 - 20 = - 4ft

Answer:

C) Both sets have an interquartile range of 27.

Step-by-step explanation:

Sorted data

Set 1: 65, 66, 77, 79, 81, 93, 104, 105

Set 2: 1, 29, 56, 59, 60, 67, 72, 74

Median position: (8+1)/2 = 4.5th value

Ranges:

Set 1: 105 - 65 = 40

Set 2: 74 - 1 = 73

Medians:

Set 1: (79+81)/2 = 80

Set 2: (59+60)/2 = 59.5

IQR:

Set 1: (93+104)/2 - (66+77)/2

= 27

Set 2: (67+72)/2 - (29+56)/2

= 27

Answer:

c

Step-by-step explanation:

Answer:

x= [tex]\frac{135}{7}[/tex]

Step-by-step explanation:

1. [tex]-\frac{7}{3} (x-3)=-52[/tex]

2. combine -7/3(x - 3)

  =    [tex]-\frac{7}{3}x-7 = -52[/tex]

3. Do combine like terms on both sides

   =   -52 + -7 = -45

4. left with, [tex]-\frac{7}{3}x = -45[/tex]

5. divide -45 by -7/3

6. left with, [tex]x = \frac{135}{7}[/tex]

Answer:

21

Step-by-step explanation:]

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Answer:

1) a) yes

b) no

c) a² - 39

(a)² - (sqrt(39))²

(a - sqrt(39))(a + sqrt(39))

This quadratic can be split into real factors, but not rational

sqrt(39) is a real number, but not rational

2) real

Answer:

160 pages.

Step-by-step explanation:

That is 125 - 0.20 * 125

= 125 - 25

= 160 pages.

Answer:

The answer is you saved $25.00 and the new total is $100.00

Step-by-step explanation:

so first you set up the equation of is over of = percent over 100

[tex]\frac{a}{125}=\frac{20}{100}\\\\[/tex]

then simplify the [tex]\frac{20}{100}=\frac{1}{5}[/tex]

then you see if 5 can go into 125. It can so you divide 125 by 5=25

so you multiply the [tex]\frac{1}{5}=\frac{25}{125}[/tex]

so now you just [tex]\frac{a}{125}=\frac{25}{125}[/tex]

then you just subtract the 25 because that is how much you are saving and your total will be $100.00

Answer:

$9

Step-by-step explanation:

12 + 18 = $30 Total

30 - 21 = $9 Discount

30 - 9 = $21 After discount

Answer:

[tex]slope=-\frac{1}{3}[/tex]

Step-by-step explanation:

Use the slope formula for two points:

[tex]\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}[/tex]

Insert values

[tex]\frac{-12-(-10)}{11-5}[/tex]

Simplify

[tex]\frac{-12+10}{11-5} \\\\\\\frac{-2}{6} \\\\-\frac{2}{6}[/tex]

Simplify

[tex]-\frac{1}{3}[/tex]

The slope of the linear equation will be negative 1/3.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The points are given below.

(5, -10) and (11,−12)

The equation of the line that passes through (5, -10) and (11,−12) will be given as,

(y + 10) = [(-12 + 10) / (11 - 5)](x - 5)

y + 10 = - (1/3)x + 5/3

y = -(1/3)x + 5/3 - 10

y = -(1/3)x - 25/3

The slope of the linear equation will be negative 1/3.

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Answer:

Goldbach’s Conjecture precipitated from letters in 1742 between German mathematician Christian Goldbach and legendary Swiss mathematician Leonhard Euler, considered one of the greatest in math history. As Euler put it, “I regard [it] as a completely certain theorem, although I cannot prove it.”

Euler may have sensed what makes this problem counterintuitively hard to solve. When you look at larger numbers, they have more ways of being written as sums of primes, not less. Like how 3+5 is the only way to break 8 into two primes, but 42 can broken into 5+37, 11+31, 13+29, and 19+23. So it feels like Goldbach’s Conjecture is an understatement for very large numbers.

Still, a proof of the conjecture for all numbers eludes mathematicians to this day. It stands as one of the oldest open questions in all of math.

Answer:

dividing and multiplying decimals

Step-by-step explanation:

Answer:

t

Step-by-step explanation:

Line [tex] \purple{\boxed{\bold{t}}} [/tex] is the transversal.

Answer:

you take all the point from around then multiply and do the same with the base

Step-by-step explanation:

Answer:

7 cans

Step-by-step explanation:

6 cans of paint  kids need to cover the bedroom wall.

The formula for calculating the area of a rectangle with dimensions l and w is: A = lw (rectangle). In other words, the length times the width equals the area of a rectangle.

Given

length = 12 m

width = 7.875 m

area = 12 * 7.875 = 94.5 sq. m

area 1 can can fill = 15 sq. m

no. of cans that can fill 94.5 = 6

therefore, 6 cans of paint  kids need to cover the bedroom wall.

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Answer:

  yes

Step-by-step explanation:

We can estimate* that the total price including tax of the game will be less than ...

  $43.31 +10% of 43.31 = $43.31 +4.33 = $47.61

Todd easily has enough to pay for the game, including tax.

_____

You can work this more exactly a couple of ways.

  1. Price + tax = 1.085×$43.31 = $46.99 . . . less than Todd's budget

  2. Most Todd can afford: $55.50/1.085 = $51.15 . . . more than the game price

_____

* For estimating purposes, we like to use numbers that are easy to compute with. 10% is one such number, as it only requires moving the decimal point.

Answer:

a) 95% Confidence Interval = (8.832%, 13.168%)

b) The 8% claim for the pundit falls outside the range of the confidence interval, hence, it isn't a very plausible claim given the poll data.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 11% = 0.11

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the sample proportion)

Critical value will be obtained using the z-distribution. This is because the sample size is large enough for the t-distributoon valur to approximate the z-distribution value

Critical value for 95% confidence = 1.960 (from the z-tables)

Standard error = σₓ = √[p(1-p)/n]

where

p = sample proportion = estimated to be 11% = 0.11

n = Sample size = 800

σₓ = √[p(1-p)/n]

σₓ = √[0.11×0.89/800]

σₓ = 0.0110623234 = 0.01106

95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.11 ± (1.960 × 0.01106)

CI = 0.11 ± 0.02168

95% Confidence Interval = (0.08832, 0.13168)

95% Confidence Interval = (8.832%, 13.168%)

b) The 8% claim for the pundit falls outside the range of the confidence interval, hence, it isn't a very plausible claim given the poll data.

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Answer:

subtract 4 from both sides

divide both sides by 5

take the square roots of both sides

add 3 to both sides

Step-by-step explanation: