At first, Mrs. Hanrahan's students thought that a linear model might describe the relationship between a pendulum's length and its period pretty well. After fitting a least-squares regression model to data, they decided that a better model be available. Perform this analysis yourself, and explain why the students didn't favor the linear model.

Answer: 8

Step-by-step explanation:

The capacity required for a kitchen size, given the additional BTU recommended, is A. 10, 000 BTUs.

The area of the kitchen would be:

= Length x Width

= 16 x 10

= 160 ft ²

At this capacity, it means that the recommended capacity would be over 5, 000 BTUs which is for 150 ft² kitchens.

The next recommended capacity is 6, 000 BTUs and with a kitchen requiring 4, 000 BTUs over the capacity, the BTUs is :

= 6, 000 + 4, 000

= 10, 000 BTUs

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The profit was maximum when the current price raised by $2 then the profit falls in further increase of price.

The axis graph displays the point where two real number lines—one vertical and one horizontal (X axis)—intersect (Y axis). The X axis is referred to as the data set's independent variable, while the Y axis is referred to as the data set's dependent variable.

Given:

We have the Graph in which X- axis shows increase in price over the current value of Milkshake and, Y- axis shows Weekly profit Earned.

From the graph we can see that when the amount increased by $2 that gave the maximum profit.

After that it rising the money in prices leads to falls in profit.

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When h is very small, then the slope would be equal to 6

We have

m = y2 - y1 / x2 - x1

where 2.97² - 3² / 2.97 - 3

we would have

-0.1791 / -0.03

m = 5.97

We have to do the same for   x = 3.001

3.001² - 3² / 3.001 - 3

m = 6.001

finally we have to solve for x = 3 + h

m = [tex]\frac{(3 + h)^2-(3)^2}{3+h-3}[/tex]

m = [tex]\frac{9+h^2+6h-9}{h}[/tex]

m = [tex](\frac{h}{h})*(\frac{h+6}{1} )[/tex]

m = h + 6

if h is close to 0 then m = 6

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The man should pull rope A to lift the load more easily

From the question, we have the following parameters that can be used in our computation:

The diagram

To determine the rope to pull, we calculate the moment at the point

This is calculated as

Moment = Force * Perpendiculat Distance

Using the above as a guide, we have the following:

Point A = F * (6 + 2)

Point B = F * (3 + 1)

Evaluate

A = 8F

B = 4F

8F is greater than 4F

Hence, the man should pull from point A

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Answer:

60%

Step-by-step explanation:

9/15 converted = 0.6 = 60%

Answer:

D=5=14 I hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total marbles = 0
Number of green marbles = 6
so,
Probability of getting 2 green marbles = 2/20 = 1/10

The probability that Jerod selects two green marbles at random from the bag is 1/10

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that Jerod has a bag of 20 marbles containing 12 red, 6 green, and 2 blue marbles.

Total marbles = 0

Number of green marbles = 6

Therefore,

Probability of getting 2 green marbles ;

= 2/20 = 1/10

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Answer:

triangle ABC ~ triangle GHJ

Step-by-step explanation:

The similarity statement compares the two triangles based on their corresponding sides. If two triangles have proportional corresponding sides, then they are similar.

In this case, triangle ABC and triangle GHJ have corresponding sides that are proportional. Specifically, side AB is half the length of side GH, side BC is three-fifths the length of side HJ, and side AC is two-fifths the length of side GJ. Therefore, by the definition of similarity, triangle ABC is similar to triangle GHJ.

Answer: Let's call the number of cookies Trey has "x".

Gerald has 8 less cookies than Trey, so he has x - 8 cookies.

Trey bought five times the number of cookies as Gerald, so he has 5 * (x - 8) = 5x - 40 cookies.

Combining these two equations, we have:

x + (x - 8) = 5x - 40

Simplifying, we get:

2x - 8 = 5x - 40

Solving for x, we find:

3x = 32

And finally, x = 10.

So Trey has 10 cookies and Gerald has 2 cookies.

Step-by-step explanation:

As per the given triangles given in the question, the corresponding names are mentioned accordingly in the answer.

A triangle is a basic polygonal geometry with three sides and three interior angles. This is a fundamental geometric shape that is particularly related. Its three vertices are joined together. Depending on their sides and angles, triangles can be classified into a wide range of groups.

In geometry, there are six different kinds of triangles. There are two categories into which they can be divided. The three triangles are categorized as equilateral triangles, isosceles triangles, and scalene triangles based on their sides. Triangles can be classified as acute, obtuse, or right-angled depending on the angle at which they are formed. There are so six different kinds of triangles in geometry.

As per the given information in the question,

a. 1, 2

b. 1

c. 2

d. 6

e. 5, 6, 7

f. 7

g. 6

h. 6

i. 4, 6

j. 4, 6

k. 4, 8

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Complete question -

The statement that the probability of obtaining a sample mean greater than 46 is: p = 0.8413.

The parameters given are;

Sample size; n = 9

Population mean; μ = 50

Population standard deviation; σ = 12

Sample mean; x' = 46

Formula for the z-score here is;

z = (x' - μ)/(σ/√n)

z = (46 - 50)/(12/√9)

z = -4/4

z = -1

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

p-value = 0.8413

Thus, the statement is true

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The length and the width of the fencing are 85 feet and 30 feet respectively.

The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his rectangular front yard.

The length is five feet less than three times the width.

Let w be the width.

Then, 3w - 5 is the length.

So, the perimeter of the rectangular fence = 200 + w.

Now, 2(3w - 5 + w) = 200 + w

6w - 10 + 2w = 200 + w

7w = 210

w = 30

Then length = 85

Therefore, length = 85 feet and width = 30 feet.

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Answer:

35280 blinks

Step-by-step explanation:

1 day = 24 hours

24 - 8 = 16 hours

1 hour = 3600 seconds

16 hours = 50400 seconds

Now we have to find how many blink in 1 second

14 divided by 20 = 0.7 blink in 1 second

Now we take

0.7 times 50400 = 35280 blinks

So, Sam blink 35280 times a day

The weighted average length of the nails in the drawer is given as follows:

D. 3.50 cm.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

For the weighted mean, each observation is multiplied by it's weight.

Considering the percentages as the weights, the weighted average length of the nails in the drawer is obtained as follows:

0.705 x 2.5 + 0.19 x 5 + 0.105 x 7.5 = 3.5.

Meaning that option D is the correct option for this problem.

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Based on the given triangle, we can find that:

First, we will focus on the triangle NLP. NLP is a right triangle, then we can use the formula of sinus to find the length of NP, where:

Sin ∠NLP = NP / LP

Sin 35° = NP / 20

0.57 = NP / 20

NP = 11.47

NP ≈ 11

Next, we will focus on triangle GLP. GLP is a right triangle with hypotenuse of 52 and the base of 20. Using the Phytagoras theorem we can try to find the triangle's height.

GL² = GP² + LP²

52² = GP² + 20²

2704 = GP² + 400

GP² = 2304

GP = 48

GP = GN + NP

48 = GN + 11

GN = 37

To find the size of angle ∠GLN, we have to find the size of angle ∠PGN first. We will use the Sines Law:

LP / sin ∠PGN = GL / sin ∠GPN

20 / sin ∠PGN = 52 / 1

sin ∠PGN = 20/52

∠PGN = 22.5°

∠PGN ≈ 23°

∠GLP + ∠GPL + ∠PGN = 180°

∠GLP + 90° + 23° = 180°

∠GLP = 67°

∠GLP = ∠GLN + ∠NLP

67° = ∠GLN + 35°

∠GLN = 32°

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Step-by-step explanation:

75.00 - 25.00 = 50.00

50.00 / 20.00 = 2.50

So, she needs to mow 2.5 lawns or more to have enough money to buy the skateboard.

The inequality can be expressed as:

20.00 * x >= 50.00

x >= 2.50

So, the inequality "x >= 2.50" can be used to determine the number of lawns she needs to mow to have enough money to buy the skateboard.

The expression for the time of the number of games remaining for shoes will be T = 225 - 2W.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jacob just bought a new pair of basketball shoes. He expects the shoes to last for two hundred twenty-five games. He plays two games a week.

The expression for the life of the shoes will be written as:-

T = 225 - 2W

Here, T is the time and W is the number of weeks.

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Part A:

Complete table becomes:
Age (x)               Probability (p)                (x × p)

15                          9/40 = 0.225              3.375

16                         12/40=0.30                     4.8

17                         8/40=0.20                      3.4

18                         11/40=0.275                   4.95

....................................................................................................

Total                     1.00                    16.525

Part B:

Mean becomes: 16.525

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Fundamentally, probability is a discipline of mathematics that uses computations to foretell the potential outcomes of a certain occurrence. It provides you the power to forecast the outcomes of future occurrences, which makes it seem cool.

Part A:

Age (x)               Probability (p)                (x × p)

15                          9/40 = 0.225              3.375

16                         12/40=0.30                     4.8

17                         8/40=0.20                      3.4

18                         11/40=0.275                   4.95

....................................................................................................

Total                     1.00                    16.525

Part B:

mean (μ) = ∑⁴(i = 1) xi pi

mean (μ) = 16.525

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Answer:

B) Linear Pair

D) Adjacent

E) Supplementary

Step-by-step explanation:

Because the sum of the two angles is 180°, we conclude that the correct options are:

B, D, and E.

We want to find the relationship between angles a and b.

Notice that if we would add these two angles, we would get a plane angle, then we could write:

∠a + ∠b = 180°.

That means 3 things:

The angles are adjacent because share a vertex and a common side, and the angles are supplementary because their sum is equal to 180°, and also are a linear pair, because their sum is equal to 180°.

Then the correct options are:

B, D, and E.

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Answer:

Below

Step-by-step explanation:

y - y1   = m ( x - x1 )     is point slope form of a line  m = slope

For point ( -1,3) :

y-3 = 3 (x- -1)

y -3 = 3x + 3        add 3 to both sides

y = 3x + 6         The underlined equations are the same line just different forms....you'll need to pick the one you need

Answer:

Step-by-step explanation:

Quadratic X €

Evaluate -20

Answer:

[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Lets solve for [tex]x[/tex] in

[tex]-2^2-2x^2+2x+1=0[/tex]

Evaluate [tex]2^2[/tex]

[tex]-4-2x^2+2x+1=0[/tex]

Add [tex]-4[/tex] and [tex]1[/tex].

[tex]-2x^2+2x-3=0[/tex]

Divide both sides of the equation by [tex]-2[/tex].

[tex]x^2-x+\frac{3}{2}=0[/tex]

Now the equation is in standard form.

[tex]ax^2+bx+c=0[/tex]

We can solve this quadratic by completing the square.

Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation.

[tex]x^2-x=-\frac{3}{2}[/tex]

Take one half of the coefficient of [tex]x[/tex] and square it, then add it to both sides.

Add [tex]\frac{1}{4}[/tex] to both sides.

[tex]x^2-x+\frac{1}{4} =-\frac{3}{2}+\frac{1}{4}[/tex]

[tex]x^2-x+\frac{1}{4} =-\frac{5}{4}[/tex]

The left hand side is a perfect trinomial square.

Factor the left hand side by writing it as a square.

[tex]\left(x-\frac{1}{2}\right)^2 =-\frac{5}{4}[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]x-\frac{1}{2} =\pm\sqrt{-\frac{5}{4}}[/tex]

Rewrite [tex]\frac{5}{4}[/tex] as [tex]\left(\frac{i}{2} \right)^2 *5[/tex]

[tex]x-\frac{1}{2} =\pm\sqrt{\left(\frac{i}{2} \right)^2 *5}[/tex]

Pull terms out from under the radical.

[tex]x-\frac{1}{2} =\pm \frac{i}{2} \sqrt{5}[/tex]

Combine [tex]\frac{i}{2}[/tex] and [tex]\sqrt5[/tex].

[tex]x-\frac{1}{2} =\pm \frac{i\sqrt{5}}{2}[/tex]

Add [tex]\frac{1}{2}[/tex] to both sides of the equation.

[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]

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The number of acres that will be pollinated by the bees in 18 beehives is given as follows:

D. 48.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

From the table, the constant is obtained as follows:

3k = 8

k = 8/3.

Hence the equation is of:

y = 8x/3.

The number of acres that will be pollinated by 18 beehives is then given as follows:

y = 8(18)/3

y = 48 acres.

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Answer: D. 48.

Step-by-step explanation:

because the table shows 3k = 8k = 8/3. y = 8x/3. So then it turns into y = 8(18)/3 = y = 48 acres.

Answer:

No, the equations are not balanced.

Step-by-step explanation:

Let's solve 50² - 40 × 6 + 19 - 2.

The equation is now 2500 - 40 × 6 + 19 - 2.

    2. 40 × 6 = 240.

The equation is now 2500 - 240 + 19 - 2.

    3. 240  + 19 = 259.

The equation is now 2500 - 259 - 2.

    4. 2500 - 259 = 2241.

The equation is now 2241 - 2.

    5. 2241 - 2 = 2.

50² - 40 × 6 + 19 - 2 = 2241.

Now, lets solve 2279 - 2.

2241 ≠ 2277. In addition, 2241 is not equal to 2277, meaning that the equations are not balanced.

Answer:

y= -4/5x -3

Step-by-step explanation:

Answer:

[tex]\frac{6}{15} - \frac{5}{15} = \frac{1}{15}[/tex]

Step-by-step explanation:

Answer:

The ratio of ozone used to the total amount of water treated per day can be calculated as follows:

Ozone used = 25,000 mg

Amount of water treated = 16,000,000 liters = 16,000,000 x 1000 ml = 16,000,000 x 1000 x 1000 mg = 16,000,000,000,000 mg

Ratio of ozone used to water treated = 25,000 / 16,000,000,000,000 = 1.5625 x 10^-11

So, the ratio of ozone used to the total amount of water treated per day is approximately 1.5625 x 10^-11.

[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.

16,000,000 liters of water

25,000 milligrams of ozone

A ratio is basically telling how much of one thing corresponds to a unit of another thing. Hence, let's express this as a division in the following fashion:

[tex]\frac{25,000}{16,000,000} =\\ \\\frac{0.0015625}{1} =\\ \\\frac{15.625*10^{-4} }{1}[/tex]

[tex]15.625*10^{-4}[/tex] miligrams of ozone / liter of water.

The partition and shade to show 5/7 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

partition and shade to show 5/7

To do this, we can make use of a tape diagram

Such that the size of each partition is equal

Using the above as a guide, we have the following:

5/7 implies that we create 7 partitions and shade 5 sections

Next, we make the tape diagram (see attachment)

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