Hooke's law states that the force F required to stretch a spring x units beyond its natural length is directly proportional to x.
(a) Express F as a function of x by means of a formula that involves a constant of proportionality k. F=kx
b) A weight of 8 pounds stretches a certain spring from its natural length of 10.4 inches to a length of 10.7 inches. Find the value of k in part (a). k = ____________
c) (c) What weight will stretch the spring in part (b) to a length of 13.1 inches?
F = ​

Answer:

I believe this what you're asking:

To estimate the sum of 3.456 and 8.79, we can round each number to one decimal place, and then add them:

3.456 ≈ 3.5

8.79 ≈ 8.8

So, 3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3

Therefore, we can estimate that the sum of 3.456 and 8.79 is approximately 12.3.

In equation form, this can be written as:

3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).

b) The probability that the sum of the numbers drawn is 4 is 2/9.

c) The probability that the sum of the numbers is at least 4 is 2/3.

a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:

P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)

Hence, the probability space can be written as a set, S = {1,2,3}.

b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:

P = 2/9

c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:

(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)

Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3

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Answer:b

Step-by-step explanation:

let's move like the crab, backwards.

B)

profit is simply the surplus amount or 3.75 - 2.50 = 1.25.

A)

since the item was bought for $2.50, that's our origin amount, and thus that's our 100%, what's 1.25 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 2.50 & 100\\ 1.25& x \end{array} \implies \cfrac{2.50}{1.25}~~=~~\cfrac{100}{x} \\\\\\ 2.5x=125\implies x=\cfrac{125}{2.5}\implies x=50[/tex]

The difference between the total and the initial contribution, which is: Interest [tex]= $5,409.09 - $5,000, I[/tex] nterest $409.09, is the amount of interest earned. Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.

We can use the compound interest calculation to determine how much money Lupita will receive after 48 months:

Where: [tex]A = P(1 + r/n)(nt)[/tex] A represents the whole sum after t years.

P represents the primary sum.

The yearly interest rate is r.

Given that interest is compounded yearly, [tex]P = $5,000, r = 0.02, n = 1,[/tex]and[tex]t = 48/12 = 4[/tex] (since the time is given in months, we need to convert to years by dividing by 12).

Hence, the equation is: [tex]A = $5,000(1 + 0.02/1)^(1*4)[/tex]

[tex]A = $5,000(1.02)^4\sA ≈ $5,409.09[/tex]

The amount that differs between the total and the original deposit that represents interest earned is: Interest equals [tex]$5,000 - $5,409.09$409.09[/tex] in interest

Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.

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From the listed factor pairs, there are no factor pairs for 36x² that add up to 15x.

A factor pair is a set of two numbers that can be multiplied together to get a specific product.

The factor pairs for 36x² are:

1 x 36x²

2 x 18x²

3 x 12x²

4 x 9x²

6 x 6x²

To identify which pair adds to 15x, we need to look for the factor pair whose two terms add up to 15x. None of the above factor pairs add up to 15x. Therefore, there is no factor pair for 36x² that adds up to 15x.

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Solving a system of equations we can see that the correct option is A.

Here we can define the variables:

g = snacks in one pack of granola bars.

f = snacks in one pack of fruit rolls.

And we can write a system of equations like:

10g + 6f = 152

7g + 12f = 200

If we take the difference between two times the first equation and the second, we will get:

2*(10g + 6f) - (7g + 12f) = 2*152 - 200

13g = 104

g = 104/13 = 8

There are 8 snacks in a pack of granola, and with that value we can find f.

10g + 6f = 152

6f = 152 -10g

f = (152 - 10*8)/6 = 12

We conclude that the correct option is A.

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Answer:

(x + 3)

Step-by-step explanation:

Answer:

Part A 4 Part B 20 Part C C

there are total 28 balls. 1 / 7 = 4 balls.

Answer:

a = 24

b = 10

c = 26

======================================================

Explanation:

We're given a list of possible b values and they are:

4, 5, 8, 10, 12, 24

Let's make a table to show what each value of 'a' would be based on those b values above.

[tex]\begin{array}{|c|c|} \cline{1-2}b & a\\\cline{1-2}4 & 12\\\cline{1-2}5 & 14\\\cline{1-2}8 & 20\\\cline{1-2}10 & 24\\\cline{1-2}12 & 28\\\cline{1-2}24 & 52\\\cline{1-2}\end{array}[/tex]

Example calculation: If b = 4, then a = 2b+4 = 2*4+4 = 12 (first row)

I recommend using spreadsheet software to quickly compute these values. Also, a spreadsheet is useful to organize the data into a table.

Next we'll add a third column c.

This column will be computed using the formula [tex]c = \sqrt{a^2+b^2}[/tex] which is based from the pythagorean theorem [tex]a^2+b^2 = c^2[/tex]

So,

[tex]\begin{array}{|c|c|c|} \cline{1-3} & & \\b & a & c = \sqrt{a^2+b^2}\\\cline{1-3}4 & 12 & 12.6491\\\cline{1-3}5 & 14 & 14.8661\\\cline{1-3}8 & 20 & 21.5407\\\cline{1-3}10 & 24 & 26\\\cline{1-3}12 & 28 & 30.4631\\\cline{1-3}24 & 52 & 57.2713\\\cline{1-3}\end{array}[/tex]

Each decimal value mentioned is approximate. The only time c is an integer is when a = 24 and b = 10.

So that's how I got a = 24, b = 10, c = 26 as the final answer.

Answer:

Given as steps.

Step-by-step explanation:

Step 2: Opposite angles of a parallelogram are Equal
Step 4 ( After " Definition of a parallelogram"): Given
Step 5: ASA congruency Property / Therom
Step 6: CPCTC


P.S: It is ASA congruency Therom as both angles are adjacent to the side they are trying to prove.


Hope It Helps!

The ratios for the similar triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The length of one side of one triangle is 4 times that of the corresponding side of the other, hence the constant of the proportional relationship for the side lengths is given as follows:

k = 4.

The perimeter is measured in units, just like the side lengths, while the area is measured in units squared, hence the ratios are given as follows:

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Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

Answer:

a. 6 and 2

b. 3 and 8

Step-by-step explanation: Supplementary angles add up to 180 degrees. In this figure angles 6,2 lie on the same line and a straight line has an angle measure of 180 degrees. Vertical angles are opposite to each other and have the same value. 8 and 3 are one example and on that same area, 7 and 4 are too.

Answer:

It will have a rise of 20.

Step-by-step explanation:

We can use ratios:

Rise : Run = 16 : 4 = 4 : 1 = 20 : 5

Hope this helps!

The product shown below in simplest form (x+5) (x-5) and we can use this product to determine that (15) (5)= 75.

First, we need to find the product shown below in simplest form:

we have = (x+5) (x-5)

we need to explain how you can use this product to determine that,

(15) (5) = 75

for us to get the solution we will let x = 10

Then (x + 5) (x - 6) will be:

(10 + 5) (10 - 5), or we can also say that: (15)(5) = 75

Also, this could be calculated as:

10(10 - 5) + 5(10 - 5) = 100 - 50 + 50 - 25 = 75

Therefore we can say that the product shown below in simplest form (x+5) (x-5) and we can use this product to determine that (15) (5)= 75

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Full question: Find the product shown below in simplest form: (x+5) (x-5) explain how you can use this product to determine that (15) (5) = 75

As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) equation exceeds the size of T, which contradicts the premise that T has the greatest area.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.  

The area of a triangle in hyperbolic geometry is determined by the formula:

Area = K ∙ (α + β + γ - π)

where K is a constant that depends on the curvature of the space and,, and are the triangle's angles.

we want to emphasise the expression + + -.

Consider the following two situations:

Case 1: T has angles that add up to be less than.

Moreover, the total of the areas of triangles PTA, PTB, and PTC is larger than the area of T since their angles add up to more than T's angles. As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) exceeds the size of T, which contradicts the premise that T has the greatest area.

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As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.

Finding a value of a single unit or the ratio of two values, then using this value to determine the value of a bigger or smaller number, is the unitary method, a problem-solving strategy used in mathematics. The unit method, single unit method, and percentage method are additional names for the unitary approach. The unitary method, which can be used to address issues in a number of disciplines including mathematics, algebra, geometry, and physics, entails using a ratio, proportion, or factor. The approach is founded on the proportionality concept, according to which two ratios or quantities are proportional if they have the same ratio or proportion.

given

Three and a half pounds of apples, which can be expressed as a mixed amount or an incorrect fraction, were harvested by the Martinez family:

3 1/2 = 7/2

Ana selected one-fourth of those apples, so the quantity she selected can be calculated by dividing by the total number of apples selected by the Martinez family:

1/4 × 7/2 = (1 × 7)/(4 × 2) = 7/8

As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.

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The relatiοnship in the given diagram is nοt a functiοn, because fοr each input there is nοt exactly οne οutput. Sο Optiοn A is cοrrect

Functiοn is a relatiοn between a set οf inputs and a set οf οutputs which are permissible. In a functiοn, fοr particular values οf x we will get οnly a single image in y. It is denοted by f(x).

Vertical line test:-

Whenever we want tο check whether a given expressiοn is a functiοn οr nοt we can apply a vertical line test, in this test we check fοr a single image οf x , we are getting a single image οr mοre.

If we get mοre images then it will nοt be a functiοn.

Fοr example, let us take, y² = 4ax

y = ±√4ax

Fοr single value οf x we get twο values οf y

Hence, it will nοt be a functiοn.

Given that,

Values οf x and values οf y

In given diagram,

fοr x = 0,

there are twο values οf y, -4 and -2

but accοrding tο definitiοn οf y, it shοuld give οnly οne value

Hence, it is nοt a functiοn

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The set o rates that Frank could use to finish the events within 7.5 hours is (0.75 km/h, 25 km/h, 12.5 km/h).

To determine the rates at which Frank must complete each event to finish the triathlon within 7.5 hours, we can use the formula:

time = distance / rate

where;

Let x be the rate at which Frank completes the swim,

y be the rate at which he completes the bike ride, and

z be the rate at which he completes the run.

Then, we have the following three equations:

2.25 / x + 65 / y + 20 / z = 7.5

x > 0, y > 0, z > 0

We want to find the set of rates (x, y, z) that satisfy these equations and inequalities.

Here is one possible set of rates that would allow Frank to complete the triathlon within 7.5 hours:

x = 0.5 km/hour

y = 20 km/hour

z = 10 km/hour

Using these rates, we can calculate the time it would take Frank to complete each event:

Swim: 2.25 km / 0.5 km/hour = 4.5 hours

Bike ride: 65 km / 20 km/hour = 3.25 hours

Run: 20 km / 10 km/hour = 2 hours

The total time would be:

4.5 + 3.25 + 2 = 9.75 hours

This is greater than 7.5 hours, so Frank would need to increase his rates to finish within the time limit.

Here are some possible sets of rates that would allow him to do so:

x = 0.75 km/hour, y = 25 km/hour, z = 12.5 km/hour

x = 1 km/hour, y = 30 km/hour, z = 15 km/hour

x = 1.25 km/hour, y = 35 km/hour, z = 17.5 km/hour

Using any of these sets of rates, Frank would be able to complete the triathlon within 7.5 hours.

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According to the given information, the coordinates of C′ are (-7, 3.5).

What is the scaling of a triangle?

Scaling is a type of transformation in which the size of an object, in this case, a triangle, is changed while its shape and orientation are maintained. In other words, scaling involves multiplying the coordinates of the vertices of the triangle by a factor called the scale factor.

To dilate a triangle using a scale factor of 3.5, we need to multiply the distance between each vertex and the center of dilation by 3.5. The center of dilation can be any point, but for simplicity, we can choose the origin (0,0).

So, the coordinates of the new vertex C′ can be found by multiplying the distance between the old vertex C(-2,1) and the origin (0,0) by 3.5, and then adding this to the coordinates of the origin.

The distance between C and the origin is [tex]\sqrt{(-2-0)^2+(1-0)^2}[/tex] = [tex]\sqrt{5}[/tex] so the distance between C′ and the origin is [tex]3.5*\sqrt{5}[/tex].

Therefore, the coordinates of C′ are (-23.5, 13.5) = (-7, 3.5).

So, the answer is C′(-7, 3.5).

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Answer: Let's call the first term of the arithmetic progression "a" and the common difference "d". Then we can use the following formulas to find the second, fifth, and seventh terms:

- The second term is a + d.

- The fifth term is a + 4d.

- The seventh term is a + 6d.

We are given that the sum of the second and seventh terms is 25:

(a + d) + (a + 6d) = 25

Simplifying this equation, we get:

2a + 7d = 25 ...(1)

We are also given that the fifth term is 15:

a + 4d = 15 ...(2)

Now we can solve for the common difference "d" by using equations (1) and (2) to form a system of two equations in two variables. One way to do this is to solve equation (2) for "a" in terms of "d", and then substitute that expression for "a" into equation (1):

a = 15 - 4d ...(3)

Substituting equation (3) into equation (1), we get:

2(15 - 4d) + 7d = 25

Simplifying this equation, we get:

30 - 8d + 7d = 25

Solving for "d", we get:

d = -5

Therefore, the common difference is -5.

Step-by-step explanation:

Answer:

12%

Step-by-step explanation:

147/ 1225 x 100/ 1

0.12 x 100 = 12%

Answer:

Therefore, 147 is 12% of 1225.

The solution to the inequality  - 11y -13>42 is y < -5.

An inequality is a mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥ to indicate whether one is less than, greater than, less than or equal to, or greater or equal to the other.

To solve the inequality -11y - 13 > 42, we need to isolate y on one side of the inequality.

-11y - 13 > 42

First, we can add 13 to both sides:

-11y > 55

Next, we can divide both sides by -11, remembering to reverse the direction of the inequality because we are dividing by a negative number:

y < -5

To graph this on a number line,

Here is a rough sketch of the number line:

<=====(●)------------------------

-5

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Therefore , the solution of the given problem of probability comes out to be  the likelihood that they have four girls is 1/15.

The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.

Here,

Given that the family has at least one girl, we can use Bayes' theorem to determine the likelihood that they have four girls:

=> P(4 girls | at least one girl) = P(4 girls)

=> Times P(at least one girl | 4 girls) / P. (at least one girl)

Additionally, we are aware that the probability of having at least one female is

=> P(at least one girl = 1 - P(no girls) = 1 - (1/2)4 = 15/16.

The likelihood of not having any females is equal to the likelihood of having four boys,

which is

=>  (1/2)4 = 1/16.

Given that all four of the children are female, the likelihood of producing girls is one.

Combining everything, we have:

=> P(4 females | a girl)

=> 1 * (1/16) / (15/16) = 1/15

Given that the household has at least one girl, the likelihood that they have four girls is 1/15.

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The strengths and weaknesses of the data will help to identify the areas that need to be improved.

The steps that are to be taken to apply hypothesis tests to the case of Bayview University are given below:Open the dataset of Bayview University and read the case in its entirety at the end of Chapter 9. After opening the dataset of Bayview University, read the case in its entirety at the end of Chapter 9. It is important to read the case carefully in order to understand it properly. This is the first step that is to be taken in order to apply hypothesis tests to the case of Bayview University.

Use descriptive statistics to summarize the data and comment on your findings. Once the case has been read carefully, descriptive statistics are to be used to summarize the data. Descriptive statistics are statistical techniques that are used to describe and summarize the data. They are used to summarize the data in a way that is meaningful and easy to understand. The descriptive statistics will help to identify the central tendency and the variability of the data. After summarizing the data, comments are to be made on the findings. These comments will help to identify the strengths and weaknesses of the data. The strengths and weaknesses of the data will help to identify the areas that need to be improved.

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Answer:

No, it is not reasonable. The scaled drawing would be 12 inches wide by 30 inches tall.

Step-by-step explanation:

First, scale down the sides. 48in divided by 4 is 12in , and 120 in divided by 4 is 30 in. So no, it would not fit on her paper.

Answer:

B.

Step-by-step explanation:

The proportions should be exactly the same for each set of questions and correct questions.

Based on Raven's history, she get 5 of 7.

Choice B. shows exactly that with a scalar of 2, 3, and 4. For Row 2, the set is twice as large, so Raven gets exactly twice as many questions correct and exactly twice as many incorrect.

For Option B., the [tex]\frac{correct}{total}[/tex] always simplifies to [tex]\frac{5}{7}[/tex] for every row.

Based on the information provided, the total Diane will need to pay is $11.6.

Let's start by calculating the total from the items she ordered, the process is shown below:

Now, let´s apply the coupon by using the 10% as a reference:

12.05 x 0.9 (she will paid only 90%) = $10.845

Finally, let's calculate the tax by using its percentage and let's add it:

$10.845 x 0.0775 = $0.84

$10.845 + $0.84 = $11.6

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