Lucy’s dog weighs nine and seventy-five hundredths kilograms. what is the weight, in kilograms, of lucy’s dog written in expanded notation?

\(\\ \rm\hookrightarrow (3^8.2^{-5})^{-2}(2^{-2}3^{-3})^4.3^{28}\)

\(\\ \rm\hookrightarrow 3^{-16}

.2^{-10}.2^{-8}.3^{-12}>3^{28}\)

\(\\ \rm\hookrightarrow 3^{-16-12+28}2^{-10-8}\)

\(\\ \rm\hookrightarrow 3^02^{-18}\)

\(\\ \rm\hookrightarrow \dfrac{1}{2^{18}}\)

The natural length of the spring is approximately 3.97 cm.

The natural length (in cm) of the spring can be found by the following steps:

Given that 2.4 J of work is needed to stretch a spring from 15 cm to 19 cm  and 4 J is needed to stretch it from 19 cm to 23 cm.

We know that the work done in stretching a spring is given by the formula;

W = ½ k (x₂² - x₁²)

Where,W = work done

k = spring constant

x₁ = initial length of spring

x₂ = final length of spring

Let the natural length of the spring be x₀.

Then,

2.4 = ½ k (19² - 15²)

Also,4 = ½ k (23² - 19²)

Expanding and solving for k gives:

k = 20

Next, using the value of k in any of the equations to solve for x₀,

x₀² - 15² = (2 × 2.4) ÷ 20

x₀² = 15² + (2 × 2.4) ÷ 20

x₀² = 15.72

x₀ = √15.72

x₀ ≈ 3.97

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The measure of the side r is 13.29 in

To determine the value of the side of the triangle:

We need to take note of the six trigonometric identities. These identities are;

From the information shown in the diagram, we have that;

side q is the opposite side of angle Q

r is the hypotenuse side

s is the adjacent side

Using the sine identity, we have;

sin 37 = 8/r

cross multiply the values, we have;

r = 13. 29 in

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The equation of the regression line that predicts carbon dioxide emissions from GDP is y = 166.9x + 115.725. This regression line provides a simplified representation of the relationship between GDP and carbon dioxide emissions, allowing for predictions and further analysis of their association.  

The regression line equation is in the form of y = mx + b, where y represents the dependent variable (carbon dioxide emissions) and x represents the independent variable (GDP). The slope of the regression line, denoted by m, indicates the rate at which carbon dioxide emissions change with respect to GDP. In this case, the slope is 166.9, meaning that for every unit increase in GDP, carbon dioxide emissions are predicted to increase by 166.9 units.

The y-intercept, represented by b, gives the value of the dependent variable (carbon dioxide emissions) when the independent variable (GDP) is zero. In this equation, the y-intercept is 115.725, implying that when GDP is zero, the predicted carbon dioxide emissions are 115.725 units. By substituting the given values into the equation, y = 166.9x + 115.725, we can estimate carbon dioxide emissions based on a given GDP value.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

See below

Step-by-step explanation:

Center:   (-3, 4)

radius = r = \(\sqrt{25}\) = 5

diameter = 2r = 10

Answer:

Center= (3,-4)   Radius=5   Diameter=10

Step-by-step explanation:

The numbers (3,-4) are the coordinates in the center of a circle. The radius is squared to get the end number so to get the radius, you have to find its square root- \(\sqrt{25\) =5. The diameter is 2 times bigger than the radius so 5 times 2= 10.

Answer:  + or - 8

Step-by-step explanation:

A.  x^2 could be represented by the area of a square.  Length and width are the same, so the area would be x^2.  The answer is clearly wrong, since a square with sides of 32 would create a much larger area than 64.

B.  x^2 = 64

  What number times itself equals 64? =  8

This could be either positive or negative, since (-8)^2 is also equal to 64.

a. The total of the three cards is 12. 36

b. The number that should replace the question mark is 1.36

The mean of a given set of data is defined as the average of the values.

The formula for the mean of a set of data is given as;

Mean = sum of the data/number of data

From the information given, we have that;

Mean = 5

The data = 8 + 3 + x

Substitute the values, we have;

5 = 8 + 3 + x/3

cross multiply the values, we have;

15 = 11x

Divide both sides by the coefficient, we have;

x = 1. 36

The total of these cards = 8 + 3 + 1.36 = 12. 36

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There are 8,222,286 different ways that six students can form a group for an activity in a class of 29 students.

To find the number of ways to form a group of 6 students from a class of 29, we can use the concept of combinations, which are arrangements of items without regard to order.

The number of combinations of n items taken r at a time is denoted by C(n,r) and is given by the formula:

C(n,r) = n! / (r!(n-r)!)

where n! denotes the factorial of n, which is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

To apply this formula to the problem, we have:

n = 29 (number of students in the class)

r = 6 (number of students in the group)

So, the number of ways to form a group of 6 students from a class of 29 is:

C(29,6) = 29! / (6! * (29-6)!) = (29 x 28 x 27 x 26 x 25 x 24) / (6 x 5 x 4 x 3 x 2 x 1) = 8,222,286

Therefore, there are 8,222,286 different ways that six students can form a group for an  activity in a class of 29 students.

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Answer:

Here ya go, buddy:

situation:  

Katy wants to know how much money she needs to bring to the craft store to buy sixteen yards of fabric that cost $2.40 per yard.

y=2.4x  where x represents the number of yards of fabric and y represents the total amount of money she needs to bring to the store.

can i get brainliest please?

the slope of the line is 8 and equation line is y = 8x.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

slope m = 24-16 / 3-2

m = 8/1 = 8

y = 8x

Hence the slope of the line is 8 and equation line is y = 8x.

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Answer:

4x(5 − x^2)

Step-by-step explanation:

20 − 4x^3

= 4x(5 − x^2)

The equivalent expression after taking a common factor is,

⇒ 2 (10 - 2x³)

What is Mathematical expression?

The combination of numbers and variables by using sign addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The expression is;

⇒ 20 - 4x³

Now, Take common factor as;

⇒ 20 - 4x³ = 2 × 10 - 2 × 2x³

                 = 2 (10 - 2x³)

Thus, The equivalent expression after taking a common factor is,

⇒ 2 (10 - 2x³)

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Answer:

The Answer is 5/9 in the simplest form.

Answer:

a. 36 blueberries and 12 strawberries

b. 16 blueberries and 4 strawberries

Step-by-step explanation:

The computation of each berry in the bowl is shown below;

a. Total 48 berries

The Ratio of blueberries to strawberries is 9:3

So, the blueberries is = 48 × 9 ÷ (9  + 3) = 36

And, the strawberries is = 48 × 3 ÷ (9 + 3) = 12

b. Total 20 berries

The Ratio of blueberries to strawberries is 4:1

So, the blueberries is = 20 × 4 ÷ (4 + 1) = 16

And, the strawberries is = 20 × 1 ÷ (4 + 1) = 4

Answer:

Step-by-step explanation:a. 36 blueberries and 12 strawberries

b. 16 blueberries and 4 strawberries

Step-by-step explanation:

The computation of each berry in the bowl is shown below;

a. Total 48 berries

The Ratio of blueberries to strawberries is 9:3

So, the blueberries is = 48 × 9 ÷ (9  + 3) = 36

And, the strawberries is = 48 × 3 ÷ (9 + 3) = 12

b. Total 20 berries

The Ratio of blueberries to strawberries is 4:1

So, the blueberries is = 20 × 4 ÷ (4 + 1) = 16

And, the strawberries is = 20 × 1 ÷ (4 + 1) = 4

Answer:

\(5\)

Step-by-step explanation:

3/4+12/8+3/2+10/8=5

The comparison distribution in a t test for dependent means is a distribution of the differences between the pairs of scores on the dependent variable.

This distribution is used to determine whether the observed differences between the means of two related groups are statistically significant or could have occurred by chance. The t statistic is calculated by dividing the mean difference between the pairs of scores by the standard error of the mean difference, which is based on the variance of the differences in the sample. The t statistic is then compared to a t distribution with degrees of freedom equal to the number of pairs of scores minus one to determine the probability of obtaining the observed difference by chance.

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The volume of the pyramid is: 192 cubic inches
The surface area of the pyramid is: 181.01 inches
Cost of material is approximately 0.90 cents


To find the volume of the pyramid, we can use the formula:

V = (1/3) * base area * height

where base area is the area of the base of the pyramid and height is the height of the pyramid.

The base of the pyramid is a rectangle with dimensions 8 inches by 6 inches, so its area is:

A = length * width = 8 in * 6 in = 48 sq in

The height of the pyramid is given as 12 inches.

Therefore, the volume of the pyramid is:

V = (1/3) * 48 sq in * 12 in = 192 cubic inches

To find the surface area of the pyramid, we need to find the area of each face and add them up. Since the pyramid has four triangular faces, the surface area is:

A = area of one face * 4

To find the area of one face, we can use the formula for the area of a triangle:

A = (1/2) * base * height

where base is one of the sides of the base of the pyramid and height is the height of the pyramid.

The base of the pyramid is 8 inches, so the height can be found using the Pythagorean theorem:

h^2 = 12^2 - (8/2)^2 = 144 - 16 = 128

h = sqrt(128) = 8*sqrt(2) inches

Therefore, the area of one face is:

A = (1/2) * 8 in * 8sqrt(2) in = 32sqrt(2) sq in

And the surface area of the pyramid is:

A = 4 * 32sqrt(2) sq in = 128sqrt(2) sq in

To find the cost of material, we need to multiply the surface area by the cost per square inch:

cost = surface area * 0.005 cents/sq in

Substituting the value for the surface area, we get:

cost = 128sqrt(2) sq in * 0.005 cents/sq in = 0.64sqrt(2) cents

Rounding to two decimal places, the cost of material is approximately 0.90 cents.
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a. The maximum number of jobs that can be in progress at once is 3. b. The maximum number of idle tape drives at a given time is 3, and the minimum number of idle tape drives depends on the scheduling algorithm and job execution order.

a. The maximum number of jobs that can be in progress at once is determined by the number of available tape drives. In this case, there are 15 tape drives available. Since each job requires exactly 4 tape drives, the maximum number of jobs that can be in progress at once is 15 divided by 4, which is 3.75. However, since we cannot have a fraction of a job, the maximum number of jobs that can be in progress at once is 3.

b. The maximum number of tape drives that may be left idle at a given time is determined by the number of tape drives and the number of jobs in progress. Since there are 15 tape drives and a maximum of 3 jobs in progress, the maximum number of idle tape drives at a given time is 15 - (3 * 4) = 3.

The minimum number of tape drives that may be left idle depends on the scheduling of the jobs. If all the jobs are scheduled such that they fully utilize all available tape drives, then there would be no idle tape drives. However, if the jobs are not scheduled optimally and there are gaps in the execution of jobs, then some tape drives may be left idle. The minimum number of idle tape drives would depend on the specific scheduling algorithm and the order in which the jobs are executed.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above.

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{0}}} \implies \cfrac{ -2 }{ 1 } \implies - 2\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- 2}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=-2x+3 \end{array}}\)

Answer:

x= 21

Step-by-step explanation:

\( \frac{x}{3} = 7 \\ \\ multiply \: both \: sides \: by \: 3 \\ \\ 3 \times \frac{x}{3} = 3 \times 7 \\ \\ \implies \cancel 3 \times \frac{x}{\cancel 3} = 21 \\ \\ \implies \: x = 21\)

The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.

This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.

According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.

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There are two valid solutions

1. A is a knight, B is a knight, and C is a knave.

2. A is a knave, B is a knave, and C is a knight.

In this scenario, we have three natives on the island: A, B, and C. It is known that knights always tell the truth, while knaves always lie. Let's analyze the statements made by each native:

A says: "If B is a knight, then C is a knave."

B says: "If C is a knight, then A is a knave."

C says: "If A is a knight, then B is a knave."

To determine the true identities of A, B, and C, we need to examine the consistency of their statements.

Let's consider the possibilities:

1. If A is a knight:

  - A's statement would be true.

  - B and C's statements would also need to be true.

  - This implies that B is a knight and C is a knave.

2. If A is a knave:

  - A's statement would be false.

  - B and C's statements would also need to be false.

  - This implies that B is a knave and C is a knight.

Now let's evaluate these possibilities:

1. If A is a knight, B is a knight, and C is a knave:

  - A's statement is true, as B is a knight and C is a knave.

  - B's statement is true, as C is indeed a knave.

  - C's statement is false, as A is a knight, not a knave.

  - This configuration is consistent with the rules.

2. If A is a knave, B is a knave, and C is a knight:

  - A's statement is false, as B is not a knight.

  - B's statement is false, as C is a knight.

  - C's statement is true, as A is indeed a knave.

  - This configuration is consistent with the rules.

Therefore, there are two valid solutions:

1. A is a knight, B is a knight, and C is a knave.

2. A is a knave, B is a knave, and C is a knight.

These solutions are consistent with the statements made by A, B, and C, considering the behavior of knights and knaves on the island.

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Answer:

10m

Step-by-step explanation:

Difference means minus (-)

55/100 - 45/100

lcm=100

multiply through by 100

100×55/100 -100×45/100

 =55 - 45

 =10m

Answer:

-------------------

There are 13 clubs and 13 hearts in the deck.

First, find the number of ways to choose 2 clubs out of 13:

Next, find the number of ways to choose 3 hearts out of 13:

Now, multiply these two results:

Answer:

Step-by-step explanation:

Answer is D. There is multiple y values for x =0.

Answer:

  see attached

Step-by-step explanation:

You want the steps to simplify the sum of two rational expressions.

In general, the steps will be ...

See the attachment for the order for the given sum.

__

Additional comment

You can also look for factors in the combined numerator that will cancel denominator factors. And, you can expand the denominator to standard form.

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