Emma recorded the weight of her kitten in ounces on certain days for 24 days. The data are shown in the scatter plot​

Using the triangle proportionality theorem, the missing lengths that are indicated are:

1. 35

2. 14

3. 28

4. 18

The triangle proportionality theorem states that when a line is drawn to be parallel to any side of a triangle that it intersects two of the side of the triangle at two different points, then the two sides are divided proportionally or in the same ratio.

Apply the triangle proportionality theorem to find all the missing length that are indicated. Let the missing side be represented as x.

Problem 1:

x/28 = 15/12

x = (28)(15)/12

x = 35

Problem 2:

x/28 = 6/(18 - 6)

x/28 = 6/12

x/28 = 1/2

x = 28/2

x = 14

Problem 3:

x/35 = 12/(12 + 3)

x/35 = 12/15

x/35 = 4/5

x = (35)(4)/5

x = 28

Problem 4:

x/54 = 8/24

x/54 = 1/3

x = 54/3

x = 18

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Answer:

AM=M-A

-3 -1. -2

2 -. -3. = 5

-3. -2. -5

2. +. 5. =. 7

A bicycle rider rides 24 km riding at a rate greater than 8 km/ h.

Given that, a bicycle rider is riding at a rate of 15 km/h for 4/9 of his ride.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Let total number of km be x.

Distance1 =4/9 x

Distance2 =2/9 x

Remaining distance = x-(4x/9 + 2x/9)

= x-6x/9

=(9x-6x)/9

= 3x/9

Now, time =1 hour

8 = 3x/9 ÷ 1

⇒ 8×9=3x

⇒ x=24 km

Hence, a bicycle rider rides 24 km riding at a rate greater than 8 km/ h.

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[tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex]  for the equation that models.

Jada sells b books and m magazine subscriptions to raise money for a choir trip. She earns $4 for each book and $3 for each magazine subscription she sells, and she earns a total of $96 toward the cost of her choir trip.

Given that

1. Jada sells b books and m magazines

2. She earns $4 for each book and $3 for each magazine

3. Total amount she earned is $96

Given equation is

4b + 3m = 96

Solve 4b + 3m = 96 for b

Subtract 3m from both sides

4b + 3m - 3m = 96 - 3m

4b = 96 - 3m

Now divide both sides by 4

= [tex]b = \frac{96-3m}{4}[/tex]

So, the answer for b is [tex]\frac{96-3m}{4}[/tex]

Now, solve 4b + 3m = 96 for m

Subtract 4b from both sides

4b + 3m - 4b = 96 - 4b

= 3m = 96 - 4b

Now divide both sides by 3

= [tex]m = \frac{96-4b}{3}[/tex]

So, the answer for m is [tex]\frac{96-4b}{3}[/tex]

Hence the answer is [tex]b = \frac{96-3m}{4}[/tex] and [tex]m = \frac{96-4b}{3}[/tex] for the equation that models.

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The decimal place should be after only 1 digit so the answer is e

Answer:

it is c

Step-by-step explanation:

you do 9x2 6+1 = 7 + 18 =25

Based on the data the correct interpretation of the interval is that we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. (Option B)

In statistics, a confidence interval indicates the probability that a population parameter will lie between a set of values around the population mean. It measures the degree of certainty or uncertainty in a sampling method. It is a range of values which are bounded above and below the statistic's mean that likely would contain an unknown population parameter. Confidence level is the percentage of certainty or probability of the confidence interval would include the true population parameter when a random sample is repeatedly drawn. Hence, in the given case based on the information we are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches.

Note: The question is missing options which are A. We are 94% confident that the population mean height of college basketball players is 66.35 inches. B. We are 94% confident that the population mean height of college basketball players is between 65.6 and 67.1 inches. C. A 94% of college basketball players have heights between 65.6 and 67.1 inches. D. There is a 94% chance that the population mean height of college basketball players is between 65.6 and 67.1 inches.

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The equation of the line in point slope form is (c) y - 6 = -2(x + 2)

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (2, -2) and (-2, 6)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2, -2) and (-2, 6)

Substitute the known values in the above equation

So, we have the following equation

m = (6 + 2)/(-2 - 2)

Evaluate

m = -2

The equation of a line can be represented as

y  - Y = m(x - X)

Where

Slope = m = -2

(X, Y) = (-2, 6)

So, we have

y - 6 = -2(x + 2)

Hence, the line has an equation of y - 6 = -2(x + 2)

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The two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).

In the given question we have to find the two x intercept of the equation.

The give equation is [tex]y=\frac{1}{2}(x+2)^2-4[/tex].

We can find the x intercept by putting y=0. Then solving the equation for x.

Now putting y=0 in the given equation.

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

Add 4 on both side, we get

[tex]\frac{1}{2}(x+2)^2[/tex] = 4

Multiply by 2 on both side, we get

[tex](x+2)^2[/tex] = 8

Taking square root on both side, we get

x+2 = √8

x+2 = ±2√2

Subtract 2 on both side we get

x=±2√2-2

Taking 2 common

x=2(±√2-1)

Now the values of x

x={2(-√2-1), 2(√2-1)}

x={-2(√2+1), 2(√2-1)}

Hence, the two x intercept of the equation [tex]y=\frac{1}{2}(x+2)^2-4[/tex] is -2(√2+1) and 2(√2-1).

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Answer:

hope this will help you..

1. The patterns regarding the polygons are given as follows:

2. The relationship between the number of sides of the polygon, and the number of non-overlapping triangles in the polygon is:

The number of non-overlapping triangles in the polygon is two less than the number of sides.

3. The relationship between the number of sides of the polygon and the sum of the interior angles is:

The sum of the interval angles of a triangle is given by the multiplication of 180º and the number of non-overlapping triangles in the polygon.

The patterns in the context of this problem are all obtained from the last row of the table, and they are all axioms for polynomial relations.

For item 2, the relationship is given by the third column of the last row, and for item 3, by the fourth column.

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The population of white tailed deer was increased by 40 times .

What are white tailed deer?

The medium-sized white-tailed deer is a native of North America, Central America, and South America as far south as Peru and Bolivia. It is often referred to as the white tail or Virginia deer.

Main body:

population of white tailed deer in 1905 = 5*10^5

population of white tailed deer in 2000 = 2*10^7

Population increase can be calculated by using simple division ,

calculating :

⇒ 2*10⁷/5*10⁵

⇒ 2*10⁽⁷⁻⁵⁾/ 5

⇒ 2*10²/ 5

⇒ 200/5

⇒ 40

Hence population increased by 40 times from 1905 to 2000 for white tailed deer.

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The solution of the equation is -3, 5+2i, 5-2i

What is solution of equation?

The solution of an equation is the array of all values that, when replaced for unknowns, make an equation true. For equations requiring one unknown, raised to a power one, two basic algebra rules involving the additive property and the multiplicative property are used to decide its solutions.

given equation is [tex]x^3+87=7x^2+x[/tex]

we can write it as

[tex]x^3+7x^2+x+87=0[/tex]

solving this cubic equation, we get

(x+3)(x2-10x+29)=0

x = -3 is the first root of the equation.

x2-10x+29 = 0

x =(-b±√b2-4ac)/2

x =(10±√-16)/2

x =5±2i

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Answer are

a) The Excepted value (p-hat) of p is 0.57

b) The Standard error of p is 0.05

c) Sampling distribution of p is Normal distribution

d) E(p-hat) = 0.57 , σ(p-hat) = 0.05

Excepted value or "p-hat" is defined as the ratio of number of succes in any sample or event to the total the size of sample . It is also known as sample proportion.

P-hat = X/ N

we have given that,

Sample size (N) = 100

Probability of an event occuring (p) or population proportion = 0.57

The Excepted value of sample proportion i.e p-hat is equal to population proportion i.e p

a) so, excepted value of p = 0.57

b) Standard error of p-hat is equal to square roots of product of p and (1-p) divided by sample size .

Standard error of p- hat = √p(1-p)/n

= √0.57 × 0.43/100= 0.05

c) Sampling distribution of sample mean is normal distribution using central limit theorem.

d) Sampling distribution of p shows

E(p-hat) = 0.57

σ(p-hat) = 0.05

Hence, we get all the required values of excepted value of p , standard error of p , distribution of p.

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For the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].

As given in the question,

Given matrix are equal to :

A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]

Simplify the equation which satisfy the equation 3X = -3A + 4B is given by :

Substitute the value of matrix A and matrix B in the given equation we get:

3X  =  [tex]-3\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right] + 4\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex]

⇒ 3X =  [tex]\left[\begin{array}{ccc}-24&12\\21&0\\\end{array}\right] + \left[\begin{array}{ccc}8&20\\8&0\\\end{array}\right][/tex]

⇒ 3X = [tex]\left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]

To get the value of X divide both the side by 3 we have,

⇒ X   = [tex]\frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex]

Therefore, for the given matrix A = [tex]\left[\begin{array}{ccc}8&-4\\-7&0\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}2&5\\2&0\\\end{array}\right][/tex] then value of matrix X which satisfy the given equation 3X = -3A + 4B is equal to [tex]X = \frac{1}{3} \left[\begin{array}{ccc}-16&32\\29&0\\\end{array}\right][/tex].

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Answer:

Step 3 is wrong. If 3x+28=15, then 3x= 15-28

Answer:

x= 0.41

Step-by-step explanation:

tan 9° =[tex]\frac{x}{2.6}[/tex]

x= 2.6 tan9°  (cross multiply)

x= 0.41          (solve trignomatic function)

The angle measures are ∠1 = 66°, ∠2 = 114°.

Given that m<1 = (x+81)° and m<2=2x°.

Here ∠ 1 and ∠ 2 are adjacent angles and are supplementary ( sum to 180°), then

2x + x + 81 = 180 , that is

3x + 81 = 180 ( now subtract the number 81 from both the sides )

3x = 99 ( now divide both the sides by the number 3 )

So that, x = 33

Thus, putting the value of x in the below equations:

∠ 1 = 2x = 2 × 33 = 66°

∠ 2 = x + 81 = 33 + 81 = 114°

Hence the answer is the angle measures = ∠1 = 66°, ∠2 = 114°.

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Answer:

600 miles

Step-by-step explanation:

1 Inch = 100 Miles

6 Inches = 600 Miles

Answer:

a^2 - 5ab

Step-by-step explanation:

[3a * (a-b)] - [2a * (a+b)]

[3a(a) - 3a(b)] - [2a(a) + 2a(b)]

3a^2 - 3ab - (2a^2) - (2ab)

3a^2 - 2a^2 - 3ab - 2ab

a^2 - 5ab

The pounds of berries that Gabrielle put in each container, given the pounds of berries she picked, are  5/6 pounds

Gabrielle was able to pick 5 ⁵/₆ pounds of berries. First convert this to an improper fraction for easier calculations:

= 5 ⁵/₆

= ((6 x 5) + 5) / 6

= 35 / 6

The pounds of berries that went into each container is:

= Pounds of berries / Number of containers

= 35 / 6 ÷ 7

= 35 /6 x 1/7

= 35/42

= 5/6 pounds

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Answer:

43446

Step-by-step explanation:

52 weeks in an year

835.5*52

= 43446

Answer:

y = 2 ; y = -7

Step-by-step explanation:

sum of two numbers = 5

product of two numbers = -14

the two numbers are 7 and -2

(y-2)(y+7) = 0

y = 2

y = -7

Answer:

105

Step-by-step explanation:

627-102=525

525 divided by 5 is 105

Check the picture below.

Answer:

Incomplete question.

Step-by-step explanation:

4 cm = 50 km

1 cm = 50/4 = 12.5 km

Use above ratio or

50 km = 4 cm

1 km = 4/50 = 0.08 cm

The standard deviation of the sum of the 4 random variables is 10.23

The question is incomplete the complete question is  

For each of the 4 stroke categories 2,4,6,8 consider a random variable representing the time of a randomly selected swimmer in that category is 0.6,0.8,0.2,0.7. What is the standard deviation of the sum of the 4 random variables?.

To calculate the Expected Value, we need to multiply each value by its probability and then sum the products up.

μ = E(x) = ∑xp(x)

That is, (0.6x2) + (0.8x4) + (0.2x6) + (0.7x8) = 1.2 + 3.2 + 1.2 + 5.6 = 11.2

Mean = 11.2

Now we take the first and second steps,

(2- 11.2)² x 0.6 = 84.64 x 0.6 = 50.78

(4 - 11.2)² x 0.8 = 51.84 x 0.8 = 41.47

(6 - 11.2)² x 0.2 = 27.04 x 0.2 = 5.4

(8 - 11.2)² x 0.7 = 10.24 x 0.7 = 7.16

Now we take the the third step and add our products together to get the variance V,

V = σ2 = ∑(x−μ)2P(x)

V = 50.78 + 41.47 + 5.4+ 7.16 = 104.81

Now we take the last step by taking the square root of the variance to get the standard deviation SD,

SD = σ = √σ2

Standard Deviation SD = √104.81 = 10.23

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The range of the given graph is [5, ∞).

Range.

Range refers the set of possible output values, and if we have the graph, then the set of all possible y values on the graph is defined as the range.

Given,

Here we have the graph.

Through the given graph we have to find the range of the line.

As per the definition of range, we have identified that the range take the value of y axis.

While we lookin into the given graph, we have identified that the starting point of the line is

=> (0, 5)

In this point 0 refers the x coordinate and 5 refers the y coordinate. So, the starting range is 5.

And the end of the line is not pointed.

So, we can consider that this line goes infinitely.

So, the range of the graph is  [5, ∞).

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