Determine the unknown length or angle measurement. Round each answer to the nearest whole number

(C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.

To find what fraction of the marbles now in the bag is blue:

Therefore, (C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.

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Complete question:

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

(A) 1/5

(B) 1/4

(C) 1/3

(D) 2/5

(E) 1/2

Between 48% and 54% believe that their health is extremely important.

According to the statement

Given that a random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important.

Here

Sample size n =1001

sample proportion p = 0.51

By these values we calculate the Standard error of proportion.

So, Standard error of proportion = 0.0158.

Since sample size is sufficiently large we can take Z critical value for confidence interval

Z critical value for 95% = 1.96

Margin of error = ±1.96*std error

= ±0.0310

confidence interval = 0.51 ±0.0310

= (0.48, 0.54)

So, Between 48% and 54% believe that their health is extremely important.

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The length of hypotenuse when the value of legs of a right angled triangle are 7 and 7 feet is 9.9 feet.

Given that a and b are legs and c is the hypotenuse. length of legs of a right angled triangle  are 7 feet and 7 feet.

We have to find the value of c in the right angled triangle.

In this we have to apply pythagoras theorem because it says tat the square of hypotenuse is equal to the sum of squares of base and perpendicular of that right angled triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex]

H=c

P=7 feet

B=7 feet.

Put the values in the above rule:

[tex]c^{2} =7^{2} +7^{2}[/tex]

[tex]c^{2}[/tex]=49+49

[tex]c^{2}[/tex]=98

c=9.899

After rounding off to nearest tenth we will get c=9.9.

Hence the value of c is 9.9 which is the length of hypotenuse.

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Performing subtraction operations on the given vectors gives;

u - v = <-2 - 3, -7 - (-4) > = <-5, -3>

Therefore;

u - w = <-2 - 5, -7 - 1> = <-7, -8>

u - w = <-7, -8> which corresponds with graph 2

Therefore;

w - v = <5 - 3, 1 - (-4)> = <2, 5>

w - v = <2, 5> which corresponds with graph 3

Therefore;

v - u = <3 - (-2), -4 - (-7)> = <5, 3>

v - u = <5, 3> which corresponds with graph 4

Therefore;

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Answer:

15.78°

Step-by-step explanation:

Let the angle be x.

From the x, the known sides are the opposite side, O(13) and the adjacent side, A(46)

Therefore, The trigonometric ratio is the tangent ratio.

tan x = O/A

tan x =13/46

x = 15.78°

Answer: 27

Step-by-step explanation:

Mean = Sum of data/Number of data = (2 + 7 + x)/3 = 12

(x+9)/3 = 12

x+9 = 36

x = 27

Answer:

Step-by-step explanation:

B is the answer

The corresponding range of the domain is (11, -4, -29)

The function is given as:

5x + y = 1

Make y the subject

y = 1 - 5x

The domain is given as:

(-2,1,6)

Substitute these values in y = 1 - 5x

y = 1 - 5(-2) = 11

y = 1 - 5(1) = -4

y = 1 - 5(6) = -29

Hence, the corresponding range of the domain is (11, -4, -29)

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Answer:

12.2 cm

Step-by-step explanation:

we are going to use the formula (below).

Our a and b are going to be our two legs: 10cm and 7cm

[tex]C^{2} =10^{2} +7^{2} \\C^{2}=100+49\\C^{2}=149\\C=\sqrt{149} \\C=12.2cm[/tex]

Answer:

2

Step-by-step explanation:

• Multiplying two numbers with same bases is the same as adding their powers:

∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

• Dividing two numbers with same bases is the same as subtracting their powers:

∴  [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒  [tex](4^{1})^{\frac{1}{2} }[/tex]

⇒  [tex]4^{\frac{1}{2}[/tex]

• Raising anything to the power of  [tex]\frac{1}{2}[/tex] is the same as square-rooting it:

∴  [tex]4^{\frac{1}{2}[/tex]

⇒ [tex]\sqrt{4}[/tex]

⇒ 2

The diagram where angles 1 and 2 form a linear pair is option D which is that a horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

Given that angle 1 and 2 form a linear pair.

We know that a linear pair is an angle that are formed when two lines intersect each other at a single point.

In our case when a horizontal line has 1 line extending from it and when angles 1 and 2 are formed shows a linear pair.

In first part when two lines intersect they donot form 4 angles.

In second part when 3 lines extend from a point they don't form right angle between the lines.

Hence the linear pair angles are shown by the statement that a horizontal line has 1 line extending from it. Angles 1 and 2 are formed.

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The sine and cosine rule is typically used to find the measure of angles in trigonometry.

It should be noted that the sine rule is used when we are given:

The cosine rule is used when we are given:

The advantage is that it can help us understand the connections between the sides and their angles.

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There are 2 people are stepping onto the roller coaster per minute at peak time

According to statement

Given Flow time = 10 minutes.

Given Inventory = 20.

We use the formula then

I = R × T,

Therefore R = I / T.

Substitute the values in formula then

Flow rate = 20 / 10 = 2 people per minute.

So, There are 2 people are stepping onto the roller coaster per minute at peak time

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The surface area of the square pyramid is: 220 units².

Surface area of a square pyramid = 1/2(base perimeter)(slant height) = 1/2(P)(l).

Given the following:

Perimeter of base (P) = 4(10) = 40 units

Slant height (l) = 11 units

The surface area of the square pyramid = 1/2(40)(11)

Surface area of the square pyramid = 220 units²

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Using an exponential function, it is found that:

An exponential function is modeled by:

[tex]y = ab^x[/tex].

In which:

The parameters for this problem are given as follows:

a = 2, b = 2.

Hence the number of bacteria after x hours is given by:

[tex]y = 2(2)^x[/tex]

After 6 hours, the amount is:

[tex]y = 2(2)^6 = 2^7 = 128[/tex]

After 24 hours, the amount is:

[tex]y = 2(2)^{24} = 2^{25} = 33554432[/tex]

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Answer:

Find the rate of sales tax

R= 9000/120000

=0.075

=7.5%

So, the rate is 7.5%

Option D. What we can conclude is that  If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

An operation is done on a first column of numbers. When this operation is repeated on the second column, we would have option D.

If the sum of the numbers that are in the third can be seen to be greater than three, then the sums are not going to be seen as equal

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One column of numbers consists of 28, 42, and 14. When the digits of the numbers are added together, the result is 2 + 8 + 4 + 2 + 1 + 4 = 21, and when the digits of 21 are then added together, the end result is 2 + 1 = 3. If the same process is performed on the numbers in a second column, what can be concluded?

A. If the end result from the second column is also 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

B. If the end result from the second column is not 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

C. If the end result from the second column is also 3, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.

D. If the end result from the second column is not 3, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column.

Using the given recipe, he will need 6 cups of milk to make 18 servings.

We know that the recipe for 6 servings, calls for 2 cups of milk.

Miguel wants to do 18 servings, Then he needs to use the recipe:

18 = x*6

Solving the linear equation for x:

x = 18/6 = 3

So he needs to use his recipe 3 times.

And we know that for 6 servings he needs 2 cups of milk, then for 18 he needs:

3*(2 cups) = 6 cups of milk.

Using the given recipe, he will need 6 cups of milk to make 18 servings.

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Answer:

(x+9) (x-8)

Step-by-step explanation:

Edmentum/Plato

Answer:

Q₂ = 10

Step-by-step explanation:

Given data set:  3, 9, 12, 4, 6, 40, 25, 14, 10

Q₂ is the median (the middle value) of the given data set when the data set is ordered from smallest to largest.

Order the values in the data set:

3, 4, 6, 9, 10, 12, 14, 25, 40

As the number of values is odd, the middle value is the 5th value.

Therefore, the median (Q₂) of the given data set is 10.

If the number of data values is even, and therefore there are two middle values, the median is halfway between them.

Answer:

9a^3b^3

Step-by-step explanation:

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number

Find the prime factors of each term in order to find the greatest common factor (GCF).

Answer:

Step-by-step explanation:

the third one is correct

[tex]6 \times 3 - \frac{18}{9} \\ (6 \times 3) - (18 \div 9)[/tex]

More than 93 percent of all blank coupons are distributed as freestanding inserts in newspapers.

What is percent?

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The rate at which Sean drank the slushy is 5 milliliters  per second.

The time it would take to drink all the slushy is 55 seconds.

In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.

Speed = slushy drank in 13 seconds / time

(275 - 210) / 13

65 / 13 = 5 milliliters  per second

Time it would take to drink all the slushy =total milliliters of the slushy / speed

275 / 5 = 55 seconds.

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The linear function that shows that the number of cars seen each week by the mechanic is:

f(x) = -5x + 200.

A linear function is modeled by:

y = mx + b

In which:

During the first week analyzed, the amount of cars was of 200, hence the y-intercept is of 200. In 5 weeks, the amount decayed by 25, hence the slope is given by:

m = -25/5 = -5.

Thus the linear function that shows that the number of cars seen each week by the mechanic is:

f(x) = -5x + 200.

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Answer:

f(x) = −5x + 250

Step-by-step explanation:

First, we must find the slope. We can take 2 points. (10, 100) and (15,175)

Using y2-y1/x2-x1=m, we find that the slope =-5. to find the y-intercept, we have to find that y= when x=0. Since 10 weeks passed since the begining, we can inverse the slope to find 5(cars)x10(weeks)=50.

so, 200(week10)+50(week 1)=250

f(x)=-5x+250.

Another name for AXW is <X

The arrow on XW implies that the segment XW is a ray, such that any of the points X or W can be the starting point

Hence, another name for XW is WX

A ray with an endpoint X is a ray that ends at point X

An example of such ray is XY

The arrow on WX implies that the segment WX is a ray, such that any of the points X or W can be the starting point

Hence, another name for WX is XW

The name AXW represents an angle

An angle can be named after its middle point

Hence, another name for AXW is <X

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The standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.

Dispersion is measured by variance. A metric called a "measure of dispersion" is used to assess how variable data are concerning an average value. There are two sorts of data: grouped and ungrouped. Data is referred to as grouped data when it is presented as class intervals. On the other hand, it is referred to as ungrouped data if it comprises just individual data points. For both types of data, the sample and population variances may be calculated.

The variance of the provided data is obtained by taking the square of the standard deviation. The standard deviation is used to determine how widely distributed the data points are about the mean. In other words, the standard deviation is used to determine how observations in a data collection deviate from the mean. While the standard deviation has the same unit as the population or the sample, variance is represented in square units.

In the question, we are asked to find the standard deviation, if the variance is 0.01545.

We know that Variance = (Standard Deviation)².

This gives us:

Standard Deviation = √Variance,

or, Standard Deviation = √0.01545,

or, Standard Deviation = 0.12429802894 ≈ 0.1243.

Thus, the standard deviation is 0.1243, given the variance to be 0.01545, making option B the right choice.

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Answer:

ray

Step-by-step explanation:

Rays only have one endpoint, so it continues infinitely in one direction. Segments have TWO endpoints.