What is a numerical expression? Give an example.

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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Answer:

Step-by-step explanation:

the third one is correct

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

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:

Find the rate of sales tax

R= 9000/120000

=0.075

=7.5%

So, the rate is 7.5%

(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

Answer:

Step-by-step explanation:

7+6-8x5=

7+6-40=

13-40=

-37

if the x is multiplying

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

What is percent?

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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°

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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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

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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The value is J = 1.71*10^-6 kmol/m^2.s

According to the given conditions we get,

The length the tube l= 0.20m

The diameter of the tube d= 0.01m

The total pressure inside the tube P= 101.32kPa

The partial pressure of CO2 at the first end is

P1= 456mm Hg = 60794.832 Pa

The partial pressure of CO2 at the other end is

P2= 76mm Hg = 10132.472 Pa

The temperature is T = 298 K

The diffusion coefficient D= 1.67* 10^-5 m^2/s

Generally the molar flux of CO2 is mathematically represented as

J= D{p1-p2} / R.T

Here R is the gas constant with value R= 8.314 j/kmol

So we get J= 1.71 * 10^-3 mol/m^2.sec

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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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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

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).

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.

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:

(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.

The reference angle after rotating the unit circle anti-clockwise is;  π/3 Radians

To draw the angle θ = -120° in the unit circle, we will move clockwise 90°, and thereafter another angle of 30°.

This tells us that we pass the fourth quadrant and stop in the third quadrant.

The reference angle of an angle theta in the third quadrant, is; θ + 180°.

Thus, the reference angle of -120° is; -120° + 180° = 60°.

Converting 60° to radians gives; (60/360) * 2π Radians = π/3 Radians

Thus, the Reference angle is π/3 Radians

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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:

ray

Step-by-step explanation:

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

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:

Step-by-step explanation:

B is the answer

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 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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