Calculate the side lengths a and b to two decimal places

A. a= 10.92 b=14.52 <--- My answer

B. a= 11 b= 15

C. a=4.18 b=3.15

D. a= 11.40 b=13.38

Answer:

The answer is option A

Step-by-step explanation:

Since the lines are perpendicular the slope perpendicular line is the negative inverse of the original line and when they are multiplied should give - 1

Let m be the slope of the perpendicular line

That's

1/3 × m = - 1

multiply through by 3

m = - 3

The slope of the perpendicular line is - 3

Hope this helps you

Answer:

-3

Step-by-step explanation:

Answer:

i feel as if in the United States, both the metric system and the English system of measurement are used, although the English system predominates. This discussion question has three parts:

Look around you to find something in the U.S. that is measured in metrics. Describe it to the class.

Give an example of how you think the metric system will be used in your future career.

Do you think the U.S. should switch to metric system exclusively? Why or why not?

This week we learned about the metric and U.S. customary measurement systems. Please upload and submit your responses to the following questions in at least 150 words:

In reflecting on both measurement systems, what did you find most important?

Explain how both measurement systems could relate to your life, community, or current/future career.

Expert Answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given : A right triangle

To do : Solve for x

Solution,

[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )

[tex]0.5736 = \frac{x}{20} [/tex]

multiply both sides of the equation by 20

[tex](0.5736) \times 20 = x[/tex]

Calculate the product

[tex]11.471 = x[/tex]

Swipe both sides of the equation

[tex]x = 11.471[/tex]

Round answer to nearest hundredth

[tex]x = 11.47[/tex]

Hope this helps...

Best regards!!

Answer:

The answer is

Step-by-step explanation:

3+ – 5(4+ – 3v) can be written as

3 - 5( 4 - 3v)

Expand and simplify

That's

3 - 20 + 15v

15v - 17

Hope this helps you

Answer:

[tex]\mathbf{V = 1296 \pi }[/tex]

Step-by-step explanation:

Given that :

Find the volume of the region enclosed by the cylinder [tex]x^2 + y^2 =36[/tex] and the plane z = 0 and y + z = 36

From y + z = 36

z = 36 - y

The volume of the region can be represented by the equation:

[tex]V = \int\limits \int\limits_D(36-y)dA[/tex]

In this case;

D is the region given by [tex]x^2 + y^2 = 36[/tex]

Relating this to polar coordinates

x = rcosθ    y = rsinθ

x² + y² = r²

x² + y² = 36

r² = 36

r = [tex]\sqrt{36}[/tex]

r = 6

dA = rdrdθ

r → 0 to 6

θ to 0  to 2π

Therefore:

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r sin \theta ) (rdrd \theta)[/tex]

[tex]V = \int\limits^{2 \pi} _0 \int\limits ^6_0 (36-r^2 sin \theta ) drd \theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [\dfrac{36r^2}{2}- \dfrac{r^3}{3}sin \theta]^6_0 \ d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648- \dfrac{216}{3}sin \theta]d\theta[/tex]

[tex]V = \int\limits^{2 \pi} _0 [648+\dfrac{216}{3}cos \theta]d\theta[/tex]

[tex]V = [648+\dfrac{216}{3}cos \theta]^{2 \pi}_0[/tex]

[tex]V = [648(2 \pi -0)+\dfrac{216}{3}(1-1)][/tex]

[tex]V = [648(2 \pi )+\dfrac{216}{3}(0)][/tex]

[tex]V = 648(2 \pi )[/tex]

[tex]\mathbf{V = 1296 \pi }[/tex]

Let x be the number.

Set up an equation:

2x - 2/3x = 20

Simplify:

1 1/3x = 20

Divide both sides by 1 1/3

X = 15

The number is 15

do not know because my brain cant focus on this sorry :/

Answer:

The correct answer for the best line of fit is C: y = 1/3x+12

Step-by-step explanation:

So our goal here is to find the best equation that matches the line of fit.

So right away we can already eliminate two of the options because in the scatter point it shows that the starting y-intercept is 12 and two of the options have a y-intercept of 15. So we are able to tell that Option B and Option D isn't the equation for the lien of fit.

Now we are left with Option A and Option C, which both have a y-intercept of 12. To find the right equation that best matches the line of fit we look at the slope. Option A has a slope of 3x while Option C has a slope of 1/3x, to tell what slope the line of has we applied both option's slope and see which one matches it.

When we match Option A's slope which is 3x it doesn't match because a slope of 3x is going first going up the y-axis 3 times then moving through the x-axis 1 time. Which would had made the line of fit more steep.

Next we match Option C's slope which is 1/3x this slope matches the line of fit because in the scatter plot it clearly shows  it going up 1 time on the y=axis and 3 times through the x-axis. Which made the line of fit not that steep.

So the correct answer to this question is C:  y = 1/3x+12.

Here a picture of the line of fit if it has a slope of 3x.

Answer:

correct answer  C: y = 1/3x+12

Step-by-step explanation:

i just did the problem

It is possible to draw a single straight line to pass through more than one point on the red curve. Therefore, the graph fails the vertical line test. We have cases where one input leads to more than one output.

Answer:

C. (x-3)(x+2)(x+1)

Step-by-step explanation:

We can use the rational roots test to help factor out the original equation.

The leading term is 1 and the constant is 6

p/q= 6/1

Now we find factors (all these are plus and minus)

1,2,3,6

1

We find the common ones (+1 and -1) and use -1 because it ends up being the root of the function

Factor, (x+1)

Now we have (x+1)(x^2-x-6)

Factor this with whatever method you perfer, I use AC method

Find two that are a product of -6 and add to -1 (-3 and 2)

We get (x+1)(x-3)(x+2)

C

Answer:

[tex]\boxed{C}[/tex]

Step-by-step explanation:

Let's solve all of the option and see which equals x³-7x-6

Option A)

[tex](x-4)(x-2)(x+1)[/tex]

=> [tex](x^2-6x+8)(x+1)[/tex]

=> [tex]x^3+x^2-6x^2-6x+8x+1\\x^3-5x^2+2x+1[/tex]

So, A is not correct

Option B)

[tex](x-6)(x-1)(x+1)\\(x+6)(x^2-1)\\x^3-x+6x^2-6\\x^2+6x^2-x-6[/tex]

This is also not correct

Option C)    ← Correct

[tex](x-3)(x+2)(x+1)\\(x^2-x-6)(x+1)\\x^3+x^2-x^2-x-6x-6\\x^3-7x-6[/tex]

This equals to x³-7x-6, So, this is the correct option. No need to do Option D since we have the right option now!

Answer:

Adjusted-R2

Step-by-step explanation:

When evaluating a multiple regression model, a commonly used goodness of fit is the adjusted-R2. It allows for a comparison of regression models with multiple predictors or independent variables. The addition of independent variables usually causes the model to be more reliable. The adjusted-R2 considers the effect of additional independent variables. It usually adjusts for the number of terms in the model.

1

Step-by-step explanation:

p(x≤20)=p(x=-10) +p(x=-5)+p(X=0) +p(x=5) +p(x=10)+ p(X=15)+p(X=20)

This, p(X≤20)=0.20+0.15+0.05+0.1+0.25+0.1+0.15

=1

Answer:

3

Step-by-step explanation:

336 / n = k + 2/n, where k is an integer

336 = kn + 2

334 = kn

2007 / n

(2004 + 3) / n

(334×6 + 3) / n

334×6/n + 3/n

6k + 3/n

The remainder is 3.

Answer:

Total number of required ways = 18480

Step-by-step explanation:

Given that

Total appetizers = 11

Total main courses = 8

Total desserts = 4

To be selected 9 appetizers

3 main courses and

2 desserts.

To find:

Number of ways of selecting them.

Solution:

Number of ways to select 'r' number of items out of 'n' number of items is given as:

[tex]_nC_r = \dfrac{n!}{(n-r)!r!}[/tex]

One important property:

[tex]_nC_r = _nC_{n-r}[/tex]

Here we have 3 items, we will find each items' number of ways of selecting and then will multiply all of them.

Number of ways to select 9 appetizers out of 11 appetizers:

[tex]_{11}C_9\ or\ _{11}C_2 = \dfrac{11 \times 10}{2} = 55[/tex]

Number of ways to select 3 out of 8 main courses:

[tex]_{8}C_3= \dfrac{8 \times 7 \times 6}{6} = 56[/tex]

Number of ways to select 2 desserts out of 4:

[tex]_{4}C_2= \dfrac{4 \times 3}{2} = 6[/tex]

Total number of ways = [tex]55 \times 56 \times 6[/tex] = 18480

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

[tex] Range= 71[/tex]

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

[tex]Mean value =58.7[/tex]

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

[tex]Variance=546[/tex]

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

[tex]Standard deviation= 23.4[/tex]

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Answer:

x = 40

Step-by-step explanation:

4/x = 50/500

Simplify the right side

4/x = 1/10

Using cross products

4*10 = 1*x

40 = x

Step-by-step explanation:

4/x = 50/500

4/x = 0.1

x = 4/0.1

x = 40

Answer:

79.67%

Step-by-step explanation:

To find the percentage correct, take the number correct over the total

98/123

.796747967

Change to a percent by multiplying by 100 %

79.6747967%

Round to the nearest hundredth

79.67%

Answer:

79.67%

Step-by-step explanation:

percent = part/whole * 100%

percent = 98/123 * 100%

percent = 79.67%

Answer:

[tex]7.5cm^2[/tex]

Step-by-step explanation:

Well using the following formula,

[tex]\frac{b*h}{2}[/tex]

5*3 = 15

15 / 2

7.5cm^2

Answer:[tex]7.5cm^{2}[/tex]

Step-by-step explanation:

h=3

b=5

area=1/2 x b x h

1/2 x 5 x 3

area=7.5

An outlier in statistics is a data point that deviates considerably from other observations. The given data set has no outlier.

An outlier in statistics is a data point that deviates considerably from other observations. An outlier can be caused by measurement variability or by experimental mistake; the latter is sometimes eliminated from the data set.

To find the outlier for the given data set follow the given steps.

Step one: The first step is to find the quartiles for the data set.

For this data set, the quartiles are:

Q1 = 45.5

Q3 = 62.5

Step Two: Find the Interquartile Range

The interquartile range is the difference between the first and third quartiles.

IQR = Q3 - Q1

IQR = 45.5 - 62.5

IQR = 17

Step Three:

The next step is to set up a fence beyond the first and third quartiles using the interquartile range.

Lower Fence = Q1 - (1.5 × IQR)

Lower Fence = 45.5 - (1.5 × 17)

Lower Fence = 20

Upper Fence = Q3 + (1.5 × IQR)

Upper Fence = 62.5 + (1.5 × 17)

Upper Fence = 88

Step Four: Find the Outliers

Any numbers in the data that are above or below the fences are outliers.

Since there are no numbers outside the two fences. Hence, it can be concluded that the given data set does not have, any outlier.

Learn more about Outlier:

https://brainly.com/question/26958242

#SPJ2

Answer:

x = -4/3 and x = 5/2.

Step-by-step explanation:

6x² - 7x = 20

6x² - 7x - 20 = 0

To solve this, we can use the quadratic formula to solve this.

[please ignore the A-hat; that is a bug]

[tex]\frac{-b±\sqrt{b^2 - 4ac} }{2a}[/tex]

In this case, a = 6, b = -7, and c = -20.

[tex]\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}[/tex]

= [tex]\frac{7±\sqrt{49 + 80 * 6} }{12}[/tex]

= [tex]\frac{7±\sqrt{49 + 480} }{12}[/tex]

= [tex]\frac{7±\sqrt{529} }{12}[/tex]

= [tex]\frac{7±23 }{12}[/tex]

[tex]\frac{7 - 23 }{12}[/tex] = [tex]\frac{-16 }{12}[/tex] = -8 / 6 = -4 / 3

[tex]\frac{7 + 23 }{12}[/tex] = [tex]\frac{30}{12}[/tex] = 15 / 6 = 5 / 2

So, x = -4/3 and x = 5/2.

Hope this helps!  

Answer:

Step-by-step explanation:

[tex]6 {x}^{2} - 7x = 20[/tex]

Move constant to the left and change its sign

[tex] {6x}^{2} - 7x - 20 = 0[/tex]

Write -7x as a difference

[tex]6 {x}^{2} + 8x - 15x - 20 = 0[/tex]

Factor out 2x from the expression

[tex]2x(3x + 4) - 15x - 20 = 0[/tex]

Factor out -5 from the expression

[tex]2x(3x + 4) - 5(3x + 4) = 0[/tex]

Factor out 3x + 4 from the expression

[tex](3x + 4)(2x - 5) = 0[/tex]

When the product of factors equals 0 , at least one factor is 0

[tex]3x + 4 = 0[/tex]

[tex]2x - 5 = 0[/tex]

Solve the equation for X1

[tex]3x + 4 = 0[/tex]

Move constant to right side and change its sign

[tex] 3x = 0 - 4[/tex]

Calculate the difference

[tex]3x = - 4[/tex]

Divide both sides of the equation by 3

[tex] \frac{3x}{3} = \frac{ - 4}{3} [/tex]

Calculate

[tex]x = - \frac{4}{3} [/tex]

Again,

Solve for x2

[tex]2x - 5 = 0[/tex]

Move constant to right side and change its sign

[tex]2x = 0 + 5[/tex]

Calculate the sum

[tex]2x = 5[/tex]

Divide both sides of the equation by 2

[tex] \frac{2x}{2} = \frac{5}{2} [/tex]

Calculate

[tex]x = \frac{5}{2} [/tex]

[tex]x1 = - \frac{4}{3} [/tex]

[tex]x2 = \frac{5}{2} [/tex]

Hope this helps...

Best regards!!

Answer:

x = 65°

Step-by-step explanation:

Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.

Angle A = 2x (vertically opposite angles are equal)

Angle A = Angle C (opposite angles of a parallelogram are equal)

Angle A = Angle C = 2x

(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)

2x + 50° = 180°

2x = 180° - 50° = 130°

x = (130°/2) = 65°

Hope this Helps!!!

Answer:

65 degrees

Step-by-step explanation:

Answer: a) Mean = [tex]=37.80[/tex]

Standard deviation=[tex]=1.9442[/tex]

b) Mean = [tex]56.00[/tex]

Standard deviation=[tex]4.0988[/tex]

c) Mean = [tex]=24[/tex]

Standard deviation=[tex]2.4495[/tex]

Step-by-step explanation:

To compute Mean and standard deviation , we use following formula:

Mean = [tex]n\pi[/tex]

Standard deviation=[tex]\sqrt{n\pi(1-\pi)}[/tex]

a. [tex]n=42,\ \pi=0.90[/tex]

Mean = [tex]42\times0.90=37.80[/tex]

Standard deviation=[tex]\sqrt{42(0.90)(0.10)}=\sqrt{3.78}\approx1.9442[/tex]

b. [tex]n=80,\ \pi=0.70[/tex]

Mean = [tex]80\times0.70=56.00[/tex]

Standard deviation=[tex]\sqrt{80(0.70)(0.30)}=\sqrt{16.8}\approx4.0988[/tex]

c. [tex]n=32,\ \pi=0.75[/tex]

Mean = [tex]32\times0.75=24[/tex]

Standard deviation=[tex]\sqrt{32(0.75)(0.25)}=\sqrt{6}\approx2.4495[/tex]

Answer:

Option (B)

Step-by-step explanation:

Given question is not complete; find the complete question in the attachment.

In the graph attached,

Parent function is an absolute value function,

f(x) = |x|

When this graph is shifted 4 units left, rule for the translation will be,

f(x) → f(x + 4)

Therefore, the new function of above translation will be,

g(x) = f(x + 4) = |x + 4|

Now the graph is shifted 2 units down so the translated function will be,

h(x) = g(x) - 2

h(x) = |x + 4| - 2

If we rewrite the function in the form of an equation, graph will be represented by

⇒ y = |x + 4| - 2

Therefore, Option (B) will be the answer.

Answer:

57.6 km/h

Step-by-step explanation:

We are told that At noon, ship A is 70 km west of ship B.

Thus, coordinates of initial position of A and B is;

A(0,0) and B(70,0)

Now, we are told that Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. Thus, the final position of ship A and B after t hours are;

A(0,-35t) and B(70,25t)

Thus, distance between the two ships at time t hours is;

d(t) = √[(70 - 0)² + (25t - (-35t))²]

d(t) = √(4900 + 3600t²)

Now, to find how fast the distance between the ships changing, let's differentiate using the chain rule;

d'(t) = [1/(2√(4900 + 3600t²))] × 7200t

d'(t) = 3600t/√(4900 + 3600t²)

d'(t) = 3600t/10√(49 + 36t²)

d'(t) = 360t/√(49 + 36t²)

Now, at 4pm,it would have been 4 hours from noon. Thus, t = 4.

So;

d'(t) = (360×4)/√(49 + 36(4²))

d'(t) = 1440/√(49 + 576)

d'(t) = 1440/√625

d'(t) = 1440/25

d'(t) = 57.6 km/h

Answer:

C. It is an angle that has its vertex at the center of a circle.

Step-by-step explanation:

That's the definition.

A. is wrong. An angle with a measure greater than 180° is an obtuse angle,

B. is wrong. An angle that has its vertex on the circle is an inscribed angle.

D. is wrong. Part of the circumference of a circle is an arc.

Answer:

Bridge = 300 m

Speed = 10 m/s

Step-by-step explanation:

If a goes past you in 10 seconds, it means the train has speed of

100 m/ 10 seconds as it is 100 m long

The speed in m/s is:

Then it take 3 times of 10 seconds to cross the bridge, so

The length of the bridge is:

Answer:

Length  : 50m

Speed   : 5 m  /  s

Answer:median:249    

Step-by-step explanation:

median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369

246 +252=498

498/2=249

as for the mean  i will give you that later

Answer:

2n + 10.

Step-by-step explanation:

2(n + 5)

= 2 * n + 2 * 5

= 2n + 10.

Hope this helps!

Answer: 2n + 10

Explanation: In this problem, the 2 "distributes" through the parenthses which means that it multiplies by each of the terms inside.

So we have 2(n) + 2(5) which simplifies to 2n + 10.

Answer:

Step-by-step explanation:

tan(pi\4+A)tan(3pi\4+A) =-1

using the tangent sum of angle formula

Answer:

A

Step-by-step explanation:

[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.