5 (u + 1) -
7 = 3
3 (u - 1) + 2u​

Answer:

156.7 miles

Step-by-step explanation:

Since [tex]x[/tex] is tangent to the circle, then it is also a right angle with the radius, from here, just do Pythagorean theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to solve for [tex]x[/tex].

Since 1 leg and the hypotenuse is given to you, you want to solve for the other leg, which is [tex]x[/tex] (either [tex]a[/tex] or [tex]b[/tex]). Lets use [tex]b[/tex] for [tex]x[/tex] and set up the equation.

[tex]b^{2}=c^2-a^2[/tex]

[tex]b^2=(3959+3.1)^2-3959^2[/tex]

[tex]b^2 = 3962.1^2 - 3959^2[/tex]

[tex]b^2 = 15,698,236.41 - 15,673,681[/tex]

[tex]b^2 = 24,555.41[/tex]

[tex]\sqrt{b^2}=\sqrt{24,555.41}[/tex]

[tex]b=156.7016592[/tex]

[tex]b=156.7[/tex] (round to nearest tenth)

The distance to the earth’s horizon from point P is 281.6 miles

The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

here, we have,

to determine the distance to the earth’s horizon from point P:

The tangent line from P meets the radius of the earth at a right angle.

This means that the triangle is a right triangle.

The length of x is then calculated as:

(3959 + 10)^2= 3959^2 + x^2

Rewrite as:

x^2 = (3959 + 10)^2- 3959^2

Evaluate

x^2 = 79280

Take the square root of both sides

x = 281.6

Hence, the distance to the earth’s horizon from point P is 281.6 miles

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Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

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

5x = 10

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{10}{5} [/tex]

Calculate

[tex]x = 2[/tex]

Now, substitute the given value of X in the equation

3x + y = 3

[tex]3 \times 2 + y = 3[/tex]

Multiply the numbers

[tex]6 + y = 3[/tex]

Move constant to R.H.S and change it's sign

[tex]y = 3 - 6[/tex]

Calculate

[tex]y = - 3[/tex]

The possible solution of this system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equation

[tex]2 \times 2 - ( - 3) = 7[/tex]

[tex]3 \times 2 - 3 = 3[/tex]

Simplify the equalities

[tex]7 = 7[/tex]

[tex]3 = 3[/tex]

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

The 95%   confidence interval is   [tex]768.44 < \mu <777.55[/tex]

Step-by-step explanation:

From the question we are told that  

    The  sample size is n = 48

    The sample mean is  [tex]\= x = 773 \ lb[/tex]

     The standard deviation is  [tex]\sigma = 16.1 \ lb[/tex]

Now given that the confidence level is  95% , then the level of significance is mathematically represented as

          [tex]\alpha = 100 - 95[/tex]

          [tex]\alpha = 5 \%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the  critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

              [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The reason we are obtaining critical values of   [tex]\frac{\alpha }{2}[/tex] instead of    [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (   [tex]1-\alpha[/tex] ) did not cover which include both the left and right tail while

[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error

 The  margin of error is mathematically represented as

      [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

     [tex]MOE = 1.96 * \frac{ 16.1 }{ \sqrt{48} }[/tex]

     [tex]MOE = 4.555[/tex]

The 95% confidence interval to estimate the mean breaking weight for this type cable is mathematically evaluated as

      [tex]\= x - MOE < \mu < \= x - MOE[/tex]

substituting values

    [tex]773 - 4.555 < \mu < 773 + 4.555[/tex]

     [tex]768.44 < \mu <777.55[/tex]

Answer:

d = 115.4 mi

Step-by-step explanation:

Since it gives us the distance in between the locations, we simply label the distances:

From the Garbage to the Hotel is 58.3 miles.

From the Hotel to the Hardware Store is 57.1 miles.

We are trying to find the distance from the Garbage to the Hardware Store, we simply add the distances between:

58.3 mi + 57.1 mi = 115.4 mi

From the odd-degree terms, take out one copy and rewrite the series as

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x+5x^3+\cdots[/tex]

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)[/tex]

Then if |x| < 1, we can condense this to

[tex]\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}[/tex]

Since the series we invoked here converge on -1 < x < 1, so does this one.

The explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

The function definition is given as:

[tex]f(x) = 1 + 6x + x^2 + 6x^3 + x^4 + ...[/tex]

Expand the terms of the expression

[tex]f(x) = 1 + 5x + x + x^2 + 5x^3 + x^3 + x^4 + ...[/tex]

Split

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x + 5x^3 + .. ...[/tex]

Factor out 5x

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express 1 as x^0

[tex]f(x) = (x^0 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express x as x^1

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Also, we have:

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(x^0 + x^2) + .. ...[/tex]

Rewrite the series using the summation symbol

[tex]f(x) = \sum\limits^{\infty}_{n=0}x^n+ 5x\sum\limits^{\infty}_{n=0}x^{2n}[/tex]

The sum to infinity of a geometric progression is:

[tex]S_{\infty} = \frac{a}{1- r}[/tex]

Where:

a represents the first term, and r represents the common ratio

Using the above formula, we have:

[tex]\sum\limits^{\infty}_{n=0}x^n = \frac{1}{1 - x}[/tex]

[tex]5x\sum\limits^{\infty}_{n=0}x^{2n} = 5x * \frac{1}{1 - x^2} = \frac{5x}{1-x^2}[/tex]

So, we have:

[tex]f(x) = \frac{1}{1-x}+ \frac{5x}{1-x^2}[/tex]

Take the LCM

[tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

Evaluate the like terms

[tex]f(x) = \frac{1 + 6x}{1-x^2}[/tex]

Hence, the explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

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Answer:

Step-by-step explanation:

a. To identify the alternative hypothesis, we have to examine the claim

The claim is that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm

Thus, alternative hypothesis is μ > 21.21

b. The test statistics is

z score = x - u /(sd/√n)

Where x (sample mean) is 23.375, u is pop. mean is 21.21, sd is 5.29 and n (sample size) is 40

z = 23.375 - 21.21 /(5.29/√40)

z = 2.165 / (5.29/6.3246)

z = 2.165/0.8364

z = 2.588

c. The critical value is

Alpha for this case study is 0.01. Then the critical probability is 1 - (alpha/2) =

1 - (0.01/2) = 1 - 0.005 = 0.995

To express the critical value as a z score, find the z score corresponding to the critical probability using the z table. Which is 0.8389.

Answer:

125975100 the population in 7 years

Step-by-step explanation:

the population in 7 more years : 127,484450(1-0.0017)^7=125975100.1919 close to 125975100

Answer: 125,976,376 IN 7 YEARS

Step-by-step explanation:

A=127,484,450

R=-0.0017/YEAR

T=7/YEARS

Answer:

-4,4,16

Step-by-step explanation:

They are all even integers.

-4^2=16

4^2=16

16^2=256

the square of the third,16 is 256 which is more than the square of the second,4=16

The three consecutive even integers such that the square of the third is 60 more than the square of the second are -18, -16 and -14.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

Let the three even consecutive integers are 2n-2, 2n and 2n + 2.

According to the question,

So,

(2n + 2)² = (2n)² - 60

4n² + 4 + 8n = 4n² -60

8n = -64

n = -8

That means, the integers are -18, -16 and -14.

Therefore, the required even integers are -18, -16 and -14.

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Answer:

180 goats

Step-by-step explanation:

3/3-1/3=2/3.

2/3=4/6 remaining.

4/6-1/6=3/6 which also equals 1/2.

If 90=1/2 then 90*2=180.

Hope this helps!! <3

Answer:

ln(60)

Step-by-step explanation:

We have the equation [tex]5e^x=300[/tex]. We can divide both sides of the equation by 5, getting [tex]e^x=60[/tex]. Finally, we can take the natural log of both sides, getting that x is equal to [tex]\ln(60)[/tex].

Answer:

The frequency of f(x) is two times the frequency of the parent function.

Step-by-step explanation:

We can say that the number that is beside the x is equal to [tex]2\pi *f[/tex], where f is the frequency.

Then, for the parent function, we get:

[tex]1 = 2\pi f_1[/tex]

or solving for [tex]f_1[/tex]:

[tex]f_1=\frac{1}{2\pi }[/tex]

At the same way, for f(x), we get:

[tex]2=2\pi f_2\\f_2=2(\frac{1}{2\pi })[/tex]

But [tex]\frac{1}{2\pi }[/tex] is equal to [tex]f_1[/tex], so we can write the last equation as:

[tex]f_2=2f_1[/tex]

It means that the frequency of f(x) is two times the frequency of the parent function.

Answer:

Step-by-step explanation:

even function are symmetrical about the y axis or f(-x)=f(x)

odd function are symmetrical about the origin -f(-x)=f(x)

f(x)=x^6 + 10x^4-11x^2+19

f(-x)=(-x)^6+10(-x)^4+11(-x)^2+19=x^6 + 10x^4-11x^2+19

the function is even

Answer:

Solution,

∆ ACB = ∆ EFD

finding the value of X,

[tex] \frac{x}{3.8} = \frac{15}{5} [/tex]

Apply cross product property

[tex]x \times 5 = 15 \times 3.8[/tex]

Calculate the product

[tex]5x = 57[/tex]

Divide both sides by 5

[tex] \frac{5x}{5} = \frac{57}{5} [/tex]

Calculate

[tex]x = 11.4[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

option (c) 4

Step-by-step explanation:

sides opposite to equal angles are equal

so ML = MN

that is 4x = x+3

4x - x = 3

3x = 3

x= 1

ML= 4x = 4*1 = 4 units

MN = x+3= 1+3= 4 units

so answer is option (c) 4

hope this answer help you

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!

Answer:

Taylor sold 42 pizzas

Step-by-step explanation:

Make a system of equations where t represents the number of pizzas Taylor sold and j represents the number that Jeff sold:

t + j = 126

j = 2t

We can solve this system by substitution, since we can substitute 2t as j.

t + j = 126

t + 2t = 126

3t = 126

t = 42

Taylor sold 42 pizzas.

Answer:

Step-by-step explanation:

Let x represent the number of pizzas that Tailor sold.

Let y represent the number of pizzas that Jeff sold.

Together they have sold a total of 126 pizzas. This means that

x + y = 126- - - - - - - - -1

Taylor has sold half as many

pizzas as Jeff. This means that

x = 1/2 × y = y/2

Substituting x = y/2 into equation 1, it becomes

y/2 + y = 126

Multiplying both sides of the equation by 2, it becomes

y + 2y = 252

3y = 252

y = 252/3

y = 84

x = y/2 = 84/2

x = 42

Taylor sold 42 pizzas

Answer:

A. The mean represents the center.

A. The median represents the center.

B. The mode does not represent the center because it is the smallest data value.

Step-by-step explanation:

Mean

(9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11)/13 = 120/13 = 9.2

The mean 9.2 and it represents the center of data.

Median

By arranging the set of data, the median, the median is the center number

8,8,8,8,8,8,(9),9,9,10,11,12,12

The median is 9 and it represents the center of data.

Mode

The mode is the number that appears most in the set of data.

The number that appears most in the set of data is 8 and does not represent the set of data.

Given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

Given the following data set:

9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11

Let's find the mean, median, and mode.

Mean of the data set:

Mean = sum of all values / number of values

Mean = [tex]\frac{9 + 9 + 12 + 12 + 9 + 8 + 8 + 8 + 10 + 8 + 8 + 8 + 11}{13}[/tex]

Mean = [tex]\frac{120}{13} = 9.2[/tex]

Median of the data set:

Order the data from the least to the greatest then find the middle value.

8, 8, 8, 8, 8, 8, (9,) 9, 9, 10, 11, 12, 12

The middle value is 9.

Mode of the data set:

The mode = the data value that appears most

8 appeared the most, therefore, the mode = 8

If you observe, you will note that the mean and median of the data set are similar. We can as well conclude that the mean represents the center of the data set.

In summary, given the data set, 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8,11:

A. The mean does represents the center of the data set

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Complete Question

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 ​respondents, 12 ​% chose chocolate​ pie, and the margin of error was given as plus or minus 5 percentage points.What values do ​ [tex]\r p , \ \r q[/tex], ​n, E, and p​ represent? If the confidence level is 90​%, what is the value of [tex]\alpha[/tex] ​?

Answer:

a

   [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

   [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

   [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e                        [tex]\r q = 1- \r p[/tex]

b

   [tex]\alpha = 10\%[/tex]

Step-by-step explanation:

Here

    [tex]\r p[/tex] is the sample proportion   [tex]\r p = 0.12[/tex]

   [tex]n[/tex] is the  sample size is  [tex]n = 500[/tex]

    [tex]\r q[/tex] represents the proportion of those that did not chose chocolate​ pie i.e  

      [tex]\r q = 1- \r p[/tex]

      [tex]\r q = 1- 0.12[/tex]

      [tex]\r q = 0.88[/tex]

     [tex]E[/tex] is the  margin of error is [tex]E = 0.05[/tex]

Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as

     [tex]\alpha = ( 100 - C )\%[/tex]

Where  [tex]C[/tex] is the confidence level which is given in this question as  [tex]C = 90 \%[/tex]

So  

    [tex]\alpha = ( 100 - 90 )\%[/tex]

    [tex]\alpha = 10\%[/tex]

Answer: -4/3

Step-by-step explanation: To find the negative reciprocal of a fraction, all you have to do is flip the fraction and change the sign.

So the negative reciprocal of 3/4 is -4/3.

Step-by-step explanation:

Tell the whole question please

Answer:

[tex]\huge\boxed{a_3=9,216}[/tex]

Step-by-step explanation:

[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]

Answer:

D. (the last one)

Step-by-step explanation:

The horizontal row lists the 3 outcomes of the spinner.

The vertial column lists the 2 outcomes of the card selection.

In the resulting sample space of 2x3=6, each table cell should contain the combination of the row value and the column value.

So in the "Orange" column, all cells below it should start with Orange. Same for the other columns.

In the Purple row, each cell should end with Purple.

Only that way, each table cell represents a possible outcome.

Answer: the intersection point is (2.4, -4.8)

Step-by-step explanation:

A) we have the function:

y = 0.5*x - 6.

First we want to know if this function intersects the line y´ = -1.5*x

Now, first we can recall that two lines are parallel only if the slope is the same for both lines, here we can see that the slopes are different, so the lines are not parallel, which means that the lines must intersect at some point.

Now, to find the intersection point we asumme y = y´ and want to find the value of x.

0.5*x - 6 = -1.5*x

(0.5 + 1.5)*x - 6 = 0

2.5*x = 6

x = 6/2.5 = 2.4

Now, we evaluate one of the functions in this value of x.

y = 0.5*2.4 - 6 = -4.8

So the intersection point is (2.4, -4.8)

Answer:

[tex]y=\frac{4}{3}x-1.75[/tex]

Step-by-step explanation:

If the slope of a line is 4/3,

and we wanna find the equation of a line that is parallel to it and crosses through (5,5).

So we already have the slope because the slope of 2 parallel lines are the same.

y = 4/3x

Look at the image below↓

So now we just need to find the y-intercept.

After some numbers we got,

[tex]y=\frac{4}{3}x-1.75[/tex]

Look at the other image below↓

Thus,

the equation of the parallel line is [tex]y=\frac{4}{3}x-1.75[/tex].

Hope this helps :)

Step-by-step explanation:

Answer:

[tex]z^5-y^5[/tex]

Step-by-step explanation:

=> [tex](z^3*z^2)-(y^4*y)[/tex]

When bases are same, powers are to be added

=> [tex](z^{3+2})-(y^{4+1})[/tex]

=> [tex]z^5-y^5[/tex]

P.s. Yessss, Wishing should be a moderator so that he can delete all the absurd or plagiarized answer!!!!!!!!

Answer:

Categorical independent variables are ___FACTORS__

The independent variables that are categorial should be factors.

In terms of mathematics, factor represents the no of algebraic expression where it split the other number that contains the zero remainder. As the factor of 12 should be 3 and 4. So based on this, the independent variables that are categorical should be considered as the factors.

Therefore, we can conclude that The independent variables that are categorial should be factors.

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Answer:

A: (–0.3, 2.1)

Answer:a

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Inverse variation on a graph is depicted by the movement of the graph diagram (line) in a downward motion

Answer:true

Step-by-step explanation:

Answer:

[tex]C.\ 200[/tex]

Step-by-step explanation:

Given

Let R represents rows and C represents Columns

When R = 8, C = 25

When R = 10, C = 20

Required

Given that there exist an inverse variation, determine the constant of proportionality;

We start by representing the variation;

[tex]R\ \alpha \ \frac{1}{C}[/tex]

Convert proportion to an equation

[tex]R\ = \ \frac{k}{C}[/tex]

Where k is the constant of proportion;

[tex]R * C\ = \ \frac{k}{C} * C[/tex]

Multiply both sides by C

[tex]R * C\ = k[/tex]

Reorder

[tex]k = R * C[/tex]

When R = 8, C = 25;

The equation  [tex]k = R * C[/tex] becomes

[tex]k = 8 * 25[/tex]

[tex]k = 200[/tex]

When R = 10, C = 20;

The equation  [tex]k = R * C[/tex] becomes

[tex]k = 10 * 20[/tex]

[tex]k = 200[/tex]

Hence, the concept of proportionality is 200

Answer:

The required probability for the high temperature which 90% of the August days exceed. is 0.0333

Step-by-step explanation:

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 61° F  to 91° F   . Find the high temperature which 90°  F of the August days exceed.

Let assume that X is the random variable

The probability mass function is:

[tex]f(x) = \dfrac{1}{b-a}[/tex]

[tex]f(x) = \dfrac{1}{91-61}[/tex]

[tex]f(x) = \dfrac{1}{30}[/tex]

Thus; The probability density function of X can be illustrated as :

[tex]f(x) = \left \{ {{ \ \ \dfrac{1}{30}} \atop { \limits }}_ \right. _0[/tex]       61 <  x < 91  or otherwise

The required probability for the high temperature at 90°  F can be calculated as follows:

[tex]P(X> 90) = \int\limits^{91}_{90} {f(x)} \, dx[/tex]

[tex]P(X> 90) = \int\limits^{91}_{90} \ {\dfrac{1}{30} \, dx[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} \int\limits^{91}_{90} \ \, dx[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} [x]^{91}_{90}[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} (91-90)[/tex]

[tex]P(X> 90) = {\dfrac{1}{30} \times 1[/tex]

[tex]P(X> 90) = 0.0333[/tex]

The required probability for the high temperature which 90% of the August days exceed. is 0.0333