How do you solve an expansion?

Answer:

10

Step-by-step explanation:

Solution 1: At first, you might think that because there are 5 ways to choose the first store and 4 ways to choose the second store, the answer is 5 * 4 = 20 but this is over-counting by a factor of 2. Say that two of the stores are A and B. If she went to A then B, that's the same as going to B then A since you still go to the same stores, therefore, the answer is 20 / 2 = 10.

Solution 2: We need to find the number of ways to choose 2 stores from 5, we can do this by calculating ₅C₂ which equals:

5! / 2!  * 3!

= 5 * 4 * 3 * 2 * 1 / 2 * 1 * 3 * 2 * 1

= 5 * 4 / 2 * 1

= 10

9514 1404 393

Answer:

  240 m²

Step-by-step explanation:

The lateral surface area is given by the formula ...

  LA = πrs . . . . . cone with radius r and slant height s

The base area is given by the formula ...

  BA = πr²

The total surface area is the sum of these:

  SA = BA +LA = πr² +πrs = πr(r+s)

The radius is half the diameter, so is 9m/2 = 4.5 m. Then the surface area is ...

  SA = π(4.5 m)(4.5 m +12.5 m) = 76.5π m² ≈ 240 m²

Answer:

1: A. 448 2: 209 pi cm^2 3: D. 351 m^2 4. B 240 cm^2 5. C. 561.1 cm^2

Step-by-step explanation:

just took the test!!!

Answer:

102 cm

Step-by-step explanation:

[tex]\boxed{\sf I=\dfrac{PRT}{100}}[/tex]

[tex]\\ \sf\longmapsto I=\dfrac{2000(12)(2.5)}{100}[/tex]

[tex]\\ \sf\longmapsto I=\dfrac{24000(2.5)}{100}[/tex]

[tex]\\ \sf\longmapsto I=\dfrac{60000}{100}[/tex]

[tex]\\ \sf\longmapsto I=600[/tex]

[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} [/tex]

As we know that , first we need to convert 2 years 6 months into years.

[tex] \sf \ \implies \: 1 \: \: year \: = \: 12 \: \: months[/tex]

[tex] \sf \implies \: 2 \: \: years \: \: and \: \: 6 \: \: months \: = \: 30 \: \:months[/tex]

[tex] \sf \implies \: \:\frac{ \cancel{30} \: \: ^{2.5 \: \: years} }{ \cancel{12 \: }} \\ [/tex]

[tex]\bf{\blue{ Time \: = \: 2.5 \: \: years}}[/tex]

[tex]\Large\rm{\orange{ \begin{cases} \large\begin{gathered} {\underline{\boxed{ \rm {\purple{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} \end{cases}}}[/tex]

[tex] \tt \large \longrightarrow \: \: S.I \: = \: \frac{2000 \: × \: 12 × \: 2.5}{100} \\ [/tex]

[tex] \tt \large \longrightarrow \: \: S.I \: = \frac{60000}{100} \\ [/tex]

[tex]\tt \large \longrightarrow \: \: S.I \: = \frac{600 \cancel0 \cancel0}{1 \cancel0 \cancel0} \\ [/tex]

[tex]\tt \large \longrightarrow \: \: S.I \: = \: 600[/tex]

[tex]\large \underbrace{\textrm {{{\color{navy}{Simple Interest \: = \: 600}}}}}[/tex]

9514 1404 393

Explanation:

You can check your answer by making sure that each of the primes you found is actually a prime. (Compare to a list of known primes, for example.) After you have determined your factors are primes, multiply them together to see if the result is 73. If so, you have found the correct prime factorization.

__

Additional comment

73 is prime, so its prime factor is 73.

  73 = 73

Answer:

1 +3i

Step-by-step explanation:

(4 - 2i) - (3 - 5i)

Subtract the reals

4 - 3 =1

Subtract the imaginary

-2i - -5i

-2i + 5i = 3i

1 +3i

Answer:

A

Step-by-step explanation:

Subtract all real numbers

4 - 3 = 1

Subtract all imaginary numbers

-2i - (-5i) = 3i

Put back together

1 + 3i

Best of Luck!

Answer:

a

  The 95% confidence interval is  [tex]0.0503 < p < 0.1297[/tex]

b

The sample proportion is  [tex]\r p = 0.09[/tex]

c

The critical value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

d

 The standard error is  [tex]SE =0.020[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  200

     The number of defective is  k =  18

The null hypothesis is  [tex]H_o : p = 0.08[/tex]

The  alternative hypothesis is  [tex]H_a : p > 0.08[/tex]

Generally the sample proportion is mathematically evaluated as

            [tex]\r p = \frac{18}{200}[/tex]

            [tex]\r p = 0.09[/tex]

Given that the confidence level is  95% then the level  of significance is mathematically evaluated 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]

Generally the standard of error is mathematically represented as

          [tex]SE = \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]

substituting values

         [tex]SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }[/tex]

        [tex]SE =0.020[/tex]

The  margin of error is  

       [tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]

=>    [tex]E = 1.96 * 0.020[/tex]

=>   [tex]E = 0.0397[/tex]

The  95% confidence interval is mathematically represented as

     [tex]\r p - E < \mu < p < \r p + E[/tex]

=>   [tex]0.09 - 0.0397 < \mu < p < 0.09 + 0.0397[/tex]

=>  [tex]0.0503 < p < 0.1297[/tex]

We want to factor the expression x - a, in such a way that we have one factor written as:

(√x - √a)

We will find that the factorized expression is:

(√x - √a)*(√x + √a)

Here we need to remember two things:

First, (√x)^2 = √(x^2) = x

also:

(x^2 - y^2) = (x + y)*(x - y)

Now, using the first property, we can rewrite our original expression as:

(x - a) = ( (√x)^2 - (√a)^2)

Now, using the second property, we can rewrite it as:

( (√x)^2 - (√a)^2) = (√x - √a)*(√x + √a)

Then we have:

(x - a) = (√x - √a)*(√x + √a)

Thus, we have factorized (x - a) in such a way that one of the factors is  equal to (√x - √a)

If you want to learn more, you can read:

https://brainly.com/question/19386208

Answer:

B) same side interior

Step-by-step explanation:

Supplementary angles are angles that can add up to the sum of angles on a straight line, [tex]180^{0}[/tex]. While a transversal in a line that passes through two parallel lines at two points.

If two lines are parallel to each other and a transversal through the lines, the sum of either same side interior angles would be supplementary.

The correct option for the given question is B, same side interior.

Answer:

B

Step-by-step explanation:

Answer:

72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees

Step-by-step explanation:

The number, 72.3 degrees, can be rewritten by breaking up the place value of each digit in the expression as folliws,:

70 degrees + 2 degrees + 0.3 degrees

The place value of 7 is tens

The place value of 2 is ones

The place value of 3 is tenths

[tex] 72.3 degrees = 70 degrees + 2 degrees + 0.3 degrees [/tex]

Answer:

72.3 + (-39.1) = 70 + 2 + 0.3 + (-30) + (-9) + (-0.1)

Step-by-step explanation:

got the off the assignment

Answer:

75°

Step-by-step explanation:

Let's find the size of x°

BCFE has four sides so the sum of its angles sizes is 360°.

● CBE + 110 + 110 + CFE = 360

CFE is equal to 65° since they have the same vertex

● CBE + 220 + 65 = 360

● CBE + 285 = 360

● CBE = 360-285

● CBE = 75

CBE and x° have the same size since they share the same vertex.so:

● x° = 75°

Answer:

75°

Step-by-step explanation:

CBE = x (vertically opposite angles are equal)

CFR = 65° (vertically opposite angles are equal)

C+F+E+B= 360 (angles in a quadrilateral sum up to 360°)

110+65+110+x=360

x= 75°

Answer:

35 or 25

Step-by-step explanation:

Answer B.ED

Step-by-step explanation:

This problem is about creating a linear regression model.

First, we should take note of the points:

(-4,8)

(-2,4)

(-1,2)

(1,5)

(2,2)

(6,-5)

(7,6)

It's necessary to find a equation y = ax + b that brings us the least MSE (Mean Squared Error). You can calculate at hand, but I bet it is going to be tiresome.

So, basically intuitively you just need to choose a line that fits closer to the given points.

First: remember if y = ax+b, a is the slope which means if a > 0 the line is " / " and a < 0 the line is " \ ".

A) No, this equation is " / "

B) It could be this one.

C) It could be this one too.

D) Nope. " / "

B) a = -1/2

C) a = -4

You can draw those two lines and see that B) gets closer to the points.

Equation:

Y = -0.4957*X + 3.780

Answer:

[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]

Step-by-step explanation:

Using a graph,

we can see that the line y = -1/2x + 7/2 best fits for the data.

Answer:

The correct choice is option B. y+1/y-1

Step-by-step explanation:

Answer:

[tex]y=4x[/tex]

Answer:

y = -4x

hope that helped.........

Answer:

85.36 far north from the center

10.36 far east from the center

Step-by-step explanation:

The extra direction taken in the north side is x

X/sin(360-315)=50/sin 90

Sin 90= 1

X/sin 45= 50

X= sin45 *50

X= 0.7071*50

X= 35.355 steps

X= 35.36

Then the west direction traveled

West =√(50² - 35.355²)

West = √(2500-1249.6225)

West= √1250.3775

West= 35.36 steps

But this was taken in an opposite west direction

From the center

He is 35.36 +50

= 85.36 far north from the center

And

25-35.36=-10.36

10.36 far east from the center

The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.

Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

In the given figure, three triangles is shown with base and height. Here,

Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.

Learn more about the base and height of the triangle here;

https://brainly.com/question/26043588

#SPJ2

Answer:

C. Cubic expression.

Step-by-step explanation:

The highest exponent is 3 ( in the term 7x^3) so it is cubic.

Answer:

C. Cubic Expression.

Step-by-step explanation:

5x + 3x^2 - 7x^3 + 2

= 3x^2 - 7x^3 + 5x + 2

= -7x^3 + 3x^2 + 5x + 2

The highest value of exponent in the equation is 3.

For a linear expression, the highest exponent is 1.

For a quadratic expression, the highest exponent is 2.

For a cubic expression, the highest exponent is 3.

For a quartic expression, the highest exponent is 4.

So, this is C. Cubic Expression.

Hope this helps!

Answer:

x = 3/4

Step-by-step explanation:

2(4x + 2) = 10           Remove the brackets

8x + 4 = 10               Subtract 4 from both sides

8x = 6                       Divide by 8

x = 6/8

x = 3/4

Check

2(4*3/4 + 2) =?10

2( 3 + 2) = 10

2*5 = 10

10 = 10

Answer:

a ≈ 1.59

b ≈ 6.69

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Step 1: Find c using Law of Sines

[tex]\frac{6}{sin58} =\frac{c}{sin13}[/tex]

[tex]c = sin13(\frac{6}{sin58})[/tex]

c = 1.59154

Step 2: Find a using Law of Sines

[tex]\frac{6}{sin58} =\frac{a}{sin109}[/tex]

[tex]a = sin109(\frac{6}{sin58} )[/tex]

a = 6.68961

Answer:

y=0x+9. Hope this helped.

Step-by-step explanation:

slope intercept form: y=mx+b

m represents slope

b represents the y intercept. Please give me the brainliest:)

[tex](B)\:\:35.8\:\text{m/s}[/tex]

Step-by-step explanation:

[tex]80\:\dfrac{\text{mi}}{\text{hr}}×\left(\dfrac{1609\:\text{m}}{1\:\text{mi}}\right)×\left(\dfrac{1\:\text{hr}}{3600\:\text{s}}\right)[/tex]

[tex]= 35.8\:\text{m/s}[/tex]

Answer: b

Step-by-step explanation:

Answer:

y > 1

Step-by-step explanation:

-2(7 + y) > -8(y + 1)

-14 -2y > -8y -8

-2y +8y > -8 +14

6y > 6

6y/6 > 6/6

y > 1

Answer:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 1 to 3.

= -196.5

Step-by-step explanation:

Given

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to infinity

The expression that includes all terms up to order 3 is:

∑(-1)^k/(2k+1)! (5x)^2k+1

From k = 0 to 3.

= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)

= -125/2 + 100000/6 - 759375/5040

= -62.5 + 16.67 - 150.67

= - 196.5

Answer: the radians should be 125

Step-by-step explanation: