Two similar data sets are being compared. The standard deviation of Set A is 4.8. The standard deviation of Set B is 6.5.

Answer: min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

Step-by-step explanation:

The five-number summary for this data set consists  of  min, Q1,

median, Q3, max.

Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.

Minimum value = 12

Maximum value = 37

since , number of observations = 10 (even)

So , Median = Mean of middle most terms

Middle most terms = 22, 25

Median =[tex]\dfrac{22+25}{2}=23.5[/tex]

First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)

= middle most term

= 17

Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)

= middle most term

= 30

Hence, five-number summary for this data set :

min = 12, Q1 =17,  median =23.5 , Q3 = 30, max = 37 .

obviously 4 is bigger coz 12/7 will yeild you 1.71

Answer:

[tex] x+y = 125[/tex]   (1)

[tex] 5x+8y = 775[/tex]   (2)

We can solve for y from equation (1) and we got:

[tex] y = 125-x[/tex]   (3)

And replacing (3) into (2) we got:

[tex] 5x +8(125-x) = 775[/tex]

And solving for x we got:

[tex] 1000-3x = 775[/tex]

[tex] 3x= 225[/tex]

[tex] x=75 [/tex]

And solving for y from (3) we got:

[tex] x= 125-75 =50[/tex]

And the solution would be x = 50 and y =75

Step-by-step explanation:

For this problem we have the following system of equations:

[tex] x+y = 125[/tex]   (1)

[tex] 5x+8y = 775[/tex]   (2)

We can solve for y from equation (1) and we got:

[tex] y = 125-x[/tex]   (3)

And replacing (3) into (2) we got:

[tex] 5x +8(125-x) = 775[/tex]

And solving for x we got:

[tex] 1000-3x = 775[/tex]

[tex] 3x= 225[/tex]

[tex] x=75 [/tex]

And solving for y from (3) we got:

[tex] x= 125-75 =50[/tex]

And the solution would be x = 50 and y =75

Answer:

Step-by-step explanation:

[tex]A=\pi r^2\\Area = 36\pi\\r = ?\\36\pi = \pi r^2\\Divide \:both \:sides \:of\: the \:equation\: by\: \pi\\\frac{36\pi}{\pi} = \frac{\pi r^2}{\pi} \\r^2 = 36\\Find\: the\: square\: root\: of\: both\: sides\: \\\sqrt{r^2} =\sqrt{36} \\\\r = 6\: feet\\[/tex]

Answer:

Step-by-step explanation:

[tex](2, 1) (5, 3)\\x_1 =2 \\y_1 =1\\x_2=5\\y_2 =3\\m =\frac{y_2-y_1}{x_2-x_1} \\\\m = \frac{3-1}{5-2} \\\\m = 2/3[/tex]

Answer:

Step-by-step explanation:

40.50/2 = 20.25

You have to divide by 2. This way both of the people will get the same amount of money.

Answer:

each friend will get

Step-by-step explanation:

20 .25

as 40 .50 ÷ 2 = 20 .25

hope this helps

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Answer:  2149

Step-by-step explanation:  If the sum of the first two digits is 3, the choices must be 1 and 2 (or 2 and 1)  In order to satisfy the other specifications, "the tens digit is 4 times the hundreds digit." the hundreds digit can't be 2 because that would make the tens dight 8.  and the ones digit would also have to 8 in order to satisfy the "seven more than the thousands digit" which would be a 1. And that violates the condition, "No two digits are equal."

So the only possible combination is 2149

4 is 4 times 1

9 is 7 +2

Answer:

Beryllium, 2 times

Step-by-step explanation:

1.12×10⁻¹⁰ has a higher exponent than 5.6×10⁻¹¹.

-10 > -11

The ratio between them is:

(1.12×10⁻¹⁰) / (5.6×10⁻¹¹)

(1.12 / 5.6) (10⁻¹⁰ / 10⁻¹¹)

0.2 × 10¹

2

Answer:

A.50,000 units

B.62,500 units

C.Process A with a profit of $700,000 to maximize profit

Step-by-step explanation:

A.Calculation for the breakeven volume for Process A

Using this formula

Breakeven volume for Process A= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process A=500,000/(35-25)

Breakeven volume for Process A=500,000/10

Breakeven volume for Process A=50,000 units

B.Calculation for the breakeven volume for Process B

Using this formula

Breakeven volume for Process B= Fixed cost/(Sales per units-Variable cost per units)

Let plug in the formula

Breakeven volume for Process B=750,000/(35-23)

Breakeven volume for Process B=750,000/12

Breakeven volume for Process B=62,500 units

C. Calculation for what the company should do if the total demand (volume) is 120,000 units

Using this formula

Profit=(Total demand*(Sales per units-Variable cost per units for Process A)- Process A fixed cost

Let plug in the formula

Profit =120,000*($35-$25)-$500,000

Profit=120,000*10-$500,000

Profit=1,200,000-$500,000

Profit= $700,000

Therefore If total demand (volume) is 120,000 units, then the company should select Process A with a profit of $700,000 to maximize profit.

Answer:

$12.10

Step-by-step explanation:

First, you have to set up a proportion to find what 20% of $60.50, or 60.5, is. On one side of the proportion you have 20/100 to represent the percent, anytime you have a percent it will always go over 100. On the other side you'll have x/60.5 because you are trying to find a value out of 60.5. This gives you the proportion 20/100=x/60.5. In order to solve this you have to cross multiply using the equation 20(60.5)=100x. First, you multiply to get 1210=100x, then divide both sides by 100 to get 12.1=x. In order for this to represent money, we add a zero on the end. This means that 20% of $60.50 is $12.10, so $12.10 is the tip.

Answer:

[tex]\boxed{\frac{-3b^4 }{a^6 }}[/tex]

Step-by-step explanation:

[tex]\frac{-18a^{-8}b^{-3}}{6a^{-2}b^{-7}}[/tex]

[tex]\frac{-18}{6} \times \frac{a^{-8}}{a^{-2}} \times \frac{b^{-3}}{b^{-7}}[/tex]

[tex]-3 \times \frac{a^{-8}}{a^{-2}} \times \frac{b^{-3}}{b^{-7}}[/tex]

Apply the law of exponents, when dividing exponents with same base, we subtract the exponents.

[tex]-3 \times a^{-8-(-2)} \times b^{-3- (-7)}[/tex]

[tex]-3 \times a^{-8+2} \times b^{-3+7}[/tex]

[tex]-3 \times a^{-6} \times b^{4}[/tex]

[tex]{-3a^{-6}b^{4}}[/tex]

The answer should be without negative exponents.

[tex]a^{-6}=\frac{1}{a^6 }[/tex]

[tex]\frac{-3b^4 }{a^6 }[/tex]

Answer:

Step-by-step explanation:

[tex] \frac{ - 18 {a}^{ - 8} {b}^{ - 3} }{6 {a}^{ - 2} {b}^{ - 7} } [/tex]

Reduce the fraction with 6

[tex] \frac{ - 3 {a}^{ - 8} {b}^{ - 3} }{ {a}^{ - 2} {b}^{ - 7} } [/tex]

Simplify the expression

[tex] \frac{ - 3 {b}^{4} }{ {a}^{6} } [/tex]

Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b \: } [/tex] to rewrite the fraction

[tex] - \frac{3 {b}^{4} }{ {a}^{6} } [/tex]

Hope this helps...

Best regards!!

Answer:

B. -3x

Step-by-step explanation:

A term is defined as either a constant or a variable with a coefficient.

-3 is incorrect because there is no constant -3 in the expression.

-3x is correct because there is a -3x in the expression

(x + 4) is incorrect because that is a linear binomial and has yet to be distributed.

-7 is incorrect because it has to be distributed.

Answer:

Step-by-step explanation:

If you take 10 percent of a number and get 35, then what is that number?

In other words, you know that 10 percent of a number is 35 and you want to know what that initial number is.

To solve this problem you multiply 35 by 100 and then divide the total by 10 as follows:

(35 x 100) / 10

When we put that into our calculator, we get the following answer:

350

Therefore, you can derive that 10 percent of 350 equals 35.

Answer:

The zeros are x=-3,-2,1

end behavior is one up one down

Step-by-step explanation:

The zeros are x=-3,-2,1

The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.

Answer:

x=60

Step-by-step explanation:

This is an equilateral triangle which means all the sides are equal.

If all the sides are equal then all the angles are equal

180/3 = 60

x=60

Answer:

x= 60°

Step-by-step explanation:

We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°

Answer:

-10

-5 * 2 = -10

Hope this is right

Mensuration:

Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.

Plane Figure: A figure which lies in a plane is called a plane figure.

For e.g:  a rectangle, square, a rhombus, a parallelogram, a trapezium.

Perimeter:

The perimeter of a closed plane figure is the total length of its boundary.

In case of a triangle or a polygon the perimeter is  the sum of the length of its sides.

Unit of perimeter is a centimetre  (cm), metre(m) kilometre(km) e.t.c

Area: The area of the plane figure is the measure of the surface enclose by its boundary.

The area of a triangle are a polygon is the measure of the surface enclosed by its sides.

A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.

Circumference of a circle is the perimeter of a circle.

In a circle the radius is half of the diameter.

The approximate value of π( Pi) is= 22/7 

==========================================================

Answer:

The answer is

Step-by-step explanation:

(x² + 3x + 4)(3x² - 2x + 1)

Expand the terms

We have

3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4

Group like terms

That's

3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4

Simplify

We have the final answer as

Hope this helps you

Answer:

A. 24

Step-by-step explanation:

4/9 = x/54

x= 54*4/9     ===== multiplying both sides by 54

x= 24

Answer is 24, choice A is correct one

Answer:

-8 i + 19 j , 105.07°

Step-by-step explanation:

Solution:

- Define two unit vectors ( i and j ) along x-axis and y-axis respectively.

- To draw vectors ( v and w ). We will move along x and y axes corresponding to the magnitudes of unit vectors ( i and j ) relative to the origin.

  Vector: v = 2i + 5j

Vector: w = 4i - 3j

- The algebraic manipulation of complex numbers is done by performing operations on the like unit vectors.

                      [tex]2*v - 3*w = 2* ( 2i + 5j ) - 3*(4i - 3j )\\\\2*v - 3*w = ( 4i + 10j ) + ( -12i + 9j )\\\\2*v - 3*w = ( 4 - 12 ) i + ( 10 + 9 ) j\\\\2*v - 3*w = ( -8 ) i + ( 19 ) j\\[/tex]

- To determine the angle ( θ ) between two vectors ( v and w ). We will use the " dot product" formulation as follows:

                     v . w = | v | * | w | * cos ( θ )

                     v . w = < 2 , 5 > . < 4 , -3 > = 8 - 15 = -7

                     [tex]| v | = \sqrt{2^2 + 5^2} = \sqrt{29} \\\\| w | = \sqrt{4^2 + 3^2} = 5\\\\[/tex]

- Plug the respective values into the dot-product formulation:

                     cos ( θ ) = [tex]\frac{-7}{5\sqrt{29} }[/tex]

                      θ = 105.07°

Answer:

3 <1<4<2

hope it worked

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BRAINLIEST

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Answer:

3>1>2>4

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

x + 0.30x = 78

1.30x = 78

x = 60

Answer:

The answer is 60.

Step-by-step explanation:

here, let another number be x.

according to the question the number when increased by 30% will be 78. so,

x+ 30% of x =78

now, x+ 30/100×x =78

or, x+0.3x=78

or, 1.3x=78

Therefore the another number is 60.

Hope it helps...

Answer:

  1.2b

Step-by-step explanation:

When we say, "a number that is 20% greater than b," we're talking about a number that is ...

  b + 20%×b

  = b + 0.20b

  = b(1 + 0.20)

  = 1.2b

Answer:

80

Step-by-step explanation:

Answer:

The 99% confidence interval  is  [tex]0.3003 < I < 0.3997[/tex]

Step-by-step explanation:

From the question we are told that

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

      The the number that are parents  x =  175

The  proportion of parents is  mathematically represented as

       [tex]\r p = \frac{x}{n}[/tex]

substituting values

      [tex]\r p = \frac{175}{500}[/tex]

     [tex]\r p = 0.35[/tex]

The  level of confidence is given as 99%  which implies that the level of significance is  

       [tex]\alpha = 100 - 99[/tex]

       [tex]\alpha =[/tex]1%

      [tex]\alpha = 0.01[/tex]

The critical value for this level of significance is obtained from the table of critical value as

          [tex]t_{x, \alpha } = t_{175, 0.05} = 2.33[/tex]

Generally the margin of error is mathematically evaluated as

       [tex]M =\frac{ t_{175, 0.01 } * \sqrt{\r p (1-\r p)} }{\sqrt{n} }[/tex]

substituting values

     [tex]M =\frac{ 2.33 * \sqrt{\r 0.35 (1-0.35)} }{\sqrt{500} }[/tex]

     [tex]M = 0.0497[/tex]

Generally the 99% confidence interval is mathematically represented as

        [tex]I = \r p \pm M[/tex]

    [tex]\r p -M < I < \r p + M[/tex]

substituting values

    [tex]0.35 -0.0497 < I < 0.35 + 0.0497[/tex]

    [tex]0.3003 < I < 0.3997[/tex]

Answer:

Option b and d

Step-by-step explanation:

With the following data,

H0:p=0.11

Ha:p≠0.11

The p-value was determined to be 0.106 and significance level of 0.05.

Since the p value (0.106) is great than 0.05, then we will fail to reject the null hypothesis and conclude that There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%

Answer:  438.5L = 438000ml

Step-by-step explanation:

Answer:

The answer is option B

Step-by-step explanation:

To solve for x we use tan

tan ∅ = opposite / adjacent

From the question

The adjacent is x

The opposite is 19

So we have

tan 29 = 19/ x

x = 19/ tan 29

x = 34.276

Hope this helps

Answer:

x ≈ 34.28

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan29° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19}{x}[/tex] ( multiply both sides by x )

x × tan29° = 19 ( divide both sides by tan29° )

x = [tex]\frac{19}{tan29}[/tex] ≈ 34.28 ( to the nearest hundredth )

Answer:

[tex]\large \boxed{\sf 15 \ \ and \ \ 24 \ \ }[/tex]

Step-by-step explanation:

Hello,

We can write the following, x being the second number.

[tex](2x-6)^2+x^2=801\\\\6^2-2\cdot 6 \cdot 2x + (2x)^2+x^2=801\\\\36-24x+4x^2+x^2=801\\\\5x^2-24x+36-801=0\\\\5x^2-24x-765=0\\\\[/tex]

Let's use the discriminant.

[tex]\Delta=b^4-4ac=24^2+4*5*765=15876=126^2[/tex]

There are two solutions and the positive one is

[tex]\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{24+126}{10}=\dfrac{150}{10}=15[/tex]

So the solutions are 15 and 15*2-6 = 30-6 = 24

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A.y = −8x + 80B

Step-by-step explanation:

first you have to find the slope :

P1(2,64). P2(6,32)

slope=Y2-Y1/X2-X1

slope=64-32/2-6

slope= -8

y= -8x + b. now solve for "b" by using one of the coordinates given above.

y= -8x + b. I will use coordinate p(2,64)

64= -8(2) + b

64 + 16 = b

80= b

you can use any of the coordinates i.e either P1(2,64)or P2(6,32) it doesn't affect the value of "b".

line of equation is :

.y = −8x + 80B

Answer: y= -8x+80

Step-by-step explanation: