In the standard Normal distribution, 43% of observations lie below which z-score?

Find the z-table here.

–1.08
–0.18
0.18
1.08

Picture posted below

By definition of the binomial coefficient,

[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]

so we have

[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]

as required.

Answer:

e4fodor8rsidididi2f2

Answer:

9

Step-by-step explanation:

3:4

AB:12

cross multiply giving

3×12:4AB

36: 4AB

divide both sides by 4,thus

AB=9

Answer:

[tex]2\sqrt{x+1}-3\\domain:[-1, \infty)[/tex]

Step-by-step explanation:

[tex]g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\[/tex]

the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1

It looks like you're asking to solve for the coefficients [tex]a,b,c[/tex] such that

[tex]2x^2 - 5 = a(x+2)^2 - b(x+1) + c[/tex]

Expanding the right side gives

[tex]2x^2 - 5 = ax^2 + 4ax + 4a - bx - b + c[/tex]

[tex]2x^2 - 5 = ax^2 + (4a - b)x + (4a - b + c)[/tex]

The coefficients on both sides must be equal, so

[tex]\begin{cases}a = 2 \\ 4a-b = 0 \\ 4a - b + c = -5\end{cases}[/tex]

Solving the system yields [tex]\boxed{a=2 \implies b = 8 \implies c = -5}[/tex].

Answer:

30.5 cm^2

Step-by-step explanation:

Recall the formula for the area of a circle: [tex]A_{circle}=\pi r^2[/tex] where [tex]\pi \approx 3.14[/tex], and "r" is the radius of the circle (distance from center to any point on the edge).

From the diagram, the radius is 5cm.

[tex]A_{circle}=\pi r^2[/tex]

[tex]A_{circle}=(3.14)(5[cm])^2[/tex]

[tex]A_{circle}=78.5[cm^2][/tex]

Recall the formula for the area of a rectangle: [tex]A_{rectangle}=bh[/tex] where "b" is the base of the rectangle (length of bottom or length of top), "h" is the height of the rectangle (distance from bottom to top).

From the diagram, the base is 8cm, and the height is 6cm.

[tex]A_{rectangle}=bh[/tex]

[tex]A_{rectangle}=(8[cm])(6[cm])[/tex]

[tex]A_{rectangle}=48[cm^2][/tex]

Having found the areas for each of the first parts, we can find the difference to find the shaded area:

[tex]A_{shaded}=A_{circle}-A_{rectangle}[/tex]

[tex]A_{shaded}=(78.5[cm^2])-(48[cm^2])[/tex]

[tex]A_{shaded}=30.5[cm^2][/tex]

Answer:

X= 5.52

Step-by-step explanation:

1. Solve the equation:

e×2x + 12= 42

x=15/e

2. Round x=15/e to the required place

x=5.52

Answer:

X=1.15

Step-by-step explanation:

Answer:

cp = rs 400

loss = 10%

Then SP = 400 - 10% of 400

= 400 - 40

= 360

Therefore SP = Rs. 360

Answer: Each child gets 1/3

Step-by-step explanation: x/3

Answer:

1/2

Step-by-step explanation:

First parabola  f(x1)   =  a ( x+4)(x-6)    use point 0,-12 to find a = 1/2

                                = 1/2 (x+4)(x-6)

Second parabola    a ( x+4) (x-6)       using point  0, -24    shows a = 1

                       f(x2)       = (1)(x+4)(x-6)

Difference between the 'a' values =  1 - 1/2 = 1/2

Answer:

[tex]648[/tex]([tex]x^{3} + 3x^{2} - 4x + 2[/tex])

Step-by-step explanation:

When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.

Answer:

(3x – 6)4

Step-by-step explanation:

Answer:

yes.

but it will be in decimals if you divide by two. And if you divide it by another rank, it will surely give a whole number. please this all I can do for you and add me to your followers

Answer: For this real-valued function;

[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]

Step-by-step explanation:

If f and g are functions, then the composite function or composition, of g and f is defined by

[tex]( f o g ) (x) = f(g(x))[/tex]

Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],

Now composition for this;

[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]

[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]

[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]

The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.

[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]

As a result, the range of the variable x must only include values that are larger than or equal to 1.

Hence, Domain = [1, )

Learn more about Composition and Domain here; https://brainly.com/question/6390405

#SPJ10

Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. The current in the amp is 1.2 × 10⁻³.

Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms.

The current in amps = (2.4×10³ volts)/(2× 10⁶ ohms)

                                  = 1.2 × 10⁻³ amp

Hence, the current in the amp is 1.2 × 10⁻³.

Learn more about Ohm' Law:

https://brainly.com/question/14796314

#SPJ1

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

Correct Expression :

[tex]\qquad \tt \rightarrow \: |10| + | - 6| [/tex]

[tex]\qquad \tt \rightarrow \: distance = 16\:\: units\degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Using distance formula -} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{( - 6 - 10) {}^{2} + (4 - 4) {}^{2} } [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{( - 16) {}^{2} + 0} [/tex]

[tex]\qquad \tt \rightarrow \: \sqrt{256} [/tex]

[tex]\qquad \tt \rightarrow \: 16 \: \: units[/tex]

For short it can be expressed as :

[tex]\qquad \tt \rightarrow \: |10| + | - 6| = 10 + 6 = 16[/tex]

[ y - coordinate of both the points are same ]

Correct option - D

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Based on the amount of federal taxes withheld till date, the percent of Mary Brown's year-to-date that have been withheld is A. 10%.

The percent of the gross pay that has been withheld for all taxes and voluntary dues is C. 17%.

= Fed tax till date / YTD Gross

= 662.26 / 6,318.17

= 10%

= (Fed tax + ST Tax + Med tax + Vol Due) / Current gross

= (111.42 + 17.09 + 12.25 + 2.5) / 845.10

= 17%

Find out more on gross earnings and deductions at https://brainly.com/question/24278391.

#SPJ1

Answer:

[tex]\textbf {B}[/tex]

Step-by-step explanation:

f(x) = 2x²

f [f(x)]

f [2x²] = 2(2x²)²

f[f(x)] = 2(4x⁴)

f[f(x)] = 8x⁴

Answer:

- x + y - 4

Step-by-step explanation:

Given polynomial:

[tex] \rm \: x+2y+1-(2x+y+5)[/tex]

Solution:

Removing parentheses,we obtain

Collecting and combining like terms,we obtain

Done!

A firm should go out of business in the long run when its price level is less than the average total cost.

The long run is a period where all factors of production are varied. It is known as the planning time of a firm. In the long run, if the if the average total cost is greater than the price, the firm should exit the market.

To learn more about when a firm should exit the market, please check: https://brainly.com/question/13034691

#SPJ1

Answer:

  (a)  9, 8, 7, 6, 5, ...

Step-by-step explanation:

The solution to the inequality can be done a couple of ways. The solution is similar to that for a one-step linear equation.

__

We know that multiplying numbers by a negative value reverses their order. For example, 1 < 2, but -1 > -2. That is, multiplying by -1 requires a change in the comparison operator if it is to remain true.

For our inequality, we want to solve it by multiplying both sides by -1/4:

  -4y > -40

  (-1/4)(-4y) < (-1/4)(-40) . . . . . multiply both sides by -1/4 (reverses order)

  y < 10 . . . . . . . . . . . simplify

The first few decreasing integer values that are part of this solution are ...

  {9, 8, 7, 6, 5, ...}

__

We can add 4y+40 to both sides of the inequality. The result will be an inequality with positive coefficients. This can be solved in one step.

  -4y > -40 . . . . . given

  (-4y) +(4y +40) > (-40) +(4y +40) . . . . . . add 4y+40 to both sides

  40 > 4y . . . . . . . . . . . . . . . simplify

  10 > y . . . . . . . . . . . . divide by 10 (order is unchanged)

  y < 10 . . . . . . . . . rearrange to put y on the left

Integer solutions to this inequality are ...

  {9, 8, 7, 6, 5, ...}

Answer:

Obtuse and the rest of the question is incomplete.

Step-by-step explanation:

Therefore,

We know that :

Substituting the values :

>> V = π × (7 / 2)^2 × 8

>> V = π × (49 / 4) × 8

>> V = π × 49 × 2

>> V = 98π

Henceforth,

We know , the volume of a cylinder is given by the formula – πr²h, where r is the radius of the cylinder and h is the height.

Therefore, putting the values, we get,

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: {r}^{2}h[/tex]

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \times \: \bigg(\frac{7}{2} \bigg)^{2} \: \times \: 8 \\ [/tex]

[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{2} \: \times \: 8 \\ [/tex]

[tex] \Large \mathcal \purple {Volume } \large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{ \cancel2} \: \times \: \cancel{8} \: ^{ \orange4} \\ [/tex]

[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{ \cancel2} \: \times \: {7} \: \times \: \cancel4 \: ^{ \orange2} \\ [/tex]

[tex] \\ \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: 7 \: \times \: 7 \: \times \: 2[/tex]

[tex]\Large \mathcal \purple {Volume }\ \large\red\implies \tt \large \:\pi \: \times \: 49 \: \times \: 2[/tex]

[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:98 \:\pi[/tex]

Hence , the volume of cylinder is 98 pi

Answer:

=8x+14 or

=16x²+56x+49

[tex]\bf{(4x+7)2 }[/tex]

[tex]\bf{=2(4x+7)}[/tex]

[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]

[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]

[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]

[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]

Answer:

(1, 1)  (1, 2)  (1, 3) (1,4)

(1,5)  (2,1)   (2,2) (2,3)

(2,4)  (3,1)  (3,2)   (3,3)

(4,1)   (4,2) (5,1)

Step-by-step explanation:

An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.

An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.

Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.

(1, 6)

(2, 6)

(3, 6)

(4, 6)

(5, 6)

(6, 6)

(2, 5)

(3, 5)

(4, 5)

(5, 5)

(6, 5)

(3, 4)

(4, 4)

(5, 4)

(6, 4)

(4, 3)

(5, 3)

(6, 3)

(5, 2)

(6, 2)

(6, 1)

Hence, the number of possible outcomes that Event E has is 21.

Learn more about the Event:

https://brainly.com/question/12961938

#SPJ2

Answer:

K

Step-by-step explanation:

(1*500 * 5) + (10 * 3*500)

The expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.

Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

The question is incomplete.

The complete question is:

A hot dog vendor at the zoo recorded the average temperature in degrees, x, and the average number of hot dogs she sold, y.

The equation for the line of best fit for this situation is shown below.

[tex]\rm y=\dfrac{3}{10}x+8[/tex]

Based on the line of best fit, complete the given statements.

We have a line of best fits:

[tex]\rm y=\dfrac{3}{10}x+8[/tex]

Plug x = 50 in the line of best fit.

y = (3/10)50 + 8

y = 15+8

y = 23

Plug y = 35

35 = (3/10)x + 8

27 = (3/10)x

x = 90 degree

Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

Thus, the expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees, and based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

Learn more about the line of best fit here:

brainly.com/question/14279419

#SPJ1

The equation that represents the given data is  [tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.

It is a statement where two variables , one dependent and one independent are related.

It is given that

a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).

The equation given in the options are

[tex]\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}[/tex]

The function goes through (8,2)

Substituting the values

f(x) = -2

f(x) = [tex]\sqrt[3]{7}[/tex]

f(x) = -3

f(x) = 2

The equation that represents the given data is

[tex]\RM \\f(x) = -\sqrt[3]{-x} ,[/tex] Option D is the correct answer.

To know more about Function

https://brainly.com/question/12431044

#SPJ1

Answer:

D

Step-by-step explanation:

Answer:

E; 10% off %20 sweater with $6 shipping

Step-by-step explanation:

Similar to what I said last time,

this time is with percentages,

How to calculate percent off?

Divide the number by 100 (move the decimal place two places to the left).

Multiply this new number by the percentage you want to take off.

Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
  0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
    which the total would be $26.75

B. 20% off $35 is
   0.2x35=7 and 35-7 = 28 so your total is $28

C. 30% off $30 with $6 for shipping is

   0.3x30=9 and 30-9 is $21 plus the shipping fee
   $27

D.  $20 sweater with $5 shipping is $25 no discount involved :D

E. 10% off %20 sweater with $6 shipping is

    0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.