Out of a pool of 26 men and 29 women what is the probability of 12 women jurors being chosen?

Answer:

4

Step-by-step explanation:

A mode is the number having the highest frequency, that is, the number which occurs the most times. (The number which occurs the most here is 4, there are two 4s. You only have one of the rest of the numbers.)

The estimate for the number of females in marketing is given as follows:

225 females.

A bar graph shows the output considering a given input. In the context of this problem, the inputs are the prices, and for each input there are two outputs, which are the number of male employees and the number of females employees in each department.

For this problem, the second input is the number of male employees and the number of females employees in the marketing departments.

Hence the number of employees is given as follows:

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Answer:

See attachments.

Step-by-step explanation:

The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.

Given function:

[tex]y=\dfrac{5}{x}-2, \quad x > 0[/tex]

Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:

[tex]\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}[/tex]

[tex]\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}[/tex]

[tex]\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}[/tex]

[tex]\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}[/tex]

Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

[tex]\hrulefill[/tex]

Given function:

[tex]y=\dfrac{-2}{x+1}+3, \quad x < -1[/tex]

Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:

[tex]\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}[/tex]

[tex]\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}[/tex]

[tex]\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}[/tex]

Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.

End behaviour:

Answer:

x = 8 and y = -4

Step-by-step explanation:

3x + 4y = 8    (call this equation '1')

x - y = 12      (call this '2')

multiply '2' by 3:

3x - 3y = 36  (call this '3')

subtract '1' from '3':

(3x - 3y = 36)  -  (3x + 4y = 8)

0x + -7y = 28

-7y = 28

y = -4.

sub that back into '1':

3x + 4y = 8

3x + 4(-4) = 8

3x - 16 = 8

3x = 8 + 16 = 24

x = 8.

sub both y =-4 and x =8 into '2' to check if everything adds up:

x - y = 12

8 - -4 = 8 + 4 = 12

so x = 8 and y = -4

The horizontal variance of sales between 2021 and 2022 is 340

By removing the sales figure of 2021 from that of 2022, we are able to arrive at the above figure.

That is Amount of 2022  – Amount of 2021 = Absolute Change.

Figure for 2022 = 3800

Less

Figure for 2021 = 3,460

Variance                340

Excel formula : = Cell no. of amount of 2022 - Cell no of amount of 2021

Note that a negative amount means decrease and positive amount means increase.

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The solution of the System of equation are,

⇒ x = 1

⇒ y = 5

We have to given that;

System of equation are,

⇒ 3x - 5y = - 22

⇒ 4x + 2y = 14

Now, We can simplify as;

From (ii);

2x + y = 7

y = 7 - 2x

Put above value in (i);

3x - 5 (7 - 2x) = - 22

3x - 35 + 10x = - 22

13x = - 22 + 35

13x = 13

x = 1

From (i);

⇒ 3x - 5y = - 22

⇒ 3 - 5y = - 22

⇒ 3 + 22 = 5y

⇒ 25 = 5y

⇒ y = 5

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Answer:

$60

Step-by-step explanation:

Based on the regression equation, the best prediction for the price of a 70-pound container of detergent can be found by substituting x = 70 into the equation:

y^ = 0.86x + 0.52

y^ = 0.86(70) + 0.52

y^ = 60.2 + 0.52

y^ ≈ $60.72

Therefore, the best prediction for the price of a 70-pound container of detergent is approximately $60.72. However, since we are dealing with prices, it is reasonable to round this value to the nearest dollar, which would be $61. But since none of the answers are 61 it would be $60.

The probability that event A or B takes place is 17/19

Probability is defined as the ratio of the required to the total possible outcomes of an event.

The probability of event A or B taking place can be defined as ;

P(A or B) = P(A) + P(B)

P(A) = 10/19

P(B) = 7/19

Hence,

P(A) + P(B) = 10/19 + 7/19

L.C.M of 19 and 19 = 1

P(A) + P(B) = (10 + 7)/19

P(A) + P(B) = 17/19

Therefore, the probability that event A or B takes place is 17/19

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Answer:

55°

Step-by-step explanation:

if angle 4 = 105°, then angle 3 must be 180 - 105 = 75° (angles in straight line add up to 180°).

angles in a triangle also add up to 180°.

so we expect angle 2 to be 180 - angle 6 - angle 3

= 180 - 50 - 75

= 55°.

The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

The mean of the data is 9 students because there are 45 students total and 5 meetings.

When 15 students attend the next meeting, the mean increases to 10.5 students because there are now 60 students total and 6 meetings.

Mean of the first 5 meetings:

There are 45 students total.

There are 5 meetings.

Therefore, the mean is:

= 45 / 5

= 9 students.

There are 60 students total.

There are 6 meetings.

Therefore, the mean is:

= 60/6

= 10 students.

The mean increases from 9 to 10 because the value of 15 is greater than the mean of 9. When a larger value is added to a set of data, the mean will increase.

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Mbhalati's statement is valid.

The charge of R180 is less than the total value of his deposit is R2000.

To determine whether Mbhalati's statement is valid, we need to calculate the total value of his deposit and compare it to the stated charge.

Given information:

Value of notes deposited: R1500

Value of coins deposited: R500

Charge for the deposit: R180

To calculate the total value of Mbhalati's deposit, we add the value of the notes and the value of the coins:

Total deposit value = Value of notes + Value of coins

Total deposit value = R1500 + R500

Total deposit value = R2000

Now, let's compare the total deposit value to the stated charge:

Total deposit value = R2000

Stated charge = R180

Mbhalati's statement would be valid if the stated charge (R180) is equal to or less than the total deposit value (R2000).

Let's check:

Is R180 ≤ R2000?

Yes, R180 is less than R2000.

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Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

Answer:

Step-by-step explanation:

3.14 . 11= 150/360

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer: 10 cheeseburgers

Step-by-step explanation: 25/2.5=10

Answer:

10

Step-by-step explanation:

To determine the number of cheeseburgers you can get with $25, you can divide the total amount of money by the cost of each cheeseburger.

$25 ÷ $2.50 = 10

Therefore, with $25, you can get 10 cheeseburgers if each cheeseburger costs $2.50.

Answer:

Arc EG = 23.21 units

Step-by-step explanation:

Arc length:

Arc length could be found by the below mentioned formula.

         [tex]\boxed{\bf Arc \ length =\dfrac{\theta }{180}*\pi r}[/tex]

r - radius of circle = 19 units

Ф - central angle of arc = 70°

                             [tex]\sf arc \ EG = \dfrac{70}{180}*3.14*19\\\\[/tex]

                                         = 23.21 units

The solution of the equation for B over the interval [0,2π] is undefined

From the question, we have the following parameters that can be used in our computation:

-√3tan(β) = tan(β)sin(β)

Divide both sides of the equation by tan(β)

so, we have the following representation

-√3 = sin(β)

Rewrite as

sin(β) = -√3

Take the arc sin of both sides

β = undefined

Hence, the solution of the equation for B over the interval [0,2π] is undefined

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Answer:

x=i[tex]\sqrt{2}[/tex], x=-i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

This equation can be factored. In order to do so, we can split the expression into two parts: (x^3-3x^2) and (2x-6). The greatest common factor of the first group is x^2, factoring it out gives us x^2(x-3). The greatest common factor of the second group is 2, factoring it out gives us 2(x-3). Since both x^2 and 2 are being multiplied by x-3, we add them into a factored form of (x^2+2)(x-3)=0

x-3 provides us with one real root, so we can disregard it.
x^2+2=0 ---> x^2=-2--->x=±[tex]\sqrt{-2}[/tex]
Factoring out the imaginary number i (equals [tex]\sqrt{-1}[/tex]), we get x=±i[tex]\sqrt{2}[/tex]

Answer:

1) 5/6
2) 19/30
3) They are mutually exclusive.

Step-by-step explanation:

Let's break the diagram down.
We have four types of smoothies:

Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8

From here, we find that there are 30 smoothies in total.

In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.

Therefore,

[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]

Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.

[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]

We can check if the events are mutually exclusive using the formula:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).

[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.

If the two sides are equal, the cases are not mutually exclusive.

[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]

Therefore, the events are mutually exclusive.

The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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Reema should use 3 hooks. The distance between the hooks is approximately 4 inches, and the distances of each hook from the left edge of the wood are approximately 1.75 inches, 5.75 inches, and 9.75 inches.

Given:

Wall length: 4 feet

Wood length: 28 inches

Space between hooks: about 7 or 8 inches

Minimum distance from each end: 1 3/4 inches

To center the coat rack on the wall, we need to find the remaining space on either side of the wood after accounting for the minimum distances from each end.

Convert measurements to inches:

Wall length: 4 feet = 48 inches

Calculate the available space for the wood on the wall:

Available space on each side = (Wall length - Wood length) / 2

Available space on each side = (48 inches - 28 inches) / 2

Available space on each side = 20 inches / 2

Available space on each side = 10 inches

Determine the number of hooks and the space between them:

Space between hooks: about 7 or 8 inches

Let's assume we choose a space of 8 inches between hooks for this calculation.

Remaining space for hooks = Wood length - (Minimum distance from each end × 2)

Remaining space for hooks = 28 inches - (1 3/4 inches × 2)

Remaining space for hooks = 28 inches - (3 1/2 inches)

Remaining space for hooks = 28 inches - 7/2 inches

Remaining space for hooks = 28 inches - 3.5 inches

Remaining space for hooks = 24.5 inches

Number of hooks = Remaining space for hooks / Space between hooks

Number of hooks = 24.5 inches / 8 inches (approximately)

Number of hooks ≈ 3.06 (rounded to the nearest whole number)

Since we cannot have a fraction of a hook, we'll round down to 3 hooks.

Calculate the distance between hooks:

Distance between hooks = Space between hooks / (Number of hooks - 1)

Distance between hooks = 8 inches / (3 hooks - 1)

Distance between hooks = 8 inches / 2

Distance between hooks = 4 inches

Calculate the distance of each hook from the left edge of the wood:

Hook 1 distance from the left edge = Minimum distance from each end

Hook 2 distance from the left edge = Minimum distance from each end + Distance between hooks

Hook 3 distance from the left edge = Minimum distance from each end + (Distance between hooks × 2)

Using the given minimum distance from each end of 1 3/4 inches (or 1.75 inches), we can calculate the distances for each hook:

Hook 1 distance from the left edge = 1.75 inches

Hook 2 distance from the left edge = 1.75 inches + 4 inches

Hook 2 distance from the left edge = 5.75 inches

Hook 3 distance from the left edge = 1.75 inches + (4 inches × 2)

Hook 3 distance from the left edge = 9.75 inches

So, Reema should use 3 hooks. The distance between the hooks is approximately 4 inches, and the distances of each hook from the left edge of the wood are approximately 1.75 inches, 5.75 inches, and 9.75 inches.

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Question

a Reema wants to build a coat rack for the front hallway. The wall is 4 feet long, and the piece of wood she has for the rack is 28  Checklist Did You... inches long. She wants to center the coat rack on the wall. There Draw a detalled needs to be an equal amount of space, about 7 or 8 inches, diagram? between the coat hooks. The first and last hooks should be no Check all your less than 1 inches from either end of the wood. How many calculations? Complete all parts hooks should Reema use? What is the distance between the of the problem? hooks? What is the distance of each hook from the left edge of the wood? Draw and label a diagram of the coat rack on the wall. Mark all the measurements for - inches placing the wood on the wall, and for attaching the hooks on the wood. You can use either fractions or decimals to label and calculate the measurements. Reflect Reflect on Mathematical Practices After you complete the task, choose one of the following questions to answer. • Model What models helped you to solve this problem? How did they help? • Be Precise When was it easier to use fractions, and when was it easier to work with decimal numbers? 213 1.75 left 1.75 edge Right edge

Answer:

To calculate the value of (-3/4)^-4, we need to apply the exponentiation rules.

When a negative number is raised to an even power, the result is positive. Thus, we can rewrite (-3/4)^-4 as (4/-3)^4.

Now, let's evaluate the expression:

(4/-3)^4 = (4^4)/(-3)^4 = 256/81

So, the value of (-3/4)^-4 is 256/81

Step-by-step explanation:

The number of squares that are in 384 sq ft is 0

From the question, we have the following parameters that can be used in our computation:

Area expression = 384 sq ft

The above expression is an area expression

This means that it cannot be compared to quantities other then squares

The term "how many squares" is not an area expression

Hence, there are no squares in 384 sq ft

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -4}{2}~~~ ,~~~ \cfrac{ y +5}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M} }{(5~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -4 }{2}=5\implies x-4=10\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +5 }{2}=-1\implies y+5=-2\implies \boxed{y=-7}[/tex]

[tex]\cfrac{x}{4}-\cfrac{x+10}{2}=3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{x}{4}-\cfrac{x+10}{2} \right)=4(3)}\implies x-(2x+20)=12 \\\\\\ x-2x-20=12-x-20=12\implies -20=12+x\implies \boxed{-32=x} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{2x+1}{5}-\cfrac{x-3}{7}=-2\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{35}}{35\left( \cfrac{2x+1}{5}-\cfrac{x-3}{7} \right)}=35(-2) \\\\\\ 14x+7-(5x-15)=-70\implies 14x+7-5x+15=-70 \\\\\\ 9x+22=-70\implies 9x=-92\implies \boxed{x=-\cfrac{92}{9}}[/tex]

The equation for the circle is

(x - 1)² + (y + 2)² = 9

Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.

Remember that for an equation for a circle of radius R and center (a, b), the equation is:

(x - a)² + (y - b)² = R²

Here we have the equation of the circle:

x² + y² - 2x + 4y - 4 = 0

We need to complete squares, we will get:

(x² - 2x) + (y² + 2*2y)  = 4

Now we can add in both sides (-1)² and (2)², then we will get:

(x² - 2x + (-1)²) + (y² + 2*2y +  (2)²)  = 4 +  (2)² + (-1)²

(x - 1)² + (y + 2)² = 4 + 4 + 1

(x - 1)² + (y + 2)² = 9 = 3²

Then we can see that the center is (1, -2), and the radius is 3.

The graph of this circle is on the image at the end.

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The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate [tex]= (1 + r/m)^m - 1[/tex]

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate [tex]= (1 + 0.145/2)^2 - 1[/tex]  

Simplifying the expression inside the parentheses:

Nominal rate [tex]= (1 + 0.0725)^2 - 1[/tex]

Calculating the exponent:

Nominal rate [tex]= (1.0725)^2-1[/tex]

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

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Answer: 132 cm cubed

Step-by-step explanation:

0.5*3*4*2=12

10*5=50

4*10=40

3*10=30

30+40+50+12=132 cm cubed