I need help with the question above. I took a pic.

Answer:

87

Step-by-step explanation:

Answer:87

Step-by-step explanation:

Using the normal distribution, the probabilities are given as follows:

a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.

b. More than 16 cases with side effects: 0.0174 = 1.74%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the equation presented below:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution in this problem are given as follows:

p = 0.05, n = 200.

Hence the mean and the standard deviation of the approximation are given as follows:

For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:

X = 12.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (12.5 - 10)/3.08

Z = 0.81

Z = 0.81 has a p-value of 0.7910

X = 7.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (7.5 - 10)/3.08

Z = -0.81

Z = -0.81 has a p-value of 0.2090.

0.7910 - 0.2090 = 0.582 probability.

For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (16.5 - 10)/3.08

Z = 2.11

Z = 2.11 has a probability of 0.9826.

1 - 0.9826 = 0.0174 = 1.74% probability.

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Associative property of the sum states that the order the operations are done doesn't matter as long as the sequence of operands also doesn't change. This property is given by:

Therefore, the equation that illustrates the associative property is:

Answer:

a. 5.6

b. 38.4

c. 8.25

d. 24

Step-by-step explanation:

Answer: -3/4

Step-by-step explanation: Lucky I just learned about this last week! Multiply 7 and -1 by -2 which makes the equation -14x + 2 = 14. Subtract 2 from both sides to make -16x = 12. Then divide each side by -16 and you get -3/4 = x.

Nice helping out!

Answer:

There are no solutions.

Step-by-step explanation:

Hello!

Isolate the absolute value equation first:

Now stop and think.

An absolute value equation always has a positive outcome, because you are finding the positive value of what's inside. The outcome here is negative, so there is no value of x that makes it so that the absolute value is negative.

So the solution is No Solutions.

The scale factor which takes circle m to circle n as depicted in the attached image is; 3.

It follows from the task content that the scale factor which takes circle m and transforms it to circle n is to be determined.

Hence, since both circles have the same center, the center can be taken as a point of reference.

Therefore, the distances between the center of the circles m and n to any point on their circumferences are; 3 units and 9 units respectively.

On this note, since circle n is; 9/3 = 3 times as large as circle m, it follows that the required scale factor is; 3.

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When Allison arrived, Austin still had 24 miles to go. Allison drive 116 miles per hour.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

As given, Allison drove home at 58 mph, but her brother Austin, who left at the same time, could drive at only 46 mph.  Allison arrived, Austin still had 24 miles to go.

Let t be the time they drove.

Then you have this "distance" equation

58t = 46t + 24

saying that both parts of the equation represent the same distance.  Then

58t - 46t = 24

12t = 24

t = 2  hours.

Hence the distance is, 2 x 58 = 116 mph.

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a) 50 elements are in the union of three pairwise disjoint sets if the sets contain 10, 15, and 25 elements.

b) 229 are there to select a student whose major is in one of the departments of the school of science if there are seven departments in this school with 31, 88, 19, 11, 41, 22, and 17 students in each.

c) 23 are there to select a person who lives on a street with five houses if the number of people in these houses are 5, 3, 2, 7, and 6.

The problem we are dealing with is related to union sets.The union of two sets is a set containing all elements that are in set A and set  B or including more sets

For the first problem, the sets  contain:

n(A)=10, n(B)=15, n(C)=25, n(A∩B)=0 ,n(B∩C)=0 ,n(C∩A)=0,n(A∩B∩C)=0

So,  n(A∪B∪C)=n(A)+n(B)+n(C)−n(A∩B)−n(B∩C)−n(C∩A)+n(A∩B∩C)

               = 10 +15+25-0-0-0-0-0

              =  50

For the second  problem, since no student can have  more than one major.

So, (A∪B∪C∪D∪E∪F∪G)=n(A)+n(B)+n(C)+n(D)+n(E)+n(F)+n(G)

As  we know : n(A)=31, n(B)=88, n(C)=19, n(D)=11, n(E)=41, n(F)=22, n(G)=17

So ,  (A∪B∪C∪D∪E∪F∪G) =  31+88+19+11+41+22+17= 229

For the third problem,  we have

n(A)=5

n(B)=3

n(C)=2

n(D)=7

n(E)=6

So, the number of elements will be (A∪B∪C∪D∪E) =  5+3+2+7+6 =23

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Answer:

+ 9

Step-by-step explanation:

x²+ 6x

to complete the square

add ( half the coefficient of the x- term )² to x² + 6x

x² + 2(3)x + 3²

= x² + 6x + 9

= (x + 3)² ← a perfect square

Step 1

Write the slope, y-intercept form of the equation of a line.

Given

8 times the quantity of X and 8

Find

Translate into an expression

Explanation

Quantity be X

so , according to the question ,

8 (X + 8)

Final Answer

Hence , the required expression is 8 (X + 8)

Answer:

(a)Vertex

(c)3 seconds

Explanation:

Part A

The maximum point on a parabola is called the Vertex.

Part C

To find out how much the plain was in the air, find the values of t at which the height, h=0.

Next, subtract the second value of t from the first value.

First, set h=0:

Factorize:

Therefore, the plane hits the ground after 3 seconds.

Answer:

-7

Step-by-step explanation:

-7 is the greatest because it is closer to 0 on the number line.

The solutions are x = -1,  y = 1 and z = 5  

In Mathematics, the equation which has highest degree 1 is known as a Linear equation. Linear equations are used to calculate unknown values. Here to represent unknown values we will use variables like x, y, z  or a, b, c .. etc.  

According to the number of variables in given equations, the given equations will be called a Linear equation in one variable or Linear equation in two variables and so on. To solve linear equations we will use Elimination method

Here, we have three linear equations with 3 and 2 variables

4x - 2y + 3z = 9 ----(1)

x - 2y = -3 -----(2)

2x + 3y = 1​ -----(3)

Here, to find x, y and z we will use Elimination method

First of all solve (2) and (3) as given below

2 × (2) ⇒  2x - 4y = - 6 -----(4)

1 × (3) ⇒  2x + 3y = 1​  

Now subtract (3) from (4)

(4) - (3) ⇒ 2x - 4y -2x - 3y  = - 6 - 1

⇒ - 7y = -7

⇒   y = 1

Substitute y = 1 in (2)

(2) ⇒ x - 2(1) = -3

x - 2 = -3

x = -1    

Now substitute x = -1 and y = 1 in (1)

(1) ⇒ 4(-1) - 2(1) + 3z = 9  

- 6 + 3z = 9

3z = 15

z = 5

From above calculations

The values of x = -1,  y = 1 and  z = 5

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By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

Solution

2 + 3 + 4 = 9

180 ÷ 9 = 20

Hence, we get the quotient of 20.

20 × 2 = 40

20 × 3 = 60

20 × 4 = 80

Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80

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Answer:

x = 2

Step-by-step explanation:

The Question was:
7x + 14 = 28

Subtract 14 from both sides.

7x = 28 − 14

Subtract 14 from 28 to get 14.

7x = 14

Divide both sides by 7.

x = 14/7

​

Divide 14 by 7 to get 2.

x = 2

Answer:

x=2

Step-by-step explanation:

To solve a question like that, we have to isolate the variable.

What is the variable? A variable is a letter partaking in an equation that is in place of a number or solution that makes the equation true.

In this case, the variable is x.

To isolate the variable, we must do the opposite action that is being done to the number.

For example, if a number was added to one side by 28, we can subtract both sides by 28 so it negates the addition and does not alter the original equation.

7x+14=28                We can subtract the 14 on both sides to negate the                                -14  -14                     addition.

7x=14                      Divide each side by 7 to isolate x.

x=2

The length of the side SU will be equal to 4√2.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the sum of the square of the other two sides.

The formula for the Pythagorean theorem will be given as:-

H² = P² + B²

Here,

H = Hypotenuse

P = perpendicular

B= Base

The length of the sides of the triangle is formed by joining the midpoints of the bigger triangle are xw=2, xv=2, and vw = 3.

Here sv = vt = xw = 2 units. Apply the Pythagorean theorem in a triangle xsv.

H² = P² + B²

sx² = xv² + sv²

sx = √ ( 2² + 2² )

sx = √8

sx = √ ( 2 x 2 x 2 )

sx = 2√2

SU = 2 sx

SU = 2 x 2√2

SU = 4√2

Therefore, the length of the side SU will be equal to 4√2.

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Answer:

y = -x + 4

Step-by-step explanation:

(-1, 5), (2. 2)

(x₁, y₁)  (x₂, y₂)

       y₂ - y₁        2 - 5          -3           -3

m = ----------- = ----------- = --------- = ------- = -1

        x₂ - x₁        2 - (-1)       2 + 1        3

y - y₁ = m(x - x₁)

y - 5 = -1(x - (-1))

y - 5 = -1(x + 1)

y - 5 = -x - 1

  +5        +5

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

y = -x + 4

I hope this helps!

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = 8, - 4) and (x₂, y₂ ) = (- 1, 5) ← 2 ordered pairs from the table

m = [tex]\frac{5-(-4)}{-1-8}[/tex] = [tex]\frac{5+4}{-9}[/tex] = [tex]\frac{9}{-9}[/tex] = - 1 , then

y = - x + c

to find c use any ordered pair from the table

using (2, 2 ) , then

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = - x + 4 ← in slope- intercept form

with y- intercept c = 4

Answer:

The selling price is:  [tex]\$77,520[/tex]

Step-by-step explanation:

Step 1: Identify the profit made

A profit of 14% is made on the article.

This means that the article was sold at a price that had 14% of its original price added to it.

The 14% of the original price is:

[tex]14\% \times 68000\\=\frac{14}{100}\times 68000\\\\\text{Calculate the value}\\\frac{14}{100}\times 68000\\=9520[/tex]

So, a profit of $9520 was made

Step 2: Calculate the selling price

The selling price will be the sum of the original price and the profit.

The selling price is:

[tex]68000+9520\\=77520[/tex]

Answer:

Step-by-step explanation:

it 10

Answer:

a. 6

b. 16

Step-by-step explanation:

a.

The mode is the number that appears the most

3 appears once

13 appears once

6 appears twice

8 appears once

10 appears once

5 appears once

Since 6 appears the most, it is the mode in this set of numbers

b.

Again, The mode is the number that appears the most

12 appears once

0 appears once

15 appears twice

13 appears twice

19 appears once

16 appears three times

Since 16 appears the most, it is the mode in this set of numbers

The correct answers are:  [A]:  "6 " ; and:   [B]: " 16 ."

____________________

Step-by-step explanation:

The question asks to find the modes of the following sets of numbers:
 Set a)   "{3, 13, 6, 8, 10, 5, 6}."

 Set b) "{12, 0, 15, 15, 13, 19, 16, 13, 16, 16}."

Note that the mode is the number that occurs most frequently within a data set.

To begin:  let's find the mode of Set: a:
_____
First, let's list all the values within Set: a: in order of smallest to largest—to simplify matters:
       →  " { 3, 5, 6, 6, 8, 10, 13 }."  
In this data set, there is only one value that occurs more than once—  
which is 6.   As such, the mode of "Data Set: a" is  6 .

Then:  To continue: let's find the mode of Set: b:
_____

Second, Let's list all the values within Set: b:  in order of smallest to largest—again; to simplify matters:
         →  " { 0, 12, 13, 13, 15, 15, 16, 16, 16, 19 } ."
In this data set, we see the following:
 Each of the three values:   0, 12, and 19 appear only once;
                      13 and 15 individually, appear twice; and:  
                      16 appears "three times".
As such:
     The value, 16 appears the most in this data set;  and:
          →  The mode of "Data Set: b"—is 16.
_____
The correct answers are:  [A]:  "6 " ;  and:  [B]: " 16 ."
_____
Hope this is helpful to you!  

  If you have any questions—Please "comment" below!
_____

Triangle ABC and the triangle EFG are congruent by the first and third statement.

What is the congruent diagram?

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

In the given example triangle ABC and triangle EFG having one same side of length 2.

By the ASA (Angle side angle) criteria, we want two angles are same then the triangles are congruent.

When "m ∠ B and m ∠ F"  and "m ∠ A and m ∠ E" are same then the triangles are congruent.

Therefore, the first option is correct.

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Answer:

15

Step-by-step explanation:

Answer:

I think the answer is 0.

Step-by-step explanation:

-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4

The ratio House blend/Organic Free Trade blend is the same and must remain the same.

So, the proportion is:

Where x is the unknown amount of the Organic Free Trade blend.

So, from the proportion, we have:

Answer: 156 pounds of Organic Free Trade blend

THE DOMAIN & RANGE OF THE FUNCTION g(x)=|x + 4| is

This is further explained below.

Generally, The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

[tex](-\infty, \infty)[/tex]

Set-Builder Notation:

[tex]$\{x \mid x \in \mathbb{R}\}$[/tex]

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

[tex]$[0, \infty)$[/tex]

Set-Builder Notation:

[tex]$\{y \mid y \geq 0\}$[/tex]

Determine the domain and range.

Domain: [tex]$(-\infty, \infty),\{x \mid x \in \mathbb{R}\}$[/tex]

Range: [tex]$[0, \infty),\{y \mid y \geq 0\}$[/tex]

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The length in feet of the pole is 13 ft.

The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.

Use the Pythagorean relationship:

c²= a² + b²

= 5²  +  12²

= 25 + 144

= 169

c = 13

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The average change in sales income per month is $ 3 million.

What is average change and how is it assessed?
The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Given, for 3 months, the average change in the company's sales
= $ 9 million
Also, for x months, the average change in the company's sales
= $ (9x/3) million
Therefore, for one month, the average change in the company's sales
= $ (9*1/3) million = $ 3 million
Thus, the average change in sales income per month is $ 3 million.

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Answer:

The formula for finding the percentage of something is given as: (No. of items you want to find÷Total no. of items)×100

Percentage of red pins = (21÷70)×100

= 30%

A complex number z is given in the form:

z = (x.y) = (realpart) x + imaginary part (iy)

In this case:

z1 = -7i

z2 = 3+3i

To write in trigonometric form:

Multiplication in trigonometric form:

Multiplication in standard form: