Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
μ = 35 and o = 9; n = 60; x = 32

Answers

Answer 1

The standard score (z-score) of the given sample is -20.

Given,

[tex]u[/tex] = 35

[tex]o[/tex] = 9

n = 60

x = 32

To calculate standard score (z-score) use formula,

[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]

Thus, the standard score(z-score) of given sample mean is -20.

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Related Questions

x = 15.3568 - (1+x)^25

Answers

The value of x in the algebraic equation x = 15.3568 - 1(1+x)^25 is 0.115

Mathematical Operation

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

In this case, we have to solve for x in the algebraic equation using mathematical operation.

x = 15.3568 - (1 + x)^25

Collect like terms

x + (1+x)^25 = 15.3568

Solving for x

x = 0.115

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Can anyone help?? Question is attached!

Answers

Answer:

9.37

Step-by-step explanation:

twelve surgeons

112.44 / 12 = 9.37

Answer:

$9.37

Step-by-step explanation:

112.44 ÷ 12

Can you please help me

Answers

How to graph an absolute value function?

First, find its vertex.Second, find its x-intercepts,Third, connect the vertex with the x-intercepts.

Step 1

How to find the vertex?

The general form of an absolute value function:

y = a|x - h| + k, where (h, k) is vertex and a - coefficient

Given function is:

y = |x + 3| - 2

Its vertex is (- 3, - 2), this is our first point to plot, point A.

Step 2

How to find x-intercepts?

Set y = 0 and solve for x:

|x + 3| - 2 = 0|x + 3| = 2x + 3 = 2 and x + 3 = - 2x = - 1 and x = - 5

So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.

Step 3

Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.

Willis borrowed $1400 at 9% simple interest to be paid back in 2 years. How much interest will he pay?

Answers

If he borrowed $1400 at 9% simple interest to be paid back in 2 years. The  interest he will pay is $1,663.34.

How to find the interest?

Using this formula

Interest = Principal ( 1+ Interest rate)^ time

Where:

Interest =?

Principal = $1400

Interest rate = 9% or 0.09

Time = 2 years

Let plug in the formula

Interest = $1,400 ( 1+ 0.09) ^ 2

Interest = $1,400 ( 1.09) ^2

Interest = $1,400 ( 1.1881)

Interest = $1,663.34

Therefore he will pay the amount of $1,663.34 as interest.

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Can someone please help me with this??

Answers

Answer:

3 * (8 + (n - 1)*x*1/3 ) = 3 * ( 0 )

..

Select the values that make the inequality -2h ≤ -40 true. Then write an equivalent inequality, in terms of h. (Numbers written in order from least to greatest going across.) The answers are
10,15,17,
19,20,21,
23,25,30.

Answers

The values that make the inequality -2h ≤ -40 true are

23,25,30

Equivalent form of the inequality is written as

h ≥ 20

How to find the values of the unequally

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using only "equal to"

solving the inequality

-2h ≤ -40

dividing through by a negative number changes the inequality

diving through by -2 gives

h ≥ 20

Therefore, h are values greater than 20 and 23, 25, and 30 are all greater than or equal to 20

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-
1) The difference quotient for f(x)=√x at the point (16, 4) is
a) 16 + h 16
h
b) √4 + h - √16
h
c) √4 + h - 16
h

d) √16 + h - 4
h

Answers

Difference quotient for f(x) = √x at (16,4) is  √16+h - 4 / h

Difference quotient is mathematical operation used to solve derivation of function by using following formula :

difference quotient = [tex]\frac{f(x+ h) - f(x) }{h}[/tex]

For the function f(x) =  √x at point (16,4)

f(x +h) = [tex]\sqrt{x+h}[/tex]  

putting value in formula

difference quotient =  [tex]\frac{\sqrt{x+h} -\sqrt{x} }{h}[/tex]

now , putting x = 16 ,

difference quotient = √16+h - √16 / h

taking square root of 16 ,

= √16+h - 4 / h

So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h

option (d) is correct

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which solution for the value of x in the figure below is incorrect? explain

Answers

B is incorrect since the equations are supposed to be set equal to each other because they are alternate interior angles

5. Find x, y, and z. Round to the nearest thousandth.

Answers

The unknown side and angle of the triangle is as follows:

x = 63°y = 31.19 unitsz = 15.89 units

How to find the side and angles of a right triangle?

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Hence, let's find x, y and z.

The sum of angles in a triangle is 180 degrees.

Hence,

180 - 27 - 90 = x

x = 63 degrees.

sin 63° = opposite / hypotenuse

sin 63 = y / 35

cross multiply

y = 35 sin 63

y = 31.1852283466

y = 31.19 units

sin 27 = z / 35

z = 35 sin 27

z = 15.8896674909

z = 15.89 units

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PEMDAS Simplify using order of operations.
7 + 3 x 5​

Answers

Answer: 22

Step-by-step explanation:

3 times 5 then add 7

Unit form 3 tens 8 ones x 1000

Answers

The expression 3 tens 8 ones × 1000 can be evaluated and the value is; 38,000.

What is the value of the word phrase as given?

It follows from the task content that the value of the expression represented by the word phrase as given is to be determined.

On this note, it follows that we have;

First, 3 tens and 8 ones can be written as;

(3 × 10) + (8 × 1)

= 30 + 8

= 38.

Therefore, the result of the evaluation is; 38 × 1000 = 38, 000.

Ultimately, the result of the expression is; 38,000.

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Which of the following uses set builder notation to denote the set of all real numbers that are greater than or equal to 3 and less or equal to 9?

Answers

The given set written on set builder notation is:

{x| x ∈ R, 3 ≤ x ≤ 9}

How to write the set?

We want to write the given set using set builder notation, the set is the set of all real numbers that are greater than or equal to 3 and less or equal to 9.

So the set can be written as an inequality as:

3 ≤ x ≤ 9

To define the set using the set builder notation, we also need to clarify that x belongs to the real number set, this is x ∈ R.

Then the set that we need to write is:

{x| x ∈ R, 3 ≤ x ≤ 9}

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The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.

Answers

Answer: base = 23  height = 31

Step-by-step explanation:

Area of triangle = (bh)/2

A = 356.5 cm2

h = b+8

356.5 = (b(b+8)) / 2

2(356.5) = b2 + 8b

0 = b2 + 8b - 713

Use quadratic equation to solve for b (there are on-line quadratic equation solvers, or you can do it manually)

b = -31 , 23

23 is the base    23 + 8 = 31 = height

Write the equation of the line that passes through
the points (-6,-3) and (2, 0). Put your answer in
fully simplified point-slope form, unless it is a
vertical or horizontal line.

Answers

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{3 }{ 8 }}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +3 = \cfrac{3 }{ 8 } ( x +6) \end{array}}[/tex]

My answer and step by step explanation is provided as an attachment.

The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?

PLEASE HELP

Answers

24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

According to the question,

We have the following information:

The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.

Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

So, we have:

x+y = 40

x = 40-y ...(1)

55x/100+80y/100 = 40*65/100

55x+80y = 40*65

Putting the value of x from equation 1:

55(40-y)+80y = 2600

2200-55y+80y = 2600

2200+25y = 2600

25y = 2600-2200

25y = 400

y = 400/25

y = 16 pints

Putting this value in equation 1:

x = 40-y

x = 40-16

x = 24 pints

Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

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the third term of the sequence is 165 find the 1st term subtract 2 and multiply by 3

Answers

Answer:

Step-by-step explanation:

Formula for geometric sequence is:

[tex]a_{n} =a_{1} (r)^{n-1}[/tex]

Now we substitute the values in:

[tex]165=a_{1} (3)^{3-1}[/tex]

165=a1(-2x3)^2

165=a1x9

Answer is 23

1.
In Triangle QRS, A is the midpoint of QR, B is the midpoint of RS, and C is the
Rubric midpoint of SQ.
Also, QA = 10, BR = 15, and SQ = 28.
What is the perimeter of triangle ABC?
Use words, number, and/or pictures to show all of your work.

Answers

The perimeter of the triangle ABC with respect to the given information is 78.

What is meant by perimeter?

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. A circle's or an ellipse's circumference is its furthest boundary. Numerous real-world uses exist for calculating perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given,

In triangle QRS,

A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ.

And also given that QA=10, BR=15, SQ=28

Let p represent the triangle ABC's perimeter.

QR + RS +SQ = p

2(QA) + 2(BR) + SQ = p

2(10) +  2(15)+ 28 = p

20 + 30+ 28 = p

78=p

Therefore, the perimeter of triangle ABC is 78

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In the football club, 36 footballers are Latvians, while there are 4 times less footballers of other nationalities. How many total athletes does the football club have?

Answers

Answer:

45

Step-by-step explanation:

Number of Latvian footballers(n¹) = 36

Numer of footballers of other nationalities(n²)=36/4=9

Now total number of footballers= n¹+n²= 36+9 =45

2. Katie is planting a garden for her science fair project. She needs of a cup of soil to go in 8 different pots. How many cups of soil does she need in total?

Answers

Answer:

She needs 8 cups of soil
one cup per pot

Step-by-step explanation:

50 POINTS PLEASE HELP The graph represents a quadratic function. Write an equation of the function in standard form.

Answers

The equation of the graph is y = 2[tex]x^{2}[/tex] + 9x + 4

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x

a[tex]x^{2}[/tex]+bx +c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

From the graph the roots of the equation are -4 and -1/2

so if x = -4, them x + 4 = 0 is a factor,

Also, if x = -1/2, then x + 1/2 = 0 is a factor

Multiply and expand the two factors

(x + 4)(x + 1/2) = 0

[tex]x^{2}[/tex] + x/2 +4x + 2 = 0

multiply through by 2

2[tex]x^{2}[/tex] + x +8x + 4 = 0

2[tex]x^{2}[/tex]  +9x +4 = 0

In conclusion, the equation of the function in standard form is 2[tex]x^{2}[/tex]  +9x +4 = 0

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The graph of a quadratic function with vertex (-3, 1)
Find the range and the domain.
Write the range and domain using Interval notation.

Answers

Answer:

Domain: (negative infinity, positive infinity)

Range: (negative infinity, 1]

Step-by-step explanation:

Z
E
140⁰
180
D120°
40
mZAOC
60
135⁰
80
C
90°
80⁰
What is the measure for the following <?

m
40
60
80

Answers

Answer:

Question 1:

The angle m∠DOX is greater than 90 degrees, but less than 135 degrees.

Looking at the diagram we see that:

m∠DOX = 120 degrees.

Question 2:

The angle m∠COX is the sum of two angles that in total are 80 degrees.

Therefore, the equation is:

m∠COX = m∠AOX + m∠COA

Question 3:

The BOA angle measurement is given by:

BOA = 60 - 40

BOA = 20 degrees

Therefore, an angle that measures 20 degrees is:

BOA.

Question 4:

From the previous question we have:

m∠BOA = 60 - 40

m∠BOA = 20

The measure of m∠BOA is 20 degrees

Question 5:

The measure of the angle EOD is given by:

m∠EOD = 140 - 120

m∠EOD = 20 degrees

THANKS

50

4.8

(41 votes)

Step-by-step explanation:

If 3 oranges cost $1.75,how much would 20 oranges cost?

Answers

Answer:$12

Step-by-step explanation:

1.75/3= 0.6 (1dp)

0.6 x 20 = 12

Answer:

$11.67

Step-by-step explanation:

3 oranges = 1.75

1 orange = 0.58333333333

20*0.58333333333 = 11.6666667


A florist makes centerpieces.
18 roses in each centerpiece.
best way to use compatible numbers to
estimate the number of roses the florist
needs for 24 centerpieces?
A 10 x 25 = 250
B 20 x 25 = 500
D
25 X 30 = 750
30 × 30 = 900

Answers

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Option B is the correct answer.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of roses in one centerpiece = 18 roses.

The number of roses in 24 centerpieces.

= 24 x 18

= 432

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Thus,

The best compatible number to use for 24 x 18 = 432.

24 can be written as 25

18 can be written as 20.

So,

20 x 25 = 500

Option B is the correct answer.

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P(H)=
P(T)=
let me know if you know how to do this

Answers

After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

As given in the question,

After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails ,

Number of total outcomes = { H , T }

Total number of outcomes = 2

Number of favourable outcomes to represent heads = 1

Number of favourable outcomes to represent tails = 1

Probability =(Number of favourable outcomes)/ (Total number of outcomes)

Probability of getting heads from the total outcomes is equal to

P(H) = 1 / 2

Probability of getting tails from the total outcomes is equal to

P(T) = 1/2

Therefore, after flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

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You are playing a game in which a single die is rolled. If a 2 or a 5 comes up, you win $36, otherwise you lose $30. What is your expected value for the game?

Answers

The expected value for the game is -12.

What is probability?

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The probability of rolling a 2 or 5:

= P(2 or 5)

= 1/6 + 1/6 = 1/3

The probability of not rolling a 2 or 5:

= 1 - 1/3

= 2/3

The expected return:

= (1/3)(36) + (2/3)(-36)

= 12 - 24

= -12

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Marcus is on an Olympic training programme.
As part of the programme, he has to have a
blood test and a fitness test at regular
intervals.
Marcus has a blood test every 42 days and a
fitness test every 44 days.
On the day before the training programme
started, Marcus had a blood test and a fitness
test.
After how many days will he next have a blood
test and fitness test on the same day?

Answers

Answer:

Step-by-step explanation:

so if it takes 42 days and 44 days just add them up

42 plus 42 = 82 plus 42=124 plus 42= 166plus 42= 208 plus 42 = 250 plus 42 = 292 plus 42= 334 plus 42= 376 plus 42=418

44 plus 44= 88 plus 44=132 plus 44=176 plus 44 = 220 plus 44= 274 plus 44= 318 plus 44= 362 plus 44=406 plus 44= 450 plus

just keep going

Copy and complete the workings below to
calculate the value of c.
c² = 9² + 40²
C² =...
c=...

Answers

Answer:

41

Step-by-step explanation:

9² + 40² = 1681

the s.r of 1681 is 41

We s.r the answer because we need the singular of C, not C²

Hope this helps

Consider the equation below 5(3a - 1) - 2(3a + 2) = 3(a + 2) + v select two expressions that are equivalent to v

Answers

The two expressions equivalent to v are:

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v6a - 15 = v

How to find the two expressions equivalent to v?

Here we have the equation:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

And we want to find expressions equivalent to v, so to do that, we just need to isolate the variable v in one side of the equation, if we subtract:

3*(a + 2) in both sides we will get:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

That is one of the equivalent expressions, to get the other, we can just simplify the left side.

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

15a - 5 - 6a - 4 - 3a - 6 = v

Now we can group like terms:

15a - 6a - 3a - 5 - 4 - 6

6a - 15 = v

That is the other equivalent expression to v.

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Equation of the line that passes through the points given (0,2) and (-2,0)

Answers

The slope of the line is change in y over change in x. In this case, we have 0-2/-2-0 this gives us -2/-2 which is 1
So we have y =x + c where c is the y value at the y intercept (in this case 2)
So your equation is y = x + 2
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