Answer:
The 95% confidence interval is [tex] 17.932 < \mu < 20 + 22.068[/tex]
Step-by-step explanation:
From the question we are told that
The population standard deviation is [tex]\sigma =7 \ inches[/tex]
The sample size is n = 20
The sample mean is [tex]\= x = 20[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{7 }{\sqrt{20} }[/tex]
=> [tex]E = 2.068[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 20 - 2.068 < \mu < 20 + 2.068[/tex]
=> [tex] 17.932 < \mu < 20 + 22.068[/tex]
Perform the following operation
and express the answer in
scientific notation.
6.300x10^-5 – 7.200x10^-3
[?]*10
Answer:
Step-by-step explanation:
6.3 x10^-5 -7.200 x10^-3= - 0.007137=7.137x10-3
Answer:-7.137 x 10^-3
Step-by-step explanation:
Can two fraction with the same numerator and different denominators be equal? Use words and numbers to explain.
Step-by-step explanation:
Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator. Once the two fractions have the same denominator, you can check to see if the numerators are equal.
The two fractions with the same numerator and different denominators can not be equal.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A division number is a number that addresses the piece of the entire, where the entire can be any number. It is a numerator and a denominator.
The fraction is in the form of a numerator and denominator. The two fractions can be equal if and only if their numerator and denominator are equal.
The two divisions with similar numerators and various denominators can not be equivalent.
More about the Algebra link is given below.
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Find the indicated probability.
If P(A or B) = 0.8, P(A) = 0.4, and P(A and B)= 0.15, find P(B).
P(B)=
(Simplify your answer. Type an integer or a decimal.)
Answer:
[tex]P(B) = 0.55[/tex]
Step-by-step explanation:
Given
[tex]P(A\ or\ B) = 0.8[/tex]
[tex]P(A) = 0.4[/tex]
[tex]P(A\ and\ B) = 0.15[/tex]
Required
Find P(B)
In probability, we have:
[tex]P(A\ or\ B) = P(A) + P(B) - P(A\ sd B)[/tex]
Substitute values
[tex]0.8 = 0.4 + P(B) - 0.15[/tex]
Collect Like Terms
[tex]P(B) = 0.8 - 0.4 + 0.15[/tex]
[tex]P(B) = 0.55[/tex]
Lucy $154 made for 11 hours of work. At the same rate, how much would she make for 8 hours of work?
Answer:
19.25
Step-by-step explanation:
Mr.Farrar spent a total of $43.87 after tax on new clothes at a clothing store. He brought 1 pair of sandals for $8.02 t-shirts fo $9.49 each and 1 pair of jeans. The tax on the purchase was $2.87 how much did Mr.Farrar pay for the pair of jeans?
Answer:
43.87 - 8 = 35.87 (sandals)
9.49 + 9.49 = 18.98 ( for two t-shirts)
35.87 - 18.98 = 16.89 (t-shirts)
16.89 - 2.87 = 14.02 (taxes)
Andrea payed $14.02 for a pair of jeans
Hopes this helps you!
Step-by-step explanation:
Which graph below represents the solution to the inequality 6 x − 12 − x ≤ 3
Answer:
The solution is:
[tex]6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}[/tex]
The graph of the solution is attached below.
Both the number line and graph is attached below.
Step-by-step explanation:
Note: you missed to add the graph options. Therefore, I am solving the inequality and adding the corresponding graph which would anyways clear your concept.
Given the inequality expression
[tex]6\:x\:-\:12\:-\:x\:\le \:3[/tex]
Group like terms
[tex]6x-x-12\le \:3[/tex]
Add similar elements: 6x-x=5x
[tex]5x-12\le \:3[/tex]
Add 12 to both sides
[tex]5x-12+12\le \:3+12[/tex]
simplify
[tex]5x\le \:15[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}\le \frac{15}{5}[/tex]
simplify
[tex]x\le \:3[/tex]
Therefore, the solution is:
[tex]6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}[/tex]
The graph of the solution is attached below.Both the number line and graph is attached below.
Solve for n.
below
.....................
Answer:
n = 12
I hope this helps!
The high temperatures for two consecutive days were 83°F and 79°F. If the average(mean) high temperaature, including a third day, was greater than 82°F, then what was the high temperature on the third day? Write an inequality representing the problem.
Answer:
83F+79F+X
----------------- >82F
3
Step-by-step explanation:
X is the unknown temp, which is the third day. adding all those up and dividing that by 3 will give you the average. if the average is above 82F, then you just add a > symbol showing that its higher than 82F
3/5+(-7/5)= can someone help me with this please
Answer:
[tex]-\frac{4}{5}[/tex]
Step-by-step explanation:
Because both of the fractions have a common denominator they can be subracted without any other work.
Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?
Answer:
50%
Step-by-step explanation:
*In this question, the 6 does not matter*
If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.
Percentages are just fancy fractions and decimals. 50% means 1/2.
Thus, the answer is 50%
Delete this already.
How many natural numbers are between 34 and 72? and, how many whole numbers between -2 and 25?
Answer:
There are 37 natural numbers between 34 and 72.
There are 25 whole numbers between -2 and 25.
Step-by-step explanation:
1. Natural numbers between 34 and 72
2. Whole numbers between -2 and 25
1.35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71.
2.0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24.
Please help I'll give brainlest
Which of the following is 1,215 divisible by? Select all that apply.
A.3
B.2
C.9
D.10
E.5
F.8
G.4
H.6
Answer: A,C,E
Step-by-step explanation:
All of the other answers give you a decimal.
Answer:
ACEStep-by-step explanation:
A
1215 divided by 3 = 405
B
1215 divided by 9 = 135
C
1215 divided by 5 = 243
*The other answers can give a decimal answer.
I need help with this
Answer:
A.
Step-by-step explanation:
I gotchu fam. The first thing that you would want to do is find the slope. The slope is the change in y divided by the change in x. Based on the points on the line, the change in y is 2 because it goes up two, and the change in x is one because it goes over 1. This would make your slope 2/1, or just 2! Now we have our slope, so we want to find our y-intercept. There are two ways that we can do this. The first way is just eyeballing it, but sometimes that's not always accurate. We're just going to do that because its faster (lol). It looks around -2. With this information, we have our entire equation! y=mx+b. we can plug in our information. y=2x-2. And that's how your answer's A! Hope this helps.
Find the LCM of the denominators in these fractions
5/6 and 1/14
Answer:
35/42 and 3/42
Step-by-step explanation:
Multiply by 3.
HOPE THIS HELPS :)
The LCM of the denominators in the fractions 5/6 and 1/14 is 42.
What is Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers.
A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers.
To find the least common multiple (LCM) of two numbers, you can list the multiples of each number and find the smallest number that is a multiple of both.
The multiples of 6 are 6, 12, 18, 24, 30, and so on. The multiples of 14 are 14, 28, 42, 56, and so on. The smallest number that is a multiple of both 6 and 14 is 42, so the LCM of 6 and 14 is 42.
Therefore, the denominators in the fractions 5/6 and 1/14 have an LCM of 42.
To learn more about the Least Common Multiple(LCM) here :
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Helpppp pleaseeeeeeee
Answer:
x= 6.85 or 89/13
Step-by-step explanation:
perimeter is sum of all sides added, so add them all and set them equal to 84
4(x-3) + 3x - 1 + 6x + 8 = 84
distribute
4x + 12 + 3x - 1 + 6x + 8 = 84
combine like terms
13x - 5 = 84
solve for x
x = 89/13 = 6.85
A pipe is leaking in the school bathroom . it leaked 3 gallons of water in 6 hours.
Find the constant of proportionality
Answer:
0.5 gallons per hour
Step-by-step explanation:
What is the only number that is a factor of every number?
A.5
B.2
C.1
D. 3.54
Answer:
the answer of the question is c.1
A salesperson at a jewelry store earns 5% commission each week. Last week, Heidi sold 640 worth of jewelry. How much did Heidi make in commission? How much did the jewelry store make from sales?
Answer:
12,800 Dollars USD
Step-by-step explanation:
What is the slope of a horizontal line?
Answer:
Slope of a horizontal line. When two points have the same y-value, it means they lie on a horizontal line. The slope of such a line is 0, and you will also find this by using the slope formula.
Which substitution method should be the best used to solve which system of equations
Answer: 6x+2y=1
Step-by-step explanation:
because it just is
What’s the value of x? :/
Answer:
[tex] x = 27 [/tex]
Step-by-step explanation:
According to congruent chords and arcs theorem, if [tex] \overline{XY} \cong \overline{ZY} [/tex] then [tex] \arc{XY} \cong \arc{ZY} [/tex].
This means that [tex] \arc{XY} = \arc{ZY} = (6x - 20) degrees [/tex]
Thus:
[tex] \arc{XY} + \arc{ZY} + \arc{ZX} = 360 [/tex] (full circle = 360°)
[tex] \arc{XY} = (6x - 20) [/tex]
[tex] \arc{ZY} = (6x - 20) [/tex]
[tex] \arc{ZX} = 76 [/tex]
Plug in the values into the equation
[tex] (6x - 20) + (6x - 20) + 76 = 360 [/tex]
[tex] 6x - 20 + 6x - 20 + 76 = 360 [/tex]
Add like terms
[tex] 12x + 36 = 360 [/tex]
Subtract 36 on both sides
[tex] 12x = 360 - 36 [/tex]
[tex] 12x = 324 [/tex]
Divide both sides by 12
[tex] x = 27 [/tex]
A large rectangle is made by joining three identical small rectangles as shown.
The perimeter of one small rectangle is 21cm. The width of one small rectangle is x cm.
Work out the perimeter of the large rectangle. The final line of your answer should be the form, perimeter of large rectangle is ...cm
Answer: 35 cm
Step-by-step explanation:
As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,
The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:
2(length + width) = Perimeter
2(2x + x) = 21
2(3x) = 21
6x = 21
x = 21/6 = 3.5 cm
x = 3.5 cm
From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:
2(length + width) = Perimeter
2(3x + 2x) = Perimeter
Perimeter = 2(5x)
Perimeter = 10x
Perimeter = 10(3.5)
Perimeter = 35 cm
Step-by-step explanation:
What is the area of a hexagon with a side length of 10? it also has a rectangle in it with other measurements but the question is asking for the area of the hectagon.
Answer:
there is a formula for a hexagon .. it's
Area = 3[tex]\sqrt{3\\}[/tex]/2 * [tex]length^{2}[/tex]
where length is the length of one side, assuming all sides are equal
Step-by-step explanation:
3*[tex]\sqrt{3}[/tex]/2= 7.348469228.........
since the length is 10... the length squared is 100
then the total area of the hexagon is 734.8469228...... [tex]units^{2}[/tex].. what ever they are
if you want to work with some concepts.. you could also say that a hexagon is just a box with the corners cut off and the triangles that are missing are the equilateral right triangles with a hypotenuse of 10 . and since 2 pieces of those triangles make a square.. you can subtract two squares of that size from the bigger box that the hexagon fits into. this is a long way to figure this out but might be good for trigonometry practice :)
it will also be 734.8463288..... see if you can work that out :)
Thee questionn is beloww
Given:
[tex]m\angle ABC=60[/tex]
To find:
The [tex]m\angle ADC[/tex].
Solution:
In circle B, [tex]\angle ABC[/tex] is central angle and [tex]\angle ADC[/tex] is inscribed angle from two points A and C.
According to central angle theorem, central angle is always twice of inscribed angle.
[tex]m\angle ABC=2(m\angle ADC)[/tex] [Central angle theorem]
[tex]60=2(m\angle ADC)[/tex]
Divide both sides by 2.
[tex]\dfrac{60}{2}=m\angle ADC[/tex]
[tex]30=m\angle ADC[/tex]
Therefore, [tex]m\angle ADC=30[/tex].
The value of y varies directly with the value of x. When y = 18, x = 3.
What is the value of x when y = 54?
Answer:
9
Step-by-step explanation:
y is 6 times x, so if you divide 54 by 6, you get 9. Hope this helps :)
Nate has $50 to spend at the grocery store. he fills his shopping cart with items totaling $46 at checkout he willhave to pay 6% sales tax on all items in the cart. Does he have enough money to buy everything in his cart?
Answer:
Yes
Step-by-step explanation:
This is becuase 46 x 1.06= 48.76, thats less than $50.
Answer:
yes
Step-by-step explanation:
tax will be $2.76 therefore it will come up to $48.76
Kevin and his children went into a restaurant and he bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each drink costs $2.25. He bought 3 times as many hotdogs as drinks.
Answer:
He bought 6 hotdogs and 2 drinks
Step-by-step explanation:
System of Equations
Kevin and his children went into a restaurant and bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each drink costs $2.25.
To solve the system of equations, we'll call the variables:
x = number of hotdogs
y = number of drinks
The first condition yields the equation:
4.50x + 2.25y = 31.50 [1]
It's also known he bought 3 times as many hotdogs as drinks, thus:
x = 3y [2}
Substituting [2] in [1]:
4.50(3y) + 2.25y = 31.50
Operating:
13.5y + 2.25y = 31.50
15.75y = 31.50
y = 31.50/15.75
y = 2
And
x = 3*2 = 6
He bought 6 hotdogs and 2 drinks
Find the size of the angle 2 x
Answer:
Given - Angles measure 2x , X and 3x
To find - Measures of 2x
Solution -
2x + X = 180° ( forming linear pair )
3x = 180°
x = 180/3
x = 60°
2x = 2 × 60 = 120°
Answer:
120°
plz give brainlist
Step-by-step explanation:
since 2x and x form a straight angle you get the equation
2x + x = 180
combine like terms
3x = 180
devide by 3
x = 60
evaluate 2x
2(60) = 120
Express as a fraction or a mixed number
1 1/2%
Answer:
5 and 1/2
Step-by-step explanation:
Simplify the expression 12 a to B minus AAA +582B minus to a B minus 4AB2 minus 6AB plus to a plus 3AB
Question:
Simplify:
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Answer:
[tex]17a^2b - 4ab^2 - 10a + ab[/tex]
Step-by-step explanation:
Given
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Required
Simplify
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Open brackets
[tex]12a^2b-8a+5a^2b-2ab-4ab^2+6ab-2a-3ab[/tex]
Collect Like Terms
[tex]12a^2b + 5a^2b - 4ab^2 - 8a - 2a + 6ab - 3ab- 2ab[/tex]
[tex]17a^2b - 4ab^2 - 10a + ab[/tex]