The expected mean for a sample of 150 women is 168.5 pounds.
What is expected mean?Expected mean can be defined as the mean weight of a number . Based on the given data we were told that the mean weight of the us women was 168.5 pounds which implies that the expected mean is 168.5 pounds.
The formula for expected mean is :
E ( X ) = μ = ∑ x P ( x )
Where:
x = values of the random variable X
P(x) = Corresponding probability
∑ =Sum of all products xP(x)
μ = mean
Therefore the expected mean is 168.5 pounds.
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Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian also paid $11.40 for granola bars and a box of tissues.
If Sebastian filled 10 gallons of gas, how much did he spend in all at the gas station?
A. $3.92
B. $24.71
C. $40.50
D. $116.91
If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.
How is the total amount determined?Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.
We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.
Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.
The cost of gas per gallon = $2.91
The number of gallons of gas bought = 10
The total cost of gas = $29.10 ($2.91 x 10)
The total cost of granola bars and tissues = $11.40
The total amount spent = $40.50 ($29.10 + $11.40)
Thus, mathematically, Sebastian spent C. $40.50 at the gas station.
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The digit 7 appears twice in
the product.
Answer:
The numbers in which 7 appears are. 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 87, 97, 107. So, counting all. ∴ Number of times 7 appears = 21
Find the difference between the sums to ten terms of the AP and GP whose first two terms are-2 and 4.
The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
What is Arithmetic Progression and Geometric Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
First term = -2
Second term = 4
A)
For Arithmetic Progression
First term a = -2
Second term = 4
Common difference d = Second term - First term
= 4 - ( -2 )
= 6
And Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
n = 10 terms
Sₙ = ( 10/2 ) [ (2x- 2) + ( 9 ) x 6]
Sₙ = 5 [ -4 + 54 ]
Sₙ = 5 x 50
Sₙ = 250
Therefore , Sum of first 10 terms of an AP is 250
B)
For Geometric Progression
First term a = -2
Second term = 4
Common ratio = Second term / First term
= 4 / -2
= -2
And Sum of first n terms of an GP : Sₙ = a( 1 - rⁿ ) / ( 1 - r )
n = 10
Sₙ = 2( 1 - ( -2 )¹⁰ ) / 1 - ( -2 )
Sₙ = 2 ( 1 - 1024 ) / 3
Sₙ = ( 2 x (-1023) ) / 3
Sₙ = 2 x ( - 341 )
Sₙ = - 682
Therefore , Sum of first 10 terms of an GP is -682
The difference between the sum of first 10 terms of AP and GP is GP - AP
= -682 - 250
= -932
Hence , The difference between the sum of first 10 terms of AP and GP where the first term and second term is 2 and 4 respectively is -932
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How do I solve this question
Answer:
the answer is down there
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y> 2x+4
x+y≤6
The graph of inequalities equation on coordinate plane is given below ↓↓↓
Difference between equality and inequality equations
Both mathematical phrases, equality and inequality , are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequalities equation is ,
y> 2x+4
x+y≤6
so, the graph is ↓↓↓
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Is 4.5 greater, less than, or equal to 4 and 1/2
Answer:
equal to
Step-by-step explanation:
4 + 1/2= 4+ 0.5= 4.5
4.5=4.5
Which ordered pair is a solution of the equation? 2 x + 4 y = 6 x − y 2x+4y=6x−y
The solution to the equation given as 2x + 4y = 6x − y has the ordered pair of (3, 4)
How to determine the ordered pair of the solution?From the question, we have the following equation that can be used in our computation:
2x+4y=6x−y
Solving further, we need to collect the like terms
So, the equation becomes
2x - 6x = -4y - y
Next, we evaluate the like terms in the above equation
So, we have the following representation
-4x = -3y
Divide both sides by -3
The equation becomes
x = 3/4y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x = 3/4 * 4
Evaluate the products
x = 3
So, we have
x = 3 and y = 4
Express as ordered pairs
(x, y) = (3, 4)
Hence, the ordered pair of the solution is (3, 4)
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3. Simplify the expression below.
√-100-2√√-16
A. -12i
B. -2i
C. 12i
D. 2i
Which ratio is equivalent to 9 : 180?
Answer:
18:360 is the correct answer
“on the following checking account record, enter the figures and add or subtract them to keep the running total correct”
will mark brainliest and 100 points :))
The running total is $95.27.
There are two types of records, Active and Inactive. There are also two major classifications, Vital and Important.
Why is record keeping important?In order to create reliable financial statements, you need good records. These consist of balance sheets and income (profit and loss) statements. These statements might assist you in managing your business and dealing with your bank or creditors.He opened the account with $299.88. He subsequently wrote many cheques, from which you deduct the sum of 299,88.
He deposited a check, thus 299.88-90.48= 209.40, 209.40 - 65.00= 144.40, and then he added $381.33 to 144.40 to get 525.73.
then you need to deduct more since he wrote more checks.
Consequently, 525.73-54.47=471.26, and 471.26-375.99=95.27, giving him a balance of $95.27.
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The current total is $95.27. Active and Inactive records are the two types of records. There are two major classifications as well: Vital and Important.
Why is record keeping important?Good records are required to create reliable financial statements. Balance sheets and income (profit and loss) statements are included. These statements may help you manage your company and deal with your bank or creditors.
Good Records are documents that contain recorded data that demonstrate the effectiveness of the quality management system, regardless of format or feature.
Given,
He deposited into the account = $299.88
He then wrote a number of cheques, from which you deduct = $299,88.
He deposited a check, thus 299.88 - 90.48
= 209.40, 209.40 - 65.00
= 144.40
and then he added $381.33 to 144.40 to get 525.73.
then you need to deduct more since he wrote more checks.
Consequently,
525.73 - 54.47
=471.26
and 471.26-375.99
= 95.27
As a result, The gives him a balance of $95.27.
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Alex house is 15 blocks from school. Carlene lives 7 blocks from Alex's house. Which equation represents the location of Carlene's house in relation to the school?
|x+7|=15
|x-7|=15
|x+15|=7
|x-15|=7
Answer:
Answer is b
Step-by-step explanation:
Because
|x-7|=15--->x=15+7, x=2211. Corey bought 25 gallons of gas to fill up his pickup truck. He paid for the part of the total with a $25 gift card and was left owing $26. How much did he pay per gallon for the gas?
Answer:
I believe that the answer is $2.04, per gallon.
Step-by-step explanation:
I added the $25 he paid with the gift card, and the $26, which was $51 that Corey paid in total. Corey had gotten 25 gallons and they want to figure out how much he paid for each gallon. So we take the total he spent divided by the number of gallons he had gotten. So 51/25=2.04
Hope this helps!!!!
Last year, Leila opened an investment account with $8800. At the end of the year, the amount in the account had decreased by 6%.
Answer:
The new value is $8,272
Step-by-step explanation:
8800 x (1 - 0.06) = 8272
Eugene has a collection of 140 pet rocks. Of these rocks, 35% are sedimentary, 40% are igneous, and the rest are metamorphic. How many are metamorphic?
Answer:
25% or 35 rocks.
Step-by-step explanation:
To find this answer, simply add up 40% and 35% to get 75%. Now, 100% is the most we can have. So, 100 - 75 = 25%.
To find even more in depth of exactly how much 25% of 140 is, we can simply move the decimal point from 25 over twice to get 0.25. The term "of" means multiply:
0.25 x 140 = 35 rocks.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Does anyone know the answer to this problem?
It is a scalene triangle .
What is a scalene triangle?A triangle called a Scalene Triangle in geometry is one with equally spaced-apart sides. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices.acc to our quesion-
all the sides of triangle are unequal
if all sides are unequal ,it is called scalene triangle.
hence,It is a scalene triangle .
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Seven of the angles of a decagon have measures whose sum is 1220. Of the remaining 3 angles, exactly two are complementary and exactly two are supplementary. Find the measures of these three angles.
The measures of the remaining three angles of the decagon are 40, 50 and 130 degrees.
How to find angles of a decagon?A decagon simony means a polygon with 10 sides. In a regular decagon, the interior angles add up to 1440 degrees, and the exterior angles add up to 360 degrees.
Complementary angles sum up to 90 degrees while supplementary angles sum up to 180 degrees.
Therefore,
1440 - 1220 = 220
Let the angles be a, b and c.
Therefore,
a + b + c =220
a + b = 90
b + c = 180
Hence,
a = 220 - 180
a = 40°
b = 90 - 40
b = 50°
c = 180 - 50
c = 130°
The angles are 40°, 50° and 130°.
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How would you investigate the complaints from renters who are
unhappy about their monthly rents?
What statistical measurement would be used?
To investigate the complaints from renters who are unhappy about their monthly rents, the mean rents can be collected
The statistical measurement that would be used is the ANOVA.
What is a mean?A dataset's mean (also known as the arithmetic mean, as opposed to the geometric mean) is the sum of all values divided by the total number of values. It is the most widely used measure of central tendency and is frequently referred to as the "average."
ANOVA is an abbreviation for Analysis of Variance. It is a statistical test invented by Ronald Fisher in 1918 that has been in use ever since. Simply said, ANOVA determines whether or not there are statistical differences between the means of three or more independent groups. The most basic type is one-way ANOVA. To know of the meansare the same, the ANOVA can be used.
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The green basilisk enclosure will include a rectangular pond in one corner. The width of the
pond will be 3 inches less than the width, w, of the enclosure.
W-3
The area of the water's surface is given by this expression: w² - w - 6.
Question
Question 1
Factor the area expression, w² - w - 6.
Replace the values of A and B to write the expression in factored form.
(w - A) (w + B)
After factorization we get the two terms ( w - 3 ) ( w + 2 )
And the values of A and B as 3 and 2 respectively .
That is A = 3 and B = 2.
The given expression is w² - w - 6.
This question can be calculated easily by middle term split
First step is to multiply the first and the last term
which will give us - 6
thus now we have to look for two number which when either added or subtracted will give us - 1
Thus we can write it as :
w² - 3 w + 2 w - 6
Now take the terms which are common
and we will get
w ( w - 3 ) + 2 ( w - 3 )
( w - 3 ) ( w + 2 )
Thus if we compare it with (w - A) (w + B)
we will get the values of A and B as
3 and 2 respectively .
That is A = 3 and B = 2
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Solve: √x-4= -2
a) x=2
b) x=8
c) There is no solution.
d) x=0
Answer: There is no solution
Step-by-step explanation:
The formatting of the question isn't clear, but I'll still explore both possibilities. If the square root is only applied to x, we can solve for the variable by adding 4 to both sides and then squaring both sides, which would give us 4. Since that is not an answer choice, it means the square root applies to x-4. With this problem, we square both sides right away. That gives us x=0, but plug 0 back into the original equation. Doing so gives us the square root of -4, which is not possible with real numbers, only with imaginary numbers.
What should be added to 5/6 to get 41/24
Answer: 26/24
Step-by-step explanation:
First we have to convert 5/6 with a denominator of 24 so 6 times what makes 24, that is 4 & whatever you do with the denominator, you have to do it with the numerator. So 5 times 4 is 20, the new fraction is 20/24. Now, we need to find what we need to add with 20/24 to get 41/24, so we subtract 20/24 from 41/24 & that is 21/24. We can check if it's correct by adding both 21/24 and 20/24 & that makes 41/24.
Pedro walks 3/8 of a mile in a 1/4 of an hour. How many miles does he walk in an hour
Answer:
S=3/8 miles
T=1/4 hour
V=S/T = 3/8 ÷ 1/4 = (3×4)÷8 = 3/2 miles in an hour
Convert 0.8 grams to grains
Answer:
12.3459 grains
Step-by-step explanation:
Answer:
12.346 grains
Step-by-step explanation:
for an approximate result, multiply the mass value by 15.432
( which is basically 0.8 times 15.432)
how many groups 1/4 are in 3/4
There are 3 1/4's in 3/4, hope this helps.
Answer: 3
Step-by-step explanation: since they are the same denominator it is basically asking how many 1s go in 3
Write log₂ A as a natural logarithm.
Answer:
ln A / ln 2
Step-by-step explanation:
Using the change of base rule: ln A / ln 2
If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 0.1 when x = 0.2
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em} \textit{we know that} \begin{cases} y=0.1\\ x=0.2 \end{cases} \\\\\\ 0.1=k(0.2)\implies \cfrac{0.1}{0.2}=k\implies 0.5=k\hspace{5em}\boxed{y=0.5x}[/tex]
Factor 64+ 60. Write your answer in the form a(b + c) where a is the GCF of 64 and 60
Whats ?? Also right an addition expression to get the same answer Answer ASAP
Answer:
p=-10
Step-by-step explanation:
-10-20=-30
Subtracting a negative from a negative will result in a higher negative, the same can be said for -10-20. Removing 10 from -20 will result in a lower answer. This is 20.
what’s the x intercept of a table with 22,27,32
The x-intercept of the table of values is 12 or (12, 0).
How to Find the X-Intercept of a Table?To find the x-intercept of a table that represents a linear relationship between x and y, first write the equation that models the table.
To write the equation, first find the slope (m) using two pairs of values, say, (22, 36) and (27, 54)
Slope (m) = (54 - 36)/(27 - 22)
Slope (m) = 18/5
Write the equation that represents the table of values by substituting (a, b) = (22, 36) and m = 18/5 into y - b = m(x - a):
y - 36 = 18/5(x - 22)
To find the x-intercept, substitute y = 0 into the equation, y - 36 = 18/5(x - 22) to find the value of x:
0 - 36 = 18/5(x - 22)
-36 = 18/5(x - 22)
5(-36) = 18(x - 22)
-180 = 18(x - 22)
-180/18 = x - 22
-10 = x - 22
-10 + 22 = x
12 = x
x = 12
The x-intercept is 12 or (12, 0).
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Choose from the drop-down menus to match the trigonometric expression with its value
The values that match the various trigonometric identity are;
1) sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀ = 1
2) cos 13 cos 47 + sin 13 sin 47 = 0.5
3) sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π = 0
How to solve Trigonometric Identities?Trigonometric identities are defined as the equations that involves the trigonometric functions that are true for every value of the variables involved.
1) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos π/₁₀ + cos²/₅π sin π/₁₀
Applying the trigonometric identity above, gives us;
sin(²/₅π + π/₁₀)
= sin(5π/10)
= sin(π/2)
= 1
2) We know that the trigonometric identity sin(A + B) is expressed as;
cos(A + B) = cosAcosB − sinAsinB.
We are given;
cos 13 cos 47 + sin 13 sin 47
Applying the trigonometric identity above, gives us;
cos(13 + 47)
= cos 60
= 0.5
3) We know that the trigonometric identity sin(A + B) is expressed as;
sin(A + B) = sinAcosB + cosAsinB
We are given;
sin²/₅π cos ⁸/₅π + cos²/₅π sin ⁸/₅π
Applying the trigonometric identity above, gives us;
sin(²/₅π + ⁸/₅π)
= sin(¹⁰/₅π)
= sin(2π)
= 0
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In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
Answer:cap
Step-by-step explanation:C A P