Answer:
x=5
Step-by-step explanation:
To find the mean, add up all the numbers and then divide by the number of numbers
(3+ 2+x+ 11+ 13+14)/6 = 8
Multiply each side by 6
(3+ 2+x+ 11+ 13+14) = 48
Combine like terms
43+x = 48
Subtract 43 from each side
x =5
Answer:
[tex]\huge \boxed{{x=5}}[/tex]
Step-by-step explanation:
The mean is the average value of a data set.
[tex]\displaystyle \sf mean = \frac{sum \ of \ terms}{number \ of \ terms}[/tex]
The mean is given solve for x.
[tex]\displaystyle 8 = \frac{3+2+x+11+13+14}{6}[/tex]
Multiply both sides by 6.
[tex]\displaystyle 8(6) = \frac{3+2+x+11+13+14}{6} \times (6)[/tex]
[tex]48=3+2+x+11+13+14[/tex]
Combine the numbers on the right side of the equation.
[tex]48=x+43[/tex]
Subtract 43 from both sides.
[tex]48-43=x+43-43[/tex]
[tex]5=x[/tex]
If a square has a side of length 3, then it’s area is 9. This square has a side of length 3, so it’s area is 9. Is it valid or invalid?
Answer:
Yes it is valid
Step-by-step explanation:
A square is a geometric shape which is also known as a Quadrilateral. This means that it has 4 sides.
For a square, it's 4 sides are equal to one another or we can put it in other words as the length of the 4 sides of a square are congruent to one another.
From the above question, we are asked that:
"If a square has a side length of 3, it's area is 9. Is it valid or invalid?"
The above statement is valid. This is because, the formula for the Area of a Square is given as
L × L = L²
Where L = Side length = 3
Area = 3 × 3 = 3²
Area = 9
Therefore, the statement is valid.
On a plane trip, baggage over 40 pounds is charged at the rate per pound of 1% of the one-way fare. The charge for a bag weighing 52 pounds on a trip where the one-way fare is $98 is:
Answer:
$11.76 is the charge for bag.
Step-by-step explanation:
Given:
One way fare = $98
Weight of bag = 52 pounds
Rate per pound Charges on baggage over 40 pounds = 1% of the one-way fare
To find:
Charge for bag = ?
Solution:
Pounds more than 40 pounds = Weight of baggage - 40 pounds
[tex]\Rightarrow 52-40 = 12\ pounds[/tex]
Charges on extra baggage = 1% of one-way fare multiplied by pounds more than 40.
Here one way fare is $98.
So, charges on extra baggage will be:
[tex]1\%\ of\ 98 \times (52-40) \\\Rightarrow 1\%\ of\ 98\times (12)\\\Rightarrow \dfrac{1}{100}\ of\ (98 \times 12)\\\Rightarrow \dfrac{1}{100}\times (98 \times 12)\\\Rightarrow \bold{\$11.76}[/tex]
So, the charge for the baggage is $11.76.
which one is irrational?
Basically everything but choice C
==========================================
Explanation:
sqrt is shorthand for square root
sqrt(4) = 2 = 2/1 showing that sqrt(4) is rational. We can write it as a fraction of two whole numbers, where 0 is not in the denominator.
-------
In contrast, we cannot write sqrt(2), sqrt(3), or sqrt(5) as a fraction of two whole numbers. Using your calculator, note how
sqrt(2) = 1.4142135623731
sqrt(3) = 1.73205080756888
sqrt(5) = 2.23606797749979
all of those decimal expansions go on forever without any pattern, which is a sign that those numbers are irrational. If they were rational, then a pattern would repeat at some point or the decimals would terminate at some point.
Answer:
a, b, d are irrational
Step-by-step explanation:
root 2 = 0.414.....
root 3 = 0.732.....
root 5 = 2.236.....
Hope this helps.....
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What is the 8th term of the sequence? −16, 24, −36, 54, ... −729/8 2187/8 −2187/8 729/8
Answer:
The answer is
[tex] \frac{2187}{8} [/tex]Step-by-step explanation:
The sequence above is a geometric sequence
For an nth term in a geometric sequence
[tex]A(n) = a ({r})^{n - 1} [/tex]
where n is the number of terms
r is the common ratio
a is the first term
From the question
a = - 16
To find the common ratio divide the previous term by the next term
That's
r = 24/-16 = -3/2 or -36/24 = - 3/2
Since we are finding the 8th term
n = 8
Substitute the values into the above formula
That's
[tex]A(8) = - 16 ({ - \frac{3}{2} })^{8 - 1} [/tex][tex]A(8) = - 16 ({ - \frac{3}{2} })^{7} [/tex][tex]A(8) = - 16( - \frac{2187}{128} )[/tex]We have the final answer as
[tex]A(8) = \frac{2187}{8} [/tex]Hope this helps you
How do you graph y=2/3x-4
━━━━━━━☆☆━━━━━━━
▹ Answer
You can use a graphing calculator.
▹ Step-by-Step Explanation
Attached is a screenshot.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
See explanation and picture attached
Step-by-step explanation:
We can break down this expression into it's core components:
Since the constant here is -4, the y intercept is -4.
Since the value we are multiplying x by is [tex]\frac{2}{3}[/tex], the slope is [tex]\frac{2}{3}[/tex]. This means for every time we go horizontal 3 units, the line increases by 2.
The graph is attached.
Hope this helped!
Solve for u.
– 22 = -8u + 6(u-7)
Simplify your answer as much as possible.
Step-by-step explanation:
- 22 = -8u + 6(u-7)
-22 = -8u + 6u - 42
8u - 6u = 22 - 42
2u = -20
u = -20/2
u = -10
Answer:
[tex] \boxed{ \boxed{ \mathrm{ \bold{ \blue{ - 10}}}}}[/tex]Step-by-step explanation:
[tex] \mathrm{ - 22 = - 8u + 6(u - 7)}[/tex]
Distribute 6 through the parentheses
⇒[tex] \mathsf{ - 22 = -8u + 6u - 42}[/tex]
Collect like terms
⇒[tex] \mathrm{ - 22 = - 2u - 42}[/tex]
Swap the sides of the equation
⇒[tex] \mathrm{ -2u - 42 = - 22}[/tex]
Move constant to R.H.S and change it's sign
⇒[tex] \mathrm{ - 2u = - 22 + 42}[/tex]
Calculate
⇒[tex] \mathrm{ - 2u = 20}[/tex]
Divide both sides of the equation by -2
⇒[tex] \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }[/tex]
Calculate
⇒[tex] \mathrm{u = - 10}[/tex]
Hope I helped!
Best regards!
Tony knew there was a solution to his math problem in one of four textbooks. He got some information from his classmates about it: Andy: "The solution is in either book 1 or 2"; Billy: "The solution is in either book 3 or 4"; Charlie: "The solution is in book 4"; Danny: "There is no solution in book 3". Emily helped Tony by saying that only one of his classmates was right, and the other three were mistaken. Which book has the solution in it?
Answer:
Charlie is the right person.
Step-by-step explanation:
The right person is Charlie because he was sure of what he was saying. Others were not sure making them mention two textbooks while Danny didn't answer the question Tony asked because he was talking about the one that doesn't have the solution.
Which of the following is a point-slope equation of a line that passes through the points (-1,4) and (8,2)
Answer:
y - 2 = -2/9( x - 8)
Step-by-step explanation:
hope this helps
let me know if u need more help
Answer:
y - 2 = -2/9(x - 8) or y - 4 = -2/9(x + 1)
Step-by-step explanation:
find slope first
(2 - 4)/(8 - -1) = -2/9
y - 2 = -2/9(x - 8)
Simplify the radical
Answer:
Step-by-step explanation:
[tex]\sqrt[3]{54c}=\sqrt[3]{3*3*3*2c} =3\sqrt[3]{2c}[/tex]
Complex numbers
[ = square root symbol
-[-64
How would I find this?
[tex]-\sqrt{-64}=-\sqrt{8^2\cdot (-1)}-8\sqrt{-1}=-8i[/tex]
The table shows the relationship between the cost of renting a car from the Wrecko Car Rental Company and the number of days for the rental. Draw a scatter plot and find an equation for the line of best fit. Use the equation to determine the cost of renting a car for 20 days. Days Cost 1 $44 2 $67 3 $90 4 $113 7 $182 10 $251
Answer:
The cost of renting the car for 20 days is $481
Step-by-step explanation:
The table of values can be formed as follows;
Day, Cost
1, $44
2, $67
3, $90
4, $113
7, $182
10, $251
From the given values and the scatter plot, there is a straight line relationship between the cost and the number of days of rental of a car.
The line of best fit is therefore a straight line and from the constant increase in cost ($23) for each extra day of rental, it is possible to find the slope, m, of the data as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
(x₁, y,) and (x₂, y₂) can be taken as (1, $44) and (3, $90) respectively to give;
[tex]Slope, \, m =\dfrac{90-44}{3-1} = \dfrac{46}{2} = 23 \ as \ stated \ above[/tex]
The equation in slope and intercept form is therefore, y - 44 = 23×(x - 1), which gives;
y - 44 = 23·x - 23
y = 23·x - 23 + 44 = 23·x + 21
The cost of renting the car for 20 days is then;
10×23 + 21 = $481
The cost of renting the car for 20 days = $481.
3kg of rump steak costs £42 adel buys 4kg of rump steak work out how much adel pays
Answer:
The answer is £ 56Step-by-step explanation:
In order to find the amount Adel paid we use ratio and proportion
3kg of rump steak = £ 42
Therefore
4kg of rump steak = [tex] \frac{4 \times 42}{3} [/tex]
We have the final answer as
£ 56Hope this helps you
Answer:
£56
Step-by-step explanation:
since 3kg costs £42
1kg will be £42/3 which will be equal to £14
4kg will cost £14×4 which will be £56
Solve the inequality for x.
7 > 2x+9
Answer:
x<-1Step-by-step explanation:
[tex]7 > 2x+9\\\\\mathrm{Switch\:sides}\\\\\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\2x+9-9<7-9\\\\2x<-2\\\\\frac{2x}{2}<\frac{-2}{2}\\\\x<-1[/tex]
whats the factored form of 6x 2 - 8x - 8 = 0
Answer:
2(x -2)² = 0
Step-by-step explanation:
2(x² - 4x - 4) = 0
2(x -2)² = 0
x = 2
Answer:
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
The factored form of [tex]6x^2-8x-8=0[/tex] is [tex]2(3x-2)(x+2)=0[/tex]
Step-by-step explanation:
[tex]6x^2-8x-8=0[/tex]
The way the quadratic equation was given, we can't have a factored form in the format: [tex](ax-b)(cx+d)[/tex]
First, divide both sides by 2
[tex]3x^2-4x-4=0[/tex]
Now, it is about thinking. From the equation, we will get something in the format: [tex](ax-b)(cx+d)[/tex]
Let's expand this: [tex](ax-b)(cx+d) = acx^2+adx-bcx-bd[/tex]
From here, we can give some values for those variables, based on the quadratic equation [tex]3x^2-4x-4=0[/tex]:
[tex](3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}[/tex]
Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.
[tex](3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}[/tex]
Therefore,
[tex](3x-2)(x+2)=3x^2-4x-4[/tex]
But we are not ready yet!
This is the factored form of [tex]3x^2-4x-4=0[/tex], to get the factored form of the problem equation, just multiply the factored form we got by 2.
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
A)40%
B)45%
C)5%
D)10%
Answer:
A) 40%
Step-by-step explanation:
25% of yards have 6-8 trees; 10% of yards have 8-10 trees; 5% of yards have more than 10 trees. So, a total of 25% +10% +5% = 40% of yards have 6 trees or more. If a yard is randomly chosen, the probability it will have 6 or more trees is 40%.
The family size bottle of sunscreen holds 12121212 fluid ounces (fl oz)(\text{fl oz})(fl oz)(, start text, f, l, space, o, z, end text, )of sunscreen. The regular bottle holds 75%75\%75%75, percent less.How many fewer fluid ounces does the regular bottle of sunscreen hold?
Answer:
The regular bottle holds 9 fl oz less
Step-by-step explanation:
Given
Family Size = 12 fl oz
Required
Determine the size held less by the regular bottle
From the question, we have that the regular bottle holds 75% less;
[tex]Regular\ Size = 75\% * Family\ Size[/tex]
Substitute 12 fl oz for Family Size
[tex]Regular\ Size =75\% * 12\ fl\ oz[/tex]
Convert percentage to fraction
[tex]Regular\ Size = \frac{75}{100} * 12\ fl \oz[/tex]
[tex]Regular\ Size = \frac{75 * 12\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = \frac{900\ fl\ oz}{100}[/tex]
[tex]Regular\ Size = 9\ fl\ oz[/tex]
Hence, the regular bottle holds 9 fl oz less
Find x. A. 22 B. 113–√ C. 222–√ D. 113√3
Answer:
x = 31.12
Step-by-step explanation:
First find the base (hypotenuse) of the smaller triangle (the isosceles triangle): Its three sides are 11, 11 and b. b can be found using the Pythagorean Theorem: b^2 = 11^2 + 11^2 = 242. Then b = √242, or b = approximately 15.56.
b (which is approximately 15.56) is the shorter leg of the large (right) triangle. The trig function needed to solve for x is the cosine:
adjacent side
cos 60 degrees = ----------------------
hypotenuse,
15.56
which becomes (1/2) = ------------
x
Solving this for x, we get: x = 2(15.56) = 31.12
determine if the following set of ordered pairs represents a quadratic function explain (5,7),(7,11),(9,14),(11,18)
Answer:the pairs are not a quadratic eqation
Step-by-step explanation:
The differences between the differences of the y value are not consistent
The set of ordered pairs (5,7),(7,11),(9,14),(11,18) does not represents a quadratic function
What is a function?A relation is a function if it has only One y-value for each x-value.
Given,
The set of ordered pairs
(5,7),(7,11),(9,14),(11,18)
We have to determine whether the (5,7),(7,11),(9,14),(11,18) is quadratic function or not.
Start by representing the function as an x-y table
x:- 5 || 7 || 9 || 11
y:- 7 || 11 || 14 || 18
The difference between the y values is not same
11-7=4
14-11=3
18-14=4
For the function to be quadratic, the above difference must be the same and since they are not, then the function does not represent a quadratic function.
Hence, the set of ordered pairs (5,7),(7,11),(9,14),(11,18) does not represents a quadratic function
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243 as a power of 3
Answer:
243 as a power of 3
= 3^5
=243
How much water will be in each bottle if the total amount of water is equally divided among the bottles?
Answer:
D
Step-by-step explanation:
add everything up devide by 3
Answer:
C. 1/2 liter
Step-by-step explanation:
First, find the total amount of water by multiplying the amounts of water by the number of bottles, then adding all 3 values together:
1/4(1) = 1/4 liter
1/2(4) = 2 liters
3/4(1) = 3/4 liter
1/4 + 2 + 3/4 = 3 liters
There are 6 bottles in total, if we count the number of dots.
To find how much water would be in each bottle if the water was equally divided, divide the total amount of water by the number of bottles:
3 / 6 = 1/2
= 1/2 liter
Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$. [tex]Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[/tex]
Answer:
[tex]x =-5\ - \sqrt{8}[/tex]
Step-by-step explanation:
Given
[tex]x^2 + 10x + 25 = 8[/tex]
Required
Find the smallest value of x
[tex]x^2 + 10x + 25 = 8[/tex]
Expand the expression on the right hand side
[tex]x^2 + 5x + 5x + 25 = 8[/tex]
Factorize
[tex]x(x+5)+5(x+5) = 8[/tex]
[tex](x+5)(x+5) = 8[/tex]
[tex](x+5)^2 = 8[/tex]
Take Square root of both sides
[tex]\sqrt{(x+5)^2} = \±\sqrt{8}[/tex]
[tex](x+5) = \±\sqrt{8}[/tex]
Remove bracket
[tex]x+5 = \±\sqrt{8}[/tex]
Subtract 5 from both sides
[tex]x+5-5 =-5\± \sqrt{8}[/tex]
[tex]x =-5\± \sqrt{8}[/tex]
[tex]x =-5\ + \sqrt{8}[/tex] or [tex]x =-5\ - \sqrt{8}[/tex]
Comparing both values of x;
The smallest value of x is
[tex]x =-5\ - \sqrt{8}[/tex]
In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$. If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?
nCr(20, 2) = 190 ways of selecting 2 from 20
nCr(10, 1) = 10 ways of selecting 1 from 10
To find the over all probability of winning,
Calculate the Harmonic Mean (19) and divide by 2
Equivalent to
1/ (1//190 + 1/10) =9.5
So the probability is 1/9.5 = 2/19.
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hour is desired. Past studies suggest that a population standard deviation of hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Complete question:
One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.28 hours is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy.
Answer:
111 students
Step-by-step explanation:
Given the following :
Margin of Error (E) = 0.28
Population standard deviation (sd) = 1.5
Recall:
Margin of Error(E) = Z * (sd/√n)
Taking a confidence interval of 95%
The Z value at a 95% confidence interval is 1.96
Plugging our values, we have :
Margin of Error(E) = Z * (sd/√n)
0.28 = 1.96 * (1.5/√n)
0.28 = 2.94 / √n
√n × 0.28 = 2.94
√n = 2.94 / 0.28
√n = 10.5
Square both sides to obtain n
n = 10.5^2
n = 110.25
standard form of 6,32,94,000
Answer:
6.3294✖️10^7
Step-by-step explanation:
To find the statdard form, you place the decimal after the largest unit, int his case 6.
Then you write down all the numbers except for "0".
This becomes:
6.3294
Then, you add the multiplying sign, and count how many digits are there after 6, and in this case, there are 7, so you add the power "7" after 10.
6.3294✖️10^7
Hope this helped!
Have a nice day:)
Juana wants to use the numbers 8, 6, 3,
and 2 to create her 4-digit ATM code.
She will not repeat any digits. How many
different codes could she create?
Geraldo recently saw a newspaper ad for a new version of his laptop. The projected price is $400.00, and the laptop will be out on the market in about one year. Geraldo wants to purchase a new laptop but is wondering if he should wait a year. With 2.5% inflation, what amount would he pay to purchase a laptop today that is the same value as the one he saw in the ad?
Answer:
The answer would be $410.00.
Cheers,
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The price he will have to pay now for laptop will be $390.
What is cost prize ?
The prize at which the good and services have been bought is known as cost prize.
here, the given information is :
The projected price is $400.00, and the laptop will be out on the market in about one year with 2.5% inflation.
Now, if he pay to purchase a laptop today that is the same value as the one he saw in the ad then the cost price he will have to pay will be 2.5% of $400 less that is:
cost price of laptop = $400 - 2.5& x 400
cost price of laptop = 97.5% x $400
cost price of laptop = $390
Therefore, the price he will have to pay now for laptop will be $390.
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Write an equation for a parabola with a focus of (1,-2) and a directrix of y=6
Answer:
y = - [tex]\frac{1}{16}[/tex](x - 1)² + 2
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-1)^2+(y+2)^2^}[/tex] = | y - 6 |
Square both sides
(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )
(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )
(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )
(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )
16y = - (x - 1)² + 32 ( divide all terms by 16 )
y = - [tex]\frac{1}{16}[/tex] (x - 1)² + 2
On a coordinate plane, triangle A B C is shown. Point A is at (negative 2, negative 4), point B is at (2, negative 1), and point C is at (3, negative 4). Triangle ABC is an isosceles triangle in which side AB = AC. What is the perimeter of triangle ABC? 5 + StartRoot 10 EndRoot units 10 + StartRoot 10 EndRoot units 10 StartRoot 10 EndRoot units 50 units
Answer:
B, 10+ /10 units
Step-by-step explanation:
Avani is building a rectangular play area. The length of the play area is 7.5 meters. The width of the play area is 5.3 meters. If she wants to cover the area in foam, how much foam does she need to buy? Due to the accuracy of the tape measure Avani used, the amount of foam needed to cover the play area is A.39 B.39.75 C.39.8 D.40
Answer:
Step-by-step explanation:
Area of the rectangle length x width
7.5x5.3 =39.75 sq.m
so, B is the correct answer.
Please help ! First one to give correct answer gets brainliest!
Answer:
(4x+1)²
Step-by-step explanation:
