12/24
Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.
Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24
Step Three: Add our new fractions: 3/24+8/24= 12/24
Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten
I hope I've help!
A 7% acid solution will be mixed with a 15% acid solution. 20 L of a 12% acid solution needs to be made.
a) Use the varialbes defined in part a to create a system of linear equations that models the given situation. SHOW YOUR WORK .
b) How many litres of each solution are needed? SHOW YOUR WORK *
c) Verify the solution. SHOW YOUR WORK *
Answer:
see below
Step-by-step explanation:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
.07r + .15 y = (r+y) .12
r+y = 20
y = 20-r
.07r + .15 (20-r) = (20) .12
0.07r+0.15(20-r)=2.4
.07r+ 3 - .15r = 2.4
-.08r = 2.4-3
-.08r = -.6
Divide by-.08
r =7.5 Liters of the 7%
y = 20-7.5
y = 12.5 L of 12%
Check
.07 *7.5 + .15 (12.5) =20*.12
.525+1.875=2.4
2.4=2.4
Please answer this correctly without making mistakes
Answer:
1/8
Step-by-step explanation:
3/8-1/8-1/8=1/8
Which expression is equivalent to the expression –6.4 – 12 + 4.6?
The answer is -13.8.
Hope this helps!
A can of lemonade holds one-third of a litre. How many litres are there in 100 can
Answer:
33 Litres
Step-by-step explanation:
Which solution value satisfies the inequality equation x – 5 ≤ 14?
Answer:
Any value that has x less than or equal to 19 is a solution
Step-by-step explanation:
x – 5 ≤ 14
Add 5 to each side
x – 5+5 ≤ 14+5
x ≤ 19
Any value that has x less than or equal to 19 is a solution
Answer:
[tex]\boxed{x\leq 19}[/tex]
Step-by-step explanation:
[tex]x-5\leq 14[/tex]
[tex]\sf Add \ 5 \ on \ both \ sides.[/tex]
[tex]x-5+5 \leq 14+5[/tex]
[tex]x\leq 19[/tex]
What function type does the table of values represent?
A) Linear
B) Exponential
C) Quadratic
D) Can't be determined
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|c|}x&y&x^2&3x^2\\---&---&---&---\\1&3&1^2&3*1^2=3\\2&12&2^2&3*2^2=12\\3&27&3^2&3*3^2=27\\4&48&14^2&3*4^2=48\\5&75&5^2&3*5^2=75\\\end{array}\\\\\\\boxed{y=3x^2\ the\ function\ is\ quadratic.}[/tex]
A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 3.74 mm
Answer:
0.0090483
Approximately = 0.00905
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 3.74
μ is the sample mean = population mean = 4 mm
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 100
σ = 1.1/√100
σ = 1.1/10 = 0.11
z = (3.74 - 4) / 0.11
z = -2.36364
Using the z score table to determine the probability,
The probability that the average thickness of the 100 sheets is less than 3.74 mm
P(x<3.74) = 0.0090483
Approximately = 0.00905
Using the normal distribution and the central limit theorem, it is found that there is a 0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means for size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean thickness of 4 mm, thus [tex]\mu = 4[/tex].Standard deviation of 1.1 mm, thus [tex]\sigma = 1.1[/tex].Sample of 100, thus [tex]n = 100, s = \frac{1.1}{\sqrt{100}} = 0.11[/tex].The probability is the p-value of Z when X = 3.74, then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.74 - 4}{0.11}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a p-value of 0.0091.
0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.
A similar problem is given at https://brainly.com/question/14228383
Help me with this please #17
9514 1404 393
Answer:
C. symmetric with respect to the origin
Step-by-step explanation:
A graph must pass the vertical line test to be called the graph of a function. No function will ever be symmetrical with respect to the x-axis, because that would mean it fails the vertical line test.
An even function is symmetrical about the y-axis. An even function has the characteristic that ...
f(-x) = f(x) . . . . an even function
An odd function is symmetrical about the origin. An odd function has the characteristic that ...
f(-x) = -f(x)
__
The given function is f(x) = -1/x. Then the value of f(-x) is ...
f(-x) = -1/-x = 1/x = -f(x)
The given function is an odd function, so is symmetrical about the origin.
is -2.75 an integer?
Answer:
yes
Step-by-step explanation:
every negative any positive number is an integer
Answer:
Step-by-step explanation:
No. Integers do not have fractions in them.
-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer
PLEASE ANSWER ASAP!!!
Fill in the box for the missing numerator in the set of equivalent expressions in the picture
Answer options are also shown in picture
any unrelated answer will be reported
Answer:
A. 14z - 28
Step-by-step explanation:
simplify z² - 3z
a. z(z - 3)
the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)
this means the numerator must also be multiplied by (z - 2)
14 x (z - 2) = 14z - 28
hope this helps :)
In recent years, the interest rates on home mortgages have declined to less than 6%. However, a
recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit
cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level
of significance, is it reasonable to conclude the mean rate charged is greater than 14%?
Answer:
Yes it is reasonable to conclude the mean rate charged is greater than 14%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.14[/tex]
The sample size is [tex]n = 10[/tex]
The sample mean is [tex]\= x = 0.1564[/tex]
The standard deviation is [tex]\sigma = 0.01561[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o: \mu = 0.14[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.14[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]
[tex]t = 3.322[/tex]
Now the p-value obtained from the z-table is
[tex]p-value = P(t > 3.322) = 0.00044687[/tex]
Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that the mean rate charged is greater than 14%
What is the domain of this graph?
Answer:
the domain is all real numbers
Andrea is buying fruit for a fruit salad. Strawberries cost $2 a pound, and blueberries cost $6 a pound. She plans to buy at least 5 pounds of berries and spend no more than $30. Which of the following is a possible combination for the number of pounds of berries she can buy?
6 pounds of strawberries and 1 pound of blueberries
I did the quiz
square with side 4 is dilated by 7
Answer:
196 in/cm/m²
Step-by-step explanation:
Given that the scale factor is a : b , then the area factor is a² : b² Here the scale factor is 1 : 7 , thus area scale factor is 1² : 7² = 1 : 49 That is the area of the dilated square is 49 times the original square. area of dilated square = 4 × 49 = 196 in/cm/m²
URGENT, PLEASE HELP ! (2/5) - 50 POINTS - ! please no wrong answers for points. ! Which scatter plot represents the data?
Answer:
A has the points plotted correctly
Step-by-step explanation:
We need to plot the data
A has the points plotted correctly
B has the point ( 10,5) plotted on (9,5)
C is missing (-6,-5)
D is missing (-6,-5) and has (-2,1) instead of (-2,-1)
Answer:
A.
Step-by-step explanation:
It would be very helpful to write the points individually from the data. Take the x value and place it with its corresponding y value:
(1,4) ; (2,2) ; (-2,-1) ; (-2,-6) ; (5,-4) ; (-6,-5) ; (10,5)
Now find the graph that has each of these points. You can write these down and cross them out if you find them on the graph, and once you find the graph where all of these points are crossed out, that's the correct graph.
The correct graph is A.
:Done
Solve this problem:
5X +8 = 53
5X + 8 = 53
5X = 53 - 8
X = 45 / 5
X = 9
Answer:
X=9
Step-by-step explanation:
5X+8=53
To solve this we need to make X the subject of the equation that means X should be alone on one side of the equation. Taking the following steps
5X=53-8
5X=45
X=45/5
X=9
Plz help me solve need help
Answer:
t=1, u=-2, w=-2
Step-by-step explanation:
please help asap
Addition prop of equality
subtraction prop of quality
multiplication prop of equality
Division prop of equality
simplifying
distrib prop
Answer:
multiplication prop of equality, (multiplying both sides by 6)
simplifying, (not distrib prop as there is no parentheses)
Addition prop of equality, (adding 18 to each side)
simplifying
Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.
Answer:
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
Step-by-step explanation:
The rules for linear transformations are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".
Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.
The appropriate choice of description is ...
b) the graph of g(x) is horizontally stretched by a factor of 3
Answer:
B
Step-by-step explanation:
Correct on Plato
I think of number I add 14 to the number and multiply the result by 3 if my final answer is 51 what number did I think of
Answer:
-1
Explanation:
Let the number be x.
Then the equation will be:
3(x+18) = 51
=> 3x + 54 = 51
=> 3x = 51 - 54
=> 3x = -3
=> x = -3/3
=> x = -1
So, the number you thought of is -1.
Answer:
The number is 3.
Step-by-step explanation:
[tex]3(14+x)=51\\42+3x=51\\3x=9\\x=3[/tex]
Digits to write five hundred seven billion,six hundred forty million,seven hundred forty-two thousand,seventy two
A general wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out ?
If you want to form a square of 7500 soldiers, the side of the square must be [tex]\sqrt{7500}\approx86.6[/tex] soliders.
But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.
That number is 7396 which when square rooted gives 86 soliders on the side.
Subtract 7396 from 7500 and get how many soliders were left out,
[tex]7500-7396=\boxed{104}[/tex]
Hope this helps :)
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Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of w
sailors. She receives a delivery of 4 tons of wood each day. The deliveries can con
afterwards the weather is too bad to allow them. Overall, she wants to build enou
least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
tons
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This question is incomplete.
Complete Question
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
280 tons of wood.
Step-by-step explanation:
From the above question:
To make 1 ship = we require 40 tons of wood.
1 ship = can accommodate 300 sailors.
Step 1
If :
300 sailors = 1 ship
2100 sailors = y ships
Cross Multiply
300 × y ships = 1 ship × 2100 sailors
y ships = 2100 / 300
y ships = 7
Hence, 2100 sailors can occupy 7 ships.
Step 2
We are told in the question that:
Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
If:
1 ship = 40 tons of wood
Since 7 ships can accommodate 2100 sailors,
7 ships =
7 × 40 tons of wood = 280 tons of wood.
Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.
To the nearest tenth, what is the area of the figure shown in the image? Segment BF is a line of symmetry of the pentagon ABCDE. Use 3.14 for pi. A. 30.3 in.^2 B. 33.0 in.^2 C. 39.3 in.^2 D. 48.3 in.^2 Please include ALL work! <3
Answer:
C, 39.3 in²
Step-by-step explanation:
Lets first find the area of the rectangle part of the house.
To find the area of a rectangle its base × height.
So its 6×4=24 in².
Now lets find the area of the top triangle.
Area for a triangle is (base × height)/2.
The height is 3 inches, because its 7-4. While the base is 6 inches.
(6×3)/2=9 in².
To find the area of the half circle the formula, (piR²)/2.
The radius of the circle is 2 because its half of the diamter which is 4.
(pi2²)/2=6.283 in².
Now we just need to add up the area of every part,
24+9+6.283=39.283in²
The mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days. Suppose that the rain pattern is Normally distributed. what is the probability of raining if the number of days are more than 23?
Answer:
The probability of raining if the number of days is more than 23 is 0.0668.
Step-by-step explanation:
We are given that the mean number of days to observe rain in a particular city is 20 days with a standard deviation of 2 days.
Let X = Number of days of observing rain in a particular city.
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean number of days = 20 days
[tex]\sigma[/tex] = standard deviation = 2 days
So, X ~ Normal([tex]\mu=20, \sigma^{2} = 2^{2}[/tex])
Now, the probability of raining if the number of days is more than 23 is given by = P(X > 23 days)
P(X > 23 days) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{23-20}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)
= 1 - 0.9332 = 0.0668
The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.
The rate at which an assembly line workers efficiency E (expressed as a percent) changes with respect to time t is given by E'(t) = 75 - 6t, where t is the number of hours since the workers shift began. Assuming that E(1) = 92, find E(t).
By the fundamental theorem of calculus,
[tex]E(t)=E(1)+\displaystyle\int_1^t E'(u)\,\mathrm du[/tex]
So we have
[tex]E(t)=92+\displaystyle\int_1^t(75-6u)\,\mathrm du[/tex]
[tex]E(t)=92+(75u-3u^2)\bigg|_1^t[/tex]
[tex]E(t)=20 + 75 t - 3 t^2[/tex]
2. If the diameter of a circle is 2V10, what is the area
of the circle.
Please help me how to do no 5
Answer:
-864
Step-by-step explanation:
The determinant of a matrix product is the product of the determinants. The determinant of a transpose is the same as the determinant of the original. Hence ...
[tex]|AB^5C^T|=(4)(-2)^5(\frac{1}{4})=-32[/tex]
The multiplication of an n×n matrix by a scalar 'a' multiplies its determinant by a^n, so the desired determinant is ...
[tex]|3AB^5C^T|=3^3(-32) = \boxed{-864}[/tex]
Simplify -3(2w - 6) +4(w + 1)
Answer:
= -2w + 22
Step-by-step explanation:
-3(2w - 6) + 4(w+1)
= (-3*2w -3*-6) + (4*w + 4*1)
= -6w + 18 + 4w + 4
= -6w + 4w + 18 + 4
= -2w + 22
NEED HELP NOW I have 31 stamps total. I have 4 more 1-cent stamps than 8-cent stamps and twice as many one cent stamps as 12 cent stamps. If my stamps are worth $1.78 altogether how many one cent stamps do I have?
x = number of 1-cent stamps
y = number of 8-cent stamps
z = number of 12-cent stamps
We have 31 stamps all together, so x+y+z = 31.
"I have 4 more 1-cent stamps than 8-cent stamps" means we have the equation x = y+8. Whatever y is, add 8 to it to get x. Solve for y to get y = x-8.
You also have "twice as many one cent stamps as 12 cent stamps", so x = 2z. Solving for z gets you z = 0.5x
-------------
x+y+z = 31
x+x-8+z = 31 ... y replaced with x-8
x+x-8+0.5x = 31 ... plug in z = 0.5x
2.5x-8 = 31
2.5x = 31+8
2.5x = 39
x = 39/2.5
x = 15.6
Your teacher made a typo somewhere because we should get a positive whole number result for x (since x is a count of how many 1-cent stamps we have).
The number of one-cent stamps is 14.
Total stamps = 31
We have three types of stamps: 1-cent stamps, 8-cent stamps, and 12-cent stamps.
The person has 4 more 1-cent stamps than 8-cent stamps.
The person has twice as many 1-cent stamps as 12-cent stamps.
We have to make equations with the given above statement.
Consider,
1-cent stamp = A
8-cent stamp = B
12-cent stamp = C
4 more 1-cent stamps than 8-cent stamps: A = 4 + B.
A = 4 + B
B = A - 4..........(1)
Twice as many 1-cent stamps as 12-cent stamps: A = 2C.
A = 2C
C = A/2...............(2)
Total number of stamps = 31
A + B + C = 31................(3)
Putting (1) and (2) in (3)
we get,
A + ( A - 4 ) + A / 2 = 31
A + A - 4 + A / 2 = 31
2A - 4 + A / 2 = 31
2A + A / 2 = 31 + 4
(4A + A) / 2 = 35
4A + A = 35 x 2
5A = 70
A = 70 / 5
A = 14
Thus the number of 1-cent stamps is 14.
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