Probability is the quantitative measure of the likelihood of the occurrence of an event.
It is mathematically expressed as:
[tex]P=\frac{number\text{ of selected outcome}}{number\text{ of total outcome}}[/tex]We can decide to call the set of numbers below 7 "A".
A = {1, 2, 3, 4, 5, 6}
|A| = 6
We call the universal set, the set containing all the numbers rollable "U"
|U| = 12
Our probability is therefore:
[tex]undefined[/tex]DIVIDE THE POLYNOMIALS USING LONG METHOD. QUESTION 1 Divide (x4 + 2x³ - 13x² - 38x - 24) + (x + 4)
Answer:
QUESTION 1: x³ - 2 x² - 5 x - 18 remainder 48
5 men take 28 days to build a boat. Assuming the men work at the same rate, calculate the number of men needed to build a boat in 20 days.
given f(x)=3x-1 and (f∘g)(x)=x^2, find g(x)
The value of g(x) is [tex]\frac{x^{2} }{3x-1}[/tex] of a function f(x)=3x-1 and (f∘g)(x)=[tex]x^{2}[/tex] .
As the composite equation is [tex]f(X)=3x^{}-1[/tex]
[tex](FOG)= x^{2}[/tex]
As [tex](FOG) =f(gx^{})\\[/tex]
∴ [tex]3x-1(gx)=x^{2}[/tex]
⇒ [tex]gx=\frac{x^{2} }{3x-1}[/tex]
How to solve the Equation of (fog)?(fog)(x) = f(g(x)) is pronounced "f of g of x" or "f constructed with g of x." Keep in mind that the letters in each expression for the composition remain in the same order.
A composite function is a fog. G(x) function is in f(x) function if (fog) is true. (Gof) indicates that f(x) function is in g(x) function.
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Please see attached question
The probability that the student is a sixth-grader or rated good grades as most important is (168 / 335) + (135 / 335) = 0.904
What is the probability?Probability is used to determine the odds that a random event would happen. The odds that the event would happen lies between 0 and 1.
The probability that the student is a sixth-grader or rated good grades as most important = (number of sixth-graders / total number of students) + (students who rates good grades as most important / total number of students)
(168 / 335) + (135 / 335) = 303 / 335 = 0.904
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Solve for U.
-3 + 2u + 6 = -8u - 7
What does U equal?
Answer:
U = -1
Step-by-step explanation:
Answer:
u=-1
Step-by-step explanation:
-3 + 2u + 6 = -8u - 7
2u-3+6=-8u-7
2u+3=-8u-7
we will collect like terms
2u+8u=-7-3
10u=-10
u=-1
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if luna adds 1/2 cups of flour to a mixing bowl for a recipe 5 times, how much flour has she added?
Answer:
10 cups
I hope this helps, have a great day/night!
Evaluate. Write your answer as a whole number or as a simplified fraction.
4^-2 / 6^3
Answer:
Your answer is [tex]\frac{1}{864}[/tex]
Step-by-step explanation:
[tex]4^{-1}[/tex] ÷ [tex]6^{3}[/tex] [tex]= 0.0011574074[/tex] or [tex]\frac{1}{864}[/tex]
Which list shows the values in order from least to greatest?
0-0.5
√(0.5)
0-0.5
20% √/0.5
○ 20% |−0.5| √/0.5
○ = √/0.5 |−0.5| 20%
20%
The values in order from least to greatest are 0-0.5,√(0.5),20%,20% √/0.5,√/0.5 |−0.5| 20%. we eliminate 0-0.5 because the value is two times in the option.
What is the percentage?Percentage represents a proportion or a fraction of a whole, expressed as a portion of 100. It is commonly denoted by the symbol "%" (percent), which literally means "per hundred."
According to the given information:
The values in the list are:
0-0.5 = a range of values from 0 to 0.5, inclusive
√(0.5) ≈ 0.7071
20% = 0.2
20% √/0.5 = 0.2 * √(0.5) ≈ 0.1414
√/0.5 |−0.5| 20% = √(0.5) * |−0.5| * 0.2 ≈ 0.0707
Therefore, the correct list in order from least to greatest is:
0-0.5
√(0.5)
20%
20% √/0.5
√/0.5 |−0.5| 20%
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A grocery store sells steak for $3.10 per pound. To feed a family, you need 2.14 lbs. of steak. How much do you pay in total
choose if the following statement is true or false: correlation is sensitive to the scale of the data; however, covariance is not sensitive to the scale of the data
Correlation is not sensitive to the scale of the data; however, covariance is sensitive to the scale of the data, so the statement is false.
Covariance is a term used in statistic and regression analysis. Covariance shows how two variables differ.
Covariance is affected by the change in scale, for example if all the value of one variable is multiplied by a constant and all the value of another variable are multiplied, by the same or another constant all together, then the covariance is automatically changed.
Correlation is also a term used in regression analysis and statistics. Correlation shows how two variables are related and therefore not influenced by the change in scale.
Hence the given statement is False
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A model rocket reaches a maximum height of 2000 feet above ground and begins to
descend at a rate of 75 feet per second. Which equation models the height above
ground, y, of the model rocket, x seconds after it reaches its maximum height?
The equation which is best representing the height above ground, y, of the model rocket and x seconds after it reaches the maximum height is 75x + y = 2000.
The height above ground, y, of the model rocket, x seconds after it reaches its maximum height can be represent by a linear equation,
The maximum height is 2000 feet, after this the rocket starts to descend with a rate of 75 feet per second.
Let us say that when the rocket starts descending, our time is started from zero,
So, on plotting these points of graph, we can one point, (0,2000).
The rate of descend is the slope m of the graph,
m = -75 ft/s
We are taking it negative because height is decreasing with time,
We can use the point slope form of equation of line,
It says, if a line passes through (a,b) and has slope m. Then the equation of line is,
(y-b) = m(x-a)
So, our line is passing through (0,2000) and has slope -75 ft/s.
So, equation of the line is,
(y-2000) = -75(x-0)
75x + y = 2000.
This above equation of line is representing the relation between the height above ground and time of the model rocket.
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Nina bought 1.725 pounds of pecans and 1.83
pounds of almonds. She also bought twice as many
pounds of walnuts as pecans. How many more
pounds of walnuts did she buy than almonds?
Nina bought 3.45 pounds of walnut.
Nina bought 1.62 pounds more walnut than almonds
Quantity of pecan bought by Nina = 1.725 pounds
Quantity of almonds bought by Nina = 1.83 pounds
The process of comparison of numbers establishes the similarities between two numbers and determines which number is greater, smaller, or equal to another number.
Quantity of walnuts = 2*Quanitity of pecans
= 2*1.725
= 3.45 pounds
So, she bought 3.45 pounds of walnut
Pounds of walnuts bought more than the almonds = Quantity of walnuts bought by Nina - Quantity of almonds bought by Nina
= 3.45 - 1.83
= 1.62 pounds
So, she bought 1.62 pounds more walnuts than almonds
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acceptance sampling is a statistical method used to monitor the quality of purchased parts and components. to ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows one defect.
Let X represent the number of defects.
When n=20 and p = 0.01,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.01)^0 * (1-0.01)^(20) + 20C1 * (0.01)^1 * (1-0.01)^(20-1) = 0.9831
When n=20 and p = 0.02,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.02)^0 * (1-0.02)^(20) + 20C1 * (0.02)^1 * (1-0.02)^(20-1) = 0.9401
When n=20 and p = 0.05,
Likelihood = P(Acceptance) = P(X=0) + P(X=1)
= 20C0 * (0.05)^0 * (1-0.05)^(20) + 20C1 * (0.05)^1 * (1-0.05)^(20-1) = 0.7358
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If g :R → R is given by g(x) = x2 + 3 , find the function f such that (g. f) (x) = 4x2 + 3. A. 3x B. 4x C. 2x D. None of these
Given:
[tex]\begin{gathered} g(x)=x^2+3_{} \\ (g\circ f)(x)=4x^2+3 \end{gathered}[/tex][tex](g\circ f)(x)=g(f(x)[/tex]Let substitute one by one from the given options.
[tex]\begin{gathered} g(3x)=(3x)^2+3 \\ g(3x)=9x^2+3 \end{gathered}[/tex]3x is not the function f.
[tex]\begin{gathered} g(4x)=(4x)^2+3 \\ g(4x)=16x^2+3 \end{gathered}[/tex]4x is not the function f.
[tex]\begin{gathered} g(2x)=(2x)^2+3 \\ g(2x)=4x^2+3 \end{gathered}[/tex]2x is the function f.
[tex]f(x)=2x[/tex]Option C is the final answer.
I need to know how to rewrite the expression using the distributive property of multiplication over addition
Given the following expression:
[tex]\text{ 10(3 + 2)}[/tex]Rewriting this using the distributive property of multiplication over addition will be:
[tex]\text{ 10(3) + 10(2)}[/tex]Therefore, the answer is letter B - 10(3) + 10(2)
12.8 = 4v solve for v
Answer:
v=3.2
Step-by-step explanation:
12.8 = 4v
v= 12.8/4 isolate the variable and divide.
v= 3.2 Answer
141% as a mixed or whole number
Answer:
1 41/100
Step-by-step explanation:
Answer:
141/100 (Already in simplest form). As a mixed number, it is: 1 41/100
Step-by-step explanation:
Suppose a batch of steel rods produced at a steel plant have a mean length of 187 millimeters, and a variance of 64.
If 416 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than
0.65 millimeters? Round your answer to four decimal places.
Please help!
6|x - 8| ≤ 12
x ≤ ?
x ≤ ?
Answer: 10, 6
Step-by-step explanation:
[tex]6|x-8| \leq 12\\\\|x-8| \leq 2\\\\-2 \leq x-8 \leq 2\\\\6 \leq x \leq 10[/tex]
Ahouseis13feettall.Itsshadowis40feetlongatthesametimetheshadowofanearbybuildingis340feetlong.Findtheheightofthebuilding.
the red triangle is the building
the black triangle is the house
x is the height of the building
we have a problem of Tales triangles semblants so we can use this equalities
[tex]\begin{gathered} \frac{x}{340}=\frac{13}{40} \\ x=\frac{13(340)}{40}=110.5\text{ f}eet \end{gathered}[/tex]the height of the building is 110.5 feet
Is y=6x proportional?
y = 6x is proportional.
Proportionality between x and y is defined if there is a constant of proportionality 'k' such that y = kx.
So here, the constant of proportionality in y = 6x is 6.
This equation also means that y varies directly with respect to x and then 6 is the constant of variation.
That is, y is directly proportional to x.
Then a change in y implies a corresponding change in x in the same direction as that of y.
If x increases, then y also increases and if x decreases, then y also decreases.
These changes are related to the constant of proportionality 6.
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At noon the temperature was 45°F. At
7 A.M. the temperature was 17°E.colder.
The temperature at 7 P.M. Was 4°F .
warmer than at 7 A.M. What was the.
temperature at 7 P.M.?
The temperature at 7 P.M is 32 °F.
What is a temperature in fahrenheit?Fahrenheit temperature scale, scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.
Given that,
Temperature at noon = 45 °F
At 7 A.M. the temperature was 17°F colder = 45-17
= 28 °F
The temperature at 7 P.M. Was 4°F warmer than at 7 A.M
= At 7 A.M. the temperature was 17°F colder + 4°F
= 28+4
= 32 4°F
Hence, The temperature at 7 P.M is 32 °F.
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What is the y intercept of the function shown?
Answer:
-2
Step-by-step explanation:
The line passes through the y-intercept at the point (0, -2)
Question 5 (05.05)Based on the graph, what is the initial value of the linear relationship?
4
1) Examining that graph, we can see that this is a decreasing function, due to the line direction. And that the initial value is the y-intercept.
2) Hence, the initial value is 4. Notice that all values after that goes decreasing for y.
The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas. Write the ratios as fractions in simplest form. Ratio (red to blue) of the perimeters: Ratio (red to blue) of the areas: pleas help
Answer:
5/8 and 25/64
What is the slope of the line that passes through the points (-4, -10)) and (-7, -19)
? Write your answer in simplest form.
Answer:
Slope = 3
Step-by-step explanation:
(-4, -10) and (-7, -19)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -19 - (-10) -19 + 10 -9
m = ------------ = ---------------- = ------------- = -------- = 3
x₂ - x₁ -7 - (-4) -7 + 4 -3
I hope this helps!
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{-19}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-19}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{-7}-\underset{x_1}{(-4)}}} \implies \cfrac{-19 +10}{-7 +4} \implies \cfrac{ -9 }{ -3 } \implies 3[/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}{(-10)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-4)}) \implies y +10= 3 (x +4) \\\\\\ y+10=3x+12\implies {\Large \begin{array}{llll} y=3x+2 \end{array}}[/tex]
Find 3 consecutive numbers whose sum is 132
Answer:
Integer 1- 43
Integer 2- 44
Integer 3- 45
Step-by-step explanation:
x+(x+1)+ (x+2)=132
3x+3-3=132-3
3x=127
/3 /3
x=43
x+1=44
x+2=45
An item costs y dollars and then a 20% discount is applied. Create an expression that could represent the price of the item after the discount. Explain your reasonin
An expression that could represent the price of the item after the discount is 0.8y.
Given that, an item costs y dollars and then a 20% discount is applied.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Cost price = $y and Discount percentage = 20%
Discount = 20% of y
= 20/100 × y
= 0.2y
The price of the item after the discount = y-0.2y
= 0.8y
Therefore, an expression that could represent the price of the item after the discount is 0.8y.
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Use your equation to complete the table. grams of fish 1500 number of calories 3000
Answer:
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
5+5=10
Find the value of x and XZ if Y is between X and Z, XY = 19, YZ = 2x+5,
and XZ = 6x + 12.
The values of x and XZ, calculated by the given equations are 3 and 30 respectively.
What is a equation?
The equals sign indicates that two expressions in an equation are equal. An equation is a mathematical formula. The meaning of the word equation and its cognates may change a bit depending on the language. An equation is defined as including one or more variables in French, as opposed to English, where an equation is defined as any well-formed formula that consists of two expressions connected by the equals sign.
Given information (and equations) in the question:
Y is between X and Z,
XY = 19,
YZ = 2x+5,
XZ = 6x+12
Since the question say Y is between X and Z, it means:
XY + YZ = XZ
Substituting the values in this equation by the values given in the question:
19 + 2x + 5 = 6x + 12
24 - 12 = 4x
x = 3
putting the value of x in the given equation:
XZ = 6x + 12
XZ = 6(3) + 12
XZ = 18 + 12
XZ = 30
Hence, the values of x and XZ are 3 and 30 respectively.
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