we have:
P(X > 6) < 0.0668
We can use the standard normal distribution to find probabilities for a normal distribution with mean u and standard deviation 2. Let Z = (X - u)/2 be the standard normal variable corresponding to X.
(A) Since f(6) > f(16), we have P(X < 6) > P(X < 16). Using the standard normal distribution, we can write this as:
P(Z < (6 - u)/2) > P(Z < (16 - u)/2)
Multiplying both sides by -1 and using the symmetry of the standard normal distribution, we get:
P(Z > (u - 6)/2) < P(Z > (u - 16)/2)
Looking up the standard normal distribution table, we can find the values of the right-hand side probabilities for different values of the argument. For example, if we use a table with z-scores and look up the probability corresponding to z = 1.5, we find that P(Z > 1.5) = 0.0668 (rounded to four decimal places).
Therefore, we have:
P(X > 6) < 0.0668
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What would be correct in this distribution math
The area under the curve between the two values is (d) 0.0750
How to determine the area?From the table, we have:
P(z = -0.45) = 0.3264
P(z = -0.67) = 0.2514
The area under the curve is calculated as:
Area = P(z = -0.45) - P(z = -0.67)
So, we have:
Area = 0.3264 - 0.2514
Evaluate the difference
Area = 0.0750
Hence, the area under the curve between the two values is (d) 0.0750
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30 times 4 times the ten power of three
Answer [tex]=7085760[/tex]
Step-by-step explanation:
Use order of operations and evaluate the exponent first
[tex]30*4*3^{10}[/tex]
[tex]30*4(59049)[/tex]
[tex]30*236192[/tex]
[tex]=7085760[/tex]
Answer: 1920
Step-by-step explanation:
4x4x4=64
64x30=1920
7. A kids furniture warehouse ships small tables and chairs in certain combinations to consumers in the United States. The weight of 3 tables and 5 chairs is 62.5lbs and the weight of 3 tables and 2 chairs is 52lbs. Create and solve a system of equations to find out how much each table and chair weighs.
The weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.
Simultaneous equationLet
Weight of tables = xWeight of chairs = yCost of 3 tables and 5 chairs is 62.5lbsCost of 3 tables and 2 chairs is 52lbs3x + 5y = 62.5
3x + 2y = 52
Subtract the equation to eliminate x5y - 2y = 62.5 - 52
3y = 10.5
y = 10.5/3
y = 3.5 lbs
Substitute y = 3.5 into
3x + 2y = 52
3x + 2(3.5) = 52
3x + 7 = 52
3x = 52 - 7
3x = 45
x = 45/3
x = 15 lbs
Therefore, the weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.
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The graph below represents the data from Part A. Use the data from Part A to correctly label the graph. Drag the labels to their appropriate locations on the graph.
The correct labels are matched to their appropriate locations on the graph as shown in the image attached below.
What is a graph?A graph refers to a type of chart that's used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
In this exercise, you're required to drag the correct labels to their appropriate locations on the graph as shown in the image attached below.
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Part A:
According to a life cycle analysis of the U.S. food system conducted by the University of Michigan, the U.S. consumes 13.9 quads of mostly fossil fuel energy to produce 1.75 quads of food energy annually. A quad is a unit of energy equal to 1 quadrillion (10¹⁵) British thermal units (BTUs). One quad is equal to the energy of 183 million barrels of petroleum.
Please help me
Marking brainliest for smart answer
Answer:
58%
Step-by-step explanation:
47/81 x 100%
≈ 58%
Hope it helps : )
How long must a ladder be to reach the top of a 12-foot wall if the bottom of the ladder is placed 3 feet from the base of the wall
Answer: 13 feet
Step-by-step explanation:
Answer:
12.37 ft
Step-by-step explanation:
Hypotenuse(c): the ladder
Cathetus: the wall (a=12) and the floor (b=3)
Equation:
[tex]c^{2} =a^{2} +b^{2}[/tex]
[tex]c^{2} =(12)^{2}+ (3)^{2} =144+9[/tex]
[tex]c^{2} =153[/tex]
[tex]c=\sqrt{153}[/tex]
[tex]c=12.37[/tex]
The ladder is 12.37 feet long
Hope this helps
For a right triangle with one leg = 3.24 cm and a hypotenuse = 7.16 cm, find the length of the missing leg
Answer:
[tex]a=\sqrt{40.768}[/tex]
Step-by-step explanation:
Given a leg and a hypotenuse we can find the third side by substituting the known values using Pythagorean theorem, let the unknown be a.
[tex]a^2+3.24^2=7.16^2[/tex]
Now all we must do is solve for a:
[tex]a^2+3.24^2=7.16^2\\a^2+10.4976=51.2656\\a^2=40.768\\a=\sqrt{40.768}[/tex]
A walking path across a park is represented by the equation y=-3x - 3. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 6). Identify the equation that represents the new path.
OA. y=-3x-6
O B. y=x+7
OC. y=3x+15
O D. y=-x+5
166
10
MAR
FREN
10-
10-
10
Answer:
y = (1/3)x + 7
Step-by-step explanation:
The general structure form of a line in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.
The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.
m = 1/3
x = -3
y = 6
y = mx + b <----- Slope-intercept form
6 = (-3)(1/3) + b <----- Insert values
6 = -1 + b <----- Multiply -3 and 1/3
7 = b <----- Add 1 to both sides
Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.
y = (1/3)x + 7
Find 20% of 150
A. 20
B. 130
C. 120
D. 30
For this, multiply 150 × .20 = 30
Therefore, 20% of 150 is 30.
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Simplify (9y²-x² )÷ (xy+3y²)
Step-by-step explanation:
[tex] \cfrac{(9y²-x² )}{ (xy+3y²)}[/tex][tex] \cfrac{3 {}^{2} (y) {}^{2} - x}{3(y {})^{2} + xy } [/tex][tex]3 {}^{2 - 1} y {}^{2 - 2 - 1} - x {}^{2 - 1} [/tex][tex]3 y { }^{ - 1} - x[/tex][tex] \cfrac{3}{y} - x[/tex]Therefore,the answer is [tex] \cfrac{3}{y} - x[/tex].
[Some of the steps I didn't show,try by yourself,to find!]Linda is filling the mold above with water and freezing it for an ice project. If a = 8 cm and b = 7 cm, what will be the volume of the frozen figure?
The volume of the frozen figure is 736 cm³
Volume of a prismFrom the question, we are to determine the volume of the frozen figure
In the given diagram,
The volume of the frozen figure = a³ + 1/2(a²b)
From the given information,
a = 8 cm
b = 7 cm
∴ Volume of the frozen figure = 8³ + 1/2(8² ×7)
Volume of the frozen figure = 512 + 1/2(448)
Volume of the frozen figure = 512 + 224
Volume of the frozen figure = 736 cm³
Hence, the volume of the frozen figure is 736 cm³
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If a side of the field is 9/10 mile and 1/2 mile what is the length of the field
Answer:
The field is 1 and 4/10 mile long.
Step-by-step explanation:
If I understand the question:
(1/2) + (9/10) =
(5/10) + (9/10) = (14/10)
(14/10) is 1 and 4/10
The field is 1 and 4/10 mile long.
Look at the rectangle and the square:
a rectangle pqrs and square lmno are drawn side by side. the length sr of the rectangle is labeled as 16 inches, and the width qr is labeled as 8 inches. the side lm of the square is labeled as 8 inches
ada says that the length of diagonal sq is two times the length of diagonal om.
is ada correct? justify your answer and show all your work. your work should state the theorem you used to find the lengths of the diagonals. (10 points) i will report you if you do it for the points!!!
Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.
For Rectangle PQRS:-
By Pythagoras Theorem, in right triangle PQS,
SQ² = PQ² + PS²,
or, SQ² = 8² + 16² sq. inches,
or, SQ² = 64 + 256 sq. inches,
or, SQ = √320 sq. inches,
or, SQ = 8√5 inches.
Thus, the length of diagonal SQ, of rectangle PQRS is 8√5 inches.
For Square LMNO:-
By Pythagoras Theorem, in right triangle LMO,
OM² = LM² + LO²,
or, OM² = 8² + 8² sq. inches,
or, OM² = 64 + 64 sq. inches,
or, OM = √128 sq. inches,
or, OM = 8√2 inches.
Thus, the length of diagonal OM, of square LMNO is 8√2 inches.
We know that 2*OM ≠ SQ, as 2*8√2 ≈ 8√5.
Thus, Ada is incorrect, as the length of diagonal SQ is not two times the length of diagonal OM. The theorem used is the Pythagoras Theorem.
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Use quadratic regression to find a function that does the following points.
(-1,-15), (1,-7), (6,-122)
Answer:
[tex]y = -x^{2} +4x-10[/tex]
Step-by-step explanation:
I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!
Complete the empty tables below with the correct values
Based on the information provided in the first table, we have the following angle and trigonometric function:
θ = 60°sin60 = √3/2cos60 = 1/2csc60 = 2/√3sec60 = 2cot60 = 1/√3How to complete the table of values?Based on the information provided in the first table, we have the following trigonometric function:
tanθ = √3
θ = tan⁻¹(√3)
θ = 60°.
In radians, we have:
θ = 60 × π/180
θ = 1.0472 radian.
sin60 = √3/2
cos60 = 1/2
csc60 = 2/√3
sec60 = 2
cot60 = 1/√3
Based on the information provided in the second table, we have the following trigonometric function:
θ = 30 × π/180
θ = 0.5236 radian.
sin30 = 1/2
cos30 = √3/2
tan30 = 1/√3
csc30 = 2
sec30 = 2/√3
cot30 = √3
Based on the information provided in the third table, we have the following trigonometric functions:
sinθ = √2/2 tanθ = 1
θ = sin⁻¹(√2/2) θ = tan⁻¹(1)
θ = 45°. θ = 45°.
In radians, we have:
θ = 45 × π/180
θ = 0.7854 radian.
cos45 = √2/2
csc45 = √2
sec45 = √2
cot45 = 1
Based on the information provided in the fourth table, we have the following trigonometric function:
sinθ = 1
θ = sin⁻¹(1)
θ = 90°.
θ = 90 × π/180
θ = 1.5708 radian.
cos90 = 0
tan90 = not defined
csc90 = 1
sec90 = not defined
cot90 = 0
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Trigonometry, please provide a simple explanation
Answer:
C
Step-by-step explanation:
cosecΘ = [tex]\frac{1}{sin0}[/tex] = [tex]\frac{2}{\sqrt{3} }[/tex] ( cross- multiply )
2sinΘ = [tex]\sqrt{3}[/tex] ( divide both sides by 2 )
sinΘ = [tex]\frac{\sqrt{3} }{2}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{\sqrt{3} }{2}[/tex] ) = 60°
Answer:
C. 60°
Step-by-step explanation:
by definition, cosec(θ) is the reciprocal of sin(θ)
In other words ,
[tex]\text{cosec} \left( \theta \right) =\frac{1}{\sin \theta }[/tex]
Then
[tex]\text{cosec} \left( \theta \right) =\frac{2}{\sqrt{3} }[/tex]
[tex]\Longleftrightarrow \frac{1}{sin \left( \theta \right) } =\frac{2}{\sqrt{3} }[/tex]
[tex]\Longleftrightarrow sin \left( \theta \right) =\frac{\sqrt{3} } {2}[/tex]
Then
θ = 60°
PLEASE HELP IM SO STUCK
If the graph of the line falls from left to right the slope is negative.
Slope = (y2 - y1)/(x2 - x1)
---> y = -2x + 3
On May 1 Geraldo Saldana opened a savings account that paid 3.5 percent
interest at Fulton Savings Bank with a deposit of $3,600. Ten days later he
deposited $3,000. Fourteen days later he deposited $5,000. No other deposits
or withdrawals were made. Six days later the bank calculated the daily interest.
Based on the amounts that Geraldo Saldana deposited in the month of May, the total simple interest comes to $18.98.
what amount of simple interest does Geraldo Saldana get?the simple interest earned can be found as:
= (3,600 x 3.5%/360 days x 30 days) + (3,000 x 3.5%/360 days x 20 days) x (5,000 x 3.5%/360 days x 6 days)
= 10.5 + 5.83 + 2.65
= $18.98
rest of the question is:
How much simple interest did his money earn?
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jordan bought a radio for $120.He paid for it with 2 coins and $5 bills.If there were half as many coins as bills, how many $2 coins were there and how many $5 bills were there
There are 20 $5 bills and 10 $2 coins.
How to find the number of $2 coins and $5 coins using equation?He bought a radio for $120. He paid for it with 2 coins and $5 bills.
let
the number of $5 bills = x
the number of $2 coins = y
Therefore,
y = 1 / 2 x
2y + 5x = 120
2(1 /2 x) + 5x = 120
x + 5x = 120
6x = 120
x = 120 / 6
x = 20
y = 1 / 2 × 20
y = 10
Therefore, there are 20 $5 bills and 10 $2 coins.
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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −32 + 150 − 1200, where x is the amount he charges per tree.
1. How much does he need to charge if he wants to break even?
2. How much does he need to charge if he wants to make a profit of $600?
Answer:
Addition form: x = 75 + √3 (675 − P) / 3
or
Subtract form: x = 75 − √3 (675 − P) / 3
Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x²?
O g(x)=-9(x + 1)²-7
Og(x) = 4(x-3)² +1
O g(x)=-3(x-4)²-6
Og(x)= 8(x-3)²-5
Answer:
Step-by-step explanation:
Discussion
A: incorrect. the minus turns the parabola upside down and you would get a maximum, not a minimum.
B: incorrect. The + 1 moves the parabola upwards not downwards.
C: incorrect. The - 3 turns the parabola upside down. You get a maximum, not a minimum.
D: correct. The parabola moves right (x - 3)^2 which anti intuitive, but it is correct. - 5 moves the parabola down. +8 the plus makes a minimum.
use the substitution method to solve the system of equaltions. choose the correct ordered pair. 2y+4x=18 and 2y-3x=4
The solution of the system of equation is x = 7 and y = 12.5.
How to solve equation by substitution?2y + 4x = 18
2y - 3x = 4
2y = 4 + 3x
y = 2 + 3 / 2 x
Hence, let's substitute the value of y in equation(1)
2( 2 + 3 / 2 x) + 4x = 18
4 + 3x + 4x = 18
4 + 7x = 18
7x = 14
x = 14 / 2
x = 7
2y - 3(7) = 4
2y - 21 = 4
2y = 25
y = 25 / 2
y = 12.5
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The two polygons are similar. Find the values of x and y.
Answer: [tex]x=11, y=9[/tex]
Step-by-step explanation:
Corresponding sides of similar figures are proportional, so:
[tex]\frac{x-2}{6}=\frac{15}{10}\\\\\frac{x-2}{6}=\frac{3}{2}\\\\x-2=9\\\\x=11[/tex]
[tex]\frac{y+3}{8}=\frac{15}{10}\\\\\frac{y+3}{8}=\frac{3}{2}\\\\y+3=12\\\\y=9[/tex]
Suppose the risk-free rate is 3.2 percent and the market portfolio has an expected return of 9.9 percent. the market portfolio has a variance of .0282. portfolio z has a correlation coefficient with the market of .18 and a variance of .3185. according to the capital asset pricing model, what is the expected return on portfolio z?
Beta = Correlation x (Variance of Z)^0.5 / (Variance of Market)^0.5
Beta = 0.18 x (0.3185)^0.5 / (0.0282)^0.5
Beta = 0.604927
CAPM equation:
Expected return = Risk free rate + Beta x (Market return - Risk free rate)
Expected return = 3.2% + 0.604927 x (9.9% - 3.2%)
Expected return = 7.25% is the answer.
Portfolio return refers to the return or loss realized on an investment portfolio that includes multiple types of investments. The portfolio is intended to provide returns based on the defined objectives of the investment strategy and the risk tolerance of the type of investor covered by the portfolio.
The basic formula for expected return is to multiply the weight of each asset in the portfolio by the expected return and then add up all these numbers. In other words, the expected return of a portfolio is a weighted average of the returns of the individual components.
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Can someone help me with these problems pleaseeee!!
Answer:
I have wrote just answer.
Find the missing side. Round your answer to the nearest tenth.
The length of the missing length in the triangle is 53.6 units
How to determine the length of the missing side?The given triangle is a right triangle.
Right triangles are triangles that have a measure of angle that is 90 degrees.
The missing side is x, and the value of x is calculated using the following sine rule
We have
sin(angle) = opposite/hypotenuse
This gives
sin(66) = 49/x
Divide both sides by sin(66)
1 = 49/x sin(66)
Multiply both sides by x
x = 49/sin(66)
Divide the expression
x = 53.6
Hence, the length of the missing length is 53.6 units
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Lines (1) and (2) are parallel. Find sides M
and N. Round your answer to the nearest
tenth.
P
A
M
(2)->
155⁰
N
Answer:
M = 4.5
N = 2.1
Step-by-step explanation:
angle p would be 25. 180 - 155 = 25
M = 5cos25 =4.5 rounded to the tenths place.
M = 5sin25 = 2.1 rounded.
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
•
1001
•
15
1001
10
143
O
133
143
Answer:
The chance of the committee being all boys is 28.57% or 29%
Classify the following function.
The function given can be classified as a function. That is option C.
What is a function in mathematics?Function can be defined as the expression that has both an x domain value and a y range value and it's being classified based on the quality of these values.
A function can be represented based on their roster forms.
Using the function equation given, f(X) = 10.2^2
Here, the first element is the domain or the x value and the second element is the range or the f(x) value of the function.
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For a population with an unknown distribution, the form of the sampling distribution of the sample mean is _____. Group of answer choices approximately normal for small sample sizes exactly normal for large sample sizes exactly normal for small sample sizes approximately normal for large sample sizes
For a population where the distribution is unknown, the sampling distribution of the sample mean will be b which is approximately normal for all sample sizes.
Given options regarding sample sizes.
We have to choose the correct option which shows the sample mean characteristics when the distribution is unknown.
Based on the central limit theorem the sampling distribution of the sample mean for either skewed variable ir normally distributed variable can be approximated given the mean and standard deviation.
The central limit theorem is said to be true when n greater than or equal to 30.
When n is greater than 30 ,z test is used, when n is less than 30 ,t test is used.
Hence for a population where the distribution is unknown ,the sampling distribution of the sample mean will be approximately normal for all sample sizes.
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Question is incomplete as it includes options in a right way:
1)exactly normal for large sample,
2) approximately normal for all sample sizes,
3) exactly normal for all sample sizes.