A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number greater than 4.
17 over 60
18 over 60
24 over 60
42 over 60
The experimental probability of landing on a number greater than 4 is 18/60
How to determine the experimental probability?The experimental probability will be given by the number of times that the outcome was greater than 4 (so a 5 or a 6) over the total number of trials.
We can see that the total number of trials is 60, and we have:
The outcome 5 a total of 10 times.
The outomce 6 a total of 8 times.
Adding these values we will get 10 + 8 = 18
Then the experimental probability of a number greater than 4 is:
E = 18/60
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A classmate simplified a rational equation 1-2/x-2 = x+1/X+2 1 - 2/x-2 = x+1/X+2
A): Explain the error in this simplification.
B): Show your work as you correct this error.
A rational equation is defined as the quotient of two polynomials, with the denominator not being zero. It is a type of algebraic expression that involves variables and rational functions with rational exponents.
The error in the given rational equation is that it's not allowed to cancel out the x-2 and X+2 terms, as they are in the denominators. It is because of the fact that it may make the denominator zero, which would result in undefined expressions. Therefore, we need to find the least common multiple (LCM) of the denominators and then convert the equation into equivalent forms with the same denominator.B):
Correction of the error1-2/x-2 = x+1/X+2Given rational equation can be re-written as:((1 - 2)/(x - 2)) = ((x + 1)/(X + 2))The LCM of x - 2 and X + 2 is (x - 2) (X + 2).Multiplying the numerator and denominator of the left side by (X + 2) and the numerator and denominator of the right side by (x - 2) we get,(1 - 2)(X + 2) = (x + 1) (x - 2)Now simplify the equation:2X - 3x = -3The given rational equation becomes 2X - 3x = -3 after correction.Note: You should always double-check if the obtained solution satisfies the initial equation.
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Lety= load in pounds andx= length in feet.In two or more complete sentences, describe the relationship between the variablesxandyin terms of length and weight.
The exact relationship between x and y may vary depending on the material and design of the object.
The relationship between the variables x and y, in terms of length and weight, is that as the length of the object (x) increases, the weight or load it can bear (y) also increases.
This is because the longer an object is, the more support it can provide, and the more weight it can hold without breaking or collapsing.
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Question
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
cm²
The area of the given triangle in the question is 48cm².
Area = (1/2) x base x height
where the base is 8cm and the height is 12cm, as given in the question.
Substituting these values, we get:
Area = (1/2) x 8cm x 12cm
Area = 48cm²
Therefore, the area of the triangle with a base of 8cm, a height of 12cm, and an angle of 59° is 48cm². A triangle is a 2-dimensional geometric shape that consists of three line segments or sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. The area of a triangle is the amount of space inside the triangle and is calculated using the formula A = (1/2) x b x h, where A is the area, b is the base of the triangle, and h is the height of the triangle. The base of a triangle is any one of its sides and the height is the perpendicular distance from the base to the opposite vertex. The area of a triangle can be used to solve various real-world problems, such as calculating the amount of material needed to construct a roof or a sail.
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A tile for a mosaic is shaped like the parallelogram shown. Find the area that is covered by 1 tile. Explain
The area covered by the tile is -
A = 1/2 x b x h
What is rotation of image?The rotation of a figure is defined as the angle about a point by which a image is rotated such that the image and the figure remains similar.
Given is triangle ΔABC.
The images of the vertices of triangle ABC after the composition is applied is -
A(0.5x₁ - 4, 0)
B(0.5x₂ - 4, 0)
C(0.5x₃ - 4, 0)
What is parallelogram?A parallelogram is a quadrilateral with two pair of equal sides. The diagonals of the parallelogram bisect each other.
Given is that a tile for a mosaic is shaped like the parallelogram shown.
The dimensions of the parallelogram tile is not given. We can assume that the dimensions of the tile are -
base = {b} units
height = {h} units
So, the area covered by the tile is -
A = 1/2 x b x h
Therefore, the area covered by the tile is -
A = 1/2 x b x h
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Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. A. C. B. D. Please select the best answer from the choices provided a b c d.
The reduced row-echelon form of the augmented matrix for the system of equations is: 1 0 0 1 | 8, 0 1 0 -2 | -2, 0 0 1 0 | 0. This means that the first equation is reduced to x_1 + x_4 = 8, the second equation is reduced to x_2 - 2x_4 = -2, and the third equation is reduced to x_3 = 0.
Step 1: Subtract 2 times row 1 from row 2 to get row 2 in the form [0 1 0 -2 | -2].
Step 2: Divide row 2 by -2 to get row 2 in the form [0 1 0 1 | 8].
Step 3: Subtract 3 times row 2 from row 1 to get row 1 in the form [1 0 0 1 | 8].
Step 4: Subtract 4 times row 2 from row 3 to get row 3 in the form [0 0 1 0 | 0].
Step 5: The reduced row-echelon form of the augmented matrix for the system of equations is now: [1 0 0 1 | 8], [0 1 0 -2 | -2], [0 0 1 0 | 0]. This means that the first equation is reduced to x_1 + x_4 = 8, the second equation is reduced to x_2 - 2x_4 = -2, and the third equation is reduced to x_3 = 0.
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if the function int volume(int x = 1, int y = 1, int z = 1); is called by the expression volume(3), how many default arguments are used?
If the function int volume(int x = 1, int y = 1, int z = 1);` is called by the expression volume(3)`, only one default argument is used.
The function volume has three parameters with default arguments: `x`, `y`, and `z`. When calling the function `volume(3)`, the argument `3` is passed as the value for parameter `x`, while parameters `y` and `z` are not specified explicitly consider default function .
In this case, the default arguments `1` for parameters `y` and `z` are used.
Therefore, only one default argument is used, specifically the default argument for parameter `y`.
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If the consumption function for Australia in 2021 is given as = 0.0052 + 0.3 + 20 where: C = total consumption of Australia in the year 2021 Y = total income of Australia in the year 2021 Calculate the marginal propensities to consume (MPC = ) and save when Y = 10. Assume that Australians cannot borrow, therefore total consumption + total savings = total income. Expert Answer
The marginal propensity to consume (MPC) for Australia in 2021, when total income (Y) is 10, is 0.3.
The consumption function for Australia in 2021 is given as C = 0.0052 + 0.3Y + 20, where C represents the total consumption and Y represents the total income. To calculate the MPC, we need to determine how much of an increase in income is consumed rather than saved. In this case, when Y = 10, we substitute the value into the consumption function:
C = 0.0052 + 0.3(10) + 20
C = 0.0052 + 3 + 20
C = 23.0052
Next, we calculate the consumption when income increases by a small amount, let's say ΔY. So, when Y increases to Y + ΔY, the consumption function becomes:
C' = 0.0052 + 0.3(Y + ΔY) + 20
C' = 0.0052 + 0.3Y + 0.3ΔY + 20
To find the MPC, we subtract the initial consumption (C) from the new consumption (C') and divide it by the change in income (ΔY):
MPC = (C' - C) / ΔY
MPC = (0.0052 + 0.3Y + 0.3ΔY + 20 - 23.0052) / ΔY
Simplifying the equation, we can cancel out the terms that don't involve ΔY:
MPC = (0.3ΔY) / ΔY
MPC = 0.3
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The functions f(x) and g(x) are shown on the graph.f(x) = 2xWhat is g(x)?y5f(x)X-55g(x)
We know that
\(f(x)=2^x\)So, we can see that g(x) is f(x) reflected in the x-axis. But, it has another change which is a downward movement in 3 units.
So, we can deduce that
\(g(x)=-2^x-3\)Sketch of the situation:
When you reflect f(x) in the x-axis, you obtain something like -f(x).
We can see that -f(x) intersect the y-axis in -1. But, g(x) intersect the y-axis in -4.
So, we need to move the function 3 units down. Whe we make the movement the graph will intersect the y-axis in -4 because -1-3=-4.
What is the value of w?
w
36°
Answer: you literally said it yourself. its 36°
Step-by-step explanation:
Find the slope of the following given points (-3, 1) and (5, 17)
Answer:
slope is 2
Step-by-step explanation:
find the change in y and x to then divide them
17-1/5- -3 = 16/8 = 2
Suppose the following expression is given: P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1). a) Write down the "realization" of the stochastic process implied by the above expression, and explain what it means.
The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.
The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.
If the process is discrete, then the function is a sequence of values at discrete points in time.
A stochastic process is one that evolves over time and the outcomes are uncertain.
The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.
To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.
The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.
The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.
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What is the absolute value of 3/2?
what is the value of 32^4?
what is the value of 32 to the fourth power?
what is the value of 42?
The value of all the given expression are as follow:
a. Absolute value of -3 / 2 is equal to 3 /2.
b. The value of 32^4 is equal to 1048576.
c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.
d. Value of 4^2 is 16
As given in the question,
Simplification of the given expressions are :
a. The absolute value of ( -3 / 2 )is
| - 3 / 2 | = ( 3/2 )
b. The value of the expression 32^4 is:
32^4
= 32 × 32 × 32 × 32
= 1048576
c. The value of the given expression ( 32 ) ^ 1/4 :
( 32 ) ^ 1/4
= ( 2⁵) ^ 1/4
= 2^(5/4)
d. Value of 4^2 is
4^2
= 4 × 4
= 16
Therefore, the value of the given expression is given by :
a. Absolute value of -3 / 2 is equal to 3 /2.
b. The value of 32^4 is equal to 1048576.
c. The value ( 32 )^ 1/4 power is equal to (2)^5/4.
d. Value of 4^2 is 16
The complete question is:
What is the absolute value of -3/2 ?
what is the value of 32^4?
what is the value of 32 to the one - fourth power?
what is the value of 4^2?
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A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours
there will be 800 bacteria.
The population after t hours is 160 x (1.3797)^t.
What is the population after t hours?The first step is to determine the growth rate of the bacteria:
growth rate = (future population / initial population) ^(1/number of years) - 1
(800 / 160)^(1/5) - 1= 37.97
The exponential function : 160 x (1.3797)^t
Here is the complete question:
A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours
there will be 800 bacteria. Express the population after t hours as a function of t. population:
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Two observers are standing on shore 20 mile apart at points A and B and measure the angle to a sailboat at a point C at the same time. one observer is 10 miles from the sailboat and the other observer is 25 miles from the sailboat. round to the nearest degree
Using the law of sines, supposing C = 30º, the angle of each observer with the sailboat is:
Observer A: 136º.Observer B: 14º.What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A has length a.The length of the side opposite to angle B has length b.The length of the side opposite to angle C has length c.The lengths and the sine of the angles are related according to the following rule:
\(\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}\)
The measure of angle B is found as follows:
sin(B)/10 = sin(C)/20
sin(B)/10 = 0.5/20 (sin(C) = 0.5)
sin(B) = 5/20
sin(B) = 0.25
B = arcsin(0.25)
B = 14º.
The measure of angle A is found as follows:
sin(A)/25 = sin(C)/20
sin(A)/25 = 0.5/20 (sin(C) = 0.5)
sin(A) = 12.5/20
sin(A) = 0.625
A = arcsin(0.625)
A = 136º.
Missing informationThe problem is incomplete, hence we suppose that the angle C is of 30º and problem asks for the angle measure of each angle.
(drawing is not to scale).
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Factor completely 81x8 − 1. (9x4 − 1)(9x4 1) (3x2 − 1)(3x2 1)(9x4 − 1) (3x2 − 1)(3x2 1)(9x4 1) (3x2 − 1)(3x2 1)(3x2 1)(3x2 1).
Answer:
(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Step-by-step explanation:
Using the identity for the difference of 2 squares;
a^2 - b^2 = (a - b)(a + b)
we put a^2 = 81x^8 and b^2 = 1 giving
a = 9x^4 and b = 1, so:
81x^8 − 1 = (9x^4 - 1)(9x^4 + 1)
Applying the difference of 2 squares to 9x^4 - 1:
= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Answer:
The answer is (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Step-by-step explanation:
Turn 5 8/25Into a decimal
Answer: 5.32
Step-by-step explanation:
8/25 as a decimal is 0.32. Add the fraction and whole number and you get 5.32
Answer:
5.32
Step-by-step explanation:
We know that the 5 in \(5 \frac{8}{25}\) will just be a 5, so we can leave that be for now.
Since we have \(\frac{8}{25}\), we want to turn it into a decimal.
A way of representing decimals is \(\frac{x}{100}\), like \(\frac{69}{100}=0.69\).
Therefore, we can convert \(\frac{8}{25}\) into hundredths and find the decimal that way.
\(\frac{8}{25} = \frac{x}{100}\)
We can cross multiply to find the value of x.
\(100\cdot8=800\\\\800\div25=32\)
This means that \(\frac{8}{25} = \frac{32}{100}\). This means the decimal is 0.32.
Adding the 5 to it, we get 5.32.
Hope this helped!
Write an exponential function and then find the value when t=7 initial value2000 annual rate:9.2%growth
Answer:
Step-by-step explanation:
Write an exponential function and then find the value when t=7 initial value2000 annual rate:9.2%growth
Exponential growth function
= y = a(1 + r)^t
Solving for y
y = 200(1 + 0.092)⁷
(A* m script file is required for this question) Plot the following surface using the surf function: z=sin(u+v) where 0≤u≤2π, and 0≤v≤2π, you need to add axis labels and a graph title.
A MATLAB script file can be used to plot the surface z = sin(u + v) using the `surf` function, with axis labels and a graph title added for clarity.
% Create a grid of u and v values
[u, v] = meshgrid(0:0.1:2*pi);
% Compute the z values based on the given function
z = sin(u + v);
% Plot the surface using surf function
surf(u, v, z);
% Add axis labels and a graph title
xlabel('u');
ylabel('v');
zlabel('z = sin(u + v)');
title('Surface Plot of z = sin(u + v)');
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Figure WXYZ is transformed using the rule. Point W of the pre-image is at (1, 6)
Answer:
d. (3, 8)
Step-by-step explanation:
the coordinates of point W " on the final image is (3 8) Solution-means first the point is translated left by 4 units and translated up by 2 units then it is reflected across y axis. (the rules follow right to left approach) The co-ordinate of point W is ( 1 6 ). After 4 units translation to left and 2 units translation to up the co-ordinates
write in slope-intercept form of the line that passes through the points (-2,-2) and (5,12)
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (the point where the line crosses the y-axis, which is represented by b).
We can use the point-slope formula to find the equation of the line that passes through the points (-2,-2) and (5,12):
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line.
Plugging in the values for the given points and solving for m, we get:
m = (12 - (-2)) / (5 - (-2))
= 14 / 7
= 2
Now that we have the slope, we can use either of the given points to find the y-intercept (b). Let's use the point (-2,-2):
y = mx + b
-2 = 2(-2) + b
-2 = -4 + b
b = -2 + 4
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = 2x + 2
This is the equation of the line that passes through the points (-2,-2) and (5,12).
Helpppppp meeeee pleaseeeeee!!!!
Answer: 15
Step-by-step explanation:
Just count the dots :)
Andrew and Kate have $30 to spend on dinner, tax, and gratuity at Mo's Restaurant. Tax is 6%, and they will give a 15%
tip on the total bill after taxes. Their dinner costs $21.00. Which statement correctly explains whether Andrew and Kate Have enough money to pay their bills
Answer:
See below ----pick the one that you need
Step-by-step explanation:
Total cost = 21 + 21 * .06 + 21 * .15
= 21 ( 1 + .06 + .15)
= 21(1.21)
Esteban is shopping for a bookshelf. He has 58 non-fiction books and 145 fiction books. He wants each shelf to have the same number of books and to have only one type of book on each shelf. If Esteban wants the greatest possible number of books on each shelf, how many shelves should the bookshelf have?
Answer:
7
Step-by-step explanation:
Criteria:
• same number of books on each shelf
⇒find a number that divides 58 and 145
• greatest number of books on each shelf
⇒find the greatest number that divides 58 and 145
Find the GCF of 58 and 145.
58 = 2 ⋅ 29
145 = 5 ⋅ 29The GCF of 58 and 145 is 29.
Each shelf will contain 29 books.
There are 203 total books (because 58 + 145 = 203).
Divide 203 by 29 to find the number of shelves there should be.
203 / 29 = 7
Therefore, there will be 7 shelves.
I need help with #41 and #42 ASAP please help me
Answer:
4 is the answer to the 1st question
mark spent 135$ on his comic book collection. he just sold it online for 310$. approximately what is the profit as a percent of his original cost?
Answer:
70% is approximately the answer
Step-by-step explanation:
135 x 2 = 270
310 - 270 = 40
35 out of 40 is 7/8.
The answer should be approx 70, I can not make sure.
MODELING WITH MATHEMATICS The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the Pythagorean Theorem to approximate
the distance between the rods where they meet the backboard. Round your answer to the nearest hundredth
Write two numbers that multiply to the value on top and add to the value on the bottom 81and 18
The two numbers that multiply to 81 and add to 18 are 9 and 9. This is determined either by factoring the number 81 or by solving the algebraic equations derived from the given conditions.
To find two numbers that multiply to 81 and add to 18, we can use factoring or algebraic methods. Let's explore both approaches:
Factoring:
Start by factoring 81 into its prime factors: 3 * 3 * 3 * 3.
Since the two numbers must multiply to 81, we can consider pairs of factors and check if their sum is 18:
Pair 1: 1 * 81 = 81 (sum = 1 + 81 = 82)
Pair 2: 3 * 27 = 81 (sum = 3 + 27 = 30)
Pair 3: 9 * 9 = 81 (sum = 9 + 9 = 18)
Therefore, the pair of numbers that multiply to 81 and add to 18 is 9 and 9.
Algebraic method:
Let's assume the two numbers are x and y.
According to the given conditions, we can write the following equations:
xy = 81 ...(1)
x + y = 18 ...(2)
To solve this system of equations, we can rearrange equation (2) to express one variable in terms of the other:
y = 18 - x ...(3)
Substitute equation (3) into equation (1):
x(18 - x) = 81
Simplifying the equation:
18x - x^2 = 81
Rearrange the equation and set it equal to zero:
x^2 - 18x + 81 = 0
Now, we can factor this quadratic equation:
(x - 9)(x - 9) = 0
The equation yields a repeated factor (x - 9) since both values are the same.
Thus, the solution is x = 9.
Substituting x = 9 into equation (3):
y = 18 - 9
y = 9
Therefore, the pair of numbers that multiply to 81 and add to 18 is 9 and 9.
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49 T
th
47 Pansy opens a savings account. She uses the
equation: y = $25x + $500 to help her keep track
of her savings, where y is the amount of money
in her account and x is the number of weeks.
Which statement is TRUE?
A. Pansy invests $500 per week.
B. Pansy started her savings account with $25.
C. Pansy plans on investing $100 every 4 weeks.
D. Pansy will take $25 per week from her account
ОО
48 The table below shows the results of a survey on
music listening preferences.
Wh
A.
Answer: D. Pansy will take $25 per week from her account
Step-by-step explanation:
Based on the information given in the question, the true statement is that Pansy will take $25 per week from her account. This is represented by $25x.
For example, if the number of weeks that he used is 8 weeks. The amount in the savings account will be:
y = $25x + $500
y = $25(8) + $500
y = $200 + $500
y = $700
Trapezoid ABCD was dilated to create trapezoid A'B'C'D'.
On a coordinate plane, 2 trapezoids are shown. Trapezoid A B C D has points (negative 4, 0), (negative 2, 4), (2, 4) and (4, 0). Trapezoid A prime B prime C prime D prime has points (negative 2, 0), (negative 1, 2), (1, 2), and (2, 0).
Which statements are true about the trapezoids? Select three options.
The length of side AD is 8 units.
The length of side A'D' is 4 units.
The image is larger than the pre-image.
Sides CD and C'D' both have the same slope, 2.
The scale factor is One-half.
Answer:
True, True, False, False, TrueStep-by-step explanation:
Trapezoid ABCD was dilated to create trapezoid A'B'C'D'.
Scale factor is 1/2 according to the coordinates.
The answer optionsThe length of side AD is 8 units.
AD = 4 - (-4) = 8TrueThe length of side A'D' is 4 units.
A'D' = 2 - (-2) = 4TrueThe image is larger than the pre-image.
False. It is 2 times smaller.Sides CD and C'D' both have the same slope, 2.
Slopes of CD and C'D' are same: m = (0 - 4)/(4 - 2) = -4/2 = -2
FalseThe scale factor is One-half.
TrueAnswer:
A,B,E
Step-by-step explanation: