The first step in solving the equation is to distribute the 5, making option D the correct choice, which results in 5x - 10 - 2x = 2.
Explanation:The first step in correctly solving the equation 5(x-2)-2x=2 would be to distribute the 5 into the parentheses of the left term. This action aligns with option D where the distribution results in 5x - 10 - 2x = 2. Doing so simplifies the equation and sets it up for further steps such as combining like terms and isolating the variable.
in a certain town, 10% of people commute to work by bicycle. if a person is selected randomly from the town, what are the odds against selecting someone who commutes by bicycle?
The odds against selecting a person who commutes by bicycle from a town where 10% of people commute that way would be 9 to 1. This is based on the percentage of people who do not commute by bicycle versus those who do.
Explanation:In statistical terms, the question is asking us to calculate the odds against selecting someone who commutes by bicycle. With 10% of people in this town commuting by bicycle, it means that 90% of them do not. Therefore, the odds against selecting someone who commutes by bicycle are 90 to 10 or 9 to 1.
This is calculated by dividing the number of unsuccessful outcomes (people not commuting by bicycle - 90%) by the number of successful outcomes (people commuting by bicycle - 10%). This gives us the odds against selecting someone who commutes by bicycle.
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The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?
Answer with explanation:
The Given Quadratic Polynomial which can be Broken into integer factors:
[tex]\rightarrow 6 x^2 + 37 x - 60\\\\ \text{Splitting the Middle term}}\\\\ \rightarrow 6 x^2 + 37 x - 60\\\\\rightarrow 6 x^2 + 45 x-8 x - 60\\\\ \rightarrow 3x \times (2 x+15)-4 (2 x +15)\\\\\rightarrow (3 x -4)(2 x+15)[/tex]
Factors of the above Expression are:
= (3 x -4)(2 x+15)
Find the slope of the line whose equation is 4y - 3x + 6 = 0.
Answer:
slope of the line will be [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
We have to find the slope of a given line whose equation is 4y - 3x + 6 = 0
If a line is in the form of y = mx + c
Then m represents slope of the line
4y - 3x + 6 = 0 [ Given equation ]
4y = 3x - 6
y = [tex]\frac{1}{4}[/tex] ( 3x-6 )
y = [tex]\frac{3}{4}x[/tex] - [tex]\frac{3}{2}[/tex]
Therefore, slope of the line will be [tex]\frac{3}{4}[/tex]
Choose all of the following that must be true for a random experiment to be binomial.
Select one or more:
A. On each trial, the event of interest either occurs or does not occur.
B. The trials are independent of one another and repeated under identical conditions.
C. The probability of occurrence is the same on each trial.
D. There is a fixed number of trials.
A binomial experiment has a fixed number of trials, all are independent and conducted under identical conditions. Only two results—success or failure—are possible with each trial, each having the same probability, fitting a binomial probability distribution.
Explanation:For a random experiment to be binomial, it must meet certain conditions. Firstly, there should be a fixed number of trials, denoted as 'n'. The results of these trials don't influence each other, meaning that the trials are independent. This signifies that the outcome of a trial, for example, the first one, does not affect the outcomes of the subsequent trials. Moreover, all these trials should be conducted under identical conditions.
In a binomial experiment, there are only two possible results, often referred to as 'success' and 'failure'. Each trial has the same probability of success, denoted as 'p'. The outcomes of a binomial experiment fit a binomial probability distribution. The random variable 'X' stands for the number of successful trials. The mean 'µ' is given by 'np', and the standard deviation 'o' by √npq. The probability of exactly 'x' successes in 'n' trials is P(X = x).
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46x12=46x(10+2), find distributive property
The sum of two numbers is equal to 70. Which of the following functions can be use to find the product of the two numbers if one of the numbers is x?
a) p = x^2
b) p = x (x-70)
c) p = x (70 - x)
d) p = (x - 70)^2
Given rectangular prism ABCD.
Choose all of the terms that best describe each of the sets of lines or points.
Points A, E, and J
collinear
intersecting
coplanar
noncollinear
noncoplanar
Answer: Fourth and Fifth options are correct.
Step-by-step explanation:
Since we have given two points i.e. A, E, and J
We can see from the graph that
A, E, J are non coplanar and non collinear.
Coplanar means that all the points lie in the same plane.
Collinear means that all the points lie in the same line.
But A, E, and J are neither in the same plane nor in the same line.
Hence, Fourth and Fifth options are correct.
Choose the value of X that makes the open sentence true
30 - x^2 < 3x + 7
A 4
B 3
C 2
D 1
Answer:
Option A - 4
Step-by-step explanation:
Given : Inequality [tex]30 - x^2 < 3x + 7[/tex]
To find : Choose the value of x that makes the open sentence true ?
Solution :
We substitute the value of x from options to check which is true,
A) x=4
[tex]30 - 4^2 < 3(4) + 7[/tex]
[tex]30-16 < 12+ 7[/tex]
[tex]14< 19[/tex]
It is true.
B) x=3
[tex]30 - 3^2 < 3(3) + 7[/tex]
[tex]30-9< 9+ 7[/tex]
[tex]21< 16[/tex]
It is false.
C) x=2
[tex]30 - 2^2 < 3(2) + 7[/tex]
[tex]30-4<6+ 7[/tex]
[tex]26< 13[/tex]
It is false.
D) x=1
[tex]30 - 1^2 < 3(1) + 7[/tex]
[tex]30-1<3+ 7[/tex]
[tex]29< 10[/tex]
It is false.
Therefore, Option A is correct.
if you are told only that you scored 80th percentile do you know from the description exactly how it wad calculated? Explain
We know that there is no universal acceptance meaning of a percentile. When someone told you that you are in the 80th percentile, the meaning of that is you have achieved the lowest score that is greater than 80 percent of the score. It is calculated by using the formula R = P/100 x (N + 1)
Final answer:
The 80th percentile represents the score below which 80% of the scores fall.
Explanation:
The 80th percentile represents the score below which 80% of the scores fall. It is calculated by finding the value at which 80% of the data is below and 20% is above. For example, if you scored in the 80th percentile on a 60-point assignment, it means that 80% of students scored equal to or below 49 points and 20% scored above.
The height of a grain of a cylindrical silo is is increasing at a constant rate of 4 feet per minute At what rate is the volume of grain in the cylinder if the radius of the silo is 10 feet?
Answer:
The rate of change of the volume of the cylinder when the radius is 10 ft is
[tex]\frac{dV}{dt}=400\pi \:{\frac{ft^3}{min} }[/tex]
Step-by-step explanation:
This is a related rates problem. A related rates problem is a problem in which we know the rate of change of one of the quantities (the height of a grain) and want to find the rate of change of the other quantity (the volume of grain in the cylinder).
The volume of a cylinder is given by
[tex]V=\pi r^2 h[/tex]
V and h both vary with time so you can differentiate both sides with respect to time, t, to get
[tex]\frac{dV}{dt}=\pi r^2 \frac{dh}{dt}[/tex]
Now use the fact that [tex]\frac{dh}{dt} = 4 \:{\frac{ft}{min} }[/tex] and [tex]r = 10 \:ft[/tex]
[tex]\frac{dV}{dt}=\pi (10)^2 \cdot 4\\\\\frac{dV}{dt}=100\cdot \:4\pi \\\\\frac{dV}{dt}=400\pi[/tex]
How do you multiply -5 that has an exponent of 4 but no parenthesis with 4? Please explain
A diver is descending to reach the bottom of a lake. After 15 seconds, she is 90 feet below the surface of the water. If positive integers represent a distance above the surface of the lake, which integer best represents the diver’s change in position in feet per second?
dive distance traveled by time
90 feet / 15 seconds = 6
since the diver is below the surface they are changing position at -6 feet per second
Write 7.625 as a mixed number in simplest form
What is the degree of the polynomial
Xy^2 + 3x^2 - 7 + x
A) 2
B) 3
C) 1
D) 4
0.5,3/16,0.755/49 least to greatest
The circumference of a circular hot tub at a hotel is 56.5 yards. What is the diameter of the hot tub?
To find the diameter of the circular hot tub, divide the circumference by π.
Explanation:To find the diameter of the circular hot tub, we need to use the formula for the circumference of a circle. The formula is C = πd, where C represents the circumference and d represents the diameter.
In this case, the circumference is given as 56.5 yards. So we can plug that value into the formula and solve for d: 56.5 = πd.
To isolate the variable d, we divide both sides of the equation by π. This gives us: d = 56.5/π.
Using a calculator, we can find the approximate value of d to be 18 yards.
The diameter of the hot tub is approximately 18 yards, calculated using the formula [tex]\(D = \frac{56.5}{\pi}\)[/tex] from the given circumference.
The circumference of a circle is given by the formula [tex]\(C = \pi \times D\)[/tex], where C is the circumference and D is the diameter. In this case, the circumference of the hot tub is given as 56.5 yards. So, the formula can be rearranged to solve for the diameter:
[tex]\[ C = \pi \times D \][/tex]
[tex]\[ 56.5 = \pi \times D \][/tex]
To find D, divide both sides of the equation by [tex]\(\pi\)[/tex]:
[tex]\[ D = \frac{56.5}{\pi} \][/tex]
Using the value of [tex]\(\pi \approx 3.14159\)[/tex], the diameter D is approximately:
[tex]\[ D \approx \frac{56.5}{3.14159} \approx 18 \][/tex]
Therefore, the diameter of the hot tub is approximately 18 yards.
6.41* 10^3 in standard form
Help me please
which graph shows a triangle and it's reflection image over the x-axis?
Belmond, a brick-cutter in a kiln, cuts 84 bricks in 3 hours. Find the unit rate.
Please Help!!
The unit rate at which Belmond cuts bricks is 28 bricks per hour, which is calculated by dividing the total number of bricks (84) by the total hours worked (3).
To find the unit rate of bricks cut per hour by Belmond, we simply divide the total number of bricks by the total time in hours. Belmond cuts 84 bricks in 3 hours, so the unit rate is:
Unit rate = Total bricks \/ Total time in hours
Unit rate = 84 bricks \/ 3 hours = 28 bricks per hour
This means that Belmond cuts 28 bricks every hour. When you need to find a unit rate, it is a matter of dividing the total quantity by the time it takes to accomplish that quantity, thus yielding the rate per single time unit (in this case, per hour).
A is an unknown number. When you round A to the nearest thousand you get 21000. When you round A to the nearest hundred you get 20,500
What is A
The unknown number A, when rounded to the nearest thousand and hundred, is determined to be within the range from 20500 to 20549. A can be any number within this range.
Explanation:In mathematics, when you're given that a number A, when rounded to the nearest thousand, ends up being 21000 or that when rounded to the nearest hundred, it ends up being 20500, you can infer that the unknown number A lies somewhere between two specific values. Since A rounds to 21000 when we round to the nearest thousand, this implies that A is between 20500 and 21499.
However, we also know that, when rounded to the nearest hundred, A is 20500. This implies that A is between 20450 and 20549. Comparing these two ranges, the unknown number A must lie within the common range, which is from 20500 to 20549. Therefore, the number A can be any number within this range.
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Mr. Green's sunflower grew 29 centimeters in one week. The next week it grew 5 centimeters more than the previous week. What is the total number of centimeters the sunflower grew in 2 weeks?
In a batch of 960 calculators, 8 were found to be defective. What is the probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary
Answer: 0.8%
Step-by-step explanation:
Given : In a batch of 960 calculators, 8 were found to be defective.
i.e. Total calculators =960
Number of defective calculator = 8
We know that the probability of any event is given by :-
[tex]\dfrac{\text{No. of favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{8}{960}=0.00833333333333[/tex]
In percent, [tex]0.00833333333333\times100=0.833333333333\%\\\\\approx0.8\%\ \ \ [\text{Rounding to the nearest tenth.}][/tex]
Hence, the probability that a calculator chosen at random will be defective=0.8%
Calculate all four second-order partial derivatives of f(x,y)=sin(2xy)
find the perimeter of the semi-circular region at leat one please
Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]
To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the interval [1/2, 2], we find the critical points and evaluate the function at the endpoints and critical points. The absolute minimum value is f(1/2) = 1/2 - ln 4 and the absolute maximum value is f(2) = 2 - ln 16.
Explanation:To find the absolute minimum and absolute maximum values of the function f(x) = x - ln 8x on the given interval [1/2, 2], we need to find the critical points and the endpoints of the interval. First, we find the derivative of the function: f'(x) = 1 - 1/x. Then, we solve the equation f'(x) = 1 - 1/x = 0 to find the critical points. The critical point is x = 1. Next, we evaluate the function at the critical point and the endpoints of the interval to determine the absolute minimum and absolute maximum values.
1. Evaluating the function at the critical point: f(1) = 1 - ln 8
2. Evaluating the function at the endpoint x = 1/2: f(1/2) = 1/2 - ln 4
3. Evaluating the function at the endpoint x = 2: f(2) = 2 - ln 16
The absolute minimum and absolute maximum values of the function on the given interval are:
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712 divided by 8 and show work
Consider the graph of the linear function h(x) = –6 + x. Which quadrant will the graph not go through and why? Quadrant I, because the slope is negative and the y-intercept is positive Quadrant II, because the slope is positive and the y-intercept is negative Quadrant III, because the slope is negative and the y-intercept is positive Quadrant IV, because the slope is positive and the y-intercept is negative
The line of linear function h(x) = –6 + x is not going to enter in the second quadrant so option second will be correct.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph is made up of some points and the distance between two. It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.
Given equation is h(x) = –6 + x
at x = 0 , h(x) = -6 so ( 0 , -6 ) is first point.
at x =1 , h(x) = -5 so ( 1 , -5 ) is second point.
If we draw a line by the two-point which I have attached then you can see it not going to the second quarter.
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"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.) f (x) = cos(πx/2)
A softball player hits the ball. The height of the ball h (in feet) at any time t seconds after the hit will be represented by the quadratic function h(t)=42t‒6t2. Use what you have learned about the zeros of a quadratic function to determine which of the following statements is true.
A. The ball will reach the ground in 3.5 seconds.
B. The ball will get to its highest point in 7 seconds.
C. The ball will stay in the air for a total of 7 seconds.
D. The highest the ball will go is about 7 feet.
In triangle ABC, a = 9, c = 5, and B = 120°. Find b2.
61
83.5
128.5
151
Answer:
The correct answer is 151.
Step-by-step explanation:
Given,
In triangle ABC,
BC = a = 9 unit,
AB = c = 5 unit,
m∠B = 120°,
We have to find : b² or AC²,
By the cosine law,
[tex]b^2=a^2+c^2-2ac cosB[/tex]
[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]
[tex]=81+25-90\times -0.5[/tex]
[tex]=81+25+45[/tex]
[tex]=151[/tex]
Hence, the value of [tex]b^2[/tex] is 151.
Answer:
Option D) [tex]b^2 = 151[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]
We have to find [tex]b^2[/tex]
The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,
[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]
Putting the values, we have,
[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]
Option D) [tex]b^2 = 151[/tex]