Answers
Related Questions
suppose that the chosen ahlete test postitive. what the probability that he or she actually used steroids?
Answers
The probability that he or she actually used steroids is 0.779.
The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn't taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have actually taken steroids. Let's choose an athlete at random and administer the drug test.
Based on prior knowledge of conditions that might be related to the event, Bayes' theorem, which is named after Thomas Bayes and is used in probability theory and statistics, describes the probability of an event.
Using Baye's theorem:
P(steroids | positive) = P(steroids)*P(positive|steroids) / P(positive) = (0.10*0.95)/0.122 = 0.779
If the selected athlete passes the test, the probability that they used steroids: 0.779
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(complete question)
A company has developed a drug test to detect steroid use by athletes. The test is accurate 95% of the time when an athlete has taken steroids. It is 97% accurate when an athlete hasn’t taken steroids. Suppose that the drug test will be used in a population of athletes in which 10% have taken steroids. Let’s choose an athlete at random and administer the drug test.
Suppose that the chosen athlete tests positive. What’s the probability that he or she used steroids?
Jack bought a coin for $200, which he sold later for $175. Find the percent of change. Did Jack make a good investment?
Answers
1. Name the inequality that is graphed. If you need use <= and >= (Use the attached photo)
2. Solve for t.
2t +7 > -3(t+1)
3. Graph (or describe the graph--give the starting point, if it is open or closed and if the graph points to the right or left)
-3y>6
4. (same instructions as #3)
y/2 <-3
5. (same instructions as #3)
4y 3x -1
Answers
1) The inequality used in graph is;
⇒ x > -2
2) The solution for t will be;
⇒ t > - 2
3) The graph of - 3y > 6 is shown in figure.
4) The graph of y/2 < - 3 is shown in figure.
5) The graph of 4y > 3x - 1 is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Now,
1) By the graph, we get;
The solution of the graph is,
⇒ x > - 2
Thus, The used inequality is '>'.
2) The inequality is,
⇒ 2t + 7 > - 3 (t + 1)
Solve for t as;
⇒ 2t + 7 > - 3t - 3
⇒ 2t + 3t > - 3 - 7
⇒ 5t > - 10
⇒ t > - 2
3) The inequality is,
⇒ - 3y > 6
⇒ - y > 2
⇒ y < - 2
4) The inequality is,
⇒ y/2 < - 3
⇒ y < - 6
5) The inequality is,
⇒ 4y > 3x - 1.
Thus, The graph of 4y > 3x - 1 is shown in figure.
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on a line segment of length 1, chooses two points independently at random. what is the probability the distance between them is more than 1/3?
Answers
The probability that the distance between the two points is more than 1/3 is 0.
The length of the given line segment is 1, so the two points chosen independently at random cannot be more than 1 unit apart.
That is, the maximum distance between the two points is 1. However, the question states that we are looking for the probability that the distance between them is more than 1/3.
Since the maximum distance between the two points is 1, and 1/3 is less than 1, it is impossible for the distance between them to be more than 1/3. Therefore, the probability that the distance between the two points is more than 1/3 is 0.
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find the measures of the numbered angles.
Answers
2=136
4=44
Mark me Brainly
Please Help this is due soon!
Answers
a + b + c = 17
First is 2 greater than two times the third:
a = 2c + 2
Sum of second and third is 9:
b + c = 9
First find the variables in terms of their relationship with other variables. We have variable a because we know that a = 2c + 2. We also know variable b because we have that b + c = 9, so b = 9 - c. We also know variable c because we have that b + c = 9, so c = 9 - b.
Now plug in the equations instead of their variables into the first equation so at the end we would only have one variable, which is easy to figure out.
First get rid of a by putting (2c + 2) instead of it. So the equation would be:
(2c + 2) + b + c = 17.
Then get rid of b by putting (9 - c) instead of it. So the equation would now be:
(2c + 2) + (9 - c) + c = 17.
To simplify this and figure out c, combine like terms so the equation would be:
2c + 11 = 17
Then get c by itself by subtracting 11 from both sides and then dividing both sides by 2 so the equation would be:
c = 3
Once you have c, you can figure out the other numbers by plugging it in:
for example, because a = 2c + 2, just plug in 3 for c to get a = 2(3) + 2, which is 6 + 2, which is 8, so a = 8.
also, because b = 9 - c, just plug in 3 for c to get b = 9 - 3, which is 6, so b = 6.
And since 8 + 6 + 3 = 17, and 8 is 2 greater than 2 x 3, and 6 + 3 = 9, those are the three numbers.
Need help Asap for 25 points
What is the solution to this inequality?
14x−5<−6
Responses
x<4
x less than 4
x<−4
x less than negative 4
x>4
x greater than 4
x>−4
Answers
Answer:
Your answer is B
Step-by-step explanation:
[tex]\frac{1}{4}x-5 < -6\\\\\frac{1}{4}x < -1 \\\\[/tex]
Multiply 4 to both sides leaving x by itself.
x < -4
Remember when you divide or multiply a negative to solve for x you switch the signs of greater than to less than or vice versa.
Write the
equation of the line that
passes through the point (3,-1) and has a slope of
2
Answers
Answer:
y = 2x - 7
Step-by-step explanation:
y = mx + b
m is known (m=2):
y = 2x + b
Since one point is known (3,-1), you can solve for b:
-1 = 2(3) + b
b = -7
So the equation is:
y = 2x - 7
What equation represents this sentence. 5 less than a number is 12.
0 5-n=12
0 5 n-12
0 5 12-n
O n-5=12
Answers
n-5=12
Step-by-step explanation:
5 less than a number equals 12 therefore the number minus 5 will equal 12.
example
say n is 17
5 less then 17 is 12 is true ( 17-5=12)
17 less than 5 is 12 is not true (5-17=12)
I hope this helps!
An airplane has stopped to re-fuel. Fuel is being added to the airplane's tanks at a constant rate. After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel. Write a function in f(t) form that describes the amount of fuel in the plane at time t.
Answers
The function in f(t) form that describes the amount of fuel in the plane at time t will be;
⇒ f (t) = 112.25t + 31.425.75
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Now,
Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (32882 - 34902.5) / ((31 - 13)
m = 2020.5 / 18
m = 112.25
Thus, The equation of line with slope 112.25 is,
⇒ y - 32885 = 112.25 (x - 13)
⇒ y - 32885 = 112.25x - 1459.25
⇒ y = 112.25x - 1459.25 + 32885
⇒ y = 112.25x + 31.425.75
Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be;
⇒ f (t) = 112.25t + 31.425.75
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the teachers are planning an ice cream party. each student gets 1 cup of ice cream. how many quarts should they buy for 60 students?
Answers
15 quarts are required to plan ice cream party for 60 students which is
[tex]\frac{1}{4}[/tex] th fraction of quart.
1 quarts = 4 cups
so 1 cup = [tex]\frac{1}{4}[/tex] th fraction of quart
so in order to plan party for 60 students we need 60 cups as it is mentioned that each student gets 1 cup of ice cream.
and 1 quarts = 4 cups
so let we need x quarts for the planning of ice cream party
so total cups = 4 *x
so 4*x =60 , x= 60/4 , x=15
so 15 quarts are required for the ice cream party of 60 students .
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why is h=root3*a/2
(equilateral triangle)
Answers
Answer:cause why not
Step-by-step explanation:
need help with this question
Answers
Answer:
y = -6x - 4
Step-by-step explanation:
Slope intercept form:
y = mx + b
m is the slope
b is the y-intercept
To find the slope, you take two points from the line and plug them into the following equation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
Let's use (0, -4) and (-2, 8):
[tex]\frac{8-(-4)}{-2-0} = \frac{12}{-2}=-6[/tex]
So m = -6
We know that the y-intercept (b) is -4, so we can plug everything into the equation:
y = -6x - 4
What are the first four terms of a sequence where he rule is 7(n+2)?
Answers
Answer:
Step-by-step explanation:
for n=1 it is 7(1+2)=21
for n=2 it is 7(2+2)=28
for n=3 it is 7(3+2)=35
what is the first word in the alternative statistical hypothesis for any experiment with three levels of a single iv?
Answers
Answer: The first word in the alternative statistical hypothesis for an experiment with three levels of a single independent variable (IV) is "differences." This is because the alternative hypothesis typically involves the existence of differences between the levels of the IV.
Step-by-step explanation:
Here is how to formulate the alternative hypothesis for an experiment with three levels of a single IV:
Identify the independent variable (IV) and the levels of the IV. In this case, there is a single IV with three levels.
Determine the relationship between the IV and the dependent variable (DV). In other words, consider how the levels of the IV may affect the DV.
Write the alternative hypothesis in terms of the relationship between the IV and the DV. The alternative hypothesis should state that there are differences between the levels of the IV in their effect on the DV.
For example, if the IV is "type of exercise" and the levels are "running," "cycling," and "swimming," and the DV is "improvement in cardiovascular fitness," the alternative hypothesis might be "There are differences in the improvement in cardiovascular fitness between the three types of exercise."
What is the null hypothesis in an experiment?
The null hypothesis in an experiment is a statement that there is no relationship between the IV and the DV, or that there are no differences between the levels of the IV in their effect on the DV. The null hypothesis is typically denoted as H0. In the example given above, the null hypothesis might be "There is no difference in the improvement in cardiovascular fitness between the three types of exercise."
This means that the hypothesis is testing whether there are significant differences between the means of the three levels of the IV. Therefore, the first word in the alternative statistical hypothesis for any experiment with three levels of a single IV is "differences."
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The first word in the alternative statistical hypothesis for any experiment with three levels of a single IV is "difference," which refers to the difference between the means of the three levels of the IV.
What is hypothesis?
Hypothesis is an educated guess or prediction made in response to a question or problem. It is based on prior knowledge and experience, as well as available evidence. The purpose of a hypothesis is to suggest a possible explanation for an observed phenomenon and then to test the validity of the hypothesis through further research or experimentation. If the hypothesis is proven correct, it can become a theory. Hypotheses can also be disproven or modified through further testing.
This is a reference to the null hypothesis, which states that there is no difference between the means of the different levels of the IV. The alternative hypothesis is that there is a difference between the means of the different levels of the IV.
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Josie is moving to a new apartment. The cost of her
rent is $850 per month, and her landlord charges a
deposit of $1000.
a) Write a linear function to represent the total cost, C,
or renting the apartment for m months.
b) What will be the total cost of renting the apartment for one year?
Answers
Answer:
b
Step-by-step explanation:
The length of the longer leg of a right triangle i 6inche more than twice the length of the horter leg. The length of the hypotenue i 9inche more than twice the length of the horter leg. Find the ide length of the triangle
Answers
The length of shorter leg is 15 inches, length of longer leg is 36 inches and the length of hypotenuse is 39 inches.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.
Let,
x = Longer leg of triangle
y = Shorter leg of triangle
h = Hypotenuse of triangle
Given: The length of the longer leg of a right triangle is 6inches more than twice the length of the shorter leg.
The length of the hypotenuse is 9inches more than twice the length of the shorter leg.
⇒ x = 6 + 2y
h = 9 + 2y
The given triangle is a right angled triangle.
⇒ x^2 + y^2 = h^2
(6 + 2y)^2 + y^2 = (9 + 2y)^2
36 + 24y + 4y^2 + y^2 = 81 + 36y + 4y^2
36 + 24y + 5y^2 = 81 + 36y + 4y^2
36 - 81 + 24y - 36y + 5y^2 - 4y^2 = 0
-45 - 12y + y^2 = 0
y^2 - 12y - 45 = 0
y^2 - 15y + 3y - 45 = 0
y(y - 15) + 3(y - 15) = 0
(y - 15)(y + 3) = 0
y - 15 = 0, y + 3 = 0
y = 15, y = -3
Since the length is not negative.
So, y = 15
Hence,
Shorter leg = 15 inchs
Longer leg = 6 + 2y = 6 + 2(15) = 36 inches
Hypotenuse = 9 + 2y = 9 + 2(15) = 39 inches
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4 tons of fertilizer cost $7,440.00. What is the price per pound?
Answers
Answer:
The correct answer would be 0.94 per pound.
Step-by-step explanation:
I'm tuck on thi quetion
A 2-gallon container of diinfectant cot $23. 76. What i the price per quart?
Answers
The price per quart of disinfectant is = $2.97
According to the information given in the question,
Quantity of the container of the disinfectants = 2 gallon
The price of a 2-gallon container of disinfectants = is $23.76
The concept used in this question is Ratio and Proportion,
The ratio is defined as the representation of two numbers in a fraction but in the case of ratio and proportion two numbers are separated by using a sign = ":"
Let us assume two numbers a and b,
If we have to present these two numbers in fractions = [tex]\frac{a}{b}[/tex].
If we have to present these two numbers in ratios = a : b.
According to the given question,
A 2-gallon container of disinfectants costs = $23.76
1 gallon = 4 quarts
So if 2 gallons = $23.762
= 2 gallons = 2 x 4
= 8 quarts
So, 8 quarts = $23.76
Now we will be dividing both sides by 8,
⇒ 1 quart = [tex]\frac{23.76}{8}[/tex]
⇒ 1 quart = $2.97
Therefore, the price per quart of disinfectant is = $2.97
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What is the length of the midsegment of a trapezoid whose vertices are I(-3, -5), J(8, -5), K(3, -9), and L(-3, -9)?
Answers
Answer:
the answer will be 4.75 units
Step-by-step explanation:
explained
The midsegment of a trapezoid is a line segment that connects the midpoints of the nonparallel sides of the trapezoid. To find the length of the midsegment, we need to first find the midpoints of the sides IJ and KL.
The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. We can find the midpoint of a line segment by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
The coordinates of the endpoints of the side IJ are (-3, -5) and (8, -5), so the midpoint of this side is:
((-3 + 8)/2, (-5 + (-5))/2) = (2.5, -5)
The coordinates of the endpoints of the side KL are (-3, -9) and (3, -9), so the midpoint of this side is:
((-3 + 3)/2, (-9 + (-9))/2) = (0, -9)
To find the length of the midsegment, we can use the distance formula to find the distance between the two midpoints:
sqrt((2.5 - 0)^2 + (-5 - (-9))^2) = sqrt(2.5^2 + 4^2) = sqrt(6.25 + 16) = sqrt(22.25) = 4.75
Therefore, the length of the midsegment of the trapezoid is approximately 4.75 units.
Look below for images I will give brainliest whoever gets its right! There are 5 trigonometry problems.
Answers
The measures of the angles and the values of the trigonometric functions are as follows;
33 (e) The angle is (450 - π)°
34 (f) The reference angle is 75°
40 (e) cos(θ) = -8/9
43 (e) sin(θ) = √3/2
What are trigonometric functions?The trigonometric functions provides the relationships between an angle and the three sides of a right triangle.
33 (e) The measure of the angle from the curve of the angle mark is found as follows;
The angle turned = 360 + (90 - θ)
Where; θ = π
Angle = 360° + (90 - π)° = (450 - π)°
34 (f) The reference angle is smallest (acute) angle made by the terminal side and the x-axis.
From the diagram, the reference angle is 360° - 285° = 75°
40 (e) The angle is in the Quadrant III
cos(θ) in Quadrant III is -cos(φ), where;
φ = θ - 180
From the diagram, cos(φ) = 8/√((-8)² + 17)
cos(θ) = -8/(√((-8)² + 17)) = -8/9
40 (f) The angle is in Quadrant II
sin(θ) = sin(φ), where; φ = 180 - θ
Therefore;
sin(φ) = 5/√((-3)² + 5²) = 5/√(34)
sin(θ) = sin(φ) = 5/√(34)
43 (e) sin(120°) = sin(180° - 120°) = sin(60°) = √3/2
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which of the following is true about sampling distributions? 1 point sampling distributions get closer to normality as the sample size increases. sampling distribution of the mean is always right skewed since means cannot be smaller than 0. sampling distributions are always nearly normal. shape of the sampling distribution is always the same shape as the population distribution, no matter what the sample size is.
Answers
A correct statement about sampling distributions is: Sampling distributions of means get closer to normality as the sample size increases.
The correct answer is an option (A)
In this question we have been given few statements.
We need to select a correct statement about sampling distributions.
We know that the sampling distribution is nothing but a probability distribution that is obtained through repeated sampling of a specific population.
Also according to central limit theorem, sampling distribution of means approaches normal when the sample size increases.
Therefore Sampling distributions of means get closer to normality as the sample size increases.
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based off of this information, what conclusions can be made about the mean value theorem? this contradicts the mean value theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 4) such that f '(c)
Answers
The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.
Explain the term Mean Value Theorem?The Mean Value Theorem says that there occurs a point c in the interval (a,b) so that f'(c) equals the function's average rate of change throughout [a,b] if a function f is continuous just on closed interval [a,b] as well as differentiable just on open interval (a,b).The function being used is;
f(x) = (x - 3)⁻²
If we separate this function according to x, we obtain;
f'(x) = -2/(x - 3)³
Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.
This suggests that;
0.06 - 0.25 = -2/(c - 3)³ x 6
-0.19 = -12/(c - 3)³
(c - 3)³ = 63.157
c = 6.98
If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).
But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.
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The complete question is-
Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This does not contradict the Mean Value Theorem since f is not continuous at x = 3. This does not contradict the Mean Value Theorem since f is continuous on (1, 7), and there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 , but f is not continuous at x = 3. Nothing can be concluded.letters x, y, and z are angle measures. which equations would guarantee that lines p and q are parallel? check all that apply.
a. x = z
b. x + y = 180 degree
c. x + z = 180 degree
d. x + y
e. y + z = 180
Answers
Answer:
Please read the assumptions that lead to the proposed answer of options a, b, and e being correct. Options c and d are easily rejected. The question is ambiguous about the locations of the angles.
Step-by-step explanation:
Parallel lines have slopes that are identical. Lines p and q have the same slopes.
It is difficult imagining what angles are represented by x, y, and z. There are only 2 lines, and they do not intersect. The locations of the angles are not identified. The lack of an intersecting point means it is free range as to where we assign the angles.
The attached graph illustrates some possibilities for x, y, and z. It uses two simple equations as examples, with the same slope to make them parallel. Assinment of any angles requires the use of an imaginary line that intersects the two parallel lines. Even then, there aren't many unique locations for the angles. To illustrate the analysis, lets assign the angles x, y, and z to thelocations shown on the graph.
Even with this huge step, there is limited information to be able to identify which of the answer options is correct. We can say that:
x = z
x+y=180
y+z=180
The answer options (below) appear to have similar relationships, so let's agree that the use of the imaginary line, plus the locations of x, y, and z are valid. Looking at the answer options, we can match choices a, b, and e to the conclusions above. d makes no sense because it is not an equation. c says that both lines must be perpendicular to the x axis, a limitation that is relatively immaterial to whether they are parallel. The condition of being parallel depends on those two angles being the same (e.g., 45 and 45, 22 and 22, etc.) and not require that they both be 90.
Answer Options Guarantee Parallel?
a. x = z Yes
b. x + y = 180 degree Yes
c. x + z = 180 degree No
d. x + y No
e. y + z = 180 Yes
Find a power series representation for the function.f(x) = x8 tan−1(x3)f(x) =[infinity] leftparen1.gifrightparen1.gifsum.gifn = 0
Answers
A power series representation for the function is:
x^8 tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^(6n + 11)/2n + 1)
In this question we need to find a power series representation for the function.
f(x) = x^8 tan^-1(x^3)
We know that the Maclaurin series:
1/(1 - x) = ∑[n = 0 to ∞] x^n
Replacing x with -x^2 we get,
1/(1 + x^2) = ∑[n = 0 to ∞] (-x^2)^n
= ∑[n = 0 to ∞] (-1)^n x^2n
Integrating above equation we get,
tan^-1(x) = ∑[n = 0 to ∞] (-1)^n (x^(2n + 1)/2n + 1) + c
For x = 0 we get c = 0
so, tan^-1(x) = ∑[n = 0 to ∞] (-1)^n (x^(2n + 1)/2n + 1)
Now we replace x by x^3, we get,
tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^3(2n + 1)/2n + 1)
Therefore, the required power series would be,
x^8 tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^(6n + 11)/2n + 1)
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Can anyone help me with this please???????
Answers
Answer:$785
Step-by-step explanation:
since she took money out already you have to add the to the pre existing total.
Liam's family has completed 40% of a trip. They have traveled 15 miles.
How far is the trip?
Answers
The number of miles the whole trip is 15 miles
What is the trip's length?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The number of miles the whole trip is 15 miles.Given that, Liam's family has completed 40% of a trip.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of miles be x.
so, 40% of x=30
⇒ 40/100 ×x=30
⇒ 0.4x=30
⇒ x=30/0.4
⇒ x=12 miles
Therefore, the number of miles the whole trip is 15 miles.
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Use this model to determine the answer.
What is 6÷1/3?
Answers
Answer:
18
Step-by-step explanation:
[tex]6/ 1/3[/tex] =
6 x 3
18
where would you have to be on this date to experience 12 hours of daylight and 12 hours of darkness? june 21
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how many bit strings of length 12 contain a) exactly three 1s? b) at most three 1s? c) atleastthree1s? d) an equal number of 0s and 1s?
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bit strings of length 12 contain a) exactly three 1s is 220 b) at most three 1s is 2700 c) atleastthree1s is 220 d) an equal number of 0s and 1s is 66.
a) To calculate the number of bit strings of length 12 containing exactly three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3).The solution is 12C3 = 220.
b) To calculate the number of bit strings of length 12 containing at most three 1s, we can use the summation formula. The formula is sum of nCr, where n is the total number of bits (12) and r is the number of 1s (3). So, the answer is (12C0 + 12C1 + 12C2 + 12C3) = 2700.
c) To calculate the number of bit strings of length 12 containing at least three 1s, we can use the combination formula. The formula is nCr, where n is the total number of bits (12) and r is the number of 1s (3). The solution is 12C3 = 220.
d) To calculate the number of bit strings of length 12 containing an equal number of 0s and 1s, we can use the combination formula. The formula is nCr
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