The directed line segment PQ is divided at this point at a 3:1 ratio (1, 8)
According to the section formula, the coordinates of a point R may be determined by dividing a line segment PQ by that point in the ratio m:n as follows:
[tex]R_x = (n * Px + m * Qx) / (m + n)\\R_y = (n * Py + m * Qy) / (m + n)[/tex]
where [tex]P_x, P_y[/tex] are the coordinates of point P, and [tex]Q_x, Q_y[/tex] are the coordinates of point Q.
In this case, we want to divide the line segment PQ in a ratio of 3:1. This means that m = 3 and n = 1.
Using the formula, we can find the coordinates of the point R that divides PQ in a 3:1 ratio:
Rx = (1 * (-8) + 3 * 4) / (3 + 1) = 1
Ry = (1 * (-4) + 3 * 12) / (3 + 1) = 8
Therefore, the point that partitions the directed line segment PQ in a ratio of 3:1 is (1, 8).
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107/103 X 101/100 =
What is 107 over 103 times 101 over 100
107 over 103 times 101 over 100 would result in 10807/10300.
Mathematical operationsIn order to multiply the fractions 107/103 and 101/100, we can simply multiply their numerators together and their denominators together:
(107/103) x (101/100) = (107 x 101) / (103 x 100)
Now we can simplify this fraction by finding the greatest common factor of the numerator and denominator and dividing both by it:
(107 x 101) / (103 x 100) = 10807 / 10300
Therefore, 107/103 times 101/100 simplifies to 10807/10300.
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Kendra is doing her math homework. For each problem, she uses 12
1
2
of a sheet of paper. How many sheets of paper will she need to complete 10 problems?
There are 5 sheets of paper will she need to complete 10 problems.
We have to given that;'
Kendra is doing her math homework. For each problem, she uses 1/2 of a sheet of paper.
Hence, For complete 10 problems, number of sheets are,
⇒ 1/2 of 10
⇒ 1/2 x 10
⇒ 5
Thus, There are 5 sheets of paper will she need to complete 10 problems.
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∠A and ∠ � ∠B are vertical angles. If m ∠ � = ( 2 � − 2 ) ∘ ∠A=(2x−2) ∘ and m ∠ � = ( 3 � − 15 ) ∘ ∠B=(3x−15) ∘ , then find the value of x.
The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees
How to find the value of x.From the question, we have the following parameters that can be used in our computation:
∠A = (2x − 2)
∠B = (3x − 15)
Since the ∠A and ∠B are vertical angles, then they are congruent angles
So, we have
3x - 15 = 2x - 2
Evaluate the like terms
So, we have
x = 13
Hence, the solution is x = 13
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Find the total cost for the month in dollars. The federal tax is 3%. Use the figure below.
Monthly phone service plan is $52.00. Four lines and 3,487 minutes are used.
Answer:
The total cost per month is $190.76 to the nearest cent.
Step-by-step explanation:
From the given table, the monthly service plan costing $52.00 is:
Monthly Service Plan = $52.00Number of included minutes per month = 2,000 minutesCost per additional line per month = $21.99Overage per minute rate = $0.06The base calling plan includes two lines.
Therefore, for 4 lines, we will need to pay for 2 additional lines per month:
⇒ $21.99 × 2 = $43.98 per month
If 3,487 minutes are used per month, then the overage of minutes is:
⇒ 3487 - 2000 = 1487 minutes per month
As the overage rate is $0.06 per minute, then the cost of the additional minutes is:
⇒ 1487 × $0.06 = $89.22 per month
Therefore, the total cost per month before tax is:
⇒ $52.00 + $43.98 + $89.22 = $185.20
To apply the federal tax of 3%, multiply the total cost by 1.03:
⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)
Therefore, the total cost per month is $190.76 to the nearest cent.
math hw for tonight
help solve this problem! Thank you!
ap cal bc
Answer:
3t^2i + 2tj is the correct answer.
Plot the coordinates on the number line provided and then find the coordinate of the indicated point
on a number line that partitions the segment into the given ratio.
A is at 1, and B is at 10. Find the point, T, so that T is two-thirds of the distance from A to B.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
4 5 6 7 89
+
10
Answer:
t = 6.8
Explanation:
We know that A is at 1, B is at 10, so that is where we place those two.
First, we need to know what 2/3 of 10 is because the distance between A and B is 10.
Solving 2/3 of 10:
_____________________
- Divide 10 by the denominator, 3
10 ÷ 3 = 3.3333......
- Multiply 3.3333..... by 2
3.3333..... x 2 = 6.6666666666667
or about 6.8 if we round up, which is prefered in these scenarios
Now that we know what 2/3 of 10 is, we can use that number as where to put it on the number line.
So t = 6.8
Hope this helps :)
Circle A has a circumference of 8π/x+2 units and Circle B has a circumference of 4π/x+2 units. What is a simplified expression for the difference in the areas of Circle A and B
The simplified expression for the difference in the area of circle A and B is 12π/(x+2)²
What is area of a circle?A circle is simply a round shape that has no corners or line segments. The area of a circle is expressed as;
A = πr²
The circumference of a circle = 2πr
for circle A;
8π/x+2 = 2πr
r = 8π/x+2 × 1/2π
r = 4/x+2
area = πr² = (4/x+2)²π
for circle B
4π/x+2 = 2πr
r = 4π/x+2 × 1/2π
r = 2/2x+2
area =( 2/2x+2)²π
difference = (4/x+2)²π - ( 2/x+2)²π
= π/(x+2)²( 4²-2²)
= π/(x+2)²(16-4)
= 12π/(x+2)²
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What is the initial value of Y=2x+3
Answer:3
Step-by-step explanation: Initial value = y-intercept
In a normal distribution, what percentage of the data falls within 2 standard
deviations of the mean?
A. 99.7%
B. 68%
C. 34%
D. 95%
The percentage of the data that falls within 2 standard deviations of the mean is B. 68%
Calculating the percentage of dataFrom the question, we have the following parameters that can be used in our computation:
Percentage = 2 standard deviations
As a general rule:
The percentage of the data that falls within 2 standard deviations of the mean is 68%
This means that the correct option is (b) 68%
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Please help me PLEASE ANYEONE?!!!?!!
Step-by-step explanation:
1/3 ÷ 3
= 1/3 ÷ 3/1
= 1/3 X 1/3 = 1/9
Similarly
1/4 ÷ 5 = 1/4 X 1/5 = 1/20
The change in water level of a pond is shown in the table.
Week
1
2
3
4
5
Water level (inches)
-1 1/4
1 3/8
2 1/2
-1 5/8
-1 3/4
Between which two weeks did the water level change the most? Calculate the change.
Between Weeks 3 and 4, the water level varied the greatest.
To determine which two weeks had the greatest change in water level, we need to find the difference between each pair of consecutive weeks and identify the largest difference.
Here are the differences between consecutive weeks:
Week 1 to Week 2: (1 3/8) - (-1 1/4) = 2 5/8
Week 2 to Week 3: 2 1/2 - 1 3/8 = 1 1/8
Week 3 to Week 4: (-1 5/8) - 2 1/2 = -4 1/8
Week 4 to Week 5: (-1 3/4) - (-1 5/8) = -1/8
The largest difference is between Week 3 and Week 4, with a difference of 4 1/8 inches.
Therefore, the water level changed the most between Week 3 and Week 4.
Note that the differences are calculated by subtracting the water level of the earlier week from the water level of the later week.
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I need help on the things in the image
The match of the given words as per the definition of the terms related to data set is as follow.
1 → g
2 →c
3 → b
4 → d
5 → f
6 → a
7 → e
The description of the each word as per the definition is ,
Mean represents the average of the data.
1→g
Spread represents the similarity or variability of the set of observed values of the data.
2→c
Center represents the middle value of the data set.
3→ b
Shape represents the values of the data set when plotted on the graph.
4 → d.
Median represents the middle value of the data set after arranging in ascending or descending order.
5 →f
Distribution represents measure of all the values of the data set spread.
6→a
variability represents the set of such values which satisfies the statistical question or relation.
7 → e.
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An online television company is sending out surveys to rank 10 TV-show genres watched. What is the probability that you guess the top 3 genres correctly and in the correct order?
Write your answer as an exact fraction which is reduced as much as possible.
Answer:
The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:
1/10 * 1/9 * 1/8 = 1/720
So the exact probability is 1/720, which is already reduced to its simplest form.
please help me i relly need help
Answer:
h(x) = 3·2^x
Step-by-step explanation:
You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).
PointsWhen x=0, the equation is ...
h(0) = a·b^0 = a
We know that h(0) = 3, so a = 3.
When x=1, the equation is ...
h(1) = 3·b^1 = 3b
We know that h(1) = 6, so 3b = 6, or b = 2.
The equation is h(x) = 3·2^x.
<95141404393>
binge drinking and auto accidents
44% engaged binge drinking
37% drank moderately
9% abstain
17% accident/binge
9% accident/non-binge
what’s p(accident/abstain)
Answer:
We can solve this problem using the following steps:
1. **Calculate the probability of being in each group.**
The probability of being in the binge drinking group is 44%.
The probability of being in the moderate drinking group is 37%.
The probability of being in the abstain group is 9%.
2. **Calculate the probability of being in the accident group.**
The probability of being in the accident group is 17% + 9% = 26%.
3. **Calculate the probability of being in the abstain group and having an accident.**
The probability of being in the abstain group and having an accident is the probability of being in the abstain group multiplied by the probability of having an accident, given that you are in the abstain group.
The probability of being in the abstain group is 9%.
The probability of having an accident, given that you are in the abstain group, is the probability of being in the accident group and being in the abstain group, divided by the probability of being in the abstain group.
The probability of being in the accident group and being in the abstain group is 9%.
The probability of being in the abstain group is 9%.
Therefore, the probability of having an accident, given that you are in the abstain group, is 9% / 9% = 1.
4. **Calculate the probability of having an accident and being in the abstain group.**
The probability of having an accident and being in the abstain group is the probability of being in the abstain group and having an accident.
The probability of being in the abstain group is 9%.
The probability of having an accident, given that you are in the abstain group, is 1.
Therefore, the probability of having an accident and being in the abstain group is 9% * 1 = 9%.
**Answer:**
The probability of having an accident and being in the abstain group is 9%.
answer quick i need done
The new vertices of the triangle after moving the triangle 5 units down, are A(1,-7), B(9,-7), and C(5,-3). So, correct option is B.
To determine the coordinates of the triangle after it is translated 5 units down, we need to subtract 5 from the y-coordinates of each vertex.
Let's start with vertex A(1,-2). If we subtract 5 from -2, we get -7. Therefore, the new coordinates of vertex A are (1,-7).
Next, let's look at vertex B(9,-2). Again, if we subtract 5 from -2, we get -7. So the new coordinates of vertex B are (9,-7).
Finally, let's consider vertex C(5,2). If we subtract 5 from 2, we get -3. So the new coordinates of vertex C are (5,-3).
In this case, we are moving the triangle 5 units down, which means that we are subtracting 5 from the y-coordinates of each vertex. This is a common transformation in geometry, and it's important to be familiar with it when working with shapes and figures in the Cartesian plane.
So, correct option is B.
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If the price of a particular chocolate bar is increased by 20%, and it used to be $2, what is the new price after the increase?
2. Solve 4.3(n + 6) > 47.3. Then graph the solution.
Answer: n>5
Step-by-step explanation:
An object is dropped from a height of 400 feet. The amount of time, in seconds, the object takes to hit the ground can be found by solving the equation - 16r2 + 400 = 0. How many seconds will it take to hit the ground?
05
O 5 or-5
O 12
O 25
It will take 5 seconds for the object to hit the ground
How many seconds will it take to hit the ground?From the question, we have the following equation that can be used in our computation:
-16r^2 + 400 = 0
So, we have
- 16r^2 = -400
Divide by -16
This gives
r^2 = 25
Take the square root of both sides
r = 5
Hence, the number of seconds is 5
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use your knowledge of transformations to find matching graph f (x) = ½ √x - 1
Answer:
Step-by-step explanation:
down 1
compress 1/2
the salaries of engineers at a computer company are normally distributed with mean $83,422 and standard deviation $8,278
The probability of observing an income between $70,000 and $90,000 for engineers at this computer company is 0.6217, or about 62.17%.
To solve this problem, we need to standardize the given income range using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can do this by using the formula:
z = (x - μ) / σ
where x is the income, μ is the mean income, and σ is the standard deviation.
For the lower bound of $70,000, we have:
z₁ = (70,000 - 83,422) / 8,278 = -1.62
For the upper bound of $90,000, we have:
z₂ = (90,000 - 83,422) / 8,278 = 0.79
We can now find the probability of observing an income between $70,000 and $90,000 by calculating the area under the standard normal curve between z₁ and z₂.
We can use a standard normal distribution table or a calculator to find this probability, which turns out to be approximately 0.6217. This means that about 62.17% of engineers at this company earn an income within this range.
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Complete question is:
The salaries of engineers at a computer company are normally distributed with mean $83,422 and standard deviation $8,278. What is the probability of observing an income between $70,000 and $90,000?
Molly has four t-shirts in her closet that she plans to wear over the next four days without wearing the same one twice. She has a blue, green, yellow, and black shirt. What are the chances that she will wear the black shirt the first day?
Write your answer as an exact fraction which is reduced as much as possible.
Answer:
Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.
Step-by-step explanation:
Which choices are equivalent to the expression below? Check all that apply.
4√3
A. 48
B. 12.4
C. √24√2
D. 3 16
E. 4.3
F. 48
The choices that are equivalent to the expression 4√3 will be ✓48 and ✓24.✓2.
How to explain the expressionIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
4✓3 will be:
= ✓4² × ✓3
= ✓48
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geometry pls helpppppp
A graph of triangle TOW is shown below.
A graph of triangle T'O'W, the image of ΔTOW after a reflection in the y-axis is shown below.
The coordinates of ΔT'O'W are: T' (5, 6), O' (-1, 8), and W' (4, -2).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (-x, y)
T (-5, 6) → (-(-5), 6) = T' (5, 6)
O (1, 8) → (-(-1), 8) = O' (-1, 8)
W (-4, -2) → (-(-4), -2) = W' (4, -2)
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F(x) = 2^x
Elija todas las siguientes afirmaciones que describen el gráfico.
A. Cuando x tiende a infinito negativo, f(x) tiende a 0.
B. Cuando x tiende a infinito negativo, f(x) tiende a infinito.
OC. Cuando x tiende a infinito, f(x) tiende a 0.
OD. Cuando x tiende a infinito, f(x) tiende a infinito.
By analyzing the end behavior of the function we can see that the correct options are A and D.
Which statements are true for the given function?Here we have the exponential function:
[tex]F(x) = 2^x[/tex]
This is an exponential growth, this means that as x increases also does the function, then the end behavior of the function is:
as x → ∞, f(x) → ∞
And when x is a really large negative number, the function tends to zero, then we have:
as x →-∞, f(x) → 0
Then the correct options are A and D.
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a parallelogram has a base of 6 centimeters and a height of 10 centimeters. this parallelogram has the same area as a triangle with a height of 5 centimeters. what is the measure, in centi,of the base of the triangle?
The area of the parallelogram can be found using the formula A = base × height:
A = 6 cm × 10 cm
A = 60 cm²
The area of a triangle is given by the formula A = 1/2 × base × height. We know the height is 5 cm and the area is also 60 cm² (since it is equal to the parallelogram). So, we can solve for the base:
60 cm² = 1/2 × base × 5 cm
Dividing both sides by 1/2 × 5 cm gives:
base = 24 cm
Therefore, the base of the triangle is 24 centimeters.
Answer:
24cm
Step-by-step explanation:
Circle the students error in the problem below and rewrite what correct step should be
The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4
Circling the students errorFrom the question, we have the following parameters that can be used in our computation:
The steps to solve the expression
From step 2 to step 3, we have
g(x) = 2(x + 1)(x + 1) - 6
g(x) = 2(x² + 1x + 1) - 6
The step 3 is incorrect
Because when the expression is expanded, we have
g(x) = 2(x² + 2x + 1) - 6
This gives a solution of
g(x) = 2x² + 4x - 4
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The constraints of a problem are listed below. What are the vertices of the feasible region?
[tex]x+y\leq 7\\x-2y\leq -2\\x\geq 0\\y\geq 0[/tex]
The vertices of the feasible region is (4, 3)
What are the vertices of the feasible region?From the question, we have the following parameters that can be used in our computation:
x + y ≤ 7
x - 2y ≤ -2
x ≥ 0
y ≥ 0
Express as equations
So, we have
x + y = 7
x - 2y = -2
Subtract the equations
3y = 9
So, we have
y = 3
Next, we have
x + 3 = 7
This gives
x = 4
Hence, the vertex of the feasible region is (4, 3)
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how much cardboard is needed to make the single slice pizza box shown
that would be 5 pieces of cardboard needed
Please please help me with my work thank you
The match to A line that has a slope of 5/3 and a y-intercept of 4 is 2y - x = -4.
We are given that;
The four equations to match from
Now,
Using the slope-intercept form, we can plug in m = 3/2 and b = -8:
y = (3/2)x - 8
This equation matches with y = 3/2x - 5 if we multiply both sides by 2:
2y = 3x - 16
Therefore, the correct equation is 2y - x = -16.
A line that contains the points (0,-2) and (4,0)
m = (0 - (-2)) / (4 - 0) m = 2 / 4 m = 1/2
Then we can plug in m = 1/2 and any of the given points to find b. For example, using (0, -2), we have:
-2 = (1/2)(0) + b -2 = b
Therefore, the equation is:
y = (1/2)x - 2
This equation matches with -5x - 3y = -12 if we multiply both sides by -6:
6y = -3x + 12
Therefore, the correct equation is -5x - 3y = -12.
A line that contains the y-intercept (0-2) and the slope of -3/4
Using the slope-intercept form, we can plug in m = -3/4 and b = -2:
y = (-3/4)x - 2
This equation matches with y = -3/4x - 2.
A line that has a slope of 5/3 and a y-intercept of 4
Using the slope-intercept form, we can plug in m = 5/3 and b = 4:
y = (5/3)x + 4
This equation matches with 2y - x = -4 if we multiply both sides by 3:
3y = (5/3)x + 12
Therefore, the correct equation is 2y - x = -4.
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