The point that divides a segment into two congruent segments is called the midpoint. Therefore, the answer is B) midpoint.
In geometry, a midpoint is a point that divides a line segment into two equal parts. It is the point on the line segment that is equidistant from both endpoints. The midpoint is important in geometry as it can be used to construct other geometric figures, such as perpendicular bisectors, which are lines that pass through the midpoint of a line segment and are perpendicular to it. For example, if we have a line segment AB, the midpoint M is the point that is exactly halfway between A and B, such that AM = MB. This can be found by drawing a perpendicular bisector of AB, which is a line that passes through the midpoint M and is perpendicular to AB. The perpendicular bisector will intersect AB at the midpoint M. It is important to note that the midpoint is not a bisector, ray, or point on a line. A bisector is a line, segment, or ray that divides an object into two congruent parts, while a ray is a part of a line that extends infinitely in one direction. The midpoint is simply the point that divides a line segment into two equal parts, and it is denoted by a symbol, such as a small vertical line with a hat on top, or by labeling the midpoint as a letter, such as M in the example above
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Which situation most accurately matches the graph?
A
im going to guess that the top of the graph has a flat line.
its easy to visualize since the graph looks like a hill, and the story describes the graph the most accurately
A travel club can spend at most 10 nights in two cities on a trip. The club needs to reserve four rooms each night and wants to spend no more than 4200 on hotels and fuel. The estimated fuel cost is 200 can the club spend 3 nights in city a and 6 nights in city b? 7 nights in city a and 3 nights in city b? justify your answer using a system of linear equations
To solve this system, we must first determine the number of available rooms in each city, as well as the per-night cost of hotel rooms. Without that information, we can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B.
Let's start by defining the variables we'll need to solve this problem:
Assume that x is the number of nights spent in City A.
Let y represent the number of nights in City B.
To determine whether the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, we must first determine whether the total cost of hotels and fuel for each scenario is less than or equal to $4200.
Given that the estimated cost of fuel is $200, the cost of hotels must be less than or equal to $4000.
The following equations calculate the cost of hotels for each scenario:
3x + 6y = cost of hotels for spending 3 nights in city A and 6 nights in city B7x + 3y = cost of hotels for spending 7 nights in city A and 3 nights in city BWe also know that the club can only spend a total of 10 nights, so x + y must be less than or equal to 10.
Finally, we must ensure that the club can book four rooms each night. This means that the number of rooms required per night in each city is four times the number of nights. As a result, we must have:
4x ≤ number of available rooms in city A4y ≤ number of available rooms in city BWhen we combine all of these constraints, we get the following system of linear equations:
3x + 6y + 200 ≤ 4200 (cost constraint for spending 3 nights in city A and 6 nights in city B)
7x + 3y + 200 ≤ 4200 (cost constraint for spending 7 nights in city A and 3 nights in city B)
x + y ≤ 10 (total number of nights constraint) (total number of nights constraint)
A city with 4x available rooms (room constraint for city A)
4y rooms available in city B (room constraint for city B)
To solve this system, we must first determine the number of available rooms in each city as well as the cost of hotel rooms per night. We can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, without that information.
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The Johnson twins were born seven years after their older sister. This year, the product of the three siblings ages is exactly 2693 more than the sum of their ages. How old are the twins?
The twins are 6 years old, and the oldest sister is 13 years old (since they were born seven years after their older sister).
What age range do twins fall into?7.3% of women under the age of 35. 6.9% of females aged 35 to 37. 6.8% of women aged 38 to 40 were female. 5.1% of females aged 41 to 42.
Starting out, let's assign some variables.
Let x represent the sister's older sister's age in years.
The twins' age is then x – 7. (since they were born seven years after their older sister).
We are told that the product of the three siblings' ages is 2693 more than the sum of their ages. This can be expressed algebraically as:
x(x - 7)(x - 7) = x + (x - 7) + (x - 7) + 2693
Simplifying this equation gives:
x³ - 21x² + 98x - 2693 = 0
We can see that x = 13 is a root of the equation, since:
13³ - 21(13)² + 98(13) - 2693 = 0
This means that (x - 13) is a factor of the equation.
We can use polynomial division or synthetic division to divide the equation by (x - 13) and obtain a quadratic equation:
x² - 8x + 207 = 0
The solutions of this quadratic equation are:
x = (8 ± sqrt(8² - 4(1)(207))) / 2 = 4 ± sqrt(241)
Since x represents the age of the older sister, which must be a positive integer, the only valid solution is:
x = 13
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The Son has got his Crown On The pharaoh’s outfitters, ‘Cloaks and Crowns’, sell Cloaks and Crowns in 3 sizes – prince, king and emperor (in increasing size order). He wants to kit out his three sons for the forthcoming festival of Ra. Ahmose chooses a bigger cloak than Kamose, but a smaller crown than Thutmose. Both Thutmose’s cloak and crown are larger than Kamose’s, but the size of Thutmose’s crown matches the size of Kamose’s cloak. Which sizes did the pharaoh’s sons each get?
The only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Let's us consider the sizes of the cloaks by C (prince), B (king), and A (emperor)
The sizes of the crowns by 1 (prince), 2 (king), and 3 (emperor).
Now let us write the following system of inequalities:
B > C
A > B
3 = C (Thutmose's crown matches Kamose's cloak)
2 > C
A > 3
A > 2 (Thutmose's crown is larger than the king size crown)
From the fifth inequality, we know that Thutmose's cloak is the largest of all three cloaks, so A must equal C.
Therefore, we can simplify the system of inequalities to:
B > C, A > B, C = 3, 2 > C, A > 3 and A > 2
Hence, the only possible solution for system is A = 2, B = 1, and C = 3, which means Thutmose got the emperor size crown and cloak, Kamose got the prince size cloak and king size crown, and Ahmose got the king size cloak and prince size crown.
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Here is a histogram showing
the times taken to complete
a task.
Estimate the percentage of
people who took less than
30 seconds to complete
the task.
Give your answer to
1 decimal place. Frequency
The percentage of people who took less than 30 seconds to complete
the task 84.4%.
The diagram shows us how many people finished the task in what time.
40 people finished in 5-10 seconds.
40 people finished in 10-15 seconds.
30 people finished in 15-20 seconds.
30 people finished in 20-25 seconds.
25 people finished in 25-30 seconds.
25 people finished in 30-35 seconds.
25 people finished in 35-40 seconds.
25 people finished in 40-45 seconds.
15 people finished in 45-50 seconds.
That is what the diagram is telling us, and what "frequency" means in this case.
Therefore,
In total, 255 people participated.
only the last 2 groups took longer than 40 seconds.
Therefore,
The estimate of how many took less than 40 seconds is
255 - 25 - 15 = 215 people.
215 people are how many % of 255 :
100% = 255
1% = 100%/100
= 255/100
= 2.55
215 is a many % as how often 1% fits into these 215 :
215 / 2.55 = 84.31372549%
≈ 84.4%
Complete Question:
Times taken to complete a task. Here is a histogram showing the times taken to complete a task.
40- Estimate the percentage of 35 people who took less than 40 seconds to complete the task.
Give your answer to 1 decimal place.
Frequency Density : 1 5 0 5
Time (Density) :
10 15 20 25 30 35 40 45 50
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the length of the altitude drawn to the hypotenuse of right triangle t is 8. if the length of the hypotenuse of t is 20, what is the length of the shortest leg of t ?
The length of the shortest leg of T is approximately 18.33 units. We are given that the length of the altitude drawn to the hypotenuse (h) is 8, and the length of the hypotenuse (c) is 20.
We can start by using the area formula for a triangle:
Area = 1/2 * base * height
In this case, the base is the length of the hypotenuse (c), and the height is the length of the altitude (h). So we have:
Area = 1/2 * c * h
Substituting the given values, we get:
Area = 1/2 * 20 * 8 = 80
We also know that T is a right triangle, so we can use the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values, we get:
a^2 + b^2 = 20^2
a^2 + b^2 = 400
We can now solve for b by substituting a in terms of h (using the formula for the area of a triangle) and simplifying:
Area = 1/2 * base * height
80 = 1/2 * 20 * h
h = 8
a = (2 * Area) / c
a = (2 * 80) / 20
a = 8
Substituting a and h in the Pythagorean theorem equation, we get:
8^2 + b^2 = 20^2
64 + b^2 = 400
b^2 = 336
b = sqrt(336)
b ≈ 18.33
Therefore, the length of the shortest leg of T is approximately 18.33 units.
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a car rental company offers two plans for renting a car: plan a: 30 dollars per day and 12 cents per mile plan b: 50 dollars per day with free unlimited mileage for what range of miles will plan b save you money for a 1 day rental? to save money the mileage must be greater than miles per day.
Plan B will save you money for a 1-day rental if you drive more than 166.67 miles.
To determine the range of miles for which Plan B will save money over Plan A for a 1-day rental, we need to set up an equation that compares the total cost of each plan.
For Plan A, the cost is given by:
Cost(A) = 30 + 0.12x
where x is the number of miles driven.
For Plan B, the cost is given by:
Cost(B) = 50
since there is no additional charge for mileage.
To determine the range of miles for which Plan B is cheaper than Plan A, we need to find the value of x for which:
Cost(B) < Cost(A)
Substituting the expressions for the costs of each plan, we get:
50 < 30 + 0.12x
Simplifying this inequality, we get:
0.12x > 20
x > 20 / 0.12
x > 166.67
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the days to maturity for a sample of five money market funds are shown here. the dollar amounts invested in the funds are provided. days to maturitydollar value ($ millions) 1515 1110 725 515 410 use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds. round your answer to decimal places. days
The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.
To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.
The calculation for the weighted mean is as follows:
Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)
where D represents the days to maturity and V represents the dollar value.
Using the given values, we can plug them into the formula and get:
Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)
Weighted Mean = 8.95 (rounded to two decimal places)
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select the correct answer. what is the solution to this equation? 3^2x = 1/3
Answer:
x= 1/27
Step-by-step explanation:
the correct answer is : X = 1/27
Answer:
- 1/2
Step-by-step explanation:
To solve for x in the equation 3^2x = 1/3, we can start by taking the logarithm of both sides with base 3:
log3 (3^2x) = log3 (1/3)
Using the logarithmic property logb (a^n) = n * logb (a), we can simplify the left side:
2x * log3 (3) = log3 (1/3)
Since log3 (3) = 1, we can simplify further:
2x = log3 (1/3)
To find the value of the logarithm on the right side, we can use the definition of logarithms: logb (a) = c if and only if b^c = a. Since 1/3 = 3^-1, we have:
2x = log3 (3^-1) = -1
Finally, to solve for x, we divide both sides of the equation by 2:
x = -1/2
So the solution to the equation 3^2x = 1/3 is x = -1/2.
Which hotkey can be used to switch from Obiect Mode to Edit Mode and back in
Blender?
please help with show work. urgent
Answer:
51
Step-by-step explanation:
How are the ordered pairs (,) and (,−) similar, and how are they different? Are the two points related by a reflection over an axis in the coordinate plane? If so, indicate which axis is the line of symmetry between the points. If they are not related by a reflection over an axis in the coordinate plane, explain how you know.
Answer: no exact answer
Step-by-step explanation:
Please Help Me!!!!!!!
Answer: the answer is sos not please help me dude
Step-by-step explanation:
but you use kami and go to files and download the pdf use kami
Mathematics: What is a mean
Find the approximate values of the five number summary for the data set represented by this box plot,
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
The Approximate values of the five number summary are ;
(i) the Minimum is 10 ,
(ii) the First quartile is 30 ,
(iii) the Third Quartile is 80 ,
(iv) the Median is 55 ,
(v) the Maximum is 100 .
The values of the data set are : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 ,55 ,60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
The Five number summary consists of the minimum , maximum , first quartile , third quartile and the median .
(i) the Minimum of the data set is = 10 ;
(ii) we split the data set into , 2 halves ;
that means ; {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } and {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
the first quartile lies in the lower half : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } ;
So , first quartile (Q₁) = 30 ;
(iii) the third quartile (Q₃) lies in the upper half : {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
So , Q₃ = 80 ;
(iv) the total number of terms in the set is = 19 ;
So , the median is = tenth term = 55 ;
(v) the maximum of the data set is = 100 .
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< A and < B are complementary angles.
< A = 3 x - 2 and < B = 2 x + 12
Find the measure of < A :
Answer: The measure of Angle A is 46 degrees.
Step-by-step explanation:
Complementary angles are angles that when both added together are equal to 90 degrees. So the measure of angle A plus the measure of angle B is equal to 90 or 3x - 2 + 2x + 12 = 90. Add like terms so you get 5x + 10 = 90. Subtract 10 on both sides you get 5x = 80. Divide by 5 on both sides and you get x = 16. To find the measure of angle A, plug in your x value. So M<A = 3(16) - 2. Ange A is equal to 46. I double checked my answer too and plugged my x value into M<B and got 44. So indeed 44 + 46 = 90.
V = Sp.v solve for v
Answer: Given the equation V = Sp.v, to solve for v, we need to divide both sides of the equation by Sp.
V / Sp = v
So v = V / Sp
Here, V is the volume of the item being sold, Sp is the price per unit, and v is the number of units being sold. By dividing V by Sp, we can find the number of units being sold (v) at a given price per unit.
Step-by-step explanation:
question 14
pls help me asap i am being timed
Answer:
164 degree is the answer
Answer:
Step-by-step explanation:
Chord PM and PN are equal
arc PM = arc PN
164=5x+4
x=32
arc PN = 5x+4 = 5(32)+4=164
Each month, Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars for his family. Crunchy granola bars come in boxes containing x bars, and chewy granola bars come in boxes containing y bars. Write two equivalent expressions for the total number of granola bars Tomas buys after 5 months. (5(__x+__y) and __x+__y)
The two equivalent expressions for the total number of granola bars Tomas buys after 5 months is 5(4x + 2y) and 20x + 10y
In mathematics, an expression is a combination of symbols (such as numbers, variables, and operators) that represent a mathematical object or value.
Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars each month. Let's assume that each box of crunchy granola bars contains x bars and each box of chewy granola bars contains y bars.
To express the total number of granola bars that Tomas buys in one month, we can use the following expression:
4x + 2y
This expression shows that Tomas buys 4 boxes of crunchy granola bars, each containing x bars, and 2 boxes of chewy granola bars, each containing y bars.
To find the total number of granola bars that Tomas buys after 5 months, we need to multiply the expression by 5, since he buys granola bars each month for 5 months. This gives us the expression:
5(4x + 2y) = 20x + 10y
Alternatively, we can also express the total number of granola bars that Tomas buys in 5 months using the following expression:
5x(4) + 5y(2) = 20x + 10y
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help asap pls. question in pic
the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
One side of rectangle is 200m
When the measure of the other side is 50 m
the area will be 50*200 = 1000m².
The expression of area A(x) = 200x,
hence the area of the rectangle is 1000m² and The expression of the area A(x) = 200x,
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Use the Pythagorean Theorem to find the distance between points F and C.
A. 2 √3
B. √41
C. 4 √3
D. 3 √5
Answer:
D. 3√5
Step-by-step explanation:
The distance between points F and C is the hypotenuse of a right triangle. Therefore we can use Pythagoras Theorem to calculate the distance between these points.
From inspection of the given graph the coordinates of the two points are:
Point C = (2, 2)Point F = (-4, -1)The horizontal difference between the x-coordinates is:
[tex]x_C-x_F=2-(-4)=6\; \sf units[/tex]
The vertical difference between the y-coordinates:
[tex]y_C-y_F=2-(-1)=3\; \sf units[/tex]
Therefore, we have a right triangle with the following dimensions:
Leg a = 3Leg b = 6Hypotenuse c = CF[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
To calculate the length of the hypotenuse, and therefore the distance between points C and F, substitute the values into the Pythagoras Theorem formula and solve for CF:
[tex]\implies a^2+b^2=c^2[/tex]
[tex]\implies 3^2+6^2=CF^2[/tex]
[tex]\implies 9+36=CF^2[/tex]
[tex]\implies CF^2=45[/tex]
[tex]\implies \sqrt{CF^2}=\sqrt{45}[/tex]
[tex]\implies CF=\sqrt{9 \cdot 5}[/tex]
[tex]\implies CF=\sqrt{9} \sqrt{5}[/tex]
[tex]\implies CF=3\sqrt{5}[/tex]
Therefore, the distance between points F and C is 3√5.
Find the missing side length using trig
Answer:
29.22
Step-by-step explanation:
convert 26kg 45g into kg
Answer:
As 1000g=1 kg ⟹1g=
1000
1
kg.
26 kg 50 g.
=26 kg+50 g
=26 kg+50(
1000
1
)kg.
=26+0.05 kg.
=26.05 kg.
Answer: 26kg, 0.045kg
Step-by-step explanation:
a college student organization wants to start a nightclub for students under the age of 21. to assess support for this proposal, they will select an srs of students and ask each respondent if he or she would patronize this type of establishment. what sample size is required to obtain a 90% confidence interval with a margin of error of at most 0.04?
A sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.
To determine the required sample size for a 90% confidence interval with a margin of error of at most 0.04, we can use the formula:
[tex]n = \left(\frac{z \cdot \sigma}{E}\right)^2[/tex]
where:
n is the sample size
z is the z-score associated with the desired confidence level (90% confidence level corresponds to z = 1.645)
σ is the standard deviation of the population (unknown, so we use 0.5 as a conservative estimate, since the proportion of students who would patronize the nightclub is unknown and assumed to be 0.5 for maximum variability)
E is the maximum desired margin of error (0.04)
Plugging in the values, we get:
n = (1.645 * 0.5 / 0.04)²
n ≈ 424
Therefore, a sample size of at least 424 students is required to obtain a 90% confidence interval with a margin of error of at most 0.04.
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Part 4: Fill in the blank. cos (56°) = sin(°)
The complete expression in the blank is cos (56°) = sin(34°)
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
cos (56°) = sin(°)
The blank expression can be calculated as
When x + y = 90;
sin(x) = cos(y)
Using the above as a guide, we have the following:
Blank + 56 = 90
Evakuate the like terms
Blank = 34
So, we have
cos (56°) = sin(34°)
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Simplify the expression.
-9(a + b) - 3a
The balance in an account after several transaction is shown in the table. Is the relationship between the balance and the number of withdrawals of linear? Blank If so, find the constant rate of change. Write the slope as a unit rate and explain your reasoning.
It should be noted that the relationship between the balance and the number of withdrawals is linear, because there is a constant amount of $10 per withdrawal.
How to express the relationshipTo confirm this, we can calculate the differences in balance for each pair of withdrawals:
Between withdrawals 3 and 2: 170 - 140 = 30
Based on the information, the starting amount is $200.
The equation to illustrate the withdrawal will be:
= 200 - 10w
where w = withdrawal.
These differences are constant, which means the rate of change of the balance is constant too.
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Use the grouping method to factor the polynomial below completely. 3x³ + 9x² + 5x + 15 O A. (3x²+3)(x + 5) O B. (3x²+5)(x+3) ○ C. (3x² + 3)(x+3) D. (3x² + 5)(x + 5)
The factor of the expression is (3x²+ 5)(x + 3)
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
3x³ + 9x² + 5x + 15
Group the terms in two's and factor each term
Using the above as a guide, we have the following:
3x²(x + 3) + 5(x + 3)
Factor out x + 3
So, we have the following representation
(3x²+ 5)(x + 3)
Hence, the solution is (3x²+ 5)(x + 3)
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What is the radius of a circle whose circumference measures 154 inches?
Answer: 77
Step-by-step explanation: to find the radius divide the circumference by 2.
Paul came in with a discovery about subtracting integers. Rather than subtracting, Paul says all he has to do I add the opposite of the second number, Create a subtraction problem with integer tiles and check out Paul's claim. Is paul right?
Answer:
Subtracting integers can be represented using integer tiles. For example, if we want to subtract -3 from 4, we can lay out 4 tiles on the number line and then add -3 tiles, like this:
4 3 2 1 0 -1 -2 -3
The subtraction problem can be represented as 4 + (-3). Adding the opposite of the second number, as Paul suggests, means finding the sum of 4 and -3, which is 1. So, Paul is correct that subtracting integers is equivalent to adding the opposite of the second number.
