The measure of CA is equal to measure of CB or CA=CB by the Side Angle Side congruence postulate.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other, known as parallel lines.
We have a statement:
a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
Consider the line segment AB,
let D be the midpoint of AB, so AD=DB
CD ⊥ AB
The triangles CAD and CBA are congruent from the Side Angle Side congruence postulate:
AD = DB, CD is common and Angle CDA = angle CDB = 90°, as CD ⊥ AB
So CA=CB
Thus, the measure of CA is equal to measure of CB or CA=CB by the Side Angle Side congruence postulate.
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the high school mathematics teacher handed out grades for his opening statistics test. the scores were as follows. 62, 66, 71, 80, 84, 88 (a) identify the lower and upper quartiles. Q1 =
Q2 =
(b) Calculate the interquartile range, Entram wat marker.
a) Q1 = 66 and Q3 = 84
b) the interquartile range is 18.
What is the domain and range?
The domain and range are fundamental concepts in mathematics that are used to describe the input and output values of a function or relation.
The domain of a function refers to the set of all possible input values, or x-values, for which the function is defined.
The range of a function refers to the set of all possible output values, or y-values.
To identify the lower and upper quartiles and calculate the interquartile range for the given scores, we need to arrange the scores in ascending order.
Arranging the scores in ascending order: 62, 66, 71, 80, 84, 88
(a) Lower and Upper Quartiles:
The lower quartile, denoted as Q1, is the median of the lower half of the data. It divides the data into two equal parts, with 25% of the scores below and 75% above.
Q1 = 66 (the value in the middle of the lower half of the data)
The upper quartile, denoted as Q3, is the median of the upper half of the data. It divides the data into two equal parts, with 75% of the scores below and 25% above.
Q3 = 84 (the value in the middle of the upper half of the data)
(b) Interquartile Range:
The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). It measures the spread of the middle 50% of the data.
IQR = Q3 - Q1
= 84 - 66
= 18
Therefore, a) Q1 = 66 and Q3 = 84
b) the interquartile range is 18.
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A box contains 20 miniature golf putt-putt balls; 10 are
yellow, 6 are red, and 4 are pink. What is the probability of
picking a red golf ball, replacing it, and then picking a
yellow golf ball? Written as a percent?
Answer: The answer is provided below
Step-by-step explanation:
From the question, a box contains 20 miniature golf putt-putt balls out of which 10 are yellow, 6 are red, and the remaining 4 are pink.
The probability of picking a red golf ball will be:
= 6/20 × 100
= 600/20
= 30%
If the red ball is replaced, the probability of picking a yellow golf ball will be:
= 10/20 × 100%
= 50%
a scale model of a building is 3 inches tall. if the building is 90 feet tall, find the scale of the model. a. 1in: 20ft c. 1:25 b. 1ft: 20in d. 1 in: 30ft
The scale of the model is 1 inch : 30 feet (option d).
To determine the scale of the model, we need to compare the height of the model to the actual height of the building. Given that the height of the model is 3 inches and the height of the building is 90 feet, we can set up a ratio to find the scale.
Let's denote the scale as "1 inch : X feet". Setting up the ratio, we have:
1 inch / X feet = 3 inches / 90 feet.
To solve for X, we can cross-multiply:
3 inches * X feet = 1 inch * 90 feet.
Simplifying the equation:
3X = 90.
Dividing both sides by 3, we find:
X = 30.
Therefore, the scale of the model is 1 inch : 30 feet (option d). This means that each inch on the model represents 30 feet in the actual building. So, for every 1 inch of the model's height, the real building's height corresponds to 30 feet.
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Helpppp quick I give brainliest
William is a window washer and needs to lean his ladder against the house to reach the windows at the top. he sets the ladder 8 feet from the house which is 14 feet tall. what is the minimum length ladder he needs to use to reach the top of the house?
a² + b² + c²
Answer:
Step-by-step explanation:
you will need a 10ft tall ladder
i hope that helped
what type of variable would necessitate using a hypothesis test of the population proportion rather than a test of the population mean? multiple choice categorical ratio-scaled incorrect interval-scaled numerical
The type of variable that would necessitate using a hypothesis test of the population proportion rather than a test of the population mean is: Categorical data.
What is Categorical data?Categorical data is another name for qualitative data and this refers to a sort of data that is not easily obtained by counting. This form of data can employ hypothesis testing. Hypothesis testing uses data to arrive at conclusions about population parameters.
A null hypothesis is first proposed after which the conclusions are made. So, instead of the numerical testing of the population mean, a hypothesis test of the population is used for the qualitative or categorical data.
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x2 +16x – 36/x2 + 6x-16
Answer:
x^4+23x^3-16x^2-36/x^2
Step-by-step explanation:
Answer:
\(\frac{x+18}{x+8}\)
Step-by-step explanation:
Assuming you require the simplification.
Given
\(\frac{x^2+16x-36}{x^2+6x-16}\) ← factorise numerator and denominator
= \(\frac{(x+18)(x-2)}{(x+8)(x-2)}\) ← cancel the common factor (x - 2)
= \(\frac{x+18}{x+8}\)
Work out (6 × 102) ÷ (3 × 10 °)
Give your answer in standard form.
Answer:
102/5
Step-by-step explanation:
* Ono 3 b) P and are the subsets of universal set U. If n (p) = 55% n (Q) = 50% and n(PUO)complement = 15% find: (i) n(PUQ) (ii) n(PDQ) (iii)n(only P) iv. n(only Q).
The probability of the sets are solved and
a) n(P U Q) = 85%
b) n(P ∩ Q) = 20%
c) n(only P) = 35%
d) n(only Q) = 30%
Given data ,
P and are the subsets of universal set U
And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%
Now , we'll use the formula for the union and intersection of sets:
n(P U Q) = n(P) + n(Q) - n(P ∩ Q)
n(P ∩ Q) = n(P) + n(Q) - n(P U Q)
n(only P) = n(P) - n(P ∩ Q)
n(only Q) = n(Q) - n(P ∩ Q)
We're given that:
n(P) = 55%
n(Q) = 50%
n(P U Q)' = 15%
To find n(P U Q), we'll use the complement rule:
n(P U Q) = 100% - n(P U Q)'
n(P U Q) = 100% - 15%
n(P U Q) = 85%
Now we can substitute the values into the formulas above:
(i)
n(P U Q) = n(P) + n(Q) - n(P ∩ Q)
n(P ∩ Q) = n(P) + n(Q) - n(P U Q)
n(P ∩ Q) = 55% + 50% - 85%
n(P ∩ Q) = 20%
(ii)
n(P ∩ Q) = 20%
(iii) n(only P) = n(P) - n(P ∩ Q)
n(only P) = 55% - 20%
n(only P) = 35%
(iv)
n(only Q) = n(Q) - n(P ∩ Q)
n(only Q) = 50% - 20%
n(only Q) = 30%
Hence , the probability is solved
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Borachio eats at the same fast-food restaurant every day. Suppose the time X between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4. 2 minutes and standard deviation 1. 3 minutes. A. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served. B. Find the probability that average time until he is served in eight randomly selected visits to the restaurant will be at least 5 minutes
The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is 0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.
Given that mean μ = 4.2 , standard deviation σ = 1.3
1. P(X >= 5) = P((X - μ)/σ >
= (5 - 4.2) /1.3
= P(Z ≥ 0.6154)
= 1 - P(Z < 0.6154)
= 1 - 0.7324
= 0.2676
The required probability is 0.2676.
2.Given that n = 8 then \(\bar x\) = σ/\(\sqrt{(n)\) = 1.3/√(8) = 0.4596
P(x-bar ≥ 5) = P((\(\bar x\) - μ)/σx-bar ≥ (5 - 4.2)/0.4596)
= P(Z ≥ 1.7406)
= 1 - P(Z < 1.7406)
= 1 - 0.9591
= 0.0409
The required probability is 0.0409.
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a retail store plans to build 4 new stores each year. they expect 1 store will go out of business every 3 1/2 years. how many years would it take to establish 30 stores core bites
It would take approximately 11.43 years to establish 30 stores.
Let's use x to represent the number of years it would take to establish 30 stores.
The store plans to build 4 new stores each year, so in x years, they will have built 4x stores.
That 1 store will go out of business every 3 1/2 years, which can be written as 7/2 years.
So in x years, 30/(4-1/2) = 40 stores will be in operation, and 40/x stores will go out of business.
So, we can write the equation:
40/x = 7/2
Solving for x, we get:
x = 80/7
Let's use x to indicate the period of time needed to open 30 shops.
The retailer intends to construct 4 additional stores year, totaling 4x stores after x years.
Every three and a half years—or seven and a half years—that one store will close its doors.
As a result, 40 stores will be open in x years and 40/x retailers will close their doors.
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in cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. one such method is called
In cluster analysis, a method can be used to reduce bias due to the difference in units of measurement. One such method is called standardization.
Cluster analysis is a data mining approach that is widely utilized in data processing, image analysis, and other data-based analytics applications. It groups items that have comparable characteristics into clusters by separating them from other objects that do not share the same features.
Standardization is the process of converting variables with various scales to a common scale so that they can be compared fairly.
Standardization involves transforming all of the variables into comparable units of measurement by converting them into z-scores. This allows for the comparison of values without being affected by the different units of measurement.
The method that can be used to reduce bias due to the difference in units of measurement in cluster analysis is standardization, which converts variables with various scales to a common scale so that they can be compared fairly. This ensures that each variable contributes equally to the distance between the clusters.
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If the company doubles the length of each edge of a
cube, how will the volume of water inside the cube
change?
It will double.
A.
B. It will triple.
C.
D.
It will be four times the initial volume.
It will be eight times the initial volume.
Answer:
It will be eight times the initial volume.
-------------------------------
Let the edge of the cube be a.
Its volume is a³.
If the edge is doubled, then the volume is:
(2a)³ = 2³a³ = 8a³As we see this is 8 times the initial volume.
1/2 + 4/7 less than are greater than 1
Ark invest estimates value of each us digital wallet user at $19,900 by 2025. assume value of latoken international client will be $1000 in 2027 and number of monthly paying clients will grow from 30,000 at 10% monthly rate till 2027 and 0 afterwards. what will be the value of latoken in 2027? *
The value of latoken in 2027 is $4731.
Given that in 2025 digital wallet users at $19900 and in 2027 latoken international clients will be $1000 and the number of monthly paying clients will grow from 30,000 at a 10% monthly rate till 2027 and 0 afterward.
The time esteem of cash states that a sum of cash is esteemed more presently than it'll be within the future. This is often due to the fact that cash can as it was extended by means of speculation. Speculation that's put off could be a missed opportunity. The time esteem of cash equation takes into consideration the amount of cash, its future esteem, the sum it can create, and the time period. The number of compounding periods is additionally a key variable for investment funds accounts.
By 2025=19900
By 2027 =1000 for client
Monthly pay =30000 each month
Rate=10%
At the end the value is computed below:
AED=30000(1+0.1)¹²
AED=30000(1.1)¹²
AED=30000×3.138
AED=94140
To find the value computation is done below:
19900x=1000×v×AED
x=(94140×1000×140)/19900
x=4.731×1000
x=4731
Hence, the value of latoken in 2027 when digital wallet user at $19,900 by 2025 and latoken international client will be $1000 in 2027 is $4731.
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The measures of two exterior angles of a decagon are 97° and 89°. What is the sum of the remaining exterior angles?
Answer:
the sum of the remaining exterior angles is 174⁰
Step-by-step explanation:
Given;
the measure of two exterior angles of a decagon = 97° and 89°
The total sum of exterior angles of a polygon is 360⁰
let the sum of the remaining exterior angles = x
sum of the given exterior angles = 97⁰ + 89⁰ = 186⁰
x + 186⁰ = 360⁰
x = 360⁰ - 186⁰
x = 174⁰
Therefore, the sum of the remaining exterior angles is 174⁰
24 I point. Afyan Company p. S24,000 annialh of an annuify for 3 kwwas at 1255 is \( 2.40183 \), the profitability index is. \( 1.96 \) 1.04 \( 0.28 \) Qi96 \( 0.04 \)
The profitability index for Aryan Company's new machine investment is 0.96.
The profitability index is a ratio used to measure the profitability of an investment by comparing the present value of future cash flows to the initial investment cost. It is calculated by dividing the present value of future cash flows by the initial investment cost.
In this case, the present value of the future cash flows can be calculated by multiplying the expected cash flow of $24,000 per year by the present value of an annuity for 3 periods at 12%, which is given as 2.40183. Therefore, the present value of future cash flows is $57,644.32.
The initial investment cost is $60,000.
To calculate the profitability index, we divide the present value of future cash flows by the initial investment cost: $57,644.32 / $60,000 = 0.96074. Rounded to one decimal place, the profitability index is 0.96.
The profitability index indicates that the present value of the expected future cash flows is approximately 96% of the initial investment cost. Generally, a profitability index greater than 1 indicates a favorable investment, while a value less than 1 suggests an unfavorable investment. In this case, the profitability index of 0.96 suggests that the investment is not expected to be highly profitable.
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The complete question is :
Aryan Company p o buy a new machine for $60.000 that will have an estimated useful site of 3 years and no savage value. The expected cash tom $24,000 annually Company has a cost of capital of 12% Given that the present value of $1 after 3 periods at 12% 071172 and the present valu of an annuity for 3ds at 12% is 2.40183, the profitability index is
1.96
1.04
0.28
0.96
0.04
Is (x − 2) a factor of f(x) = x^3 − 2x^2 + 2x + 3? Use either the remainder theorem or the factor theorem to explain your reasoning.
Answer:
\((x - 2)\) isn't a factor of \(f(x) = x^{3} - 2\, x^{2} + 2\, x + 3\).
Step-by-step explanation:
By the factor theorem, for any constant \(c\), \((x - c)\) is a factor of polynomial \(f(x)\) if and only if \(f(c) = 0\). Note that \(f(c) = 0\!\) means that substituting all \(x\) in \(f(x)\!\) with \(c\) and evaluating gives \(0\).
For example, the polynomial in this question is \(f(x) = x^{3} - 2\, x^{2} + 2\, x + 3\). The question is asking whether \((x - 2)\) is a factor of \(f(x)\).
By the factor theorem with \(c = 2\), \((x - 2)\!\) would indeed be a factor of \(f(x)\!\) if and only if \(f(2) = 0\). To find the value \(f(2)\!\), simplify replace all "\(x\)" in the definition of \(f(x)\!\) with \(2\):
\(\begin{aligned}f(2) &= 2^{3} - 2\times (2^{2}) + 2\times 2 + 3 \\ &= 2^{3} - 2^{3} + 7 \\ &= 7\end{aligned}\).
In other words, \(f(2) \ne 0\). By the contrapositive of factor theorem, \((x - 2)\) would not be a factor of \(f(x)\).
z=m+x-y, solve for x
Answer:
x= z-m+y
Step-by-step explanation:
subtract m from both sides
add y to both sides
and switch sides
If f(x) =5x2 - 3x + 1, calculate the following
Answer:
a) 199
f(-6)= 5(-6)^2 - 3 (-6) + 1 =199
b) 37
f(3)= 5(3)^2 - 3 (3) + 1 =37
in one right triangle the legs are 21cm and 28cm. the legs of the second right triangle are 15cm and 20cm. are these triangles are similar?
Answer:
Yes
Step-by-step explanation:
21÷7=3
24÷7=4
15÷5=3
20÷5=4
What is the range of the cluster in the scatter plot?
Answer:
What are clusters in scatter plots? Sometimes the data points in a scatter plot form distinct groups. These groups are called clusters.
Step-by-step explanation:
when the increase in demand is greater than the decrease in supply, the equilibrium price _____ and the equilibrium quantity _____.
Answer:
increasedeacreasesWhen the increase in demand is greater than the decrease in supply, the equilibrium price rises and the equilibrium quantity increases.
What is economic equilibrium?
Economic equilibrium, as used in economics, is a state in which forces such as supply and demand are in balance and where, in the absence of external influences, the values of economic variables will remain constant.
The equilibrium quantity rises if the rise in demand outweighs the fall in supply. The equilibrium quantity falls if the rise in demand is smaller than the fall in supply. Equilibrium price rises in each scenario.
The supply and demand curves move in opposition to one another. However, the supply curve shifted to the left while the demand curve shifted to the right (signalling a rise in demand) (indicating a decrease in supply).
In the case increase in demand > decrease in supply
In this instance, the supply curve's leftward movement is proportionally less than the rightward change of the demand curve. So, the price and the equilibrium quantity both increase.
Therefore, the equilibrium price and quantity increases.
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JK has endpoints (-2, 10) and K(10, -14). Point L divides JK into two parts with lengths in a
ratio of 5:1.
What are the two possible locations of L?
(5, 6)
(2, -4)
(8, -10)
(4, -2)
(2, 1)
(0,6)
Answer:
(8, - 10) or (0, 6)Step-by-step explanation:
There are two options as below.
1. JL/JK = 5 : 1
Find the coordinates of L:
x = -2 + 5/6(10 - (-2)) = -2 + 10 = 8y = 10 + 5/6(-14 - 10) = 10 - 20 = - 10The point is L(8, - 10)
2. JL/JK = 1 : 5
Find the coordinates of L:
x = -2 + 1/6(10 - (-2)) = -2 + 2 = 0y = 10 + 1/6(-14 - 10) = 10 - 4 = 6The point is L(0, 6)
Which of the following is a prime number between 10 and 20?
A.
14
B.
11
C.
18
D.
15
Answer:11
Step-by-step explanation:
Answer:
B - 11
Step-by-step explanation:
function or not a function
Answer: function
Step-by-step explanation:
a full-cut round brilliant diamond with a 6.50 mm girdle diameter weighs about
That a full cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat.
carat weight is determined by a combination of a diamond's size and density. A diamond's size is measured by its diameter, which is the distance across the widest part of the diamond, known as the girdle. Therefore, a diamond with a larger girdle diameter will generally weigh more than a diamond with a smaller diameter, assuming all other factors are equal.
the weight of a diamond can be estimated based on its girdle diameter, and a full-cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat. However, it's important to note that other factors, such as depth, cut, and clarity, can also affect a diamond's weight and value.
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what happens if i squish my submandibular gland
Answer:
I think you would be in lots of pain and probably lose the ability to make saliva.
Step-by-step explanation:
Let L: R² R² be a linear operator. If L((1,2)) = (-2,3), and L((1,-1)²) =(5,2),+ Find the value of L((7,8)¹) 799
L((7,8)) = (-9,23). To find the value of L((7,8)), we can use the linearity property of the linear operator L.
Since L is a linear operator, we can express any vector in R² as a linear combination of the basis vectors (1,0) and (0,1).
We have L((1,2)) = (-2,3) and L((1,-1)) = (5,2). Therefore, we can express (7,8) as (7,8) = 7(1,2) + 1(1,-1).
Using the linearity property, we can distribute the linear operator L over the linear combination:
L((7,8)) = L(7(1,2) + 1(1,-1))
= 7L((1,2)) + L((1,-1))
= 7(-2,3) + (5,2)
= (-14,21) + (5,2)
= (-9,23)
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A line passes through the points (3,0) and (4,1). What is the y—intercept of the line?
Answer: (0,-3)
Step-by-step explanation:
Use the point slope form of a line: y = mx = b, where m is the slope and b is the y-intercept
First solve for m:
m = (Y2-Y1)/(X2-X1)
m = (1-0)/(4-3)
m = 1/1 = 1
Using the slope above, plug either point into the equation and solve for b. I used (3,0) but (4,1) would give the same result:
y = mx +b
0 = 1(3) + b
0 = 3 +b
-3 = b
SOLUTION: y-intercept is (0,-3)