The acronyms SAS and SSS, which stand for Side-Side-Side and Same Side-Side-Side similarity theorems, respectively, are frequently employed.
In accordance with the Side-Side-Side (SAS) similarity theorem, two triangles are similar if their three sides are proportionate to one another. In other words, two triangles are comparable if the ratios of their respective sides are the same.
A variant of the SAS similarity theorem is known as the Same Side-Side-Side (SSS) similarity theorem. It states that two triangles are comparable if they have three pairs of corresponding sides that are proportional to one another and the angles between these pairs of sides are equal.
To assess whether two triangles are similar and to fill in any missing side lengths or angle measurements in comparable triangles, one can apply the SAS and SSS similarity theorems. These theorems are frequently applied in geometry and trigonometry to resolve triangle-related issues.
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A bicycle wheel has a circumference of 62 inches. Find the diameter of the wheel. If necessary, round to the tenths place. 39.5 inches 19.7 inches 15.5 inches 9.9 inches
Answer:
19.7 inches
Step-by-step explanation:
The formula for the circumference of a circle of radius r is C = 2πr. If the diameter is given, then the formula is C = πd.
Here C = 62 in. Dividing both sides by π yields the diameter: d = C/π:
62 in
d = ----------- = 19.7 inches
3.14
Answer:
b. 19.7
Step-by-step explanation:
did it on the ed2020 practice
To make a big batch of cookies for her father, Annmarie needs 1 1 4 pounds of chocolate chips, 3 4 pounds of walnuts, and 12 ounces of raisins. How many ounces of these three ingredients does she need in all?.
She will need 68 ounces in total for all three ingredients.
What will be the total ounces for all three ingredients?It is given that
For chocolate chips, she has = \(\dfrac{11}{4}\) pounds
For walnuts, she has = \(\dfrac{3}{4}\) pounds
For raisins, she has= 12 ounces
We know that,
\(\rm 1 \ pound = 16 \ ounces\)
\(\rm For \ chocolate \ chips, she\ has = \dfrac{11}{4} \times 16 }=44 \ ounces\)
\(\rm For \ walnuts,\ she\ has = \dfrac{3}{4} \times 16 }=12\ ounces\)
\(\rm For\ raisins, she \ has= 12\ ounces\)
so the total number of ounces she has will be the sum of all
\(=44+12+12 =68\ ounces\)
Thus she will need 68 ounces in total for all three ingredients.
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A graphed function may display different properties and characteristics over certain intervals of the graph in A and B below, describe the part of the function over the specified intervals, as “linear”or “nonlinear”and “increasing”or “decreasing”.
Help Needed,Thank you for whoever can help me out
The part of the function over the interval (-2,2) is nonlinear and decreasing.
Linear and nonlinearInterval: (-2, 2):The part of the function over the interval (-2,2) is nonlinear and decreasing.Over this interval, the graph starts at a peak of (0,2), before steadily decreasing and then sharply decreasing to a low point of (2,-2).This sharp decrease in the graph indicates that the function is nonlinear, as the rate of change is not constant.Additionally, the graph decreases over this interval, indicating that the function is decreasing. Interval: (2, 4):The part of the function over the interval (2, 4) is linear and increasing.Over this interval, the graph steadily increases; starting at the low point of (2,-2) and increasing to a peak of (4,2).This linear increase in the graph indicates that the function is linear, as the rate of change is constant.Additionally, the graph increases over this interval, indicating that the function is increasing.To learn more about Linear and nonlinear refer to:
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If the circumference of a cylinder is 32pie and it’s lateral surface area is 750cm^2 find the height of the cylinder
The height of the cylinder is approximately 5.97 cm.
Define cylinderA cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases and a curved lateral surface that connects the bases. The bases are perpendicular to the lateral surface, which means that the lateral surface forms a curved rectangle.
Given;
The circumference of the cylinder is 32π.
The lateral surface area of the cylinder is 750 cm².
Lateral surface area of a cylinder = 2πrh
Circumference of a cylinder = 2πr
We can use the circumference formula to find the radius of the cylinder:
2πr = 32π
r = 16
Now we can use the lateral surface area formula to find the height of the cylinder:
750 = 2π(16)(h)
750 = 32πh
h = 750/(32π)
h ≈ 5.97
As a result, the cylinder's height is around 5.97 cm.
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occurs when the effects of two or more explanatory variables are not separated. therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study.
The complete statement would be, confounding in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.
We know that an extraneous variable is a variable that has the potential to affect the results and it is not a independent variable.
A confounding variable is nothing but a type of extraneous variable which is related to a study’s independent and dependent variables.
These variables (confounding variables) are also known as confounders or confounding factors.
Any variable must follow following conditions to be a confounding variable:
1) A variable must be correlated with the independent variable.
2) It must be related to the dependent variable.
Thus, confounding occurs when the effects of two or more explanatory variables are not separated. therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study.
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The complete question is:
__________ in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.
5 added to the difference between a number an 12
Answer:
x-7
Explanation:
Subtract 5 5 from both sides of the equation. Subtract 5 5 from 12 12 . Divide each term in −x=7 by −1 and simplify. Divide each term in −x=7
What is the completely factor simplified form of the rational expression below?
x²+6x/x+5 4x+15/x+5
A. x²+2x-15/x+5
B. x²+2x+15x/+5
C.x+5
D. x-3
Answer:A
Step-by-step explanation:
To simplify the rational expression (x²+6x)/(x+5) + (4x+15)/(x+5), we first factor the numerator of the first fraction as x(x+6). Then, we factor the numerator of the second fraction as 4(x+3). Now, we can combine the fractions by finding a common denominator of (x+5) and adding the numerators:
(x²+6x)/(x+5) + (4x+15)/(x+5) = (x(x+6) + 4(x+3))/(x+5)
Simplifying the numerator further, we get:
(x²+6x + 4x + 12)/(x+5) = (x²+10x+12)/(x+5)
Now we can factor the numerator by finding two numbers that multiply to 12 and add to 10. Those numbers are 2 and 6. So we can write:
(x²+10x+12)/(x+5) = (x+2)(x+6)/(x+5)
Therefore, the completely factored and simplified form of the given rational expression is (x+2)(x+6)/(x+5). So the answer is A.
12:13:14 = 48:x:56
What is x?
Answer:
x = 52
Step-by-step explanation:
You are given ratios, and the 1st ratio is being multiplied by 4 to get the second ratio. How did I find this? Divide 48 by 12 and you get 4. To find x, simply multiply 13 by 4 and you should get 52
Solve for x.
8 ≤ x - (-14)
\(8 \leqslant x - ( - 14) \\ 8 \leqslant x + 14 \\ 8 - 14 \leqslant x + 14 - 14 \\ - 6 \leqslant x \\ x \geqslant - 6\)
I hope I helped you ^_^
Shopping at Savers Mart, Lisa buys her children 4 shirts and 3 pairs of pants for $85.50. She returns the next day and buys 3 shirts and 5 pairs of pants for $115.00. What is the price of each shirt and each pair of pants.
Answer:
price for one shirt
=
$
7.50
price for one pair of pants
=
$
18.50
Explanation:
Start by letting variables
x
and
y
represent the pieces of clothing from the problem.
Let
x
be the price of one shirt.
Let
y
be the price of one pair of pants.
Equation
1
:
4
x
+
3
y
=
85.50
Equation
2
:
3
x
+
5
y
=
115.00
You can solve for each variable by using elimination or substitution. However, in this case, we will use use elimination. First, we will solve for
y
, the price of each pair of pants.
To isolate for
y
, we must eliminate
x
. We can do this by making the two equations have the same
x
values. First, we find the LCM of
4
and
3
, which is
12
. Next, multiply equation
1
by
3
and equation
2
by
4
so that
4
x
and
3
x
becomes
12
x
in both equations.
Equation
1
:
4
x
+
3
y
=
85.50
3
(
4
x
+
3
y
)
=
3
(
85.50
)
12
x
+
9
y
=
256.50
Equation
2
:
3
x
+
5
y
=
115.00
4
(
3
x
+
5
y
)
=
4
(
115.00
)
12
x
+
20
y
=
460.00
Now that we have two equations with
12
x
, we can subtract equation
2
from equation
1
to solve for
y
.
12
x
+
9
y
=
256.50
12
x
+
20
y
=
460.00
−
11
y
=
−
203.50
y
=
18.50
⇒
price for one pair of pants
Now that we know that a pair of pants is
$
18.50
, we can substitute this value into either equation
1
or
2
to find price for one shirt. In this case, we will choose equation
1
.
4
x
+
3
y
=
85.50
4
x
+
3
(
18.50
)
=
85.50
4
x
+
55.5
=
85.50
4
x
=
28
x
=
7.50
⇒
price for one shirt
∴
, the price for one shirt is
$
7.50
and the price for one pair of pants is
$
18.50
.
Step-by-step explanation:
yea
Which of the following expressions are equivalent to 16a^3b^2 - 8a^5b^5 + 12a^4b? Select all that apply.
Answer:
um i don't know.... 99
Step-by-step explanation:
99 +12
THIS IS URGENT!
In orde to keep a specific bacteria alive,the temperature in a science lab cannot exceed -20 degrees farenheit. The electricity went out when the temperature was -72 degrees farenheit,but it increasing at a rate of 6.5 degrees per hour. How many hours do scientists have until the bacteria is not safe?
When Mark was looking at his monthly utility payments, he noticed that one payment was significantly lower than all the others. Which of the following would be most affected by Mark's observation? The median, average, highest, most frequent monthly payment
Answer:
The average monthly payment would be most affected by Mark's observation of one significantly lower payment. The reason is that the average is calculated by summing all the payments and dividing by the total number of payments, so any extreme values (such as the significantly lower payment) can have a substantial impact on the average value.
Step-by-step explanation:
A grain dealer sold to one customer 5 bushels of wheat, 8 of corn, and 10 of rye, for $79.10; to another, 8 of wheat, 10 of corn, and 5 of rye, for$76.60; and to a third, 10 of wheat, 5 of corn, and 8 of rye, for $74.30. What was the price per bushel for corn?
A. $2.70
B. $3.60
C. $3.70
D. $27.50
The price per bushel for corn is $3.70.
Given that,
The grain dealer sold to one customer 5 bushels of wheat, 8 of corn, and 10 of rye, for $79.10; to another, 8 of wheat, 10 of corn, and 5 of rye, for$76.60; and to a third, 10 of wheat, 5 of corn, and 8 of rye, for $74.30
We need to find the price per bushel for corn.
Let the price per bushel for wheat, corn and rye be x, y, z respectively.
According to the given data,
The selling price of 5 bushels of wheat, 8 of corn, and 10 of rye = $79.10x(5) + y(8) + z(10) = 79.10 ..........
(1)The selling price of 8 bushels of wheat, 10 of corn, and 5 of rye = $76.60x(8) + y(10) + z(5) = 76.60 ...........
(2)The selling price of 10 bushels of wheat, 5 of corn, and 8 of rye = $74.30x(10) + y(5) + z(8) = 74.30 ...........
(3)Solving the equations (1), (2) and (3),
we get y = $3.70
Hence, the price per bushel for corn is $3.70.
Therefore, option C is the correct answer.
Note: By using the same method, we can find the price per bushel for wheat and rye.
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Evaluate 86 + 14/24 + 7 13/24.
A. 93 1/8
B. 93 1/24
C. 93 24/27
D. 94 1/8
Answer:
The answer would be D. 94 1/8
Answer:
94 1/8
Step-by-step explanation:
the water cycle describes how water __ from the ocean ,plants ,animalas or waste
Answer:
evaporates
Step-by-step explanation:
Answer:
The water cycle describes how water evaporates from the ocean, plants, animals, or waste.
Step-by-step explanation:
The word evaporates is the answer.
Hope this helps!
3. Mary wants to select one shirt (white, red, black), one pant (capri,
skinny), and one footwear (shoes, boots). What is the total possible
number of outcomes? *
A 12
B 9
C 07
C 3
Answer:
3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
She wants ONE white shirt and ONE pants and shoes
Assume double[][] x = new double[4][5], what are x.length and x[2].length? a. 4 and 4
b. 4 and 5 c. 5 and 4 d. 5 and 5
The x.length is the number of rows, which is 4. x[2].length is the number of columns in the 3rd row, which is 5. The expression "new double[4][5]" creates a 2D array of doubles with 4 rows and 5 columns. The correct answer is (b) 4 and 5.
The expression double[][] x = new double[4][5] creates a 2D array x with 4 rows and 5 columns. Therefore, x.length gives the number of rows, which is 4. And x[2].length gives the number of columns in the 3rd row (since array indices start at 0), which is 5. Therefore, the correct option is (b) 4 and 5.
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Each small square on the grid is 1 cm squared. Which estimate best describes the area of this figure?
O 15 cm2
O 20 cm2
O 25 cm 2
O 35 cm2
the map is drawn to the scale of 1:4000 and the distance in between two places on the map is 4 cm what is the actual distance between those two places
Answer:
4 × 4000 = 16000cm or 160 meters
The figure is not drawn to scale. PQ and MN are straight lines. Find
Answer:
a = 138
Step-by-step explanation:
Notice that from the figure, we can see that ∠MOQ and ∠PON are vertical angles, which means that by definition, they're congruent in measure.
∠MOQ = ∠MOR + ∠ROQ = 90 + 48 = 138°
So, this means that ∠PON is also equal to 138, which means a = 138.
Thus, the answer is a = 138.
~ an aesthetics lover
the given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.
The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.
The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.
By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.
Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.
Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.
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Question
The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
Use the binomial series expansion, (1+x)r=∑n=0[infinity](rn)xn for the function f(x)=(1−2x)21 to find a third-order Maclaurin polynomial, p3(x), in order to estimate (31)21. If necessary, round your answer to three decimal places. Provide your answer below: (31)21≈
By the estimation of 3^(1/21) using the MacLaurin polynomial of the third order, we get -0.248.
First, to find the required polynomial, we use the binomial series expansion for three terms.
The general form of a binomial series expansion is given as:
(1 + x)ᵃ = ∑(n = 0 to n = inf) (ᵃCₙ) * xⁿ
where (ᵃCₙ) for each term is called its binomial coefficient.
We need only three terms expansion for the given polynomial (1−2x)²¹.
Here a = 21, and instead of x we have -2x.
Also, n = 0,1,2 and 3 for three terms.
So,
(1−2x)²¹ = (²¹C₀)*(-2x)⁰ + (²¹C₁)*(-2x)¹ + (²¹C₂)*(-2x)² + (²¹C₃)*(-2x)³
= 1 - 42x + 840x² -10640x³
For estimating we can substitute x = 1/21 into the above expansion.
which gives us
1 - 42(1/21) + 840(1/21)² -10640(1/21)³
= -0.248
Thus the approximation of the given polynomial is -0.248.
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There were some people on a bus. Half of the people get off at the first stop and 11 people get on. Now there are 20 people on the bus. How many people were on the bus to begin with?
Answer:
18 people
Step-by-step explanation:
18/2=9
9+11=20
Answer:
18.
Step-by-step explanation:
this is because in order to find out how many were on the bus, you simply do 20 - 11 = 9. Than you must multiply 9 by 2 which equals 18. That gives you your answer.
Choose the INCORRECT answer.
A Normal distribution is one of the most commonly used distribution types, because:_________.
i. Decisions based on Normal distribution insights have a good track record.
ii. Computable statistics are elegant
iii. Distributions of sample means with large enough sample sizes could be approximated to Normal
iv. All variables can be represented by the Normal distribution.
All variables cannot be represented by the Normal distribution.What is Normal Distribution?Normal distribution is a continuous probability distribution that represents data in a symmetric and bell-shaped pattern. It is a symmetric distribution with a mean (μ) equal.
The incorrect answer is option iv.
The distribution is also known as a Gaussian distribution or a bell curve. The normal distribution is the most frequently used distribution in statistics due to its well-known properties. It is a symmetric distribution with a mean (μ) equal to the median and mode. The standard deviation (σ) characterizes the variability of the data points from the mean of the normal distribution.
The incorrect option iv. All variables can be represented by the Normal distribution. This statement is not correct. Not all variables can be represented by the normal distribution. A variable that can be represented by the normal distribution must satisfy the following conditions: Values of the variable should be continuous. Values should be measured on an interval or ratio scale. The variable should have a symmetric distribution. Therefore, the correct option is iv.
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a) Find the equation of the parabola with vertex (2,5) which also passes through the point (4, -3)
In order to find the equation of the parabola, let's use the vertex form below:
\(y=a(x-h)^2+k\)Where the vertex is located at (h, k). If the vertex is located at (2, 5), therefore h = 2 and k = 5.
Now, let's use the point (4, -3) in the equation so we can calculate the value of a:
\(\begin{gathered} y=a(x-2)^2+5\\ \\ -3=a(4-2)^2+5\\ \\ -3=4a+5\\ \\ 4a=-8\\ \\ a=-2 \end{gathered}\)Therefore the equation is:
\(y=-2(x-2)^2+5\)pls help
Simplify the expression below.
4−3(9w+2(8z+1))−3z
Answer:
-27w-51z-2
Step-by-step explanation:
Suppose that a particular brand of 5 inch candles has an average life of 27 hours with a standard deviation of six hours. If all possible samples of 4 candles were selected in the average life of the samples was determined, what would the mean of the distribution of the sample means be?
5
3
4
27
The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.
This is because the sample means would be expected to be centered around the population mean.
The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:
standard deviation of sample means = standard deviation of population / square root of sample size
In this case, the standard deviation of sample means would be:
6 / square root of 4 = 3
So the answer is 3.
So, the mean of the distribution of the sample means would be 3. Your answer: 3.
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On average, Caryl's school bus arrives on time, although sometimes it is a bit early or late. If the arrival times are distributed on a normal curve, which of the following statistics would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day?
a. median
b. mean
c. standard deviation
d. correlation coefficient
If the arrival times of Caryl's school bus are distributed on a normal curve, the standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.
The standard deviation is a statistic that measures the amount of variation or dispersion from the central tendency of a set of data values. A low standard deviation indicates that the data is tightly clustered around the mean or average, while a high standard deviation indicates that the data is more spread out.
The standard deviation is particularly useful when dealing with normally distributed data, as it allows us to estimate the probability of a certain range of values occurring. In this case, Caryl can use the standard deviation to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.
Hence, option c. standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.
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f(x)=x²-3x+1
Write an expression for f(p²)
The modified function will be f(p²) = \(p^{4}\) - 3p² +1.
What is a function?
A function is a special kind of relation where each input has exactly one output. In other words, for each input value, the function returns exactly one value. A relation instead of a function is depicted in the above graph as one is mapped to intermediate values. However, if someone were instead mapped to the a single value, the relationship described above would change into a function. Furthermore, output values could match input values exactly. The function machine receives the x-values as input. After finishing its operations, the function machine outputs the y-values. Any function may be the one within.
The given function f(x) = x²-3x+1
So we can replace x ---→ p²
So f(p²) = \(p^{4}\) - 3p² +1
Hence the modified function will be f(p²) = \(p^{4}\) - 3p² +1
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Answer:
f ubiquitous uniform 8th Nii coffin stubby chin