A convex polyhedron has 20 faces that are congruent equilateral triangles. What is the name of the solid?
triangular prism
triangular pyramid
octahedron
icosahedron
Answer:
The name of the solid with 20 faces that are congruent equilateral triangles is icosahedron.
The solid you are referring to is called an icosahedron. An icosahedron is a specific type of convex polyhedron that has 20 faces. In this case, all 20 faces are congruent equilateral triangles. Option d is correct answer.
To understand why this solid is called an icosahedron, let's break down the term. "Icosa-" comes from the Greek word for twenty, while "-hedron" means face. Therefore, an icosahedron is a polyhedron with twenty faces.
Each face of an icosahedron is an equilateral triangle, meaning that all three sides of the triangle are equal in length, and all three angles are equal to 60 degrees. Since all 20 faces are congruent, they have the same side lengths and angles.
The icosahedron has a total of 12 vertices and 30 edges. The vertices are the points where three edges meet, and the edges are the line segments connecting the vertices. The icosahedron has a symmetrical and regular structure, making it one of the five Platonic solids.
An icosahedron is a convex polyhedron with 20 congruent equilateral triangle faces, 12 vertices, and 30 edges.
Option d is correct answer.
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I NEED THE ANSWER PLS :)
Answer:
x = 48
Step-by-step explanation:
It is a 90 degree angle. So first you would subtract 42 from 90 degrees. Then you'd get your answer! Hope this helped
How many people did Trevor survey?
74
92
107
137
Answer:
92 I think because in my class I heard my friend tell me
What is the product of
(7/8)(-16)(-7)(-1/14)
A -7
B -9/16
C -1/7
D 23/12
Answer:
-7
Step-by-step explanation:
(7/8)(-16)(-7)(-1/4)
(7/8)(-1/4)(-16)(-7)
(-1/16)(112)
-7
Answer:
-7
Step-by-step explanation:
multiply all the numbers together and you get -7
3cm on a map represents a distance of 60 if the scale is expressed in the ratio 1:n then n
Bob baked 175 brownies to give seven of his friends if he splits the brownies evenly and keeps none for himself how many brownies will each friend get
Answer:
25
Step-by-step explanation:
175 ÷ 7 = 25
Which phase best describes the transition from the graph y=2x^2 to the graph of y2x^2+5?
A. 5 units up
B. 5 units down
C. 5 units right
D. 5 units left?
Answer:
Anything after x determines if it goes up since it's a positive 5 it's 5 units up
Which expression represents twice the sum of w and 6?
Answer:
2(w+6)
Step-by-step explanation:
26) Evaluate the expression with its given values.
x+2y/6;x=1,y=2
Answers:
1. 1/3
2. 5/6
3. 1
4. 2/3
\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)
Here's the solution ~
The given expression is :
\(\qquad \sf \dashrightarrow \: \dfrac{x + 2y}{6} \)
Plug the required values :
x = 1 y = 2Now, the expression will be ;
\(\qquad \sf \dashrightarrow \: \dfrac{1 + (2 \times 2)}{6} \)
\(\qquad \sf \dashrightarrow \: \dfrac{1 + 4}{6} \)
\(\qquad \sf \dashrightarrow \: \dfrac{5}{6} \)
Answer:
\( \mathfrak = > \frac{x + 2y}{6} \)
\( \mathfrak = > \frac{1 + 2(2)}{6} \)
\( \mathfrak = > \frac{1 + 4}{6} \)
\( \mathfrak = > \frac{5}{6} \)
an 8 sided regular polygon (regular octagon) is inscribed in a circle whose radius is 16 feet. find the area of the polygon.
The area of the regular octagon inscribed in a circle with a radius of 16 feet can be found using the formula A = (2 + 2sqrt(2))r^2, where r is the radius of the circle. Plugging in the value for r, we get:
A = (2 + 2sqrt(2))(16)^2
A = (2 + 2sqrt(2))(256)
A = 660.254 ft^2
Therefore, the area of the regular octagon is approximately 660.254 square feet.
To derive the formula for the area of a regular octagon inscribed in a circle, we can divide the octagon into eight congruent isosceles triangles, each with a base of length r and two congruent angles of 22.5 degrees. The height of each triangle can be found using the sine function, which gives us h = r * sin(22.5). Since there are eight of these triangles, the area of the octagon can be found by multiplying the area of one of the triangles by 8, which gives us:
A = 8 * (1/2)bh
A = 8 * (1/2)(r)(r*sin(22.5))
A = 4r^2sin(22.5)
We can simplify this expression using the double angle formula for sine, which gives us:
A = 4r^2sin(45)/2
A = (2 + 2sqrt(2))r^2
Therefore, the formula for the area of a regular octagon inscribed in a circle is A = (2 + 2sqrt(2))r^2.
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Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.Given: If Elan stays up late, he will be tired the next day. Elan is tired.
Conclusion: Elan stayed up late.
Based on the explanation below, the conclusion that Elan is tired because Elan stayed up late is invalid.
How do we use reasoning to determine a conclusion?In the question, it is stated that if Elan stays up late, he will be tired the next day.
However, staying up late is not the only thing that could make Elan get tired.
This implies that there are so many other things than can make Elan get tired such as working for long hours.
It is possible that Elan was tired because Elans worked long hours.
By implication, the conclusion is invalid.
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Which is a complete list of factors of each term in the expression 15 + 20 x? 15: 1, 3, 5, 15 20x: 1, 2, 4, 5, 10, 20, x 15: 1, 3, 5, 15 20x: 1, 2, 4, 5, 10, 20 15: 3, 5 20x: 4, 5, x 15: 1, 3, 5 20x: 1, 2, 4, 5, 10, x
Answer:
15: 1 3 5 15
20: 1 2 4 5 10 20
Step-by-step explanation:
This assumes you are only factoring the coefficients of the expression. Using this assumption, we simply create a list of factors of the coefficients.
15 -> 1 * 15, 3 * 5 --> 1 3 5 15
20 -> 1 * 20, 2 * 10, 4 * 5 --> 1 2 4 5 10 20
If you don't assume factoring of just the coefficients, then 20x factors
20x: 1 2 4 5 10 20 x
Cheers.
Answer:
b
Step-by-step explanation:
Slove the system by Graphing
12x +9y = -9y
18 = 9y + 3x
The solution of the system of equations is (-6, 4)
How to solve the system of equations?Here we have the system of equations below:
12x +9y = -9y
18 = 9y + 3x
And we want to solve this graphically. To do so, we ust need to graph both of these equations in the same coordinate axis, and then find the point where the two graphs intercept.
The graph of the system of equations can be seen in the image at the end, and there you can see the graphs of the two lines, and you also can see that the lines intercept at the point (-6, 4)
So that is the solution of the system.
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chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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8. The endpoints of ST are s(-3, 2) and t(5,8). Find the coordinates of the midpoint of ST. Then find ST. OA midpoint: (1,5); ST = 5 OB midpoint: (1, 4); ST = 10 с midpoint: (1, 5); ST = 10 midpoint: (2,5); ST = 10
Answer:
The mid point of ST is (1,5) and ST = 10 units
Step-by-step explanation:
It is given that,
S(-3,2) and T(5,8). We need to find the coordinates of the midpoint of ST and also ST.
Let (x,y) be the mid point of ST. Using mid-point formula we get :
\((x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})\)
We have, x₁ = -3, x₂ = 5, y₁ = 2 and y₂ = 8
So,
\((x,y)=(\dfrac{-3+5}{2},\dfrac{2+8}{2})\\\\(x,y)=(1,5)\)
(1,5) is the midpoint of ST.
Using distance formula to find ST as follows :
\(ST=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\ST=\sqrt{(5-(-3))^2+(8-2)^2} \\\\ST=10\ \text{units}\)
Hence, the mid point of ST is (1,5) and ST = 10 units.
pirya has picked 1 1/2 cups of raspberries, which is enough for 3/4 of a cake how many cups does she need for the whole cae
Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
What is fraction?A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.
How to solve?
she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
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You decide to go to the candy store in the mall. You arrive at the store with $25 and then purchase 3 candy bars. You then buy a giant candy snake for $12.50. When you leave, you have $8.75 left in your wallet. How much did each candy bar cost? Write the equation to represent the scenario. 8.75 - x - 12.50 = 25.00 25.00 - 3x - 12.50 = 8.75 25.00 - 3x - 8.75 = 12.50 25.00x - 12.50 = 8.75
Answer:
The cost of a candy is $1.25Step-by-step explanation:
given the total amount at hand is $25
let the price of candy be x
then the cost of 3 candy will be 3x
the cost of a candy snake is $12.50.
balance at hand after the end of buying $8.75
the total expenses summed up must equal the initial amount at hand which is $25
the expression for the scenario is 3x+12.5+8.75=25
3x+21.25=25
3x=25-21.25
3x=3.75
x=3.75/3
x=$1.25
The cost of a candy is $1.25
n a given year, there are 10 million unemployed workers and 120 million employed workers in an economy.
In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.
The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.
Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.
Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.
By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.
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The point (2,-4), (x,y), A, and B all lie on the line. Find an equation relating x and y (Hint: The lope formula)
The point (2,-4), (x,y), A, and B all lie on the line. An equation relating x and y is m(x-2)=y+4.
The points (2, -4), (x, y) are lie on the line.
The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x. Slope is a ratio that includes how y changes for every unit increase of x.
The slope formula,
m\((x_{2}-x_{1})= y_{2}-y_{1}\)
Here, \(x_{1} = 2, x_{2}= x, y_{1}= -4\) and \(y_{2}= y\)
Now, we have to substitute the values in the formula,
\(m=\frac{y-(-4)}{x-2}\)
\(m= \frac{y+4}{x-2}\)
m(x-2)= y+4
Therefore, the equation is m(x-2)=y+4.
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What is the answer for x?
Answer:
x = 15
Step-by-step explanation:
7x + 5x = 180 (because parallelograms are 360 degrees)
add like terms
12x = 180
divide 12 from both sides
[x = 15]
Sarah works as a nanny and charges different rates for working during the week and the weekend. One week, she earned 902.50 working 45 hours, of which 5 hours were during the weekend. The following week she earned 1045 working 50 hours, of which 10 hours were during the weekend. What does Sarah charge per hour, in dollars, for working during the week?
Sarah's charges per hour for working during the week will be $9.5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.
Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be
45x + 5y = 902.5 ...1
50x + 10y = 1045
25x + 5y = 522.5 ...2
Subtract equation 2 from equation 1, then we have
45x - 25x = 902.5 - 522.5
20x = 380
x = 19
And the value of y will be
25 (19) + 5y = 522.5
475 + 5y = 522.5
5y = 47.5
y = 9.5
Sarah's charges per hour for working during the week will be $9.5.
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Find the GCF of 38 and 49.
Answer:1
Step-by-step explanation:
I found the factors and prime factorization of 38 and 49. The biggest common factor number is the GCF number. So the greatest common factor 38 and 49 is 1
Answer: The greatest common factor is 1
Step-by-step explanation:
49 is not even like 38 so the only one they have together in 1.
How to divide exponents with different bases and powers.
To divide exponents with different bases and powers, you need to first factor out the common factors from the exponents. This will help you simplify the expression and make it easier to solve.
For example, let's say you have the expression 4x^3 / 2x^2. To divide these exponents, you need to factor out the common factors. In this case, the common factor is x^2, so you can simplify the expression as follows:
4x^3 / 2x^2 = (4/2) * (x^3/x^2) = 2x^(3-2) = 2x
So the answer is 2x.
In general, to divide exponents with different bases and powers, you need to:
1. Factor out the common factors from the exponents
2. Divide the coefficients (if there are any)
3. Subtract the exponents of the common factors
By following these steps, you can easily divide exponents with different bases and powers.
To divide exponents with different bases and powers, follow these steps:
1. Convert the bases to their prime factorization (if needed).
2. Divide the exponents with the same base by subtracting the exponent in the denominator from the exponent in the numerator.
3. Combine the results back together as a simplified expression.
Remember, you can only directly divide exponents with the same base. If bases are different, you'll need to factorize them to find common factors.
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give bases for row(A), col(A), and null(A). [ 1 1 −8 ] A = [ 0 2 1 ] [ 1 −1 −9 ]
So, the bases for row(A), col(A), and null(A) are {[1, 0, -4], [0, 1, 0.5]}, {[1, 0, 1], [1, 2, -1]}, and {[4, -0.5, 1]}, respectively.
To find bases for row(A), col(A), and null(A) for the given matrix A, we first need to determine the reduced row echelon form (RREF) of A.
Matrix A:
[ 1 1 -8 ]
[ 0 2 1 ]
[ 1 -1 -9 ]
RREF of A:
[ 1 0 -4 ]
[ 0 1 0.5 ]
[ 0 0 0 ]
Now, we can determine the bases:
1. row(A) base:
The non-zero rows in the RREF of A form the base for row(A).
Base for row(A) = {[1, 0, -4], [0, 1, 0.5]}
2. col(A) base:
The columns of the original matrix A that correspond to the leading 1's in the RREF form the base for col(A).
Base for col(A) = {[1, 0, 1], [1, 2, -1]}
3. null(A) base:
To find the null(A) base, we need to solve the homogeneous system Ax = 0 using the RREF.
x1 - 4x3 = 0
x2 + 0.5x3 = 0
Expressing x1 and x2 in terms of x3:
x1 = 4x3
x2 = -0.5x3
Now, we write the vector solution:
x = x3[4, -0.5, 1]
Base for null(A) = {[4, -0.5, 1]}
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Which of the following lists the numbers in asending order: -3/8, -0.32, -2/7, -0.3
Answer:
its -3/8
Step-by-step explanation:
Why would you want to transform a set of raw scores into a set of z-scores? Check all that apply. a. To make a distribution with a mean of 1 and a standard deviation of 0 b. To be able to describe the location of a raw score in the distribution of raw scores c. To make all the transformed scores greater than 0 d. To make it possible to compare scores from two different distributions
For a z-score, We transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions i.e. D.
What exactly is the z-score?
The z-score is a statistical measurement that describes a value's relationship to the mean of a collection of values. The z-score formula is
z = (x - μ)/σ
x = data point
μ = mean
σ = standard deviation
Mean:- The sum of a collection of numbers divided by the total number of numbers in the set is known as the arithmetic mean, sometimes known as the arithmetic average or simply the mean or average. A survey, experiment, or observational research is usually used to create the collection.
Now,
As Z-scores are standardized scores that identify and define each score's exact placement within a distribution. We may conduct meaningful comparisons of z-scores across various samples or groups by converting our data (raw score).
hence,
We transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions.
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How many times larger is 5.4 x 10^15 than 9.0 x 10^3?
O 6.0 x 1012
O 6.0 x 1011
X
O 3.6 x 1012
O 3.6 x 1011
Answer:
6.0 x 10^11
Step-by-step explanation:
Let me know if this is wrong :) I tried
Please help I was on this for a while
Answer:
Radius R = 9 ft
Step-by-step explanation:
Given:
Volume of sphere = 972π ft³
Find:
Radius R
Computation:
Volume of sphere = (4/3)πr³
972π = (4/3)πr³
729 = r³
Radius R = 9 ft
I NEE D HALP FOR NUMBER 8 LETTERS A,B,C. I HAVE TO SHOW WORK AS WELL IM LOST RN
Answer:
a. -6
b. 3
c. 1
Step-by-step explanation:
a. 4(-5)+7(2)
-20+14= -6
b. 2(5-9)-(-3-8)
2(-4)-(-11)=
(-8)-(-11)=
(-8)+11= 3
c. (-7)²+10(-5)
49+(-50)= 1
validity coefficients greater than _________ are considered in the very high range.
When a validity coefficient exceeds 0.90, it is considered to be in the very high range.
Validity coefficients greater than 0.90 are considered in the very high range.
Validity coefficients measure the strength of the relationship between a test or measurement and the construct it is intended to assess. The coefficients range from -1.00 to +1.00, where higher values indicate stronger validity.
When a validity coefficient exceeds 0.90, it is considered to be in the very high range. This suggests that the test or measurement has a high degree of accuracy in assessing the intended construct, demonstrating a strong relationship between the two. Validity coefficients in this range provide strong evidence that the test is measuring what it is intended to measure.
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