The correct answers are given below:
1. triangular prism
2. 6 edges
3. 4 vertices
4. 3 lateral faces and a base
What is a Triangular Prism?A triangular prism is a 3-dimensional geometric figure that contains two congruent triangulated bases and three connected rectangular faces. It has an aggregate of six surfaces, nine edges, and 6 vertices.
1. square prism
2. 8 edges
3. 5 vertices
4. 4 lateral sides and a base'
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We have 2 squares. One square is shaded 2/12 and the other shaded square in the diagram is 2/15 shaded. How much of the total diagram is shaded?
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
Answer: The answer to your question is C. Brainliest?
Step-by-step explanation:
For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:
2/12 = (2 x 5) / (12 x 5) = 10/60
For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:
2/15 = (2 x 4) / (15 x 4) = 8/60
Now, we can add the two fractions:
10/60 + 8/60 = 18/60
Simplifying this fraction by dividing both numerator and denominator by 6, we get:
18/60 = 3/10
Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.
The answer is C. 0.3.
What is the likelihood
that all 21 students in a class share the same birthday? Explain.
Quick please!
Answer:
it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull
Step-by-step explanation:
Q.17> In how many ways 4 arts students and 4 science Students be arranged alternative at a round table?
Using the arrangements formula, it is found that there are 1152 ways for the students to be arranged alternatively at the table.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
\(A_n = n!\)
In this problem, we have that:
With the art students at the odd numbered places and the science students at the even numbered places, there are 4! x 4! ways.Same number of ways if they exchange, art even and science odd.Hence the number of ways is:
2 x 4! x 4! = 1152
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Find the perimeter of this shape
The perimeter of the given shape as represented in the task content is; 29 cm.
What is the perimeter of the given shape?It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.
Since each grid line has 1cm as it's length;
The perimeter of the shape is the sum of all side lengths of the shape;
Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1
P = 29 cm
Hence, the perimeter of the shape is; 29 cm.
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The graph of the equation x + 3y = 6 intersects the y-axis at what the point?
Answer:
It intersects the y-axis at point (0, 2).
Step-by-step explanation:
x + 3y = 6
3y = -x + 6
y = -1/3x + 2
Answer:
4. (6,0)
Step-by-step explanation:
Plug the points into the equation.
6+3(0)=6
6+0=6
6=6
11. A square with sides
3/8
inch has a total area of:
Answer:
\((\frac{3}{8}\,in )^2=\frac{9}{64} \,in^2=0.140625\,\,i^2\)
Step-by-step explanation:
Recall that the formula for the area of a square of side L is: \(Area=L^2\)
Therefore, for this case:
\(Area=L^2\\Area = (\frac{3}{8} \,in)^2\\Area=\frac{9}{64} \,\,in^2\\Area=0.140625\,\,in^2\)
Line EF intersects the parallel lines AB and CD.
What is the measure of angle J in the figure below?
Answer:
d, 125
Step-by-step explanation:
Answer:
d)125
Step-by-step explanation:
During practice, the players on a softball team warm up by running the bases. This graph shows the relationship between the number of hours, x, of practice the players attend and the number of minutes, y, the players spend running the bases.
How many minutes do the players spend running the bases during each hour of practice?
The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
In the context of this problem, the variables x and y are given as follows:
Variable x: number of hours.Variable y: time spent running the bases.The equation for the constant is given as follows:
k = y/x.
Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.
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Which is the correct pair?
Answer: D
Step-by-step explanation:
Since we are given that the x value is -1, we can eliminate A and C because the -1 is in the y coordinate.
To find the proper y value, we plug x into the equation.
y=-2x+5 [plug in x=-1]
y=-2(-1)+5 [multiply -2 and -1]
y=2+5 [add 2 and 5]
y=7
Now that we have the y value, we know the coordinate (-1,7) which makes D the correct answer.
Find the sum of the first 25 terms of the arithmetic sequnce 17,22,27,32.37
Answer:
Step-by-step explanation:
This sequence is adding 5 so
17 22 27 32 37 42 47 52 57 62 67 72 77 82 87 92 97 102 107 112 117 122 127 132 137 = 1925
Answer: The sum of the first 25 terms of this arithmetic sequence is 1925.
Explanation: This sequence, beginning at 17, increases by 5 per term. By simply adding 5 to the preceding term in the sequence, you can find the next term. The first term is 17, and the last term is 137. This means the list of terms is 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, and 137. The sum of these terms is 1925.
4 x 5 - (2² - 2) =?
(18 ÷ 3) + (3² - 7) =?
1. Adam opened a savings account with
$250. He saves $300 per month.
Mandy opened a savings account
with $750. She saves $200 per
month. How much more will Adam
have in his savings account after 12
months?
Answer:
$700
Step-by-step explanation:
Adam = 250 +300(12)=3850
Mandy = 750+200(12)=3150
3850-3150=700
What are the center and radius of the circle defined by the equation x^2 + y^2 -6x + 8y + 21=0
Answer:
Step-by-step explanation:
(x²-6x)+(y²+8y)=-21
(x²-6x+9)+(y²+8y+16)=-21+9+16
(x-3)²+(y+4)²=4
center=(3,-4),radius=√4=2
Need Help please, here is screenshot
1)
The axis of symmetry is x = -6.
2)
Vertex is (-6, 26).
3)
f(x) has a maximum value.
4)
f(x) is concave down.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
f(x) = -x² - 12x - 10
This is in the form of ax² + bx + c.
a = -1, b = -12, c = -10
The axis of symmetry is x = -b/2a
x = 12/(-2)
x = -6
Now,
f(x) = -x² - 12x - 10
f(x) = -(x² + 12x + 10)
f(x) = - { (x² + 12x + 36) - 36 + 10}
f(x) = -(x + 6)² + 26
This is in the form of f(x) = a (x - h)² + k
a = -1, h = -6, k = 26
Vertex = (h, k) = (-6, 26)
Now,
f(x) = -x² - 12x - 10
f'(x) = -2x - 12
f''(x) = -2
It is a negative value.
This means f(x) has a maximum value.
Now,
From the graph, we see that f(x) is concave down.
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Find the sample size required to estimate the percentage of college students who take a statistics course. Assume that we want 95% confidence that the proportion from the sample is within four percentage points of the true population percentage. Round the answer to the next larger whole number.
Answer:
The sample size is \(n = 600 \)
Step-by-step explanation:
From the question we are told that
The margin of error is E = 4% = 0.04
From the question we are told the confidence level is 95% , hence the level of significance is
\(\alpha = (100 - 95 ) \%\)
=> \(\alpha = 0.05\)
Generally from the normal distribution table the critical value of \(\frac{\alpha }{2}\) is
\(Z_{\frac{\alpha }{2} } = 1.96\)
Since the sample proportion (point estimate of the population proportion was not give we will assume it to be )
\(\^ p = 0.5\)
Generally the sample size is mathematically represented as
\(n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) \)
=> \(n = [\frac{1.96}{0.04} ]^2 * 0.5 (1 - 0.5 ) \)
=> \(n = 600 \)
Find the slope of the line on the graph.
The slope should be -1/2, because the line goes down 1 unit and then right 2 units.
Also it would be y = -1/2x+1 in y=mx+b.
The volume of a sphere is 4500cm. What is the surface area of the sphere to the nearest whole number?
The surface area of the sphere, to the nearest whole number, is 1318 cm².
How to determine the surface area of a sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
The surface area of a sphere is expressed as:
SA = 4πr²
Where r is the radius of the sphere and π is the mathematical constant pi.
Given that the volume V is 4500 cm³.
First, we solve for the radius:
Volume = (4/3)πr³
4500 = (4/3)πr³
4500 × 3 = 4πr³
13500 = 4πr³
r³ = 13500/4π
r = ∛( 13500/4π )
Now that we have the radius, we can calculate the surface area of the sphere using the formula:
SA = 4πr²
Substituting the radius we found:
SA = 4 × π × ∛( 13500/4π )²
SA = 1318 cm²
Therefore, the surface area is approximately 1318 cm².
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Discrete Mathematics
For each language L1 to L5, described below, you need to do the following:
• Create a regular expression that defines the language accurately.
The alphabet A = {a, b} will be used.
The languages are:
1. L1 which has exactly one a but any number of bs.
2. L2 which has an odd number of as and an even number of bs.
3. L3 which contains exactly two as or exactly two bs, although not necessarily adjacent.
4. L4 which has all the bs appearing before any of the as, or all the as appearing before any of the bs.
5. L5 where there can be any number of as but the number of bs must be even, although the bs do not have to be adjacent.
Note: ^ is for Start of the line, $ is for end of the line ,* means 0 or more, + means 1 or more, [ab] means either a or b and {} is for specific number of times, () is for grouping.
How to create regular expressions?A task in which it is necessary to create regular expressions to define five different languages. The alphabet used is A = {a, b}. The languages are:
L1, which has exactly one "a" but any number of "bs".
L2, which has an odd number of "as" and an even number of "bs".
L3, which contains exactly two "as" or exactly two "bs", although not necessarily adjacent.
L4, which has all "bs" appearing before any "a" or all "as" appearing before any "b".
L5, where there can be any number of "as", but the number of "bs" must be even, although the "bs" need not be adjacent.
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Given the general rotation matrix:
[cose -sine]
[sine cose]
Find the angle of rotation for the following matrix
O
O
O
√√3
NI - N/W]
1/2
√√3
2
A. 150°
B. 210⁰
C. 240⁰
D. 300
Answer is c. 210
2000
Hence, angle of rotation for given matrix is 210°.
The correct option is B.
What is trigonometric ratio?The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
cot θ = Base/Perpendicular
Given rotation matrix
[cos θ - sinθ ]
[ sinθ cos θ ]
= [-√3/2 1/2 ]
[-1/2 -√3/2 ]
Comparing elements of both matrices,
cos θ = -√3/2
cos θ = - cos 30°
cos θ = cos (180° + 30°)
cos θ = cos 210°
θ = 210°
- sin θ = 1/2
- sin θ = - (-1/2)
- sin θ = - (-sin 30°)
- sin θ = - sin(180° + 30°)
- sin θ = - sin 210°
θ = 210°
sin θ = -1/2
sin θ = - sin 30°
sin θ = sin (180° + 30°)
sin θ = sin 210°
θ = 210°
cosθ = -√3/2
cos θ = - cos 30°
cos θ = cos (180 + 30°)
cos θ = cos 210°
θ = 210°
Hence, 210° is the angle of rotation of given matrix .
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Answer:
210
Step-by-step explanation:
The radius of a circle is 1 foot. What is the length of a 90° arc?
90°
r=1ft
Give the exact answer in simplest form.
According to the given data the length of a \(90^{0}\) arc is \(\pi /2\) or approximately \(1.57\) feet.
What is meant by length of arc?In geometry, the length of an arc is the distance along the curved line that makes up the arc. It is a measure of the "length" of a portion of a circle's circumference, and it is usually expressed in the same units as the circle's radius.
According to the given information:
The length of a \(90^{0}\) arc in a circle with radius \(1\) foot can be calculated using the formula:
Length of arc = (angle/\(360\)) x \(2\pi r\)
where angle is the central angle of the arc in degrees, r is the radius of the circle, and \(\pi\) is a mathematical constant approximately equal to \(3.14159\).
Substituting the given values, we have:
Length of arc = (\(90/360\)) x \(2\pi(1 ft)\)
Length of arc = \((1/4)\) x \(2\pi ft\)
Length of arc = \(\pi /2 ft\)
Therefore, the length of the \(90^{0}\) arc is \(\pi /2 feet\) or approximately \(1.57 feet\)
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the length of the 90° arc is π/4 feet or approximately 0.785 feet
What is arc of circle?
In geometry, an arc of a circle is a portion of the circle's circumference. It is defined by two endpoints and all points along the circle between those endpoints. The measure of an arc is typically given in degrees or radians and can be used to calculate various properties of the circle, such as its length, area, and sector angles.
The formula for the length of an arc is:
L = (θ/360) × 2πr
where L is the length of the arc, θ is the central angle of the arc in degrees, and r is the radius of the circle.
In this case, θ = 90° and r = 1 ft, so we have:
L = (90/360) × 2π(1) = (1/4) × π = π/4
Therefore, the length of the 90° arc is π/4 feet or approximately 0.785 feet (rounded to 3 decimal places).
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find the lcm of each pair 14 and 18
Answer:
126
Step-by-step explanation:
Find the LCM (least common Multiple) in each 14 and 18.
126 goes in both 14 and 18.
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This table shows the results of rolling a number
cube with sides labeled 1 through 6 several
times.
What is the experimental probability of rolling a 2
or a 4?
Enter your answer as a fraction in simplest form
in the box.
Basic
7
8
9
H
y
x²
П n
O
Outcome occurred
1
2
3
5
Number of times outcome
6
10
6
4
8
6
6
Answer:
To calculate the experimental probability of rolling a 2 or a 4, we need to determine the total number of times the desired outcomes occurred and divide it by the total number of outcomes.
From the table, we can see that the number 2 occurred 6 times and the number 4 occurred 8 times. Therefore, the total number of times rolling a 2 or a 4 occurred is 6 + 8 = 14.
The total number of outcomes is the sum of all the occurrences in the table, which is 7 + 8 + 9 + 6 + 10 + 6 + 6 = 52.
Now we can calculate the experimental probability:
Experimental probability = Number of times desired outcomes occurred / Total number of outcomes
Experimental probability = 14 / 52
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 2:
Experimental probability = (14 / 2) / (52 / 2)
Experimental probability = 7 / 26
Therefore, the experimental probability of rolling a 2 or a 4 is 7/26.
A city in Texas started the day at -5 degrees Fahrenheit. The temperature increased by 15.1 degrees by nightfall. What is the final temperature at nightfall?
Step-by-step explanation:
Add 15.1 to -5-5 + 15.1 = 10.1Answer:
The final temperature is 10.1 degrees Fahrenheit
What is the surface area of a sphere with diameter 8 cm?
Answer:
As = 256\(\pi\) or 804.25cm
Step-by-step explanation:
By formula As = \(4\pi r^{2}\)
As = 256\(\pi\) or 804.25cm
Pet shelters typically have special adoption events for black cats and dogs, since their adoption rate is lower. One specific pet shelter (which has only cats and dogs) has 40% cats and 60% dogs. Twenty percent of the cats are black, and 10% of the dogs are black. The adoption percentage for black cats is 5%, and for black dogs is 10%. Cats that are not black are equally likely to be adopted as not adopted, and this is the same for dogs that are not black. For (b)-(f), write the probability statement and then calculate your answer.
a) Draw the probability tree and label all events and probabilities in it.
b) What is the probability that a randomly chosen animal is not black, a dog, and is adopted?
c) What is the probability that a randomly chosen animal is black, a cat, and is not adopted?
d) What is the probability that a randomly chosen animal is adopted?
e) Suppose a randomly chosen animal is a cat, what is the probability that it is adopted?
f) Suppose a randomly chosen animal is adopted, what is the probability that it is a cat?
a) The pet shelter has 40% cats (20% black, 5% adopted), and 60% dogs (10% black, 10% adopted). 50% are adopted in non-black cats and dogs, b) 0.45, c) 0.19, d) 0.15, e) 0.375, f) 0.6.
a) The probability tree would seem like this:
P(Cat) = 40%
P(Black Cat) = 20%
P(Adopted Black Cat) = 5%
P(Not Adopted Black Cat) = 95%
P(Not Black Cat) = 80%
P(Adopted Not Black Cat) = 50%
P(Not Adopted Not Black Cat) = 50%
P(Dog) = 60%
P(Black Dog) = 10%
P(Adopted Black Dog) = 10%
P(Not Adopted Black Dog) = 90%
P(Not Black Dog) = 90%
P(Adopted Not Black Dog) = 50%
P(Not Adopted Not Black Dog) = 50%
b) P ( Adopted & Not Black Dog ) = P(Not Black Dog) x P(Adopted | Not Black Dog) = 0.90 * 0.50 = 0.45
c) P(Not Adopted & Black Cat) = P(Black Cat) x P(Not Adopted | Black Cat) = 0.20 * 0.95 = 0.19
d) P(Adopted) = P(Adopted Black Cat) + P(Adopted Not Black Cat) + P(Adopted Black Dog) + P(Adopted Not Black Dog) = 0.05 + 0.50 + 0.10 + 0.50 = 0.15
e) P(Adopted | Cat) = P(Adopted & Cat) / P(Cat) = (0.05 + 0.50) / 0.40 = 0.375
f) P(Cat | Adopted) = P(Cat & Adopted) / P(Adopted) = (0.05 + 0.50) / 0.15 = 0.6.
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Help me please if you can
Answer:
-2
Step-by-step explanation:
Add them up: -14
Divide by how many there are: -14 / 7 = -2
Whih number produces a rational number multiplied by 0.5
The question is incomplete. Please find the full content below.
Which number produces a rational number multiplied by 0.5
(C) 2.22 produces a rational number multiplied by 0.5.
If a number can be expressed by p/q form where p and q are whole numbers and q does not equal to 0, is called a Rational number.
If a number cannot be expressed as above then that number is called Irrational Number.
In simple term, we can say that the never-ending decimal numbers and square roots of non perfect square numbers are Irrational Numbers.
Product of two rational numbers is always a rational and the product of one rational and one irrational is always an irrational number.
Here given that the number is 0.5 which is clearly a rational number.
In order to get a rational number, we have to multiply another rational number with that.
In the given choices,
\(\pi=3.14......\)
is a never-ending decimal number that is irrational.
7 is not a perfect square so
\(\sqrt{7}\)
is an irrational number.
2.020020002.... is also a never-ending decimal number hence it is irrational.
Only 2.22 is rational here.
So multiplication of 2.22 and 0.5 produces a rational number since the product of two rational numbers is always a rational number.
Hence option (C) is correct.
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Horacio is solving the equation-3/4 + 2/5x = 7/20x -1/2. Which equation represents possible ways to begin solving for x?
The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2
Which equation represents possible ways to begin solving for x?From the question, we have the following parameters that can be used in our computation:
-3/4 + 2/5x = 7/20x -1/2
The first step is to collect the like terms
So, we have
2/5x - 7/20x = 3/4 - 1/2
This represents an equation of the possible way to begin solving for x
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Is it weird i got through middle school without knowing how to solve shape degrees?
Answer:
no
Step-by-step explanation:
most people go through mid school cheating
Answer:
probably not cause same lol
Step-by-step explanation:
Tonya has 39 packages. Each package weighs 58 pounds. Choose the best estimate of the total weight of the packages.