The cardinality of a set refers to the number of elements in the set. It is found by counting the elements in the set.
What is cardinality of a set?The cardinality of a set refers to the number of elements in the set. To obtain the cardinality, we have to count the elements in the set.
a) There are 6 elements in this set hence the cardinality is 6.
b) There is only one element in the set hence its cardinality is 1.
c) There are two elements in the set hence the cardinality is 2.
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please help asap 100 points
Answers:
Problem #1: Option C, 166 yards cubed
Problem #2: Option A, 10
Step-by-step solution:
The first problem may seem a lot more confusing that it really is and this actually happened to me when I looked at it. Just because the cylinder is slanted that actually doesn't change any of the volume that we would have if it was straight up with the same diameter and height.
Using what we know about cylinders, let us plug all the information inside of the formula to determine the volume of the cylinder. However, before doing that we need to determine the radius of the circle from the diameter that was given.
Divide the diameter by two to get the radius
[tex]Radius = \frac{Diameter}{2}[/tex][tex]Radius = \frac{5.2\ yd}{2}[/tex][tex]Radius = 2.6\ yd[/tex]Plug in the values
[tex]V_{cylinder} = (\pi * radius^2)*height[/tex][tex]V_{cylinder} = (\pi * (2.6\ yd)^2)*7.8\ yd[/tex]Simplify the exponent
[tex]V_{cylinder} = (\pi * (2.6)^2 *(yd)^2)*7.8\ yd[/tex][tex]V_{cylinder} = (\pi * 6.76\ yd^2)*7.8\ yd[/tex]Simplify the expression
[tex]V_{cylinder} = (21.237\ yd^2)*7.8\ yd[/tex][tex]V_{cylinder} = 165.65\ yd^3[/tex]Therefore, after simplifying the expression using the cylinder volume formula and the given information we were able to determine that the option that best fits the description of our answer is option C, 166 cube yards.
Now that we completed the first question, we can move onto the second question. In this question we are given a figure along with 3 numbers and one unknown, x, which we need to find the value of. We need to use the Secant-Secant Power Theorem to help determine our solution.
Make an expression to represent the scenario
[tex]32(x + 32) = 28(20 + 28)[/tex]We know have an expression which we can now simplify and get the value of the unknown easily. The first step would be to distribute the 32 and 28.
Distribute both sides
[tex]32(x + 32) = 28(20 + 28)[/tex][tex](32 * x) + (32 * 32) = (28 * 20) + (28 * 28)[/tex][tex]32x + 1024 = 560 + 784[/tex]Simplify the expression
[tex]32x + 1024 = 1344[/tex]We now have a simple expression where we can now subtract both sides by 1024 to help isolate x with its coefficient.
Subtract 1024 from both sides
[tex]32x + 1024 - 1024 = 1344 - 1024[/tex][tex]32x = 1344 - 1024[/tex][tex]32x = 320[/tex]The final step that we have to help fully isolate x by itself is to divide both sides by 32 which would remove the coefficient from x.
Divide both sides by 32
[tex]\frac{32x}{32} = \frac{320}{32}[/tex][tex]x = \frac{320}{32}[/tex][tex]x = 10[/tex]After simplifying the expression completely, we are able to see that the best option that fits our description is option A, 10.
Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
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Homework Due Tomorrow please help me it would be great
Answer:
c
Step-by-step explanation:
work out the average for the data below
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
Help!!!!! Meeee!! Asappppp
Reason:
Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.
You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.
Which of the following is equal to this expression?
(256·64)^1/4
A) 4·[tex]\sqrt[4]{4}[/tex]
B) 8·[tex]\sqrt[4]{4}[/tex]
C) 8·[tex]\sqrt[4]{2}[/tex]
D) 2·[tex]\sqrt[4]{2}[/tex]
Answer:
B) [tex]8\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex](2^{8} *2^{6} )^\frac{1}{4} = (2^{8+6} )^\frac{1}{4} =(2^{14} )^\frac{1}{4} =2^{\frac{7}{2} }=\sqrt{2^{7} } =2^{3} \sqrt{2} =8\sqrt{2} = 8\sqrt[4]{2^{2} } = 8\sqrt[4]{4}[/tex]
find the perimeter of a triangular field whose length of edges are 14 m, 12m 10 m Also find the length of required to fence 4 times around it?
Answer: 36 m, 144 m
Step-by-Step Explanation:
a = 14 m
b = 12 m
c = 10 m
Perimeter = a + b + c
Therefore,
= a + b + c
= 14 + 12 + 10
= 26 + 10
=> 36
Perimeter = 36 m
Length of Fence required for Fencing 4 times = Perimeter * 4
Therefore,
= Perimeter * 4
= 36 * 4
= 144
Length of Fence required for Fencing 4 times = 144 m
a group of 20 students in four adults are going on a field trip to the museum What is the ratio of students to adults complete the statement.
Answer:
5:1
Step-by-step explanation:
Originally the ratio is 20:4
but then it is simplified to 10:2
then 5:1
X =
(19) Find the values for X and Y, and then solve for the side lengths.
Please help me! Thanks.
Answer: Answer:
The perimeter of the polygon are
PQ = 5
RS = 5
PR = √74 = 8.60
QS = √74 = 8.60
QR = 7
Step-by-step explanation:
To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula
d = √(x _2 - x_1)^2 + (y_2 - y_1)^2
Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = 4
PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2
= √ 5^2 + 0^2
= √ 25
= 5
Between R( 5 , -3) and S ( 0 , -3)
x_1 = 5
y_1 = -3
x_2 = 0
y_2 = -3
RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2
= √( -5)^2 + ( -3 + 3)^2
= √ 25 + 0
= √ 25
= 5
Between P( 0 , 4) and R (5 , -3)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = -3
PR = √( 5 - 0)^2 + ( -3 - 4)^2
= √ 5^2 + (-7)^2
= √ 25 + 49
= √ 74
= 8.60
Between Q ( 5 , 4) and S(0 ,-3)
x_1 = 5
y_1 = 4
x_2 = 0
y_2 = -3
QS = √ ( 0 - 5)^2 + ( -3 - 4)^2
= √ -5^2 + -7^2
= √ 25 + 49
= √ 74
= 8.60
Between Q( 5,4) and R(5 , -3)
x_1 = 5
y_1 = 4
x_2 = 5
y_2 = -3
QR = √ (5 - 5)^2 + ( -3 - 4)^2
= √ 0^2 + (-7)^2
= √ 0 + 49
= √ 49
= 7
Step-by-step explanation:
Please Urgent help,,,,
Answer:
This is the i-ready test, you have to try your best because if someone were to give you the answer, that will be cheating. The test provides teachers with a complete picture of student performance relating to their grade level and national norms. So, just try your best so you can get the lessons that are right for you.
(Im just saying but you don't have to listen to me ^^)
A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
can you help me with this question
( brain + 95 points ) A triangular prism has a height of 10 cm and the triangle has a base of 4 cm and a height of 6 cm. Find the volume of the triangular prism.
Area of base
1/2BH1/2(4)(6)2(6)12cm²Volume
Area of base× height12(10)120cm³Sin 0 = -8/17 and cos 0 = 15/17 find tan0
Answer:
Step-by-step explanation:
Givens
sin(theta) = - 8/17
cos(theta)= 15/17
Tan(theta) = ?
Comment
Without using the Pythagorean Theorem, you could simply use tan(theta) = Sin(theta) / cos(theta)
Tan(theta) = sin(theta) / cos(theta)
Tan(theta) =[tex]\dfrac{\dfrac{-8}{17} }{\dfrac{15}{17} }[/tex]
Now turn the bottom fraction upside down and multiply.
Tan(theta) = [tex]\dfrac{-8}{17}*\dfrac{17}{15} = \dfrac{-8}{15}[/tex]
Answer Tan(theta) = -8/15
The grade 10 class is going to bake muffins. The recipe that they are going to use requires the following ingredients: RECIPE ✓2 Egga ✔125ml Cooking oll ✓375ml brown sugar (300g) ✓800ml Milk ✓300g Whole wheat flour ✓ 375ml cake flour (210g) ✓5ml Salt ✓ 5ml Vanilla Essence ✓ 10ml Bicarbonate of soda ✓ 250ml Raisins (150g) 2.1 The volume of 150g of Whole wheat is 250ml. Calculate the volume of the Whole wheat flour in the recipe 2.2 When they are all mixed together, all the above ingredients make up 2 litres of mixture (because some parts dissolve into other parts). 2.2.1 Convert 2 litres into ml 2.2.2 How many muffins can the above recipe make if 60ml is required for each muffin? 2.2.3 Using your answer to question 2.2.2, how many eggs will the girls need to buy to make 500 muffins? 2.3 The students need to make 500 muffins, using muffin trays that hold 6 muffins par tray. They plan to put 4 trays at a time into the ovens. Each oven takes 30 minutes to bake. How long will they take to make 500 muffins if they will be using 4 ovens?
The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.
How to convert?From the information, we are told to convert 2 litres into ml. This will be:
= 1000 × 2
= 2000ml
The number of eggs that will be bought to make 500 muffins will be:
= 500 × 2
= 1000 eggs.
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Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
7) $72.45 -28.98 Rounded estimate
Answer:
$43
Step-by-step explanation:
$72.45 can be rounded down to $72.00
$28.98 can be rounded up to $29.00
$72-$29= $43
Seven increased by the product of six and the number is 19
The number is that was multiplied by 6 is 2.
What is the number?The equation that can be derived from the question is :
7 + (6a) = 19
Where a is the unknown number that 6 was multiplied with
Given the above equation, in order to determine the value of a, take the following steps:
Combine similar terms: 6a = 19 - 7
Subtract similar terms: 6a = 12
Divide both sides by 6: a = 12 / 6
a = 2
Here is the complete question:
Seven increased by the product of six and the number is 19. What is the number?
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Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?
Answer:
? = 41.41°
Step-by-step explanation:
The known side length is adjacent to the angle we need to find hence we will use cosine
cosx = adjacent /hypotenuse
cos(?) = 6 / 8
simplify fraction, cos(?) = 3 / 4
? = arccos(3 / 4)
y=-3³ +4
step by step of the rules and formula of this equation
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
the lenghts of five boxes are shown in the table which line plot shows the data from the table
Answer:
The bottom right line plot.
Step-by-step explanation:
In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.
If £2000 is placed into a bank account that pays 3% compound interest per year
how much will be in the account after 2 years?
Answer:
£ 2121.8
Step-by-step explanation:
The formula to find the compound interest is :
[tex]A=P(1+\frac{R}{100} )^n[/tex]
Here,
A = Amount ⇒ ?
P ⇒ Principal ⇒ £2000
R ⇒ Interest rate ⇒ 3%
n ⇒ Time ⇒ 2 years
Let us find now.
[tex]A=P(1+\frac{R}{100} )^n[/tex]
[tex]A=2000(1+\frac{3}{100} )^2[/tex]
[tex]A=2000(1+0.03 )^2[/tex]
[tex]A=2000(1.03 )^2[/tex]
[tex]A=2000*1.0609[/tex]
[tex]A=2121.8[/tex]
Therefore, there will be £ 2121.8 in the bank account after 2 years.
Can someone help me with this math problem?
see attached photo
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
How to determine the value of trigonometric reasons
In this question we must take into accounts the definitions of the trigonometric reasons sine and secant and the Pythagorean theorem as well.
If sec θ < 0 and csc θ > 0, then sin θ > 0 and cos θ < 0, the angle is in the second quadrant (0.5π < θ < π, x < 0, y > 0) and we have the following expression:
sec θ = r/x
[tex]\frac{r}{x}= -\frac{6\sqrt{11}}{11}[/tex]
Then x = - 11, r = 6√11 and the value of y is:
[tex]y = \sqrt{r^{2}-x^{2}}[/tex]
y = 5√11
By trigonometric expressions we have this formula for sin 2θ:
sin 2θ = 2 · sin θ · cos θ
sin 2θ = 2 · (y/r) · (x/r) = (2 · x · y)/r²
sin 2θ = [2 · (- 11) · (5√11)]/396
sin 2θ = - (5/18) · √11
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
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HELP!!!!!!!!!!!!!!!!!!!!
Answer:
D is the answer hope
Step-by-step explanation:
hope this helped
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
Which of the following is an even function?
Of(x) = (x - 1)²
Of(x) = 8x
Of(x)=x²-x
Of(x) = 7
COFFE
Sinte echinat
SUMPARNI
Answer:
Step-by-step explanation:
Solve for p: -3p + 2 > 5
To solve these types of problems:
⇒ just solve like a regular algebraic equation
⇒ with an inequality sign in the middle
Let's solve:
[tex]-3p + 2 > 5\\-3p > 3[/tex]
whenever there is any division/multiplication⇒ must change the inequality sign to face the other direction
[tex]-3p > 3\\p < -1[/tex]
Answer: p < -1
Hope that helps!
Answer:
p < -1
Step-by-step explanation:
-3p + 2 > 5
subtract 2 from both sides
-3p + 2 - 2 > 5 - 2
-3p > 3
divided both sides by -3 to get p alone
-3p / -3 > 3 / -3 reverse the inequality
p > -1