==========================================================
Explanation:
Let's write the roster notation of each set
D = {0, 1, 2, 3, ...} the dots indicate the pattern goes on forever
E = {0, 1, 4, 9, 16, 25} = list of perfect squares smaller than 36
F = {20, 22, 24, 26, 28, 30} = even numbers between 20 and 30
----------------
If we intersect sets D and E, we're looking for what numbers are in both sets at the same time. Therefore, D ∩ E = {0, 1, 4, 9, 16, 25} which is the exact same as set E. This is because all of set E is inside of set D. We say that set E is a subset of set D. So, D ∩ E = E.
Choice A is very close to being true. The problem is that 25 is missing from the set {1,4,9,16}. So this is why choice A is false.
----------------
Now let's intersect sets D and F. The numbers they have in common are {20, 22, 24, 26, 28, 30} which is exactly what set F is. So set F is a subset of set D. We can write D ∩ F = F in much the same way we can say D ∩ E = E.
D ∩ F = {12,14,16,18} is not true. A number like 12 is not between 20 and 30, so it cannot be in set F.
Choice B is false so we cross it off the list.
----------------
Choice C is true and here's why
D ∪ (E ∩ F) is the same as saying D ∪ G where G is the set of intersecting E and F together. In other words, G = E ∩ F
We don't really need to even worry about sets E, F or G. All that matters here is set D.
When we write D ∪ (E ∩ F) or D ∪ G, we're saying "a number is in set D, or it is in set G". If it is in D, then it's a whole number. Otherwise, it's in a subset of whole numbers.
Overall, D ∪ G and D ∪ (E ∩ F) form the entire set of whole numbers.
------------------
Choice D is true.
E and F have nothing in common
E = {0, 1, 4, 9, 16, 25}
F = {20, 22, 24, 26, 28, 30}
So intersecting them leads to the empty set. This is the set with nothing inside it, not even 0.
------------------
Choice F is false
These two sets below
E = {0, 1, 4, 9, 16, 25}
F = {20, 22, 24, 26, 28, 30}
union together to get
H = {0,1,4,9,16,20,22,24,25,26,28,30}
just toss all of the numbers together into one big set
Notice how each of these numbers are whole numbers, so they are part of set D. This means set H is also a subset of set D.
When we intersect sets D and H, we end up with set H. We do not simply end up with the set with 25 only inside it.
Expresa el siguiente número 14322000000000000 en notación científica *
Answer:
14322 * 10¹²
1.4322 * 10¹⁶
Step-by-step explanation:
14322000000000000
14322 * 10¹²
1.4322 * 10¹⁶
Point P is on line segment OQ. Given OP = 14 and OQ = 16, determine the
length PQ
Answer:
PQ = 2
Step-by-step explanation:
We know that OQ = OP + PQ. Since OQ = 16 and OP = 14, we know that 16 = 14 + PQ, therefore, PQ = 2.
Total hours worked for Hans Zupp is ___ .
a ) 40 hours 15 minutes
b ) 42 hours 35 minutes
c ) 44 hours 15 minutes
d ) 46 hours 15 minutes
Answer:
Option (D)
Step-by-step explanation:
Total hours worked of Monday= 4:45 hours + 5:00 hours = 9:45 hours
Total hours worked of Tuesday= 4:45 hours + 4:45 hours = 9:30 hours
Total hours worked of Wednesday= 4:30 hours + 4:30 hours = 9:00 hours
Total hours worked of Thursday= 4:45 hours + 4:15 hours = 9:00 hours
Total hours worked of Friday= 4:45 hours + 4:15 hours = 9:00 hours
Total hours worked = 9:45 + 9:30 + 9:00 + 9:00 + 9:00
= 46:15 hours
≈ 46 hours 15 minutes
Option (D) will be the answer.
Write the equation of a line with a slope of 3 and passing through the point (-5, -7).
Show steps please
Answer:
y = 3x +8
Step-by-step explanation:
[tex](-5 ,-7)=(x_1,y_1) \\m = 3\\[/tex]
Plug in values into point-slope form
[tex]y -y_1 =m(x-x_1)\\y - (-7) = 3(x - (-5))\\y +7 =3(x+5)\\y+7 =3x+15\\y = 3x +15-7\\y = 3x +8[/tex]
SimpifyWhat is x to the power of 3 times x to the power 7?
Answer:
Here is your solution-
x³ times x⁷
means, x³×x⁷
Here you just have to add the powers as aⁿ×aᵐ=aⁿ⁺ᵐ
x³⁺⁷
x¹⁰
Question 1 (1 point)
Find the volume of a cube whose side length is 2.5 feet.
Volume
3
S
side 3
Answer:
Answer:
v=15.625ft³ or 15.63ft³
Step-by-step explanation:
v=s³
v=2.5³
v=15.625
round off to the nearest hundredth
v=15.63ft³
A snack bar seils scoops of strawberry, chocolate, and
vanilla ice cream. On Monday, the snack bar sold
100 scoops in total of these flavors of ice.cream. The
snack bar sold 3 times as many scoops of chocolate as
it did strawberry and 2 times as many scoops of
vanilla as it did chocolate. How many scoops of
chocolate ice cream did the 'snack bar sell on
Monday?
Answer:
600/11
Step-by-step explanation:
scoops of
strawberry= x
chocolate= y
vanilla ice cream= z
X+y+z= 100
The snack bar sold 3 times as many scoops of chocolate as it did strawberry
3x= y
X= y/3
and 2 times as many scoops of
vanilla as it did chocolate
2z= y
Z= y/2
X+y+z= 100
Y/3 + y +y/2 = 100
2y + 6y + 3y = 600
11y= 600
Y= 600/11
William drove 35 miles per hour for a total of 105 miles. He drove for x hours.
Which equation and solution below describe the situation?
Answer:
x=35 hrs
1 hour =105
cross mutiply
105÷35=3
The equation that describes the situation is 35x = 105.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The equations are of various types, such as Trigonometric equations, and quadratic equations.
William drove 35 miles per hour for a total of 105 miles.
The total miles William drove is 105 miles.
The speed at which he drove is 35 miles/ hour.
The total time he drove is given by x hours.
The equation has to be formed for this situation.
Speed is defined as the distance traveled with respect to time.
35 = 105 / x
35x = 105
This equation describes the given situation.
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whats 5 less than 1 third
Answer:
-0.66666666666
Step-by-step explanation:
1/3-5/5
Express the quotient 36/12
Answer:
Step-by-step explanation:
36/12 = 3
12 x 3 = 36
Need help with this have no idea how to do it
Answer:
Step-by-step explanation:
x- intercept, vertex (v) and axis of symmetry, parabola form:x²+bx+c
vertex(h,k)
1- f(x)=(x+3)(x-3) change into parabola formf(x)=x²-9 a=1,b=0 ,c=-9
h=-b/2a=0
k=f(0)=-9
vertex(0,-9) , x intercept is when f(x)=0
(x-3)(x+3)=0 either x-3=0⇒ x=3 or x+3=0 then x=-3
x=3, x=-3 (-3,0) and (3,0)
the x of symmetry is the h of the vertex=0
2-g(x)=(x+1)(x-3)g(x)=x²-2x-3 a=1, b=-2,c=-3
h=-b/2a⇒-(-2)/2(1)⇒h=1
k=f(1)=1²-2(1)-3⇒k=-4
v(1,-4)
x of symmetry=h=1
(x+1)(x-3)=0
x+1=0⇒x=-1 (-1,0)
x-3=0 ⇒x=3 (3,0)
x intercept :-1,3
3-y=-x(x+6) ⇒y=-x²-6x a=-1,b=-6, c=0vertex(-3,9)
x intercept:(0,0) and (-6,0)
axis of symmetry =-3
4-g(x)=2(x-5)(x-1) ⇒ 2x²-12x+10 a=2, b=-12, c=10vertex(3,-8)
axis of symmetry=3
x intercept : (5,0), (1,0)
5) -4x(x+1)⇒-4x²-4x a=-4,b=-4vertex(-1/2,1)
x of symmetry=-1/2
x intercept : (0,0)(-1,0)
6- f(x)=-2(x-3)² ⇒-2x²+12x-18vertex(3,0)
x intercept (3,0)
axis of symmetry = 3
Find the distance between X (5, 7) and Y (-6, 6).
Round answer to the nearest tenth.
Answer: 11.0 or 11
Step-by-step explanation:
To find the distance first find the difference between the coordinates. find the change in the x and y coordinates and square them to add them to get a number and find the square root of that same number to find the distance.
x coordinates: 5-(-6)= 11
y coordinate: 7-6 = -1
Now square them
11^2 + 1^2 = l^2 where l is the distance
121 + 1 = l^2
122 =l^2
l = [tex]\sqrt{122}[/tex]
l = 11.045 Rounded to the nearest tenth is 11.0
Evaluate ( z^2 + 4 ) ( z^2 – 5)
Answer:
z^4-z²-20
Step-by-step explanation:
( z^2 + 4 ) ( z^2 – 5)
z^4+4z²-5z²-20
z^4-z²-20
Sarah received a score of 36 points on an exam. The exam consisted of multiple choice questions that were worth 3 points for a correct answer and free response questions that were worth 5 points for a correct answer. If she answered a total of 10 questions correctly, how many of each type of question did she get correct?
Answer:
Sarah answered 7 multiple choice questions and 3 free response questions correctly.
Step-by-step explanation:
Given that: she has 36 points.
3 points each for the multiple choice question (MCQ)
5 points each for the free response question (FRQ)
To determine how many of each question was answered correctly. Let the number of MCQ she answered be represented by x and FRQ by y.
3x + 5y = 36 ............ 1
Since she answered a total of 10 question, then;
x + y = 10
x = 10 - y ................ 2
Substitute equation 2 into 1,
3(10 - y) + 5y = 36
30 - 3y + 5y = 36
2y = 6
y = 3
Substitute the value of y in equation 2,
x = 10 - y
= 10 - 3
= 7
x = 7, y = 3
Therefore, Sarah answered 7 multiple choice questions and 3 free response questions.
A three-person committee is chosen at random from a group of 8. How many different committees are possible?
Solve the system of linear equation by substitution. Check your solution. x=6y-7 4x+y=-3
Answer:
X = -1
Y = 1
Step-by-step explanation:
The solution of the equations x = 6y - 7 and 4x + y = -3 will be (-1, 1).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equation is given below.
x = 6y - 7 ...1
4x + y = - 3 ...2
Simplify the equation, then we have
4(6y - 7) + y = -3
24y - 28 + y = - 3
25y = 25
y = 1
The value of the variable 'x' will be calculated as,
x = 6(1) - 7
x = 6 - 7
x = - 1
The solution of the equations x = 6y - 7 and 4x + y = -3 will be (-1, 1).
More about the solution of the equation link is given below.
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which of the following must describe an irrational number? (1pt) a number with a nonterminating decimal expansion a number with a non repeating decimal expansion a number with a repeating or terminating decimal expansion a number with a non repeating and non terminating decimal expansion.
Answer:
a number with a non repeating and non terminating decimal expansion.
Step-by-step explanation:
Irrational numbers are numbers which cannot be expressed as fractions, they are real numbers which cannot be expressed as rational numbers such as the square root of natural numbers other than perfect squares.
Irrational numbers are non repeating, non terminating decimal numbers with no group of the digits repeated. Therefore the decimal expansion does not terminate but continues without repetition example is π.
Determine ux and sigma x from the given parameters of e population and sample size.
mu = 86, sigma = 16, n = 64
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
A) Describe the sampling distribution of xbar.
B) What is P (xbar > 73)?
C) What is P (xbar 69)?
D) What is P (69.8 < xbar < 72.5)?
1) Choose the correct description of the shape of the sampling distribution of xbar.
A) The distribution is skewed left.
B) The distribution is approximately normal.
C) The distribution is uniform.
D) The distribution is skewed right.
E) The shape of the distribution is unknown.
Find the mean and standard deviation of the sampling distribution of x-.
2) P(x->73) =.
3) P (x- 69) =.
4) P (69.8 < xbar < 72.5) =.
Answer:
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 86
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 2
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 71
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 1
B) The distribution is approximately normal.
[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]
Therefore, the probability that the sample mean is greater than 73 = 0.0228
[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]
The probability that the sample mean is less than or equal to 69 is 0.0228
[tex]\mathbf{P( 69.8 \leq \overline x \leq 72.5) = 0.8181}[/tex]
Thus, the probability that the sample mean is between 69.8 and 72 is 0.8181.
Step-by-step explanation:
We are to determine the [tex]\mu_{\overline x}[/tex] and [tex]\sigma_x[/tex] from the given parameters of a population and sample size.
Given that :
population mean [tex]\mu[/tex] = 86
population standard deviation [tex]\sigma[/tex] = 16
sample size n = 64
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is equal to the population mean [tex]\mu[/tex]
∴
[tex]\mu_{\overline x}[/tex] = [tex]\mu[/tex] = 86
The standard deviation of the sampling distribution can be computed by using the formula:
[tex]\sigma_{\overline x } = \dfrac{\sigma }{\sqrt{n}}[/tex]
[tex]\sigma_{\overline x } = \dfrac{16 }{\sqrt{64}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{16 }{8}[/tex]
[tex]\mathbf{\sigma_{\overline x } = 2}[/tex]
∴
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 86
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 2
Suppose a simple random sample of size n = 36 is obtained from a population with mu = 71 and sigma = 6.
i.e
sample size n = 36
population mean [tex]\mu[/tex] = 71
standard deviation [tex]\sigma[/tex] = 6
From the central limit theorem's knowledge, we know that as the sample distribution approximates a normal distribution, the sample size gets larger. Thus, the mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is equal to the population mean [tex]\mu[/tex]
∴
[tex]\mu_{\overline x}[/tex] = [tex]\mu[/tex] = 71
The standard deviation of this sampling distribution [tex]\sigma_{\overline x}[/tex] can be estimated as :
[tex]\sigma_{\overline x }= \dfrac{\sigma }{\sqrt{n}}[/tex]
[tex]\sigma_{\overline x }= \dfrac{6 }{\sqrt{36}}[/tex]
[tex]\sigma_{\overline x } = \dfrac{6 }{6}[/tex]
[tex]\mathbf{\sigma_{\overline x } = 1}[/tex]
∴
The mean of the sampling distribution [tex]\mu_{\overline x}[/tex] is 71
The standard deviation of the sampling distribution [tex]\sigma_x[/tex] is 1
A)
The correct option from the given question is:
B) The distribution is approximately normal.
B) What is P (xbar > 73)?
i.e
[tex]P(\overline x >73) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{73 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{2 \times 6 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > \dfrac{12 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x >73) = P \begin {pmatrix} Z > 2 \end {pmatrix}[/tex]
[tex]P(\overline x >73) = 1- P \begin {pmatrix} Z < 2 \end {pmatrix}[/tex]
Using the Excel Function ( =NORMDIST(2) )
[tex]P(\overline x >73) = 1- 0.9772[/tex]
[tex]\mathbf{P(\overline x >73) = 0.0228}[/tex]
Therefore, the probability that the sample mean is greater than 73 = 0.0228
C) What is P (xbar ≤ 69)?
i.e
[tex]P(\overline x \leq 69) = P \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{69 -71 }{\dfrac{6}{\sqrt{36}}} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix}Z \leq \dfrac{-2 }{\dfrac{6}{6}} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-2 \times 6 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq \dfrac{-12 }{6} \end {pmatrix}[/tex]
[tex]P(\overline x \leq 69) = P \begin {pmatrix} Z \leq -2 \end {pmatrix}[/tex]
Using the EXCEL FUNCTION ( = NORMSDIST (-2) )
[tex]\mathbf{P(\overline x \leq 69) = 0.0228}[/tex]
The probability that the sample mean is less than or equal to 69 is 0.0228
NOTE: This text editor can't contain more than 5000 characters so the last part of the question is attached in the image below.
Determine the sum of the arithmetic series: 5+18 +31 +44 + ... 161.
Answer:
1079
Step-by-step explanation:
Hello,
18-5 = 13
31-18=13
44-31=13
161=5+13*12
So we need to compute
[tex]\displaystyle \sum_{k=0}^{k=12} \ {(5+13k)}\\\\=\sum_{k=0}^{k=12} \ {(5)} + 13\sum_{k=1}^{k=12} \ {(k)}\\\\=13*5+13*\dfrac{12*13}{2}\\\\=65+13*13*6\\\\=65+1014\\\\=1079[/tex]
Thanks
The required sum of the arithmetic series 5+18 +31 +44 + ... 161 is 1079.
Given that,
Arithmetic series: 5+18 +31 +44 + ... 161.
The Sum of the series is to be determined.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values
Here,
From the given series
First term A = 5, Common difference D = 13 and last term L = 161
Last term = An + (n -1)
161 = 5 + (n - 1)13
n - 1 = (161 - 5) / 13
n = 12 + 1
n = 13
Now the sum of an arithmetic series,
S = n /2 (A + L)
S = 13 / 2 (5 + 161)
S = 13 / 2 * 166
S = 13 * 83
S = 1079
Thus, the required sum of the arithmetic series 5+18 +31 +44 + ... 161 is 1079.
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Find the area of the isosceles triangle.
Answer:
60in^2
Step-by-step explanation:
Area of a triangle = Height x Base X 1/2
Base = 10
Other 2 sides = 13
Now, let's split the Base into 2 parts.
=> 1 part = 5 and 2 part = 5
We can find the height using Pythagorean theorem
=> Isosceles triangle
=> (1 part of the base)^2 + Height^2 = The Hypotenuse^2 = the longer side of a triangle = 13^2
=> 5^2 + Height ^2 = 13^2
=> 25 + Height^2 = 169
=> 25 - 25 + Height ^2 = 169 - 25
=> Height^2 = 144
=> Height = Square root of 144
=> Height = 12
Area = 12 x 10 x 1/2
=> 12 x 5
=> 60 in^2
So, the Area is 60 in ^2
8^15÷8^−3 im lost i dont get this whole simply thing at all
8^15 ÷ 1/8^3 = 8^15 x 8^3=8^18
1.8014399e+16
Step-by-step explanation:
So before you can divide the numbers you have to simplify the exponents. You probably learned P(parentheses) E(exponents) M(multiply) D(divide) A(add) S(subtract.
PEMDAS is important because it shows you what order to so something in. Exponents is before divide so you simplify the exponents and you get 8^15= 3.5184372e+13 and 8^-3 = 0.001953125. So after you simplify the exponents you can now divide themNow (3.5184372e+13) ÷ (0.001953125) = 1.8014399e+16help will give brainliest
Answer:
-10+4=-6
Step-by-step explanation:
evaluate 1/3(-15+3/2)
Answer:
-4 1/2
Step-by-step explanation:
1/3(-15+3/2)
1/3(-13 1/2)
1/3(-27/2)
-27/6
-4 3/6
-4 1/2
3x^2+11x+6 in factor form
Answer: (3x+2)(x+3)
Step-by-step explanation: Factor by grouping.
I hope this helps you out.
Answer:
[tex](3x+2)(x+3)[/tex]
Step-by-step explanation:
[tex]3x^{2} +11x+6[/tex]
Let's factor.
[tex]3x^{2}+11x+6[/tex]
This equals
[tex](3x+2)(x+3)[/tex]
Now you got your answer!
Hope this helps!
calculate the weight of a piece of steel to the nearest tenth of a pound. the diameter is 40" and the thickness is 2
Answer:
2513.3
Step-by-step explanation:
cylinder volume = π[tex]r^{2}[/tex]h
cylinder volume = π [tex]20^{2}[/tex](2)
cylinder volume = 2513.27
cylinder volume = 2513.3
Evaluate the expression (7+6i)−(−9−8i) and write the result in the form a+bi.
Remove the parentheses and combine the like terms:
7 - -9 = 7+ 9 = 16
6i - -8i = 6i +8i = 14i
The answer is 16 + 14i
at the mall myla bought a shirt for 25.36$ a hat for 5.09$ and a belt for 11.45$ howe much did she spend altogether?
25.36+5.09+11.45= 41.9$ intotal
Answer:
41,9
Step-by-step explanation:
25.36+5.09+11.45
Write the fraction 2/5 as an equivalent with the given denominator 25
Answer:
10/25
Step-by-step explanation:
2/5 = x/25
We need to multiply the bottom by 5 to get to 25
5*5 = 25
What we to the bottom, we do the the top
2/5 * 5/5 = 10/25
Answer:
10/25
Step-by-step explanation:
2/5 = x/25
cross multiply
2 • 25 = 50
5 • x = 5x
set equal to each other
5x = 50
divide both sides by 5
x = 10
4 times the sum of a number and 8 gives 25
Answer:
4×(x+8)=25.
use the 4 to multiply the numbers in the bracket.
which is 4x+32=25.
then collect like terms which is...
4x=25-32...
4x=-7.
x=-7/4= -1.75 or -1 whole number 3/4.
If you want to go bed a 800 o'clock
at night and set the alarm to get up at
9 in the morning how many hours
sleep would this permt you?
Answer:
13 hours
Step-by-step explanation:
8:00 plus 4 is twelve ( 12 o'clock )
then you have 9hrs left.
( 4+9=13 )