Answer:
[tex]\begin{aligned}\lbrace & \; 3,\, 5,\, 6,\, 7,\, 9,\, 10, \\ &\; 11,\, 12,\, 13,\, 14,\, 15,\, 17, \\ &\; 18,\, 19,\, 20\rbrace\end{aligned}[/tex].
Step-by-step explanation:
The integer powers of [tex]2[/tex] between [tex]1[/tex] and [tex]20[/tex] are:
[tex]2^{0} = 1[/tex].[tex]2^{1} = 2[/tex].[tex]2^{2} = 4[/tex].[tex]2^{3} = 8[/tex].[tex]2^{4} = 16[/tex].Thus, [tex]A = \lbrace 1,\, 2,\, 4,\, 8,\, 16 \rbrace[/tex].
The complement of set [tex]A[/tex] (denoted as [tex]A^{C}[/tex]) includes all elements of the universal set [tex]U[/tex] that are not in set [tex]A\![/tex].
For example, the element [tex]1[/tex] is in [tex]U[/tex] and is also in [tex]A[/tex]. Thus, [tex]1[/tex] isn't in [tex]A^{C}[/tex].
The element [tex]3[/tex] is in [tex]U[/tex] and isn't in [tex]A[/tex]. Thus, [tex]3[/tex] is in [tex]A^{C}[/tex].
Repeat this decision process for each element of [tex]U[/tex] to enumerate [tex]A^{C}[/tex]:
[tex]\lbrace 3,\, 5,\, 6,\, 7,\, 9,\, 10, \, 11,\, 12,\, 13,\, 14,\, 15,\, 17, \, 18,\, 19,\, 20\rbrace[/tex].
A city planner has to build two small parks, shown in the diagram below. Park a is a triangle and park b is a rectangle. Find the length of each side of the park.
Answer:
The answer is one yard
Step-by-step explanation:
A city planner has plans to build two small parks, shown in the diagram below. Park is a triangle, and the park is a rectangle. Each unit on the coordinate grid represents a yard.
Answer:
show the picture an i will find it out
Step-by-step explanation:
I don’t understand this question and I need help
Answer:
[tex]FIRST\ BLANK:\ 22[/tex]
[tex]SECOND\ BLANK:\ 20[/tex]
[tex]THIRD\ BLANK:\ 18[/tex]
I hope this helps you
:)
Answer:
1. 22
2. 20
3. 18
Step-by-step explanation:
1. 2(13-p) = 2(13-2) = 26-4 = 22
2. 2(13-p) = 2(13-3) = 26-6 = 20
3. 2(13-p) = 2(13-4) = 26-8 = 18
1. y = 3x - 7
y = 4x - 14
Solve each system of equations by substitution
Answer:
(7,14)
Step-by-step explanation:
y=3x-7
y=4x-14
3x-7=4x-14
-7=x-14
7=x
to find y
y=3x-7
y=3(7)-7
y=21-7
y=14
Amanda owns a local cupcake shop. She pays 1,500 each month for rent. It costs her 5.00 to make each batch of cupcakes. She sells each batch for 20.00 How many batches must she sell each month in order to make a profit? write an inequality to model this situation and solve.
Answer: 15x - 1500 > 0, 101 batches
Step-by-step explanation:
To begin, lets start by modeling this with a linear equation, (for sake of simplicity).
we can model this in the form y = mx + b, where y is 0, (meaning she isn't making profit OR losing money either).
Next, lets set up the parameters:
0 = mx + b. We can safely say that b, our constant, is -1500, because this is the money she "loses" every month.
Now we have 0 = mx -1500. We know she sells each batch for $20, so we also know that she makes 20x dollars for x batches. Our m = 20.
Now we have 0 = 20x - 1500. However, this equation is not completely correct, as we arent subtracting the cost for making each batch of cupcakes. The problem says that it costs her $5 to make each batch. So it will cost her 5x dollars for making x batches. If we subtract this from how much she sells each batch for, we get the profit she makes from selling each batch. So she makes a profit of (20x - 5x) = 15x dollars for x batches of cupcakes.
Out completed equation is 15x - 1500 = 0.
Solving this equation for x will give us how many batches she needs to sell to break even. To model this as an inequality for profit we simply replace the "=" sign with a ">" sign.
So our completed inequality is 15x - 1500 > 0
Solving this for x:
15x - 1500 > 0
15x > 1500
x > 100
Amanda needs to make more than 100 batches per month to make a profit. The greatest number of whole number batches over 100 is 101; so she needs to sell atleast 101 batches to make a profit every month.
.pleaseeeee helppppppp
Answer:
[tex]4.8038[/tex] or just [tex]4[/tex] quarts.
Hope this helps!
Noam is interested in estimating the average age of the Summer Olympians who have competed since 1980. She randomly selected 24 Olympians, and the result was this list of ages: 16, 17, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 25, 26, 27, 28, 29, 30, 32 Construct and interpret a 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics. Use the table to determine the appropriate value of t*. Enter in the degrees of freedom and the value of t* (exactly as you see it written in the table). Degrees of freedom =
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics is (20.6, 24.8). It means that we are 98% sure that the true age of all Olympians is between these two values.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In this problem, with the help of a t-distribution calculator, with a two-tailed significance level of 0.02 and 24 - 1 = 23 degrees of freedom, the parameters are:
[tex]\overline{x} = 22.7, s = 4.15, n = 24, t = 2.5[/tex]
Then, the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 22.7 - 2.5\frac{4.15}{\sqrt{24}} = 20.6[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 22.7 + 2.5\frac{4.15}{\sqrt{24}} = 24.8[/tex]
The 98% confidence interval for the true mean age of Summer Olympians since the 1980 Olympics is (20.6, 24.8). It means that we are 98% sure that the true age of all Olympians is between these two values.
More can be learned about the t-distribution at https://brainly.com/question/16162795
Please help.
Given the equation in Standard Form, change it into Slope-Intercept Form [y = mx +b]
3y - 9x = -6
Show work.
Step-by-step explanation:
the answer is y=3x-2 if you cant see the picture
A car is moving at a uniform speed of 75km /hour.
a. How far will it travel in 20 minutes
b. Find the time required to cover a distance of 250km. fast
Two forces are each applied to an area of 0.04 m2.
The first is applied with a pressure of 55 N/m2, and the second with a pressure of 40 N/m2.
Find the difference between the size of the forces.
Answer:
Example 5 If a force F1 = 100N is applied on the left in the hydraulic lift shown, where A1 = 0.02 m2 and. A2 = 0.08 m2, what force F2 will be.
Step-by-step explanation:
Fifteen full crates of walnuts weigh 585 pounds, whereas an empty crate weighs 10 pounds. How much do the walnuts alone weigh?
Answer:
435
Step-by-step explanation:
15 × 10 = 150
15 - 585 = 435
How do I compute 6 less than thrice of 120
I need help on this!
Answer:
Option A: 3 and 1/2
Step-by-step explanation:
10/3 = 3 and 1/3
11/3 = 3 and 2/3
3 and 1/2 is in between both.
Answer:
A) [tex]3\frac12[/tex]
Step-by-step explanation:
[tex]\dfrac{10}{3}=3\frac13=3\frac26[/tex]
[tex]\dfrac{11}{3}=3\frac23=3\frac46[/tex]
[tex]3\frac12=3\frac36[/tex]
so [tex]3\frac12[/tex] is between [tex]\dfrac{10}{3}[/tex] and [tex]\dfrac{11}{3}[/tex]
For selling his studio apartment, Martin had to pay the real estate agent a commission of 5%. The studio sold for $95,000. What was the agent’s commission?
y×y×y=32
If you get this correct you will be marked as the brainliest
Answer:
[tex]\sf y = 3.17[/tex]
explanation:
[tex]\sf y * y * y = 32[/tex]apply rule: a * a * a = a³
[tex]\sf y^3= 2^5[/tex]changing sides, changes cubic to cubic root
[tex]\sf y = \sqrt[3]{2^5}[/tex]simplify
[tex]\mathrm \huge {y = 2^{\frac{5}{3} }}[/tex]In decimals
[tex]\sf y = 3.174802104[/tex]In two decimal places
[tex]\sf y = 3.17[/tex]Solution:
Note that:
y × y × y = y³ = 32Taking a cube root both sides.
y³ = 32=> ∛y³ = ∛32Writing the prime factors of 32.
=> y = ∛2 x 2 x 2 x 2 x 2Simplifying ∛32
=> y = 2 x ∛2 x 2 = 2 x ∛4PLEASE HELP
Two angles are supplementary. The measure of the larger angle is 12 more than 2 times the measure of the smaller angle.
Find the measures of both angles.
Provide your answer below:
Answer:
56° and 124°
Step-by-step explanation:
If two angles are said to be supplementary then their sum is 180°
Let x = smaller angle
If the larger angle is 12 more than 2 times the smaller angle, then
⇒ larger angle = 2x + 12
Sum of the angles = 180°
⇒ x + 2x + 12 = 180
⇒ 3x + 12 = 180
⇒ 3x = 168
⇒ x = 56
Therefore, smaller angle = 56°
larger angle = 2(56) + 12 = 124°
If your grandmother gave you her wedding ring, it was appraised at $1,200, and the annual inflation rate was 6 percent, how many years would it be before it was worth $2,400?
Answer: about 12 years
Step-by-step explanation: If your grandmother gave you her wedding ring, which was appraised at $1,200 and it had an annual inflation rate of 6 percent; it would take about 12 years for the ring's worth to become $2,400.
Answer:
about 11-12 years before it was worth $2400
14 = 6x4+b
I WILL MARK BRAINLYIEST FOR 1ST PERSON
The table show the numbers of balls in the gym 12 basketballs, 18 dodgeballs, 8 soccer balls, 14 tennis balls
Answer:
52 total number of balls in the gym
Step-by-step explanation:
12+18=30
30+14=44
44+8=52
Mark wants to buy a new lap top computer. He finds one that was priced
at $1200.00. It is on sale for 25% off. What is the sale price of the lap
top?
Answer:
sale price: $900
Explanation:
original price will be always of 100%
sale price: 100% - 25% = 75%
so solve:
100% ↔ $1200
1% ↔ $1200/100
1% ↔ $12
75% ↔ (12 * 75) = $900
what fraction of 7 1/2 is 3 1/2
Answer:
Step-by-step explanation:
7 1 x 3 1
2 2
= 105 = 26 1
4 4
Result in decimals: 26.25
Calculation steps:
7 1 x 3 1
2 2
= 15 x 7
2 2
= 15 × 7
2 × 2
= 105 = 26 1
4 4
please help me for this question
Answer:
Mid-point: [tex](0,-5)[/tex]
Equation: [tex]y=\frac{7}{3}x-5[/tex]
Step-by-step explanation:
To find the mid-point of AB, simply add up their x and y coordinates and divide by 2 respectively to find their middle point.
[tex](\frac{{x__A}+{x__B}}{2},\frac{{y__A}+{y__B}}{2})[/tex]
[tex](\frac{{-7}+{7}}{2},\frac{{-2}+{(-8)}}{2})[/tex]
[tex](0,-5)[/tex]
To find the perpendicular slope that passes through the mid-point, we need to know the slope between AB first.
Slope of AB: [tex]\frac{{y__2}-{y__1}}{{x__2}-{x__1}}[/tex] = [tex]\frac{{-8}-{-2)}}{{7}-{(-7)}}[/tex] = [tex]\frac{-6}{14}[/tex] = [tex]\frac{-3}{7}[/tex]
Multiplying slopes that are perpendicular with each other always results in -1.
[tex]\frac{-3}{7}*m = -1[/tex]
[tex]m=\frac{7}{3}[/tex]
By the point slope form:
[tex]({y}-{y__1})=m({x}-{x__1})[/tex]
Plug in the coordinates of the mid-point:
[tex]({y}-{(-5)})=\frac{7}{3} ({x}-{0})[/tex]
Equation: [tex]y=\frac{7}{3}x-5[/tex]
How many whole numbers are greater than 21 to the power of 2 and less than 22 to the power of 2?
Using the concept of whole numbers, it is found that there are 42 whole numbers that are greater than 21 to the power of 2 and less than 22 to the power of 2.
What is a whole number?A whole number is a countable number, that is, 1, 2, 3, 4, ....
In this problem, the numbers are:
21^2 = 441.
22^2 = 484.
The amount of numbers between them, excluding them, is given by:
484 - 441 - 1 = 42
There are 42 whole numbers that are greater than 21 to the power of 2 and less than 22 to the power of 2.
More can be learned about whole numbers at https://brainly.com/question/10814303
ASAP 50 points!!!!!!
Given the functions f(x) = –x2 + 4x and g(x) = x - 4, describe or show Bethany how she could find where f(x) = g(x) using a system and name the value(s) for x.
Answer: x=-1, x=4
Step-by-step explanation:
GIVING OUT 50 POINTS
The area of the parallelogram below is ____ square meters. A parallelogram with height labeled with 8 meters. The top horizontal side is labeled 6 meters. The base of the left triangle formed by the height is 2 meters.
Answer:
The area of the parallelogram below is 48 square meters.
Explanation:
[tex]\sf area \ of \ parallelogram = base * height[/tex]
Given:
base: 6 mheight: 8 musing the formula:
→ base * height
→ 6 * 8
→ 48 m²
In a a school , there are 600 students and the ratio of boys to girls is 2:3 find the number of boys and girls .
PLEASE HELP! Vertical angles 5 & 6 (3x-15)° and (2x+7)°
Answer:
Angle 5 = 51 degrees
Angle 6 = 129 degrees
Step-by-step explanation:
When dealing with parallel lines like this, the picture attached shows all the angles that are equal to each other. Angle 6 and (3x-15) will sum to 180 degrees. Angle 5 is equal to 3x-15. (3x-15) will be equal to (2x+7)
The first step to solving this problem after the angle relationships are determined is to solve for x:
3x-15=2x+7
3x-2x=7+15
x=22
The second step is to determine angle 5:
angle 5 = 3x-15
angle 5 = 3(22)-15
angle 5 = 66-15
angle 5 = 51 degrees
The third step is to determine angle 6:
angle 6 = 180 - (3x-15)
angle 6 = 180 - 3x + 15
angle 6 = 195 - 3x
angle 6 = 195 - 3(22)
angle 6 = 195 - 66
angle 6 = 129 degrees
The final step is to check the angles. Angle 6 and 3x-15 should add to 180; 180 - angle 5 should be equal to angle 6.
129 + 3x - 15 =? 180
129 + 3(22) - 15 =? 180
129 + 66 - 15 =? 180
180 = 180
180 - 51 =? 129
180 - 51 =? 129
180 - 51 =? 129
129 = 129
I WILL GIVE BRAINILESTTTTT
Answer: C
Step-by-step explanation:
NO LINKS!! Help me please
Answer:
y = 7·1.5^x
Step-by-step explanation:
To find the parameters of the exponential function, substitute the given point values and solve the resulting equations for the parameters.
The form you want to find the parameters of is ...
y = ab^x
__
For (x, y) = (1, 10.5)
10.5 = ab^1
For (x, y) = (3, 23.625)
23.625 = ab^3
__
The value of 'b' can be found by dividing the second equation by the first:
[tex]\dfrac{23.625}{10.5}=\dfrac{ab^3}{ab^1}\\\\2.25 = b^2\\\\b=\sqrt{2.25}=1.5[/tex]
Then the value of 'a' can be found by substituting for b in the first equation:
10.5 = a(1.5^1)
a = 10.5/1.5 = 7
The exponential function is ...
y = 7·1.5^x
Answer:
[tex]y=7 (1.5)^x[/tex]
Step-by-step explanation:
General form of an exponential function: [tex]y=ab^x[/tex]
where:
[tex]a[/tex] is the y-intercept (or initial value)[tex]b[/tex] is the base (or growth factor)[tex]x[/tex] is the independent variableIf [tex]b > 1[/tex] then it is an increasing function
If [tex]0 < b < 1[/tex] then it is a decreasing function
Given:
(1, 10.5)(3, 23.625)Substitute these ordered pairs into the general form of the exponential function:
Equation 1: [tex]ab^1=10.5[/tex]
Equation 2: [tex]ab^3=23.625[/tex]
To find [tex]b[/tex], divide Equation 2 by Equation 1:
[tex]\implies \dfrac{ab^3}{ab^1}=\dfrac{23.625}{10.5}[/tex]
[tex]\implies b^2=2.25[/tex]
[tex]\implies b=\sqrt{2.25}[/tex]
[tex]\implies b=1.5[/tex]
Now substitute found value of [tex]b[/tex] into one of the equations to find [tex]a[/tex]:
[tex]\implies ab=10.5[/tex]
[tex]\implies 1.5a=10.5[/tex]
[tex]\implies a=\dfrac{10.5}{1.5}[/tex]
[tex]\implies a=7[/tex]
Therefore, the final exponential equation is: [tex]y=7 (1.5)^x[/tex]
What is the answer of "(2⁵ ÷ 2⁸) ÷ 2⁷" ?
I need help please and thank you