Answer:
The original price was $30
Step-by-step explanation:
40% = 40/100 = 0.4
[tex]\frac{12}{0.4} =30[/tex]
Hope this helps
How much is a one time investment of 250 be when invested at 6% for 40 years in compound annually
Hi
6% increase is multiply by 1,06
done 40 times
so : 250* 1,06^40 = 2571 ,
a rectangular floor of a room measures 5.4m long and 4.2m wide .the room is to be covered with square tiles . Calculate the minimum number of the floor
Answer: 22
Step-by-step explanation:
Number of floor tiles = (5.4m × 4.2m) ÷ 1m²
Number of floor tiles = 22.68
Minimum number of floor tiles = 22
Multiply each of the following(2x - 3y) and (x + 5y)
Answer:
[tex]2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]
Step-by-step explanation:
We can use the rainbow expansion method to find the expression.
[tex](2x - 3y)(x + 5y) \\ = 2 {x}^{2} + 10xy - 3xy - 15 {y}^{2} \\ = 2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]
Add the matrices.
What number fills in [?] ?
B
A
4
2
9 -4
3 -2 8
ܚ ܝܪ ܚ
-1
A + B =
25
9 -8
-1 5
596
1 [?]
3
4
82
4
7
-4
Entor
Answer:
3
Step-by-step explanation:
A + B is calculated by adding the same positions in both matrices.
and position (2, 3) in A+B is therefore the sum of position (2, 3) in A plus the position (2, 3) in B, which is then
-4 + 7 = 3
Find the length indicated
Answer:
23
Step-by-step explanation:
if you have 8 apples in a box, and then you put 15 additional apples into the box - how many apples are in the box ?
you see that is the same problem as the symbolized scenario with 2 lines being connected.
you have a string (e.g. for a kite) of 8 meters. and then you tie another string of 15 meters to it - how long is the new combined string ?
you really need help with that ?
8 + 15 = 23
Line l has a slope of -3. The line through which of the points is perpendicular to l
What is the measure of
Answer:
C
Step-by-step explanation:
[tex]\cos E=\frac{11}{18} \\ \\ E=\cos^{-1} \left(\frac{11}{18} \right) \\ \\ E \approx 52.33^{\circ}[/tex]
An investment pays 10% interest compounded monthly. What percent, as a decimal, is the effective annual yield? Enter your answer as a decimal rounded to four decimal places.
[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ APY=\left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ APY=\left(1+\frac{0.1}{12}\right)^{12}-1\implies APY=\left( \frac{121}{120} \right)^{12}-1\implies APY\approx 0.1047[/tex]
For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200 . The maximum capacity of the company is 100 items.
Based on the cost and revenue functions to the company for selling x items, the domain of C(x) is [0, 100].
The range of C(x) is (200, 4,200).
What is the domain and range of C(x)?The domain would be the lowest capacity and the maximum capacity. As these are physical units to sell, the lowest unit would be 0 units as units can't be negative.
The maximum capacity is given as 100 items so the domain is:
= [0, 100]
The range is:
When x is 0, the function gives C(x) as:
= 40(0) + 200
= 200
When x is the maximum of 100, the C(x) is:
= 40(100) + 200
= 4,200
Range is:
(200, 4,200)
Full question is:
What is the domain and range of C(x)?
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I need help with this question:
Simplify
The simplified form of the given expression as a fraction is 7x/x-7
Simplification of fractionsFractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.
Given the expression below;
(1/7+1/x)/(1/49+1/x²)
Find the LCM to have:
(x+7/7x)/(x²-49)/49x²
Divide to have:
x+7/7x * 49x²/(x²-49)
(x+7) * 7x/(x+7)(x-7)
Cancel out the like terms to have:
1 * 7x/x-7
= 7x/x-7
Hence the simplified form of the given expression as a fraction is 7x/x-7
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%. What is the probability that it will rain on exactly one of the three days they are there? Round your answer to the nearest thousandth.
The probability that it will rain on exactly one of the three days they are there is 0.375.
Given that Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%.
The binomial distribution is used when there are exactly two outcomes of a trial that are mutually exclusive.
Use binomial probability:
P = ⁿCʳ pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
and p is the probability of success.
probability of rain on any given day =p =0.50
total number of ways,n=3
let X is number of days with rain out of 3 days
So, [tex]X\sim Bin(3,0.50)[/tex]
P(x=X)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ
P(x=1)=³C₁(0.50)¹(1-0.50)³⁻¹
P(x=1)=3×0.50×(0.5)²
P(x=1)=1.5×0.25
P(x=1)=0.375
Hence, the probability that it will rain on exactly one of the three days they are there where the probability of rain on any given day is 50% is 0.375.
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Jolene set up a retirement account. She arranged to have $350 taken out of each of her monthly checks; the account will earn 2.1% interest compounded monthly. She just turned 33, and her ordinary annuity comes to term when she turns 60. Find the value of her retirement account at that time.
Answer:
A convenient formula to use is
S = ((1 + i)^n - 1) / i where S is the value of 1$ deposited for n periods at an interest rate of i
in this case n = 12 * 28 = 336 periods of deposit at an interest rate of
.0021 / 12 = .00175 = i
S = (1.00175^336 - 1) / .00175 = 456.8338 the value of 1$ after 336 periods
350 * 456.8338 = 159891.81 the value of 350 deposited monthly
Note that 350 * 336 would be 117,600
One must be careful to distinguish the above formula from
(1 - (1 + i)^-n) / i which gives the value of 1$ when the borrower is "paying" an interest rate of i - this would be the case for a mortgage - or what is the value of 1$ paid for n periods when paying an interest rate of i
How would you prove that Angle2 ≈ Angle4?
Angles 2 and 4 are corresponding angles. They are congruent, not supplementary because they have the same measure and do not add up to 180 degrees. Therefore, the answer is the third option. Corresponding angles are congruent.
There is a boardwalk game at Point Pleasant where you are blindfolded to throw darts at a board full of balloons. Each time a dart is popped, it is not replaced until the next turn. The board has 10 green,4 purple,5 red,and 2 tiedye and 3 black balloons.
Find the probabilities of the following outcomes:
a. Popping two reds consecutively during one turn
b. Popping a red, then a green during one turn
c. Popping a red, then a black, then a red during one turn
d. Popping anything but a tiedyed balloon on three consecutive throws
The given number of balloons, green = 10, purple = 4, red = 5, tie-dye = 2, black = 3, gives;
a. 5/138
b. 25/276
c. 5/1012
d. 35/46
How can the different probabilities be calculated mathematically?Given parameters;
Number of balls;
Green = 10
Purple = 4
Red = 5
Tie-dye = 2
Black = 3
Mode of selection = Without replacement
Number of balloons = 10+4+5+2+3 = 24
a. Probability of popping a red balloon = 5/24
Probability of popping a second red balloon = 4/23
Therefore;
Probability of popping two reds consecutively = 5/24 × 4/23 = 5/138
b. Probability of popping a red balloon = 5/24
Probability of popping a green balloon next = 10/23
Therefore;
Probability of popping a red and then a green balloon = 5/24 × 10/23 = 25/276
c. Probability that the first balloon that pops is a red = 5/24
Next balloon is a black = 3/23
Third balloon is red = 4/22
The probability, P, is therefore;
P = 5/24 × 3/23 × 4/22 = 5/1012d. The probability that the first balloon is a tie-dye = 2/24 = 1/12
Therefore;
Probability that the first balloon is not a tie-dye = 1 - 1/12 = 11/12
Probability that the second balloon is not a tie-dye = 21/23
Similarly;
Probability that the third balloon is not a tie-dye = 20/22 = 10/11
Which gives;
The probability, P, of popping anything but a tie-dye on three consecutive throws is therefore;
P = 11/12 × 21/23 × 10/11 = 35/46Learn more about probability theory in mathematics?
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2х+чу=4 and x + 2y = 3
Since the values on both sides are equal, hence the system of equation given has no solution
Solving simultaneous equationsSimultaneous equations are equations that consists of two or more equation and unknowns.
Given the equation below
2х+4у=4
x + 2y = 3
From equation 2;
x = 3 - 2y
Substitute into equation 1
2(3-2y) + 4y = 4
Expand
6 - 4y + 4y = 4
6 = 4
Since the values on both sides are equal, hence the system of equation given has no solution
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So I need to know what company changes more or less
Ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table given below. General Knowledge Math Science Acel Barek Carlin Acton Bay Acton Anael Max Anael Max Kai Kai Carl Anael Dario Dario Carlin Barek Let G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. Find G n M and G u S .
The computation shows that:
G n M = Anael and Max
G u S = Acel, Action, Anael, Max, Carl, Dario, Catlin, Kai, and Barek.
How to illustrate the information?From the information, ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table.
The subjects include general Knowledge Math Science.
Therefore, G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. The intersection is illustrated above.
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please help me! in need of help due tomorrow!
Answer:
Step-by-step explanation:
(1). A = π r²
A = 4 π
Area of shaded region is [tex]\frac{4\pi *260}{360}[/tex] = [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]
(2). C = 4 π
In this case, the length of the bigger arc and the area of shaded region happen to be the same.
The length of the arc ADB is [tex]\frac{26}{9} \pi[/tex] or [tex]\frac{26\pi }{9}[/tex]
A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use. What is the area of the tarp?
Trapezoid ABCD with base side AD labeled 15 feet, top side BC labeled 10 feet, and right side CD labeled 5 feet. Angle C measures 120 degrees.
To find the height, first find that is
. This means the height of the trapezoid is approximately
feet. So, the area of the tarp is approximately
square feet.
The area of the tarp is 54.125 square feet
How to determine the measure of D?From the figure in the question, we have the following angle measure:
DCE= 120
This means that:
<C = DCE - 90
Substitute the known values in the above equation
<C = 120 - 90
Evaluate the difference
<C = 30
The measure of D is then calculated as
<D = 90 - <C
This gives
<C = 90 - 30
Evaluate the difference
<C = 60
How to determine the height of the trapezoid?Represent the height with h.
This is then calculated as:
sin(D) = h/5
This gives
sin(60) = h/5
Multiply both sides by h
h = 5 * sin(60)
Evaluate
h = 4.33
How to determine the area of the tarp?This is calculated as:
A = 0.5 * (10 + 15) * 4.33
Evaluate
A = 54.125
Hence, the area of the tarp is 54.125 square feet
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Answer:
In the image
Hope this helps!
Step-by-step explanation:
To find the height, first find that ∠D is 60°. This means the height of the trapezoid is approximately 4.3 feet. So, the area of the tarp is approximately 53.7 square feet.
Suppose a stock qualifies as having moderate risk if the standard deviation of its monthly rate of return is less
than 10%. A stock rating agency randomly selects 36 months and decides the rate of return for a specific fund.
The standard deviation of the rate of return is computed to be 4.95%. Is there sufficient evidence to conclude
that the fund has moderate risk at the α=0.05 level of significance? A standard probability plot shows that the
monthly rates of return are typically distributed.
Test the claim using a hypothesis test.
What are the null and alternative hypotheses for the hypothesis test?
What is the conclusion based on the hypothesis test?
The conclusion of the Hypothesis Conclusion is; that there is sufficient evidence to support the claim that the fund has moderate risk.
How to test hypothesis claim?
We are given;
Sample size; n = 36
Population standard deviation; σ₀ = 10
Sample standard deviation; s = 4.95
Significance level; α = 0.05
Claim: Standard deviation less than 10
The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis needs to contain an equality and the value mentioned in the claim. If the claim is the null hypothesis, then the alternative hypothesis states the opposite of each other. Thus;
Null Hypothesis; H₀: σ = 10
Alternative Hypothesis; H₁: σ < 10
Compute the value of the test statistic:
χ2 = [(n - 1)/(σ²)] * s²
χ2 = [(36 - 1)/(10²)] * 4.95²
χ2 = 8.576
The critical value of the left-tailed test is given in the row with df = n - 1 = 36 - 1 = 35 and in the column with 1 − α = 0.95 of the chi-square distribution table online, we have;
χ2_{1 - α} = 21.77
The rejection region then contains all values smaller than 21.77
If the test statistic is in the rejection region, then reject the null hypothesis:
8.576 < 13.848
Thus, we will reject H₀ and conclude that there is sufficient evidence to support the claim that the fund has moderate risk.
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please help, I have been on this question for a while. Lotta yummy PTS
Answer:
[tex]y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3[/tex]
Step-by-step explanation:
Given equation:
[tex]y=\left|\dfrac{1}{2}x-2\right|+3[/tex]
Translation
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
When translating a graph to the right, subtract the number of units from the x variable.
Translating the given graph one unit to the right:
[tex]f(x-1) \implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3[/tex]
Simplifying:
[tex]\implies y=\left|\dfrac{1}{2}(x-1)-2\right|+3[/tex]
[tex]\implies y=\left|\dfrac{1}{2}x-\dfrac{1}{2}-2\right|+3[/tex]
[tex]\implies y=\left|\dfrac{1}{2}x-\dfrac{5}{2}\right|+3[/tex]
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Identify the vertex of the parabola ?
Step-by-step explanation:
second one
explanation: trust me bro
Write an expression involving exponents to represent the shaded area in square inches of the diagram than use that expression to calculate the shaded area in squares inches of the diagram
The expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
Expression involving exponents and shaded areaThe expression is:
6²- (3² + 2²)
The shaded area:
Shaded area=6²- (3² + 2²)
Shaded area=36-(9+4)
Shaded area=36-13
Shaded area=23 square inches
Therefore the expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.
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Hi, please help me me by demonstrating how to solve these 2 questions step by step :)
The given height of the shape is calculated to be 1,895.04 inches.
How to solve for the heightWe have the following details required to solve this problem
The distance b1 = 800 m
The angle of elevation β1 = 50°
distance b2 = 1450 m
- The new angle of elevation α = 33°
We first have to find the height of h1
800 x tan 50 degrees
= 953.40
The height of h2
1450 x tan 33
= 941.641
The height of the shape is the sum of the heights of h1 and h2
953.40 + 941.641
= 1,895.04
Hence the height of the shape is given as 1,895.04 inches.
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HELPPPPPP PLSSSSSSSSSS
Answer:
wait ewiai twia it i ti i got this soon
(1+3) x (2 x 3)
PLEASE ANSWER QUICK !!!!
Mikayla is determining the actual
distance between Harrisville and Lake Town
using a map. The scale on her map reads
1 inch = 50 miles. She measures the distance
to be 4.5 inches and writes the following
proportion:
1 in. 50 mi
x mi
4.5 in.
P
Explain why her proportion is equivalent to
50 mix mi
1 in. 4.5 in."
Answer:
100 miles and 5.5 inches
Geometry: Explaining Volume Formulas
Step-by-step explanation:
volume = area of circle × hight of cylinder ....
V = πr² × h
so V = πr²h
Answer:
10831 mm³
Step-by-step explanation:
The volume of any solid figure with a uniform cross section parallel to the base can be found using the volume formula ...
V = Bh
where B is the area of the base, and h is the height perpendicular to the base.
Base areaThe base of this cylindrical stack of pennies is a circle of diameter 19.05 mm. The area formula for a circle in terms of diameter is ...
A = (π/4)d²
The stack of pennies has a base area of ...
A = (π/4)(19.05 mm)² ≈ 285.023 mm²
VolumeThe volume formula tells us the stack of pennies has a volume of ...
V = Bh
V = (285.023 mm²)(38 mm) ≈ 10830.9 mm³
The volume of the stack of pennies is approximately 10831 mm³.
The mean of a normally distributed data set is 118, and the standard deviation is 16.
a) Use the standard normal table to find the probability that a randomly-selected data value is greater than 140.
b) Use the standard normal table to find the probability that a randomly-selected data value is less than 90.
Step-by-step explanation:
a)
z = (140 - 118)/16 = 22/16 = 11/8 = 1.375 ≈ 1.38
in the z-table this gives us the p-value : 0.91621
that is the probability of values 140 and below.
for above 140 we need to calculate the value of the other side of the bell-curve :
1 - 0.91621 = 0.08379
b)
z = (90 - 118)/16 = -28/16 = -7/4 = -1.75
in the z-table this gives us the p-value : 0.04006
that is the probability of values of 90 and below.
PLEASE HELP I will give 50 points! PLEASE ANSWER CORRECTLY
In a school, 10% of the students have green eyes. Find the experimental probability that in a group of 4 students, at least one of them has green eyes. The problem has been simulated by generating random numbers. The digits 0-9 were used. Let the number "9" represent the 10% of students with green eyes. A sample of 20 random numbers is shown. 7918 7910 2546 1390 6075 2386 0793 7359 3048 1230 2816 6147 5978 5621 9732 9436 3806 5971 6173 1430 Experimental Probability = [?]% =
Using it's concept, the experimental probability that in a group of 4 students, at least one of them has green eyes is of 0.45 = 45%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.
In this problem, there were 20 trials. The digit 9, which represents a student with green eyes, appears at least once in 9 of the the trials, hence the probability is:
p = 9/20 = 0.45 = 45%.
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Help me with this please asap?!
Answer:
None of these answers are correct.
Step-by-step explanation:
[tex]QR=\frac{25+45}{2}=35[/tex]
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
By Trapezoid mid - segment theorem :
[tex] \qquad❖ \: \sf \:QR = \cfrac{MN+ OP}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= \cfrac{25+ 45}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR = \cfrac{70}{2} [/tex]
[tex] \qquad❖ \: \sf \:QR= 35 \: \: units[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
length of segment QR = 35