1. Identify all pairs of congruent corresponding parts, then write a congruency statement.
∠A ≅ ___ AB≅___
∠B≅ __ BC≅___
∠C≅ ___ AC≅__
Congruency statement
Answers
The congruent pairs for the angles and sides of the given two congruent triangles are
∠A ≅ ∠D
∠B ≅ ∠ E
∠C ≅ ∠F and
AB ≅ DE
BC ≅ EF
AC ≅ FD
What is congruent triangles?
If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.
Let the given two triangles, ΔABC and ΔDEF are congruent.
We have to find the congruent pairs from the given two congruent triangles.
First to find the congruent pairs for angles.
∠A ≅ ∠D
∠B ≅ ∠ E
∠C ≅ ∠F
Now to find the congruent pairs for sides,
AB ≅ DE
BC ≅ EF
AC ≅ FD
These are the congruent pairs for the angles and sides of the given two congruent triangles.
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Related Questions
Which diagram shows a pair of angle measures that prove lines a and b are parallel?
Answers
Answer:
c
...................
Answer:
the answer is the option C
A store is instructed by corporate headquarters to put a markup of 11% on all items. An item costing 18$ is displayed by the store manager at a selling price of 2$. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
Answers
if the markup is 11%, well, we simply add that to the cost of the item, in this case 18.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{11\% of 18}}{\left( \cfrac{11}{100} \right)18}\implies 1.98~\hfill \underset{selling~price}{\stackrel{18 ~~ + ~~1.98}{\text{\LARGE 19.98}}}[/tex]
Question 12 of 25
Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Boys
Girls
Total
Play a sport
95
76
171
Do not play a
sport
45
59
104
Total
overe pot independent because Nair) 0.10
140
135
275
Are being a girl and playing a sport independent events? Why or why not?
Answers
Being a female and participating in sports are independent events for the provided data because P(girl) = P(girl participates in sports)
What are independent events?These are the occurrences that are independent of other occurrences.
Occurrences A and B are independent events when the likelihood of one occurring is unaffected by the occurrence of the other.
Probability of independent events formula:
"P(A∩B) = if A and B are independent occurrences P(A).P(B)
What exactly is probability?Finding the chance that an event will occur is the focus of this area of mathematics."
P(A) = n(A)/n(S), where n(A) is the number of positive outcomes and n(S) is the total number of possible outcomes for an event A.
For given question,
We have been given a table that shows the results broken down by gender.
Play sports Do not play sports Total
Boy 95 45 140
Girl 76 59 135
Total 171 104 275
Using the definition of probability:
⇒ P(girl) = Number of girls/ Number of students
⇒ P(girl) = 135/275
⇒ P(girl) = 0.49 ....................(1)
Now we find the probability of girls that play a sport.
Using the definition of probability:
P(girl plays a sport)
= Number of girls who plays a sport/ number of students who plays a sport
= 76/ 171
= 0.44 ......................(2)
From (1) and (2),
P(girl) = P(girl plays a sport)
Thus, being a girl and playing a sport are Independent events.
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Determine if the events are independent or dependent.
P(A) = 0.65 P(B) = 0.25, P(A and B)0.40
P(A) = 0.22 P(B) = 0.45, P(A and B) .0.099
P(A) = 0.42 P(B) = 0.62, P(A| B) =
0.2604
You roll a pair of dice at the same time.
You choose two marbles from a bag, without replacement.
Answers
The events P(A) = 0.22 P(B) = 0.45, P(A and B) = 0.099 and rolling a pair of dice at the same time are independent events. Others are dependent events.
What is Independent and Dependent Events?Independent events are events for which the occurrence of this event does not depend on any other events.
Dependent events are those events for which it's occurrence depends on other events.
Two events A and B are independent, if
P(A | B) = P(A)
P(A and B) = P(A) × P(B)
P(A) = 0.65, P(B) = 0.25 and P(A and B) = 0.40
P(A) × P(B) = 0.65 × 0.25 = 0.1625 ≠ P(A and B)
∴ A and B are dependent events.
P(A) = 0.22 P(B) = 0.45 and P(A and B) = 0.099
P(A) × P(B) = 0.22 × 0.45 = 0.099 = P(A and B)
∴ A and B are independent events.
P(A) = 0.42 P(B) = 0.62 and P(A| B) = 0.2604
P(A| B) = 0.2604 ≠ P(A)
∴ A and B are dependent events.
If you roll a pair of dice at the same time, probability for any number to occur on dice 1 does not affect the probability of any number to occur on dice 2.
∴ A and B are independent events.
If you choose two marbles from a bag, when the first marble is chosen, then the second marble you choose will not be the first marble in any case. So second event depends on the first event.
∴ A and B are dependent events.
Hence, as P(A and B) = P(A) × P(B) satisfies for the events P(A) = 0.22 P(B) = 0.45, P(A and B) = 0.099, is is independent events. Also rolling a pair of dice at the same time is also independent events. The rest of the events are dependent events as it does not satisfies the condition for independent events.
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The doubling period of a bacterial population is 15 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0 ?
Find the size of the bacterial population after 3 hours.
Answers
The doubling period of a bacterial population is 15 minutes. the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.
How to find the initial population?y = total amount of bacteria
a = initial bacterial at time 0
b = growth factor
t=120 minutes =15 minutes 8 times
So,
t=8
90000 = a (2)^8
90000 = a (256)
90000/256 = a
351.56 = a (initial population)
Equation:
y = 351.56 (2)t
After 3 hours (15 minutes 10 times), or at t = 10
y = 351.56 (2)^10
y= 359,997.44
Therefore the initial population at time t=0 is 351.56. the size of the bacterial population after 3 hours is:359,997.44.
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Find the equation of Straight line equally indined to the axes and cutting off an intercept 0-2 from the y-axis
Answers
The equation of the line is y = x - 2.
What is the equation of the line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
We have,
y-intercept(c) = −2 and
the line is equally inclined to the axis i.e., the same angle to the x-axis and y-axis(say)=θ
but the angle between the axes is 90°
2θ = 90° ⇒ θ = 45°
As slope and y-intercept are given.
The equation of a line is y = mx + c
c = -2 and
m = tan45°
as the line is equally inclined to the axes.
c = -2 and m = 1
Hence, the equation of the line is y = x - 2.
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Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 8 years. Assume that money is worth 5.4%, compounded quarterly. (Round your answer to the nearest cent.)
Answers
Present Value of Annuity = $4,000 × 26.1948 = $104779.2
What is a present value?
The worth of an anticipated revenue stream assessed as of the valuation date is known as the present value in the fields of economics and finance.
Here, we have
Where , Annuity Amount = $4,000
n = No. of periods = 8 years × 4 quarters per year = 32 periods but since the first payment is at beginning of the quarter,
Then, n = 31 when considered for PVAF
r = 5.4% / 4 quarters = 1.35%,
Present value of Annuity = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n, r)
PVAF(n₀,r) when the first payment is at beginning of n i.e.
n₀ = 1 + { [1-(1+r)^ -n ]/r }
= 1 + { [1-(1+0.0135)^ {-31}]/0.0135 }
= 1 + [ (1 - 0.65987 ) ] / 0.0135]
= 1 + 25.1948
= 26.1948
PVAF(32,35%) = 26.1948
Hence, Present Value of Annuity = $4,000 × 26.1948 = $104779.2
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Two functions, A and B, are described as follows: Function A y = 8x + 3 Function B The rate of change is 1 and the y-intercept is 4. How much more is the rate of change of function A than the slope of function B? (5 points) Question 12 options: 1) 1 2) 7 3) 8 4) 9
i need it now
Answers
The rate of change is 7 more of function A than the slope of function B.
What is meant by slope?Slope is calculated as the ratio of "vertical change" to "horizontal change" between any two points on a line, or any two points. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.
Since y=8x+3,
The rate of change in equation A is equal to the slope m m=8.
The rate of change, m=1, is given in equation B.
y=mx+ is the solution to equation B.
By substituting the values we get,
y=x+4
Calculate the difference between the rates of change of function A and function B.
8-1=7
Therefore, the rate of change is 7 more of function A than the slope of function B.
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Write a quadratic function to model the graph to the right.
f(x)=____
Answers
f(x) = x² + 2x + 2
Solution:
Given vertex (1,1)
a = 1
Formula of quadratic equation is :
y = a(x + b)² + c
where, a =1, x=x, b = x1, c = y1
Substituting the values in the equation, we get
y = x² + 2x + 2
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A quadratic function to model the graph to the right is f(x) = x² + 2x + 2
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Solution:
Given vertex (1,1)
a = 1
Formula of quadratic equation is :
y = a(x + b)² + c
where, a =1, x=x, b = x1, c = y1
Substituting the values in the equation, we get
y = x² + 2x + 2
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A password is required to log into a system that only recognizes numbers and letters
of the alphabet (not case sensitive). You want to create a password using 7 numbers
or letters, but cannot reuse any of them.
How many different passwords are possible?
Answers
There are total 42,072,307,200 different passwords are possible .
What are combinations ?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.
Combinations can be confused with permutations. However, in permutations, the order of the selected items is essential. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), while in permutations, the arrangements are different.
Given: A password is required to log into a system that only recognizes numbers and letters of the alphabet
Since , there are total 26 letters and 10 numbers are possible that can be used to create a password . Hence , there are 36 character in total to be used.
Also , repetition of character is not allowed. Therefore , the chance of selecting every character decreases by 1 in comparison to its preceding character .
Chance of selecting first character = 36
Chance of selecting second character = 35
Similarly for seventh = 30
Thus , different passwords that are possible using 7 numbers or letters, without reusing any of them = 36*35*34*33*32*31*30 = 42,072,307,200 .
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ABDE is an isosceles trapezoid. Select all parts that are marked congruent.
Side AB and Side AE
Angle E and Angle D
Angle E and Angle B
Angle A and Angle B
Angle A and Angle D
Side AE and Side BD
Side AB and Side ED
Answers
The concurrent parts in the given ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.
Concurrent triangles:Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. These triangles may be moved, flipped, twisted, and turned to get a similar effect. When relocated, they are parallel to one another. The concurrence sign is '≅'.
Here we have,
ABDE is an isosceles trapezoid.
Draw 2 diagonals in a given trapezoid
Then the 2 diagonal will divide the trapezoid into 4 triangles
Here ΔAOB, ΔBOD, ΔEOD, and AOE
From the formed triangles
ΔAOB and ΔEOD will be two concurrent triangles
Then Side AB ≅ Side ED
ΔBOD and AOE will be two concurrent triangles
Side AE ≅ Side BD
Therefore,
The concurrent parts in the given ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.
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Suppose the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points. It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students. Find what scores should be assigned A’s and B’s.
Answers
82.9 score should be assigned for A’s and 74.4 should be assigned for B’s
In this question we have been given the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points.
It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students.
We need to find what scores should be assigned A’s and B’s.
μ = 70, σ = 10
Using standard normal table,
P(X > x) = 10%
P(X > x) = 0.10
1 - P(X ≤ x) = 0.10
P(X ≤ x) =1−0.10
=0.90
Using standard normal z table,
(x - 70)/10 = 1.29
x = 82.9 (score for A’s)
Now, P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)
P(X>x) = 0.33
1 - P(X ≤ x) = 0.33
P(X ≤ x) = 1 - 0.33
= 0.67
Using standard normal z table,
(x - 70)/10 = 0.44
x = 74.4 (score for B’s)
Therefore, the score for A = 82.9 and the score for B = 74.4
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help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answers
Answer:
a. 18.5 million
b. 2002
Step-by-step explanation:
Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.
Population in 2000The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.
A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5
The population in 2000 was 18.5 million.
Year of 26.6 millionWe can solve for t to find the year in which the population reached 26.6 million:
26.6 = 18.5·e^(0.1708t)
26.6/18.5 = e^(0.1708t)
ln(266/185) = 0.1708t
t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000
The population will reach 26.6 million in the year 2002.
__
Additional comment
The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.
(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)
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Place the numbers in order from greatest to least 1 3/4 , 5.25 , -5/2 , -8.345
Answers
Answer: 5.25>1 3/4>-5/2>-8.345
Step-by-step explanation:
Suppose that you’d like to retire in 40 years and you want to have a future value of $ 500000 in a savings account. Also suppose that your employer makes regular monthly payments into your retirement account.
If you can expect an APR of 7% for your account, how much do you need your employer to deposit each month?
Employer Contribution =
The formulas we have been using assume that the interest rate is constant over the period in question. Over a period of 40 years, though, interest rates can vary widely. To see what difference the interest rate can make, let’s assume a constant APR of 4% for your retirement account. How much do you need your employer to deposit each month under this assumption?
Employer Contribution =
Answers
a) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 7% APR, your employer contributions should be $190.49.
b) If only your employer makes the monthly deposits into your retirement account for the future value of $500,000 in 40 years at 4% APR, your employer contributions should be $423.03.
What is the future value?The future value represents the amount expected to be the balance in the investment account after a period.
The future value can be used to determine the periodic payments required to meet the target balance, using an online finance calculator.
Periodic Deposits at 7%:N (# of periods) = 480 months (40 years x 12)
I/Y (Interest per year) = 7%
PV (Present Value) = $0
FV (Future Value) = $500,000
Results:
PMT (Periodic deposits) = $190.49
Sum of all periodic payments = $91,435.07
Total Interest = $408,564.93
Periodic Deposits at 4%:N (# of periods) = 480 (40 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $0
FV (Future Value) = $500,000
Results:
PMT (Periodic deposits) = $423.03
Sum of all periodic payments = $203,052.33
Total Interest = $296,947.67
Thus, the periodic deposits to meet the future value will depend on the interest rate.
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Valentino's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found. Type of Crust Number Sold Thin crust 293 Thick crust 216 Stuffed crust 174 Pan style 195 Based on this information, of the next 3000 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do not round any intermediate calculations. pizzas X
Answers
Answer:
1120
Step-by-step explanation:
Given the information below:
The Relative Frequency of selling a pan style pizza =
Therefore, if Valentino's Pizzeria were to sell 4000 pizzas, the expected number of Pan style pizza sold will be:
Number of Pan Style Pizza Sold = Relative Frequency of pan Style Pizza Purchase X Total Number of Sales
They should expect to sell 1120 pan Style pizzas.
Suppose an annuity pays 4% annual interest, compounded annually. If you invest $4,500 in this annuity annually for 10 years, what percentage of the total balance is interest earned? Round your answer to the nearest hundredth of a percent. Do NOT round until you have calculated the final answer.
Answers
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]
so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.
so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]
f(x) = 2(x²-7)
Find f(2).
Answers
Two machines produce sound pressure levels of approximately 80 dB(A) each. What is their approximate combined sound pressure level?
Answers
83.01dB is approximate combined sound pressure level.
What is sound pressure level?
The result of the pressure changes in the air caused by sound waves is sound pressure, often known as sound pressure level. The hearing threshold is the lowest sound pressure that a human can hear, and the pain threshold is the maximum sound pressure that a person can tolerate.
The difference between sound pressure at the pain threshold and the hearing threshold is a million times higher.
We have sound pressure level denoted as (Lp) of each machine
i.e 80 dB,(given).
Therefore, we can calulate sound pressure level from both machines combined by given formula,
SPL = 10 * Log(10^(SPL(1) /10) + 10^(SPL(2) /10) +10^(SPL(3) /10) + ............)
where,
SPL= sound pressure level(dB)
=> SPL = 10 * Log(10^(80 /10) + 10^(80 /10))
=> SPL = 10 * Log(10^8 + 10^8)
=> SPL = 10 * 8.301
=> SPL = 83.01dB
Hence, 83.01dB is approximate combined sound pressure level.
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if you form a triangle from three given side lengths, will you always get one triangle or more than one triangle?
Answers
If the three side lengths are all different then you will only get one triangle. However, if two or more of the side lengths are the same then you can get more than one triangle.
What is known as a triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total
How is a triangle made?Three diagonals must meet at three different locations to form a triangle. There are five possible arrangements of three diagonals. We categorize them according on how many different diagonal endpoints there are. The quantity of triangles with 3, 4, and 5 endpoints will be counted directly.
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You need a car for 5 days. A car rental company offers customers two rate plans. With Plan A, the
customer pays $25 per day plus $0.15 per mile driven. With Plan B the customer pays $150 for the week,
even if the car is returned early, with no per-mile charge. Which payment plan would you select if you
plan to drive a total of 100 miles?
Answers
There are five questions listed below. Each question includes the quantity 22. Match the 22 in each question on the left to which part of the problem it represents on the right -- the base, percent, or amount. Some answer options on the right will be used more than once.
Answers
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.”
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.Using concepts of percentage,
3 is 16.63% of 22.
22 is 13.41% of 164.
0.88 is 4% of 22.
8 is 22% of 36.36.
1.1 is 5% of 22.
A percentage is a number or ratio expressed as a fraction of 100.
Let 3 be x% of 22.
=x/100*22=3
=x=3*100/22=13.63
3 is 13.63% of 22.
Let 22 be y % of 164.
=y/100*164=22
=y=22*100/164=13.41
13.41% of 164 is 22.
4% of 22 = 0.88
=4/100*22=0.88
Let 8 is 22% of z.
=22/100*z=8
=8*100/22=36.36
5% of 22 = 1.1
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A waterproof speaker sells for $179, which is marked up by 30% of the selling price. What is the cost of the speaker? A. $152.30 B. $132.50 C. $123.50 D. $125.30
Answers
The original cost of the speaker will be equal to $125.3. The correct option is D.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a waterproof speaker sells for $179, which is marked up by 30% of the selling price.
The cost price of the speaker will be calculated as,
Cost price = 179 x 0.7
Cost price = $125.3
Therefore, the original cost of the speaker will be equal to $125.3. The correct option is D.
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Target charges $4.40 for 8 sodas. Walmart charges $7.08 for 12 sodas. Which store has
the best unit price? How much cheaper is it?
Answers
Answer:
Target
Step-by-step explanation:
$4.40/8 is 0.55 and $7.08/12 is 0.59
3. For the graph above, what is the approximate y-value of the point of intersection?
0-1
04
03
02
Answers
Answer: 02
Step-by-step explanation: w
Need help!!!! with geomtry
Answers
Answer: n=11 m=3
Step-by-step explanation:
2n+2=3n-9
n=11
3m+6=n+4
3m+6=11+4
3m+6=15
3m=9
m=3
Book b is twice as long as book a. book c is 30 pages longer then book b. together the three books have 280 pages.
I just need help with question number 10
It has to be solved algebraically Can someone please help me with this problem
Answers
Answer:
book c has 130 pages
Step-by-step explanation:
let book a = x pages
book b = 2x
book c = 2x + 30
according to the question:
x + 2x +2x + 30 = 280
5x + 30 = 280
5x = 280-30
5x = 250
x = 250/5
x = 50
thus book c has 2(50) + 30 = 130 pages
Expand the log completely
Answers
Answer:
1/3log₂(x) +1/3log₂(y) +1/3log₂(z)
Step-by-step explanation:
You want the complete expansion of ...
[tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}[/tex]
Relevant rulesThe rules of logs and exponents relevant to this expansion are ...
[tex]\log_b{(xy)}=\log_b{(x)}+\log_b{(y)}\\\\\log_b{(x^a)}=a\cdot\log_b{(x)}\\\\\sqrt[n]{\vphantom{b}a}=a^{\frac{1}{n}}[/tex]
ExpansionApplying these rules to the given expression, we get ...
[tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}=\log_2{((xyz)^{\frac{1}{3}})}=\dfrac{1}{3}\log_2{(xyz)}\\\\=\boxed{\dfrac{1}{3}\log_2{(x)}+\dfrac{1}{3}\log_2{(y)}+\dfrac{1}{3}\log_2{(z)}}[/tex]
Equation that passes through 4,-3 and -4,7
Answers
(7-(-3))/(-4-4)=-(5/4)
4y=-5x+c
Put one point in equation above
4y=-5x+8
5. Find all the solutions to the equation x²e^x– 2xe^x – 3e^x =0.
Answers
Answer:
[tex]x = 3, -1[/tex]
Explanation:
math