Answer:
1) 64 and 81
2) a(n) = (n + 2)^2, where n = 1, 2, 3, ...
3) a(25) = (25 + 2)^2 = 27^2 = 729
what are the roots of the equation ?-3x = -10x^2-4
Given the following Quadratic equation:
[tex]-3x=-10x^2-4[/tex]You can use the Quadratic formula to solve it:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, you need to add "3x" to both sides of the equation:
[tex]\begin{gathered} -3x+(3x)=-10x^2-4+(3x) \\ 0=-10x^2+3x-4 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} a=-10 \\ b=3 \\ c=-4 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2^{}-4(-10)(-4)}}{2(-10)} \\ \\ x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Answer
Complex roots:
[tex]\begin{gathered} x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]which fraction on the number line is equal to 3
Answer:
? can't answer if there's no number line
Justin works in a department store selling clothing. He makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 30% of his total sales for the week. How much would Justin make in a week in which he made $2425 in sales? How much would Justin make in a week if he made x dollars in
We can convert that 30% into a decimal, as: 0.3 (That's 30/100)
Now, we can multiply this 0.3 by any quantity that we want to calculate 30% from.
For example, let's take Justin's commission:
[tex]2425\cdot0.3=727.5[/tex]Adding this to his base salary,
[tex]450+727.5=1177.5[/tex]We can conclude that Justin's paycheck for the week would be $1,117.5
Similarly, the expression for Justin's paycheck in a week were he made x dollars in sales is:
[tex]0.3x+450[/tex]what is the equation of the line that passes through the point (-2, 14) and is perpendicular to the with the following equation? y = -2/5x - 1
Answer: the y = -2/5x - 1
Step-by-step explanation: hoped this help you two
1/4t = 1/3t + (-16)
pls solve t and show steps if possible
Answer:
t = 192
Step-by-step explanation:
1/4t = 1/3t + (-16)
1 1
-------t = -------t - 16
4 3
1(3) 1(4)
-------t = -------t - 16
4(3) 3(4)
3 4
-------t = -------t - 16
12 12
3 4
-------t = -------t - 16(12)
( 12 12 ) 12
3t = 4t - 192
-4t -4t
---------------------
-t = -192
÷-1 ÷-1
---------------
t = 192
I hope this helps!
The average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. The number of shoppers is normally distributed. For a random day, what is the probability that there are less than 250 shoppers at the grocery store? The answer should be typed as a decimal with 4 decimal places
For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.
The average total number of shoppers on a grocery store in 1 day is 506; the standard deviation is 115.
The number of shoppers is normally distributed.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 506 and standard deviation of 115.
Then, we can say that,
Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P(X<200)
[tex]=P(Z < \frac{200-506}{115})[/tex]
=P(Z<-2.66)
Where, Z is the standard normal variate.
ρ = -0.266
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.0039
For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.
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The population of the United States increased from 249 million in 1990 to 308 million in
2010.
The absolute change in the population was
The relative change in the population was
of a percent)
million.
% (round to the nearest tenth
The absolute change in the population was 59 million. The relative change in the population was 23.69%
The absolute population change is the magnitude of the increase or decrease in population for a defined period.
What is absolute change ?Absolute change describes the straightforward difference between the indicator over two time periods. The indicator's value in the earlier period is used to calculate the relative change, which expresses the absolute change as a percentage.
Small numbers can make relative changes appear more significant than they actually are. This is true because a minor change in the number's absolute value can generate a significant change in the percentage.
Big numbers may make relative changes appear less significant. This is so that any change in the number that represents a substantial relative change may be seen.
The relative change can be minor even when the absolute change is significant if it is a change on a larger number.
Absolute change = Final value – Initial value
= 308m- 249m = 59m
The absolute change in the population was 59 million
Relative change Formula = (Final value – Initial value) / Initial value * 100%
= 308m- 249m/ 249*100 = 23.69%
The relative change in the population was 23.69%
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a top speed an object travels 3,200 millimeters in 4 seconds how many millimeters does the object travel each second
Which of the following sentences properly uses semicolons in a serial list?
There is so much you can do to cut down on waste; such as composting, which uses food waste to help plants grow, recycling, which keeps plastic, metal, and glass out of landfills, and thrifting, which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste, such as composting; which uses food waste to help plants grow; recycling; which keeps plastic; metal; and glass out of landfills; and thrifting; which cuts down on clothing waste from fast fashion.
There is so much you can do to cut down on waste; such as composting; which uses food waste to help plants grow, recycling; which keeps plastic, metal, and glass, out of landfills, and thrifting; which cuts down on clothing waste from fast fashion.
The sentence that properly uses semicolons in a serial list is B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
What are semicolons?A semicolon is a punctuation mark consisting of a period put on top of a comma.
Semicolons can be used for the following purposes:
To join two independent clauses without the coordinating conjunctions (and, but, or, nor, for, so, yet)As a serial listTo introduce evidence for a preceding statement.Thus, the proper use of semicolons in a serial list is Option B.
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Answer:
B. There is so much you can do to cut down on waste, such as composting, which uses food waste to help plants grow; recycling, which keeps plastic, metal, and glass out of landfills; and thrifting, which cuts down on clothing waste from fast fashion.
Step-by-step explanation:
A bicyele store costs $2400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicyeIs $120How many bicycles must the store sell each month 1o break even?Write a system of equations to represent the situation, then solve*Show both the equations and the solution
Answer:
The system of equations is:
• C(x)=2400+60x
,• R(x)=120x
The number of bicycles to break even = 40
Explanation:
Let the number of bikes sold = x
• The operating cost of the store per month = $2400
,• Cost Price Per bike = $60
Thus, the total monthly cost for the store:
[tex]C(x)=2400+60x[/tex]Next, the average selling price of each bicycle is $120, therefore, the monthly revenue of the store:
[tex]R(x)=120x[/tex]The store breaks even when the cost equals its revenue.
[tex]\begin{gathered} R(x)=C(x) \\ 120x=2400+60x \end{gathered}[/tex]We then solve for x:
[tex]\begin{gathered} \text{ Subtract 60x from both sides of the equation} \\ 120x-60x=60x-60x+2400 \\ 60x=2400 \\ \text{ Divide both sides of the equation by 60} \\ \frac{60x}{60}=\frac{2400}{60} \\ x=40 \end{gathered}[/tex]The store must sell 40 bicycles in order to break even.
A line passes through the point (–2, 7) and has a slope of –5.
A coordinate plane.
What is the value of a if the point (a, 2) is also on the line?
–7
–1
1
7
Based on the fact that the line passes through (-2, 7) and the slope, the value of a can be found to be -1
How to find the value of a?To find the value of a, you first need to find the y-intercept to complete the linear equation which takes the form:
y = slope (x) + y-intercept
7 = -5(-2) + y-intercept
7 = 10 + y-intercept
y-intercept = 7 - 10
y-intercept = -3
The line equation is:
y = -5x - 3
The line y = -5x - 3 is passing through the point (a,2) is:
2 = -5(a) - 3
3 + 2 = -5a
a = 5 / -5
a = -1
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Answer:
the answer is -1
Step-by-step explanation:
75% of the marbles in a bag are orange and the rest are blue. What fraction of the orange marbles must be removed from the bag so that 50% of the remaining marbles are orange?
Answer:
1/2
Step-by-step explanation:
75% of the marbles in a bag are orange and the rest are blue. The percentage for blue will be:
= 100% - 75%
= 25%
The fraction of the orange marbles that must be removed from the bag so that 50% of the remaining marbles are orange will be:
= 75% - 25%
= 50%
= 1/2
Identify the degree and leading coefficient of the given power function
In a equation as above:
a is the leading coefficient
n is the degree
For the given equation:
[tex]-2x^2[/tex]The coefficient is: -2The degree is: 2Kirby is buying a new grill that has been reduced for an end of summer sale by 25% to $496. what was the original price of the grill?
Given:
percentage decerease = 25%
current price of the grill = $496
Let the original price of the grill be x
We can calculate percentage decrease using the formula:
[tex]\text{Percent decrease = }\frac{Orig\text{ inal value - new value}}{Orig\text{ inal value}}\text{ }\times\text{ 100}[/tex]Substituting the given values we have:
[tex]\begin{gathered} 25\text{ = }\frac{x-496}{x}\times\text{ 100} \\ 25\text{ = }\frac{(x-496)\times100}{x} \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 25x\text{ = 100x - 49600} \\ \text{Collect like terms:} \\ -75x\text{ = -49600} \\ \text{Divide both sides by -75} \\ \frac{-75x}{-75}\text{ = }\frac{-49600}{-75} \\ x\text{ }\approx\text{661.33} \end{gathered}[/tex]Hence, we can conclude that the original price of the grill is approximately $661.33
Answer:
$661.33
Kareem wrote an exam which had 30 questions. Each question he answers correctly gets him 10
marks. However, he loses 5 marks for each question he answers incorrectly. He attempted all the
questions and got a total of 180 marks. How many questions did he answer wrong?
Total number of questions = 30 questions.
Each correct answer gets = 10 marks.
Marks deducted for each wrong answer = 5 marks.
Total marks scored by Kareem = 180 marks.
If Kareem had attended all the questions, then
Let 'α' be the number of questions he answered wrong, then the number of questions answered correctly by him, will be = (30 - α)
Then we have,
Total marks obtained = (correct answers x 10 marks ) - (wrong answers x 5 marks )
that is.,
180 = [(30 - α) x 10] - [α x 5] = 300 - 10α - 5α
180 - 300 = -15α
α = 120/15 = 8 questions.
Therefore, 8 questions were answered wrong by Kareem.
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what is 11/12 ÷ 1/30 2 1/40 2 3/40 3 1/30 3 2/3
The given expression is
[tex]\frac{11}{12}\colon\frac{1}{3}[/tex]First, we change 1/3 for its reciprocal to transform the division into a product.
[tex]\frac{11}{12}\cdot\frac{3}{1}[/tex]Then, we multiply the fractions.
[tex]\frac{11\cdot3}{12\cdot1}=\frac{33}{12}=\frac{11}{4}[/tex]At last, we transform the fraction into a mixed fraction.
[tex]\frac{11}{4}=2\frac{3}{4}[/tex]Therefore, the right answer is B. 2 3/4.MTR
3 MAINTAIN ACCURACY In Exercises 27-30, determine
whether the statement uses the word function in a way
that is mathematically correct. Explain your reasoning.
27. The selling price of an item is a function of the cost of
making the item.
28. The sales tax on a purchased item in a given state is a
function of the selling price.
29. A function pairs each student in your school with a
homeroom teacher.
30. A function pairs each chaperone on a school trip
with 10 students.
Please just do 28 and 30
Answer:
28. Correctly used
30. Incorrectly used
Step-by-step explanation:
You want to know if the word "function" is correctly used in the following cases:
28. The sales tax on a purchased item in a given state is a function of the selling price.
30. A function pairs each chaperone on a school trip with 10 students.
28. Sales taxThere is exactly one value of sales tax associated with any given selling price. This means the ordered pair (selling price, sales tax) will be unique for any given selling price. Hence, the relation between selling price and sales tax is a function. The word function is used correctly in describing this relation.
29. ChaperonesThere are 10 different students associated with any given chaperone. This means there will be multiple (chaperone, student) ordered pairs for any given chaperone: (c1, s1), (c1, s2), ..., (c1, s10), (c2, s11), (c2, s12), ..., (c2, s20), .... The relation between chaperones and students is not a function. The word function is used incorrectly in describing this relation.
Write in words the meaning of P^2 - 7P.
Answer:
P squared minus 7 times P
Step-by-step explanation:
Select the correct answer. Consider the graph of f(x) given below. The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x - 5) B. g(x) = f(x) - 2 C. g(x) = f(x) - 5 D. g(x) = f(x + 2)
PLEASE OFFER ME YOUR ANSWER, I ASK OF YOU...PLS
The function that could represent g(x) is (c) g(x) = f(x) - 5
How to determine the function g(x)?The figure of the graph that completes the question is added as an attachment
From the attached graph, we have the equation of the function to be
y = f(x)
Also, the graph of the function f(x) has its intercept to be
y-intercept of f(x) = 3
From the question, we have
y-intercept of g(x) = -2
Subtract the intercepts
Difference = y-intercept of g(x) - y-intercept of f(x)
So, we have
Difference = -2 - 3
Evaluate
Difference = -5
The function g(x) is then represented as
g(x) = f(x) + Difference
So, we have
g(x) = f(x) - 5
Hence, the function g(x) is g(x) = f(x) - 5
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Solve for x. 23r + 2 = 156 + 481 + 6 A. x = 1/12 B. x = -2/5C. x = -1/10 D. x = -12/5
C) x= -1/10
1) Evaluating the following expression
23x+2= 15x + 48x + 6 Add the like terms
23x +2 = 63x +6 Subtract 63x and 2 from both sides
23x -63x = 6 -2
-40x =4 Divide both sides by -40
x = -4/40 Simplify it by 4
x= -1/10
2) Hence, the answer is x= -1/10
What is the GCF of 64a^8b^4 and 56a^5b^8
We need to find the greatest common factor of
[tex]64a^8b^4,56a^5b^8[/tex]We will find the greatest common factor of 64 and 56, first
Since the factors of 64 are
[tex]\begin{gathered} 1\times64 \\ 2\times32 \\ 4\times16 \\ 8\times8 \\ 1,2,4,8,16,32,64 \end{gathered}[/tex]Since the factors of 56 are
[tex]\begin{gathered} 1\times56 \\ 2\times28 \\ 4\times14 \\ 8\times7 \\ 1,2,4,7,8,14,28,56 \end{gathered}[/tex]Then the common factors are 1, 2, 4, 8
The greatest is 8, then
The GCF of 64 and 56 is 8
The greatest common factor of the same variables is the least power
Then the GCF of a^8 and a^5 is a^5
The GCF of b^4 and b^8 is b^4
Then the greatest common factor of the given terms is
[tex]\text{GCF}=8a^5b^4[/tex]2.1. AP-8 Write the integer value that point B represents, then write its opposite. B - 10 5 5 10 Point B represents the integer
In the line, the point B represents the integer -3, because it is 3 units left from 0.
Its opposite is the number 3, that is 3 units right from 0.
Write an equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
Please help and Thank you.
h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
What is Translation?Translation is the process of reworking text from one language into another to maintain the original message and communication.
The parent function is: g(x)=|x|
we stretch the parent function y = |x| by a factor of 3.
h= |x/3|
If the constant is between 0 and 1, we get a horizontal stretch
if the constant is greater than 1, we get a horizontal compression of the function.
Hence h= |x/3| equation that represents a horizontal stretch by a factor of 3 of the graph of g(x)=|x| .
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A basket contains 12 black marbles and 8 blue marbles. What is the probability Josiah will
select a blue marble, replace it, and then a black marble? Express your answer as a percent.
Answer:
24%=====================
GivenBlack marbles = 12,Blue marbles = 8.SolutionTotal number of marbles:
12 + 8 = 20Probability of selecting a blue marble:
P(blue) = number of blue / total = 8/20 = 2/5Probability of selecting a black marble after replacing the blue:
P(black) = number of black / total = 12/20 = 3/5Probability of selecting blue and black marbles in same order with replacement:
P(blue, then black) = 2/5*3/5 = 6/25 = 24/100 = 24%a³ = 125
Each edge of the cube is
feet long.
Answer:
each cube is 5 feet long because 5*5*5 = 125
Step-by-step explanation:
a company purchases shipments of 600 machine components and uses this acceptance sampling plan: randomly select and test 25 components and accept the whole batch if there are fewer than 3 defective components. it is known that this particular component has a 4% defective rate. what is the probability that shipment will be accepted?
25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. The probability is it that the shipment will be accepted is 0.7323.
Given that,
An organization utilizes the following acceptance sampling strategy for ordering shipments of 600 machine parts: 25 components are randomly chosen and tested; if there are no more than 3 defective components, the entire batch is accepted. This specific component is known to have a 4% fault rate.
We have to find how probability is it that the shipment will be accepted.
By binomial we get,
Binomial Problem:
n = 25 ; p = 0.04
P(0<= p <= 2)
= 0.7323
Therefore, The probability is it that the shipment will be accepted is 0.7323.
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2x(x+7) + 35 = (x + 1)x(x+1) -2
Answer:
x= -6
Step-by-step explanation:
1
Distribute
2
Distribute
3
Distribute
4
Multiply by 1
5
Combine like terms
6
Subtract the numbers
7
Move terms to the left side
8
Distribute
9
Add the numbers
10
Combine like terms
11
Multiply by 1
12
Combine like terms
13
Use the quadratic formula
14
Evaluate the exponent
15
Multiply the numbers
16
Subtract the numbers
17
Evaluate the square root
18
Add zero
19
Multiply the numbers
20
Cancel terms that are in both the numerator and denominator
I need help fast with my math homework.
Answer:15 twice
Step-by-step explanation:
Which integer is the farthest from the origin on a number line? A. -11 O B.-1 Oc. O D. 10
In order to determine the farthest integer related to the origin ona a number line, apply the absolute value of the given numbers, this gives you the distance of the specific number to the origin.
The absolute value of a number, negative or positive, is always equal to the same positive number.
Then,for the given asnwer choices you have:
|-11| = 11 where the bars |-11| expresses absolute
A cyclist leaves New York traveling at an average speed of 9 miles per hour. 4 hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 21 miles per hour. How many hours after the car leaves New York will the car catch up to the cyclist? *
The car will catch up with cyclist in 3 hours
What is time ?Time refers to the interval in seconds , minutes or hours it took for an event to take place
How to calculate How many hours it will take the car to catch up with cyclistInformation given for the question include
A cyclist has average speed of 9 miles per hour
A car leaves has average speed of 21 miles per hour
following same route when
The question is asking at what time will the distance be equal if the cyclists have advantage of 4 hours already
Calculation of distance covered by the cyclist
average speed = distance / time
distance = 9 mph * (x + 4)
Calculation of distance covered by the car
average speed = distance / time
distance = 21 mph * x
equating both gives
9 mph * (x + 4) = 21 mph * x
9x + 36 = 21x
36 = 21x - 9x
12x = 36
x = 3
hence the car will meet the cyclist in 3 hours
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