Answer: Plan to add the same number of stores each year:
Let x be the number of stores the company adds each year. To reach at least 600 stores and no more than 800 stores in 5 years, we need:
5x + 5(5) = 600 (minimum number of stores)
5x + 5(5) = 800 (maximum number of stores)
Solving these equations, we get:
x = 119.4
So, the company can add 119 stores each year for 5 years to reach at least 600 stores and no more than 800 stores.
Plan to multiply the number of stores by the same factor each year:
Let r be the factor by which the number of stores increases each year. To reach at least 600 stores and no more than 800 stores in 5 years, we need:
5(5) r^5 = 600 (minimum number of stores)
5(5) r^5 = 800 (maximum number of stores)
Solving these equations, we get:
r ≈ 1.63
So, the company can multiply the number of stores by about 1.63 each year for 5 years to reach at least 600 stores and no more than 800 stores (rounded to the nearest whole store). For example, starting with 5 stores, the company can have approximately 8, 13, 21, 34, and 55 stores after 1, 2, 3, 4, and 5 years, respectively.
Step-by-step explanation:
please
\(2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 \)
I need help
You are comparing apples and oranges in a fruit bowl. Is the ratio 2:3 the same as the ratio 3:2? Explain
Answer:
no
Step-by-step explanation:
because 3;2 is more the 2;3 as you know if you do it as a fraction it would be 3 over 2 and 2 over 3 the 3 over 2 whould be a whole and the 2 over 3 would be 3 forths of a whole and the 3 over 2 would be more
In the slope - 6/11, the 11 indicates to
A. Rise 11 units
B. Fall 11 units
C. Run 11 units
Answer:
C. run 11 units
Step-by-step explanation:
because you run down -6 you rise 11
what's the inverse of f(x)=(x+3)^5
Answer:
The inverse is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x) = (x+3)^5
Finding the inverse,
\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)
We replace x with y and vice versa
so,
\(x = (y+3)^5\)
Solving for y,
the the 5th root,
\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)
hence the inverse function is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x)=(x+3)×5
Y=5X+15
now
interxchanging x and y we get,
x=5y+15
5y=x-15
y=x-15/5
therefor f~1(x)=x-15/5
Solve. Show each step.
5.4 - 6x = -6
Answer:
x = 1.9
Step-by-step explanation:
5.4 - 6x = -6
Gotta isolate the x, so you would minus 5.4 from both sides:
5.4 - 5.4 - 6x = (-6) - 5.4
5.4 - 5.4 cancels out, and (-6) - 5.4 is -11.4 What's left is:
- 6x = -11.4
Gotta isolate the x, so divide -6 to both sides. It negative because the sign in front of it is a subtraction sign, it would be positive if there is a addition sign:
- 6x/(-6) = (-11.4)/(-6)
-6 divide by -6 cancels out, and -11.4 divided by -6 is 1.9. A negative divided by a negative is a positive. Result, x is now isolated:
x = 1.9
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
Write an expression in terms of x that represents the distance between ( 4 , 8 ) and ( x , 8 ) for x > 4 .
The distance between two points is the number of units between them
The expression that represents the distance between the points is x - 4
How to determine the expressionThe points are given as: (4,8) and (x,8)
The distance (d) between points is calculated using:
\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)
So, we have:
\(d = \sqrt{(x - 4)^2 + (8 -8)^2}\)
Evaluate the difference
\(d = \sqrt{(x - 4)^2 + 0^2}\)
Evaluate the exponent
\(d = \sqrt{(x - 4)^2 + 0}\)
Evaluate the sum
\(d = \sqrt{(x - 4)^2}\)
Evaluate the exponent
\(d = x - 4\)
Hence, the expression that represents the distance between the points is x - 4
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Find the magnitude and direction of the vector using the given information. V=<6,7>
Answer:
The magnitude of the vector is 9.165 and it's direction is 40.6°
Step-by-step explanation:
Vector Quantities:A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.
Magnitude of vector v is given by
|v| = √6²+7²
= √36+49
= √84
= 9.165
Direction of vector v is obtained by:
\( \tan( \theta) = \frac{x}{y} \)
\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)
\(\theta = {40.6°}\)
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Rewrite each subtraction equation as an addition equation.
z - (-12) = 15
Answer:
...........
Step-by-step explanation:
::
z+12=15
1 point
The scale factor between Rectangle NMS and a similar rectangle is 3/2.
What are the dimensions of the new rectangle?
10
4
NMS
12 x 30
0 7 x 13
0 8x20
0 6x15
24. There are 10 pupils in a class. Half of them are
girls. What is the probability of selecting a girl
from the class for a trip to the zoo?
Find the prime factorization of each numbera. 663b. 442
Solution:
Prime factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number.
Given:
Using a tree diagram;
\(\begin{gathered} 663=3\times221=3\times(13\times17) \\ 663=3\times13\times17 \end{gathered}\)Hence, 663 = 3 x 13 x 17
Using a tree diagram;
\(\begin{gathered} 442=2\times221=2\times(13\times17) \\ 442=2\times13\times17 \end{gathered}\)Hence, 442 = 2 x 13 x 17
One -tenth of books are picture books 2/10 are story books and half are science fiction and remainings are encyclopaedia what fraction are encyclopaedia
Answer:
1/5 of books are encyclopediaStep-by-step explanation:
Remaining fraction:
1 - (1/10 + 2/10 + 5/10) = 1 - 8/10 = 2/10 =1/51/5 of books are encyclopedia
Answer:
Let the total fraction of books be 1, then;
\(1 - ( \frac{1}{10} + \frac{2}{10} + \frac{1}{2} ) \\ 1 - ( \frac{(1 + 2 + 5)}{10} ) \\ (1 - \frac{8}{10}) = \frac{(10 - 8)}{10} \\ \frac{2}{10} = \boxed{ \frac{1}{5} }\)
Therefore, 1/5th of the books are encyclopaedia.Max had 1 litre of syrup. He used 1/5 litre of the syrup on Saturday and 5/6 of the remaining syrup on Sunday. How many litres of syrup did Max have left?
Answer:
2/15 litre
Step-by-step explanation:
There is 1 litre in total. Max used 1/5 litre.
1 - 1/5 = 4/5 litre
Then he used 5/6 of the remaining 4/5 litre. He would have 1/6 of 4/5 litre left.
1/6 * 4/5 = 2/15 litre
or
You could do 5/6 * 4/5 to find out how much syrup he used on Sunday and then subtract that from 4/5 litre. It will give you the same answer
Suppose we want to choose 7 colors, without replacement, from 9 distinct colors
If the order of the choices does not matter, how many ways can this be done?
The number of ways to choose the colors is 36
How to determine the number of ways?The given parameters are:
Colors = 9
Colors to choose = 7
Since order does not matter, then it is combination
This is calculated using:
\(^nC_r = \frac{n!}{(n - r)!r!}\)
This gives
\(^nC_r = \frac{9!}{7!2!}\)
Evaluate
\(^nC_r = 36\)
Hence, the number of ways is 36
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The jacket at the department store originally cost $199. It was selling so well that the store decided to increase the price by 25 percent. What was the new cost of the jacket?
Answer:
$248.75
Step-by-step explanation:
25% more of 199 is 248.75
Select the statement that indicates that the triangles in each pair are congruent.
50 points
Answer:
D. ∆XVW ≅ ∆XBC
Step-by-step explanation:
Angle X = Angle X (vertical angles are congruent)
Angle V = angle B (corresponding angles are congruent)
Angle W = angle C (corresponding angles are congruent)
The three angels in ∆XVW are congruent to the three corresponding angles in ∆XBC.
Therefore, the statement that indicates both triangles are congruent is:
∆XVW ≅ ∆XBC
A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2- hour reserve, and the second book can be checked out overnight. a. Construct a tree diagram to display the 12 outcomes in the sample space. b. Let A denote the event that at least one of the books selected is an even-numbered copy. What outcomes are in A? c. Suppose that copies 1 and 2 are first printings, whereas copies 3 and 4 are second printings. Let B denote the event that exactly one of the copies selected is a first printing. What outcomes are contained in B?
The event A is that at least one of the books selected is an even-numbered copy. The event B is that exactly one of the copies selected is a first printing.
A tree diagram to display the 12 outcomes in the sample space would look like this:
1st Selection | 2nd Selection
----------------------------
1 | 2
1 | 3
1 | 4
2 | 1
2 | 3
2 | 4
3 | 1
3 | 2
3 | 4
4 | 1
4 | 2
4 | 3
The event A is that at least one of the books selected is an even-numbered copy. This would include outcomes 1-2, 1-4, 2-1, 2-3, 2-4, 4-1, 4-2, and 4-3.
The event B is that exactly one of the copies selected is a first printing. This would include outcomes 1-3, 1-4, 3-1, 3-2, 3-4, 4-1, 4-2, and 4-3.
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In a class of students, the following data
table summarizes how many students have a
cat or a dog. What is the probability that a
student chosen randomly from the class has
a cat?
Has a dog
Does not have a
dog
Has a cat
2
3
Does not have a
cat
12
10
The table can be summarized as follows:
| | Has a dog | Does not have a dog |
|----------|-----------|---------------------|
| Has a cat | 2 | 3 |
| Does not have a cat | 12 | 10 |
To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.
The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.
The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.
So, the probability that a student chosen randomly from the class has a cat is 5/27.
1. The population of San Francisco is 884,363 people. The population of Sacramento is 501,901 people. About how many people live in San Francisco? Sacramento? Round your answer to the nearest thousand.
The number of people who live in San Francisco to the nearest thousand is; 884,000.
The number of people who live in Sacramento to the nearest thousand is; 502,000.
What number of people live in San Francisco and Sacramento to the nearest thousand?To round off a number to the nearest thousand, the hundreds place value digit is considered.
For San Francisco; since the hundred place digit is; 3; we have that; 884,363 ~~ 884,000.
For Sacramento; since the hundreds place digit is; 9; we have that; 501,901 ~~ 502,000.
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The diagonals of rectangle QRST intersect at P. Given that
m/PTS= 34° and
QS=10, find mSRT.
Note that since the diagonals of rectangle QRST intersect at P and m∠PTS = 34°, thus, m∠SRT is 56°.
What are the properties of a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. Rectangles have the following fundamental properties: A rectangle is a quadrilateral.
The two opposite sides are parallel and equal.Each inside angle measures 90 degrees.The total of all internal angles is 360 degrees.The diagonals cut each other in half.The diagonals are both the same length.With regard to the above problem:
Since ∠QRS = 90° (based on the qualities of a rectangle) ; and
∠QRT ≅ ∠RTS = 34° (based on the rule of alternate angles,
Thus, m∠SRT = 90° - 34°
∠SRT = 56°
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Full Question:
The diagonals of the rectangle QRST intersect at P. Given that
m∠PTS= 34° and QS=10, find m∠SRT.
See attached image.
HELP! I WILL AMKE YOU BRAINLIEST BC THIS IS DUE TODAY!!!
Answer: 27.3
Step-by-step explanation:
I took the outcomes of the Aces from the trial and found the average and the answer I got was 27.3%
Hope this helps.
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In the 2012 Olympics a U.S. athlete Nathan Adrian finished the 100-meter freestyle swim in 47.52 seconds. If nathan swam the same pace in a regular 25-meter pool what would his time have been per lap?
At the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.
To solve this problem
The idea of proportionality can be applied. The time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle. Since the tempo is constant while the distance varies, we can establish a ratio:
100 meters / 47.52 seconds = 25 meters / x seconds
where x is the unknown time for one lap in the 25-meter pool.
To solve for x, we can cross-multiply:
100 meters * x seconds = 47.52 seconds * 25 meters
100x = 1188
Dividing both sides by 100, we get:
x = 11.88 seconds
Therefore, at the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.
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S vi) The temperature in Gulmerg in Kashmir was-10°C in January and it rose by 44°c to reach the maximum temperature during summer. The maximum temperature during summer in that year was
The maximum temperature during summer in that year was 34°C.
It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.
A temperature rise of that magnitude would be extremely unusual and potentially dangerous.
However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.
The minimum temperature in January was -10°C, and if we add 44°C to it, we get:
-10°C + 44°C = 34°C
Therefore, the maximum temperature during summer in that year was 34°C.
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Yesterday a movie theater sold 280 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $610 from popcorn sales. Find how many bags of each size of popcorn were sold
Answer:
110 large bags and 170 small bags of popcorn were sold.
Step-by-step explanation:
Since yesterday a movie theater sold 280 bags of popcorn, and a large bag of popcorn costs $ 4 while a small bag of popcorn costs $ 1 and in all, the movie theater made $ 610 from popcorn sales, to find how many bags of each size of popcorn were sold, the following calculation must be performed:
280 x 4 + 0 x 1 = 1120
140 x 4 + 140 x 1 = 700
130 x 4 + 150 x 1 = 670
110 x 4 + 170 x 1 = 610
Therefore, 110 large bags and 170 small bags of popcorn were sold.
At the sixth-grade school dance, there are 132 boys, 89 girls, and 14 adults. Write the ratio of the number of boys to the number of girls. Type your answer either in the format: 3:4 with no spaces, OR in the format 3 to 4.
Answer:
the ratio will be 132 to 89
The ratio is 132 : 89.
What is ratio?A comparison of two quantities by division is called a ratio and the equality of two ratios is called proportion. A ratio can be written in different forms like x : y or x/y and is commonly read as, x is to y.
Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b
Given:
Boys= 132
girls= 89
adults= 14
So,
the ratio of number of boys to number of girls is
= 132/89
=132 : 89
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evaluate the expression 2x+3y-4w when x=2 y=3 w=4 p=1/2 and m=1.2
guys help i have a test tomorrow :')
The value of the expression is -3.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2x + 3y - 4w _____(1)
Now,
Substitute x = 2, y = 3, and w = 4 in (1).
So,
2x + 3y - 4w
= 2 x 2 + 3 x 3 - 4 x 4
= 4 + 9 - 16
= 13 - 16
= -3
Thus,
The value is -3.
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Question content area top Part 1 Think About the Process Use the algebra tiles to help you solve the equation 2x - 4 = 10. What is the first step in solving the equation using algebra tiles? What is the solution to the equation?
The solution to the equation is x = 7.
What is the linear equation in one variable?
A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.
The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.
Hence, the solution to the equation is x = 7.
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