Based on this projection, which of the following is closest to the number of t-shirts Marcus needs to sell during the first month to meet his goal? (100 brainley points plsss help)
Answers
Answer:
A. 1,500
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7cm}\underline{Sum of the first n terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the $n$th term.\\\end{minipage}}[/tex]
The given scenario can be modelled as a geometric series.
If Marcus' goal is to sell 15,000 t-shirts during the first 6 months, then:
Sum Sₙ = 15,000n = 6If he projects that the number of t-shirts he sells will increase by 20% each month then the common ratio is:
r = (1 + 0.2) = 1.2Substitute these values into the formula and solve for a:
[tex]\implies 15000=\dfrac{a(1-1.2^6)}{1-1.2}[/tex]
[tex]\implies 15000(1-1.2)=a(1-1.2^6)[/tex]
[tex]\implies a=\dfrac{15000(1-1.2)}{1-1.2^6}[/tex]
[tex]\implies a=1510.586188[/tex]
Therefore, the approximate number of T-shirts Marcus needs to sell during the first month to meet his goal is 1,500.
Check:
Month 1 = 1511Month 2 = 1511 × 1.2 = 1813Month 3 = 1813 × 1.2 = 2176Month 4 = 2176 × 1.2 = 2611Month 5 = 2611 × 1.2 = 3133Month 6 = 3133 × 1.2 = 3760Total = 1511 + 1813 + 2176 + 2611 + 3133 + 3760 = 15004
Check:
Month 1 = 1500Month 2 = 1500 × 1.2 = 1800Month 3 = 1800 × 1.2 = 2160Month 4 = 2160 × 1.2 = 2592Month 5 = 2592 × 1.2 = 3110Month 6 = 3110 × 1.2 = 3732Total = 1500 + 1800 + 2160 + 2592 + 3110 + 3732 = 14894 ≈ 15000
Related Questions
i need help with this
Answers
Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
What is a Pythagoras theorem?
The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:
a² + b² = c²
To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:
KL² = KM² + KN²
Substituting the given values, we get:
24² = 10² + KN²
Solving for KN, we get:
KN² = 24² - 10²
= 576 - 100
= 476
KN = √476
= 21.84
Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
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Rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
What is a Pythagoras theorem?
The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship is often expressed in the form of the equation:
a² + b² = c²
To find the length of KN in this right triangle, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the hypotenuse is KL, and the other two sides are KM and KN. The theorem can be written as:
KL² = KM² + KN²
Substituting the given values, we get:
24² = 10² + KN²
Solving for KN, we get:
KN² = 24² - 10²
= 576 - 100
= 476
KN = √476
= 21.84
Hence, rounding to the nearest tenth, we get that the length of KN is approximately 21.8.
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Dee chose A as the correct answer. What was her error? Answer in a complete sentence.
Answers
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
Given that, it takes Zach 10 minutes to paint [tex]40\frac{1}{2}[/tex] square feet of his bedroom wall.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, square feet = 40.5 square feet
Rate at which he paints the wall =40.5/10
= 4.05 square feet per minute
As we know 1 hour =60 minutes
Now, number of square feet
= 4.05×60
= 243 square feet
Number of square feet of wall painted in 1 hour is 243 square feet. Therefore, option C is the correct answer.
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At approximately what latitude is the sun directly overhead at noon on November 24?
Help this is due tomorrow and I have no idea how to do it I'll give 100 points
Answers
Answer:
23.5 degrees north
Step-by-step explanation:
A lione ha 4 cub that weigh 1. 7 kg, 2. 1 kg, 3 kg, and 2. 7 kg. Each cub eat 1. 25 kg of food a day. How much food will be needed to feed all the cub for one year?
Answers
The food will be needed to feed all the cub for one year is 1825 kg.
Given :
A lion ha 4 cubs that weigh 1. 7 kg, 2. 1 kg, 3 kg, and 2. 7 kg. Each cub eat 1. 25 kg of food a day.
one cub eats food = 1.25 kg
4 cubs eats food = 1.25 kg * 4
= 125 / 100 * 4 kg
= 500 / 100 kg
= 5 kg
5 kg for one day.
cub eats food for one year = 365 * 5 kg
= 1825 kg.
Therefore the food will be needed to feed all the cub for one year is 1825 kg.
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1. please Prove that the angle that an are of a circle subtends at the centre is twice that which it substends at any point on the remaining part of the circumfrence.
Answers
An arc is a portion of the circumference of a circle. If we draw an arc with central angle A, the arc will subtend an angle A at the center of the circle.
An angle is a measure of rotation. If we draw a radius from the center of the circle to any point on the arc, the angle formed by the radius and the arc will be half of the angle A.
Since the arc subtends an angle A at the center of the circle, and the angle formed by the radius and the arc is half of the angle A, it follows that the angle that an arc of a circle subtends at the center is twice that which it subtends at any point on the remaining part of the circumference.
This can be formally stated as follows:
For any arc of a circle with central angle A, the angle that the arc subtends at the center of the circle is 2 times the angle that the arc subtends at any point on the remaining part of the circumference.
This conclusion holds true regardless of the size of the arc or the size of the circle.
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Pleaseee hellpp
Which of the following is the solution to the inequality below?
s > 7
A. s = 9
B. s = 7
C. s = 1
D. s = 3
Answers
Answer:
A
Step-by-step explanation:
s must be a number greater than 7
please help its due tomorrow and im failing the class
Answers
Answer:
the slope is -1/9
Step-by-step explanation:
The first thing to do is use the slope formula y^1 - y^2 over x^1 - x^2. You substitute each value into these variables and solve, which will then give you a negative slope of -1/9.
hope this helps!! :3
Find the difference between the actual quotient and the etimated quotient of 78,070÷37. (Dividend i rounded off to nearet thouand and divior to nearet ten)
Answers
The actual quotient and the estimated quotient of 78,070÷37 is 2110 , so the difference between them is 0.
On dividing 78,070 by 37 ,
we get
78,070 /37
=2110
Since , the number gets divided completely
therefore the estimated quotient and the actual quotient will be 2110.
We first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient. When the divisor in a division sum has two or more digits, it is helpful to first estimate the quotient before attempting to discover the exact number.
The outcome of dividing two numbers is known as the quotient. Divided divisor = quotient + remainder is the formula for expressing the terms of division.
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Please help geomotry
Answers
Figure D was reflected over the y axis and translated 4 units upwards to form figure E
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
According to the given question:
On translating the figure D over y-axis, the figure E will be 4 units above.
Therefore, Figure D was reflected over the y axis and translated 4 units upwards to form figure E.
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Jon bought 6 gallons of gas for $24
A( Find the cost of 1 gallon
B( Find the cost of 12 gallons
Answers
Answer:
A/ $4 for 1 gallon
B/ $48
Step-by-step explanation:
Take 24 divided by 6 = $4 per gallon
Then take 4 times 12 = $48 for 12 gallons
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A middle chool took all 6th grade tudent on a field trip to ee a ballet. The tudent filled 702 eat leaving 35% vacant how manny eat were in the theater
Answers
There were 1080 seats in the theater.
In this question, we have been given that the 6th grade students went on a field trip to see a ballet.
The students filled 702 seats leaving 35% vacant.
We need to find the total seats in the theater.
Let there were n seats in the theater.
Given that 35 percent of total seats were vacant.
So, we get an equation,
702 + (35% of n) = n
702 + 0.35n = n
(1 - 0.35)n = 702
0.65n = 702
n = 1080
Therefore, the total seats in the theater = 1080
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Please name these last two shapes
Answers
Answer:
Step-by-step explanation:
Square, Irregular shape
A loan of $740 is taken out a daily interest of 0.66%. How much will it cost to pay off the loan after 57 days?
Answers
Answer:
$1,018.39
Step-by-step explanation:
Interest formula is I = Prt/100
where P = principal
r = interest rate (in percent)
t = number of time periods
Here we have P = 740
interest = 0.66% per day
t = 57 days
I = 740 x 0.66 x 57 /100 = 278.39 (rounded)
Total amount to pay back = 740 + 278.39 = $1,018.39
(1). 7/10 - 2/5
(2). 3/4 + 5/6
(3). 17/9 - 11/12
(4). 2/3 + 1/4 - 7/12
Answers
Answer:
1. 3/10
2. 19/12
3. 35/36
4. 1/3
Step-by-step explanation:
Help please asp before 11:59
Answers
Answer: I believe it is reflected over the y-axis.
Step-by-step explanation:
Always look for the dum (I know it is spelled wrong but Brainly won't let me type it) and dummer answer choices. The other two choices aren't even a type of transformation. Think about it. If you are reflecting over the y-axis, the y-values stay the same and the x-values change.
A certain state uses the following progressive tax rate for calculating individual income tax: Progressive Income Range ($) Tax Rate 0 - 10,000 10,001 - 50,000 50,001 - 100,000 3% 5% 5.5% Calculate the state income tax owed on a $90,000 per year salary. tax = $[ ? ] Round your answer to the nearest whole dollar amount.
Answers
The required state income tax owed on a $90,000 per year salary is $4950.
Given that,
A table shows the income tax owed by the state on the particularar salary,
Income Range ($) Tax Rate
0 - 10,000 3%
10,001 - 50,000 5%
50,001 - 100,000 5.5%
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
on $90,000
Tax owed = 5.5% of 90000, because this salary lies in the segment 50,001 - 100,000.
Tax owed = 0.055[90000] = $4950
Thus, the required state income tax owed on a $90,000 per year salary is $4950.
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A laptop computer originally priced at $2100 now ell for $2,200. What i the percent of increae?
Answers
The percent of increase is 4.761 %
Given :
A laptop computer originally priced at $2100 now and sell for $2,200.
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.
Difference = sell price - original price
= 2200 - 2100
= 100
Percent of increase = 100 * 100 / 2100
= 100 * 1 / 21
= 100 / 21
= 4.761 %
Therefore 4.761 % increase in percent.
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i am wondering what 72b=9 is
Answers
Answer:
1/8
Step-by-step explanation:
9/72 = 1/8
s is inversely proportional to t.
When s = 0.9, t = 2
Work out s when t = 0.6
Answers
Answer:
s = 3
Step-by-step explanation:
We model the proportion with the equation:
[tex]s =\frac{k}{t}[/tex]
We have s and t, but we need to find the k (i.e., the constant of proportionality) by plugging in the s and t we already have:
[tex]0.9=\frac{k}{2}\\ 1.8=k\\s=\frac{1.8}{t}[/tex]
To find s when t = 0.6, we simply plug in 0.6 for t in last equation we found with k:
[tex]s=\frac{1.8}{0.6}\\ s=3[/tex]
Factor t12 – r3s15.
A. (t4 – rs5)(t8 – rs5t4 – r2s10)
B. (t4 – rs5)(t8 + rs5t4 + r2s10)
C. (t9 – rs12)(t18 + rs12t9 + r2s24)
D. (t4 + rs5)(t8 – rs5t4 + r2s10)
Answers
The required factors of the given polynomial is (r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10).
What is factor?
A factor is a number that partitions another number, leaving no remainder portion. if multiplying two whole number gives us an item, the numbers we are increasing are variables of the item since they are separable by the item.
According to question:We have given,
t^12 - r^3(s)^15
By using formula
(a³ - b³) = ( a+ b)( a² -ab + b²)
Then,
(r^4)^3 - (rs^5)^3
(r^4 + rs^5)((t^4)^2 - rs^5t^4 + (r^5)^2)
(r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10)
Thus, required answer is (r^4 + rs^5)(t^8 - (rs^5t^4) + r^2s^10), So option (D) is correct.
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If M7=28, what is M14?
Answers
Answer:
56
Step-by-step explanation:
divide 7 into 28 which is 4.
Then substitute 4 for M so 4 times 14 which is 56.
Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100100100 pieces of sushi in total. Sofia had already ordered and paid for 242424 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 121212 pieces and costs \$8$8dollar sign, 8. Let rrr represent the number of additional rolls that sofia orders. 1) which inequality describes this scenario? choose 1 answer: choose 1 answer:.
Answers
In linear equation, Sofia will order 7 more rolls of sushi (84 pieces) and pay $56.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
They need at least 100 pieces of sushi
Sofia had ordered and paid for 24 pieces of sushi already
Sushi comes in rolls
Each roll=12 pieces at $8
R=additional rolls that Sofia orders
Additional sushi= Needed sushi - ordered sushi
=100-24
=76 pieces of sushi
Each roll has 12 pieces
76/12=6.33
Sofia has to order in rolls
So, she will order 7 more rolls of sushi of 12 pieces each
12*7=84 pieces
Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100
If Sofia orders 84 pieces + the already ordered 24 pieces
Total pieces=108 pieces
She has paid for 24 pieces (3 rolls) at $8 per roll
7 rolls=$8*7
=$56
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Indigo launches a toy rocket from a platform. The height of the rocket in feet is given by h(t)=-16t² + 80t + 96 where t represents the time in seconds after launch. What is the rocket's greatest height?
Answers
The calculated value of the rocket's greatest height is 196 feet
Calculating the rocket's greatest height?From the question, we have the following parameters that can be used in our computation:
height function, h(t) =-16t² + 80t + 96
So, we have
h(t) =-16t² + 80t + 96
The maximum value of t is calculated as
t = -b/2a
So, we have
t = -80/(2 * -16)
Evaluate
t = 2.5
The rocket's greatest height is at t = 2.5
So, we have
h(2.5) =-16(2.5)² + 80(2.5) + 96
Evaluate
h(2.5) = 196
Hence, the rocket's greatest height is 196 feet
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Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?.
Answers
180 ft2 be the area of the rectangular sheep pen .
What is rectangle?
A quadrilateral is a shape with two opposed sides that are equal and parallel.
There are four 90-degree angles on its four sides, making it a four-sided polygon. The shape of a rectangle is two dimensional.
Length of the sheep pen =60ft
150 ft of fencing bought
One side of rectangular sheep pen is covered with barn which is equaling the width
perimeter of rectangular sheep pen = 2(length +width)
length need to covered is 2 Length+ width
150 =2 length+width
150 = 2 x60 +width
150-120= width
30= width
Area of rectangle = 60 x 30
= 180 ft2
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Drag each label to the correct location in the equation. not all tiles will be used.
the density of mercury is 13.6 grams per cubic centimeter. complete the steps for converting 13.6 g/cm3 to kg/m3. (1 kg = 1,000 g, 1 m3 = 106 cm3)
13,600 10^6 1,360 1 g 1 kg 1 m3
13.6g/cm^3 x ( )/1000g x ( ) cm^3/( ) = ( ) kg/m^3
Answers
As per the given equation, the resulting conversion is written as,
13.6g/cm³ x 1kg/1000 x 10⁶cm³/m³ = 13600kg/m³
Equation:
An equation consist the value of the variable, numbers and the constants.
Given,
Here we have the density of mercury is 13.6 grams per cubic centimeter.
Now, we have to convert this one into kg/m3.
Here the process of conversion of 13.6 g/cm3 to kg/m3
We know that, 1 Kg of weight is equal to 1000 grams of weight
Then it can be written as
=> 1 g = 1 kg/1000
Then the first blank (numerator) will be filled with 1 Kg
Similarly, 1 meter is equal to 100 centimeter
So, for cubic unit it can be written as,
=> 1 cm³ = 1m³/100³
It can be simplified as,
=> 1 cm³ = 1m³/10⁶
Now, the second blank (numerator) will be filled with 10⁶
Finally, the third blank (denominator) will be filled with 1m³
Therefore, the last blank will be 13600
Hence, we have find the all the values on the blanks.
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f(x)=-x^{2}+2x+6
f(x)=−x
2
+2x+6
\text{Find }f(-7)
Find f(−7)
Answers
The value of f(-7) is -29.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)=-x² + 2x + 6
So, to find f(-7) put x= -7
f(-7) = -(7)² + 2(7) + 6
f(-7) = -49 + 14 + 6
f(-7) = -29
Hence, the value of f(-7) is -29.
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Ahley' chocolate bar i 72% cocoa. If the weight of the chocolate bar i 51 gram, how many gram of cocoa doe it contain?
Answers
Answer: 36.72 G
Step-by-step explanation:
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A bread is cut into 10 equal parts. How many children can share all parts of the bread if each child takes 0.2 parts
Answers
5 children can share all parts of the bread if each child takes 0.2 parts.
What are Fractions?Fraction are numbers of the form [tex]\frac{a}{b}[/tex] where a and b are real numbers. It is represented as a portion or part of a whole.
The number on the top is called numerator and the number on the bottom is called denominator.
There are 10 equal parts of bread and each child takes 0.2 part.
Total parts of the bread = 10
Part each child takes = 0.2 = [tex]\frac{2}{10}[/tex]
2 parts out of 10 are taken by each child.
Remaining are [tex]\frac{8}{10}[/tex] parts.
[tex]\frac{2}{10}[/tex] × 4 = [tex]\frac{8}{10}[/tex]
Remaining parts can be shared by 4 children.
Hence number of children who can share the bread if each takes 0.2 parts = 5
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1.03 of 0.054 is what number?
Answers
Answer:
1.03% of 0.054=0.0005562
A university will spend Atmos 6000 by monitors and keyboards for computer lab each monitor will cost $200 and each keyboard will cost $25 which inequality represents all possible combinations of x the number of monitors and y the number of keyboards the university can buy for the computer lab?
Answers
Answer:
Answer: 200x + 25y <= 6000
Step-by-step explanation: