Answer:
4 weeks
Step-by-step explanation:
Final answer:
After 5 weeks, you and your friend will have the same amount.
Explanation:
To find out after how many weeks you and your friend will have the same amount, we need to set up an equation and solve for the number of weeks. Let's assume the number of weeks is represented by 'w'.
Your balance in the bank after 'w' weeks can be represented by the expression: 48.50 + 9.50w. Your friend's balance after 'w' weeks can be represented by the expression: 1 + 2(9.50w). We want to find out when these two balances are equal, so we set up the equation: 48.50 + 9.50w = 1 + 19w.
Solving this equation, we get:
48.50 + 9.50w = 1 + 19w
48.50 - 1 = 19w - 9.50w
47.50 = 9.50w
w = 47.50/9.50
w = 5
After 5 weeks, you and your friend will have the same amount.
A ticket cost $4.80 the new ticket price will be 1.25 times the old price what will the new ticket be
The new ticket price after a 25% increase from the original price of $4.80 will be $6.00.
Explanation:The question asks about the new cost of a ticket if its current price is $4.80 and a 25% (or 1.25 times) increase is applied, so we perform a simple multiplication. To find out the new ticket price, we need to calculate 1.25 times the original price. Therefore, the new ticket price will be 1.25 times $4.80, which can be calculated as follows:
1.25 * $4.80 = $6.00
Hence, the new ticket price after the 25% increase will be $6.00.
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A salesperson earns a salary of $700 per month plus 2% of the sales. Which inequality correctly represents the total sales if the salesperson is to have a monthly income of at least $1800?
x ≤ $45,000
x ≤ $55,000
x ≥ $55,000
x ≥ $45,000
Answer:
C. [tex]x\geq 55000[/tex]
Step-by-step explanation:
Let x be the total monthly sales.
We have been given that a salesperson earns a salary of $700 per month plus 2% of the sales. The salesperson want to have a monthly income of at least $1800.
This means that 700 plus 2% of total monthly sales should be greater than or equal to 1800. We can represent this information in an equation as:
[tex]700+(\frac{2}{100})x\geq 1800[/tex]
[tex]700+0.02x\geq 1800[/tex]
Let us solve our inequality to find the monthly sales (x).
Subtract 700 from both sides of our inequality.
[tex]700-700+0.02x\geq 1800-700[/tex]
[tex]0.02x\geq 1100[/tex]
Divide both sides of inequality by 0.02.
[tex]\frac{0.02x}{0.02}\geq \frac{1100}{0.02}[/tex]
[tex]x\geq \frac{1100}{0.02}[/tex]
[tex]x\geq 55000[/tex]
Therefore, the total monthly sales must be greater than or equal to 55,000 and option C is the correct choice.
Factor the trinomial below
4x^2+19x-5
A: x+5
B: 4x-1
C: 2x-5
D: x-5
E: 2x+1
Answer:
A: x+5
B: 4x-1
Step-by-step explanation:
4x^2+19x-5
(4x ) ( x )
We know that 1 will be positive and 1 will be negative.
Our choices for the numbers are 5 and 1
4*5 -1 = 19
(4 x - 1) (x + 5)
At the county fair, the operator of a game guesses a contestant’s weight. For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive \$3$3. A contestant weighing xx pounds received \$15$15 when the operator guessed 120120 pounds. Which of the following equations could be used to solve for the weight of the contestant? Choose 1 answer: 3 | x - 15 | = 120
Answer: [tex]| x - \frac{15}{3} | = 120[/tex] or [tex]\frac{1}{3}| 3 x - 15|= 120[/tex] or [tex]| 3x - 15| = 360[/tex] or [tex]| x - 5 | = 120[/tex]
Step-by-step explanation:
Since, According to the question,
For each pound the operator’s guess differs from the contestant’s weight, the contestant will receive $3.
And, If a contestant weighing x pounds received $15
Then the guessed weight of contestant = [tex]| x - \frac{15}{3} |[/tex]
But, Again according to the question,
The guessed weight is 120 pounds,
Thus, [tex]| x - \frac{15}{3}|= 120[/tex]
⇒ [tex]\frac{1}{3}| 3 x - 15|= 120[/tex]
⇒ [tex]| 3x - 15|= 3\times 120[/tex] (by multiplying 3 on both sides)
⇒ [tex]| 3x - 15|= 360[/tex]
⇒ [tex]3| x - 5|= 360[/tex]
⇒ [tex]| x - 5|= 120[/tex] ( On dividing both sides by 3 )
Answer:
3|x-120|=15
Step-by-step explanation:
what's that?
your welcome ;)
If you want to know how many shirts and pairs of pants he bought, what matrix equation could you write to solve?
Answer:
A
Step-by-step explanation:
The equations are ...
... s + p = 15
... 3s + 10p = 94
Matrix equation A is equivalent.
Where can the perpendicular bisectors of an acute triangle intersect?
I. Inside the triangle
II. On the triangle
III. Outside the triangle
A. I only
B. III only
C. I or III only
D. I, II, or III
Answer:
D
Step-by-step explanation:
Answer:
I and II
Step-by-step explanation:
Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE.
Statement 1 is true because the perpendicular bisectors intersect at the center of the circumcircle.
Since the two triangles have the same circumcircle, therefore, their perpendicular bisectors intersect at the same point. So statement I is true.
Statement II: The distance from C to D is the same as the distance from D to E.
Since they both, that is distance from C to D and the distance from D to E represent the radius of the circle therefore, they both are equal in length.
Therefore, only I and II are correct.
pErIoD
Margo purchases bulk teas from a warehouse and marks up those prices by 40% for retail sale. When teas go unsold for more than two months, Margo marks down the retail price by 40%. She says that she is breaking Even that is, she is getting the same price for the tea that she paid for it. Is she correct? Complete the explanation.
Answer:
Margo is incorrect.She is selling tea in loss.
Step-by-step explanation:
Let the cost price of teas when purchased from the warehouse = $ x
Then Margo marks retail price of teas a = x + 0.40 x
a = x (1 +0.40)
a = 1.4 x
After 2 months she marks down the retail price by 40% then retail price becomes b = 1.4 x - 40% of 1.4 x
b = 1.4 x - 0.4 x 1.4 x
b = 1.4 x - 0.56 x
b = 0.84 x
Difference between cost price and selling price b is = x - .84 x
= 0.16 x
which shows now Margo is selling under the cost price so Margo is incorrect.
Margo is not correct in saying that she is breaking even by marking down the retail price by 40% when teas go unsold for more than two months. In fact, she is losing money on those teas.
Explanation:Margo is not correct in saying that she is breaking even by marking down the retail price by 40% when teas go unsold for more than two months. In fact, she is losing money on those teas. Let's break it down:
When Margo purchases bulk teas from the warehouse, she marks up the prices by 40% for retail sale. This means if she buys a tea for $10, she sells it for $14.However, when the teas go unsold for more than two months, Margo marks down the retail price by 40%. So if she initially sold the tea for $14, she now sells it for $8.40.This means that for every tea that goes unsold for more than two months, Margo is losing $1.60 ($10 - $8.40).Therefore, Margo is not breaking even, she is actually making a loss by marking down the price of unsold teas.
ILL GIVE BRAINLIEST
what is the slope of the line that passes through the pair of points -6,8 2,3
a.-3/8
b.-8/1
c.-7/8
d.-5/8
Answer:
The answer is D
Step-by-step explanation:
Answer:
d. -5/8
Step-by-step explanation:
To find slope, use the following equation
slope (m) = (y₂ - y₁)/(x₂ - x₁)
First, set each coordinate. Let:
(x₁ , y₁) = (-6 , 8)
(x₂ , y₂) = (2 , 3)
Plug in the corresponding numbers for the corresponding variables.
m = (y₂ - y₁)/(x₂ - x₁)
m = (3 - 8)/(2 - (-6))
Simplify. Note that two negative signs would result in a positive sign.
m = (3 - 8)/(2 + 6)
m = -5/8
d. -5/8 is your answer
~
Emma brandy and Damien will cut a rope that is 29.8 feet long into 3 jump ropes. Each of the three jump ropes will be the same length l. Write a division sentence using compatible numbers to estimate the length of each rope.
Answer: Length of each of rope will be 9.93 feet.
Step-by-step explanation:
Since we have given that
Length of rope that Emma brandy and Damien will cut = 29.8
Number of jumps = 3
According to question, each of the three jumps ropes will be the same length l.
Length of rope can be attained by dividing the length of rope with number of jumps.
so, length of each rope will be
[tex]l=\frac{\text{Length of rope}}{\text{Number of jumps cut into }}\\\\=\frac{29.8}{3}\\\\=9.93\ feet[/tex]
Hence, Length of each of rope will be 9.93 feet.
what are the real and imaginary parts of the complex number? -11+3i
Answer:
-11 is real and 3i is
Step-by-step explanation:
i is a imaginary number is equals to rad(-1) which doesn't exist
The real part of the complex expression is - 11 and the imaginary part of the complex number will be 3i.
What is a complex number?The complex number is the combination of the real part and the imaginary part. Then the complex number is given as a+bi where the value of i is √(-1) and the value of i² is -1.
The complex number is given below.
⇒ - 11 + 3i
The term that has iota is known as imaginary part and the term that does not have iota is known as real part.
The real part of the complex expression is - 11 and the imaginary part of the complex number will be 3i.
More about the complex number link is given below.
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help me plzzzzzzzzz!
Which values from the given replacement set make up the solution set of the inequality?
2b–4≥2 ; {1,2,3,4}
{1,2}
{3,4}
{1,2,3}
{2,3,4}
A rectangle has a perimeter 86 cm and length 36 cm what is its width
Answer: w = 7cm
Step-by-step explanation:
Perimeter = 2 x length + 2 x width = 2L + 2w
Width is 4 cm less than the length, so w = L-4
36 = 2L + 2(L-4)
36 = 2L + 2L - 8
36 = 4L - 8
44 = 4L
L = 11
w = 7
2(11) + 2(7) = 22 + 14 = 36
Length is 11, width is 7
Answer:
7cm
Step-by-step explanation:
36x2= 72
86-72= 14
14/2= 7
A middle school keeps track of its population. In 2011, the school population was 1500 students. In 2012, the student population had increased by 10%. In 2013, the student population had decreased by 10%. Andy believes that the 2013 student population is the same as the 2011 student population since the population both increased and decreased by the same percentage. Identify and explain the flaw in Andy's reasoning. Determine the percent change in the number of students from 2011 to 2013.
Answer:
-1%
Step-by-step explanation:
The population will not be the same unless the starting value is the same. Percent is a portion of the total 100%. If the total in 2011 and 2012 was different, then the change in population will be different.
In 2011, the population was 1500 students.In 2012, the population was 10% more than 1500. 1500+1500(0.10)=1500+150=1650In 2013, the population decreased by 10% from 1650. 1650-1650(0.10)=1650-165=1485.To find the percent change,
To calculate the percent increase or decrease, we:
Find the difference between the new value and the original Divide the number by the original Multiply by 100 and the % symbol.The population originally in 2011 was 1500. In 12013, the population is 1485.
1485-1500=-15
-15/1500=-0.01
100(-0.01)=-1%
0.75(100)=75%
The towns population increase by 75%
Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. The percent change in the number of students from 2011 to 2013 is a 1% decrease.
Explanation:Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. Let's calculate the population in 2012 after a 10% increase. 10% of 1500 students is 150 students. So the population in 2012 would be 1500 + 150 = 1650 students.
Now, let's calculate the population in 2013 after a 10% decrease from 1650 students. 10% of 1650 students is 165 students. So the population in 2013 would be 1650 - 165 = 1485 students.
To determine the percent change in the number of students from 2011 to 2013, we calculate the difference between the initial population (1500 students) and the final population (1485 students) and divide it by the initial population. (1500 - 1485) / 1500 = 15 / 1500 = 0.01 or 1%. Therefore, there was a 1% decrease in the number of students from 2011 to 2013.
Which of the following polynomials is the expansion of (1/2x-y)^4
Answer:
1/16 x^4 - 1/2x^3y +3/2 x^2y ^ - 2 xy^3 + y^4
Give the starting value a, the growth factor b, and the growth rate r if Q = abt = a(1 + r)t . Write r as a percent.
Answer:
Option a:
a=79
b=1.002
r=0.2%
Step-by-step explanation:
Q = 79 (1.002)^t
Q = a b^t = a (1+r)^t
Comparing with the formulas:
a=79
b=1.002
1+r=1.002
Solving for r: Subtrating 1 both sides of the equation:
1+r-1 = 1.002 - 1
r = 0.002
Writting r as percent:
r = (0.002) 100%
r = 0.2%
Translate the equation into slope-intercept form.
2x + 3y = 9
Stock in Ombor Medical Supplies earns a return of 5.3% annually, while bonds issued by Ombor Medical Supplies earns a return of 4.1% annually. If you invest a total of $2,400 in Ombor Medical Supplies, $1,400 of which is in bonds and $1,000 of which is in stocks, which side of the investment will show a greater return after six years, and how much greater will it be?
a. The stocks will earn $55.60 more than the bonds.
b. The stocks will earn $118.60 more than the bonds.
c. The bonds will earn $82.00 more than the stocks.
d. The bonds will earn $26.40 more than the stocks.
Answer:
d. The bonds will earn $26.40 more than the stocks.
Step-by-step explanation:
Assuming, the rates are uniform for 6 years.
Stock in Ombor Medical Supplies earns a return of 5.3% annually, so $1000 will yield annually;
[tex]0.053\times1000=53[/tex] dollars
Total amount in 6 years will become = [tex]53\times6=318[/tex] dollars
Bonds issued by Ombor Medical Supplies earns a return of 4.1% annually, so $1400 will yield annually;
[tex]0.041\times1400=57.40[/tex] dollars
Total amount in 6 years will become = [tex]57.40\times6=344.40[/tex] dollars
We can see that bonds have high yield than stocks.
So, difference amount is = [tex]344.40-318=26.40[/tex] dollars.
Therefore, The bonds will earn $26.40 more than the stocks.
Answer:
it is d
Step-by-step explanation:
i took the edu test :)
Brian Steve and Rita invested a total of $24,000 in a business each person invested the same amount unfortunately in the first quarter they suffered a loss of $4500 which they shared equally by what amount as each individual investment change due to the loss
Answer:
Each individual investment changed by $2250 due to the loss.
Step-by-step explanation:
It is given that Brian Steve and Rita invested a total of $24,000 in a business.
Each person invested the same amount. So amount invested by each person is
[tex]\frac{24000}{2}=12000[/tex]
Therefore invested by each person is $12000.
They suffered a loss of $4500, which they shared equally. Each individual suffered a loss of
[tex]\frac{4500}{2}=2250[/tex]
Therefore Brian Steve and Rita suffered a loss of $2250 each. So, each individual investment changed by $2250 due to the loss.
Answer:
1500
Step-by-step explanation:
Corey used the regression equation y = 1.505x − 88.21, where x is the temperature and y is the number of swimmers, to determine a possible outside temperature when 80 swimmers are at City Pool.
1. y = 1.505(80) − 88.21
2. y = 120.4 − 88.21
3. y = 32.19
4. If there are 80 swimmers at the pool, the temperature is likely to be 32.2°F.
Analyze Corey’s work to find his error. What is Corey’s mistake?
Answer: Corey substituted the number of swimmers into the variable (x) representing the temperature. Then he didn't wonder if the polar bear club really has 80 members.
Step-by-step explanation:
Answer:
A. He substituted 80 for x instead of y.
Step-by-step explanation:
Belkis is pulling a toy by exerting a force of 1.5 newtons on a string attached to the toy. The string makes an angle of 52 degrees with the floor. What could be the vertical and horizontal components of the force? a. ≈ 1.18N; ≈ 0.92 E
b. ≈ 1.07N; ≈ 0.09 E
c. ≈ 1.18N; ≈ 0.09 E
d. ≈ 1.07N; ≈ 0.92 E
Answer: (A) 1.18 North, 0.92 East
Step-by-step explanation:
The vertical component is sin 52° times the Force of 1.5 newtons
⇒ 1.5 sin 52° = 1.18
The horizontal component is cos 52° times the Force of 1.5 newtons
⇒ 1.5 cos 52° = 0.92
Answer:
a. ≈ 1.18N; ≈ 0.92 E
Which of the following is described as a line, segment, or ray that bisects a segment at a right angle?
A. Slope
B. Perpendicular bisector
C. Midpoint
D. Angle bisector
Answer:
option B
Step-by-step explanation:
the correct answer is option B
A Line, segment, or ray that bisects a segment at a right angle is Perpendicular bisector.
The slope of the is the rate of change of y-axis w r t to x-axis.
Midpoint is the center of any line segment.
An angle bisector is a line which bisects angle in equal proportion
Lisa's favorite chocolate candies are wrapped in the shape of a triangular prism with shiny gold paper as shown below. If all sides of the package are covered in the gold paper, what is the surface area of the amount that is wrapped?
Answer:
Surface Area = 150
Step-by-step explanation:
The surface area of this triangular prism is the sum of area of all the sides.
Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)
Triangle 1 area: [tex]\frac{1}{2}bh=\frac{1}{2}(8)(3)=12[/tex]Triangle 2 area: [tex]\frac{1}{2}bh=\frac{1}{2}(8)(3)=12[/tex]Lateral surface 1 (rectangle): [tex]l*w=(7)(5)=35[/tex]Lateral surface 2 (rectangle): [tex]l*w=(7)(5)=35[/tex]Bottom surface (rectangle): [tex]l*w=(7)(8)=56[/tex]Summing all these gives us the total surface area.
Total surface area = [tex]12+12+35+35+56=150[/tex]
**** The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).
Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use Pythagorean Theorem. Which is:
[tex]leg^2+leg^2=hypotenuse^2\\3^2+4^2=hypotenuse^2\\25=hypotenuse^2\\hypotenuse=5[/tex]
Hence, the side length of the hypotenuse is 5 [used above in the calculation]
Solve by elimination
2x-y=0
3x-2y=-3
To solve a system of equations by elimination, make the coefficients of one variable equal. Subtract one equation from the other to solve for one variable, then substitute this solution into one of the original equations to solve for the other variable. In this case, the solution to the given system of equations is x = 3, y = 6.
Explanation:In mathematics, specifically in algebra, the method of elimination is used to solve a system of simultaneous equations. Your equations are:
2x -y = 03x - 2y = -3To solve this system by elimination, we need to make the coefficients of y in both equations equal by multiplying if necessary. We can obtain this by multiplying the first equation by 2:
4x - 2y = 0
3x - 2y = -3
Next, we subtract one equation from the other to eliminate y:
4x - 3x = 0 - (-3) => x = 3
To find y, substitute x = 3 into the first equation:
2*3 - y = 0 => y = 2*3 = 6
So, the solution to the system of equations is x = 3, y = 6.
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One factor of f(x)5x^3+5x^2-170+280 is (x + 7). What are all the roots of the function? Use the Remainder Theorem.
a. x = –4, x = –2, or x = 7
b. x = –7, x = 2, or x = 4
c. x = –7, x = 5, or x = 280
d. x = –280, x = –5, or x = 7
Answer: (b) x = -7, x = 2, x = 4
Step-by-step explanation:
Remainder Theorem is used to determine if a given value is a root.
It is stated that (x + 7) is a root ⇒ x + 7 = 0 ⇒ x = -7
We can confirm this by plugging in x = -7 and getting a value of 0.
f(x) = 5x³ + 5x² - 170x + 280
f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280
= -1715 + 245 + 1190 + 280
= 0
CONFIRMED that x = -7 is a zero!
Next, let's try x = 2
f(2) = 5(2)³ + 5(2)² - 170(2) + 280
= 40 + 20 - 340 + 280
= 0
CONFIRMED that x = 2 is a zero!
Lastly, let's try x = 4
f(4) = 5(4)³ + 5(4)² - 170(4) + 280
= 320 + 80 - 680 + 280
= 0
CONFIRMED that x = 4 is a zero!
Tom has a large photo he wants to shrink to wallet-sized. It's width is 20 centimeters and it's len is 30 centimeters. If he wants the width to be 5 centimeters what should the length be?
A 1200 sq ft house is advertised for sale at a price of 96000. What is the cost per square foot?
Answer:$80.00
Step-by-step explanation:
APEX
Math Help:
Which two answers are correct?
Answer:
see below
Step-by-step explanation:
The odd degree (7) tells you the end behaviors are in opposite directions. The negative leading coefficient (-4) tells you the sign of y will be opposite the sign of x.
For x going toward negative infinity, y goes toward positive infinity.
For x going toward positive infinity, y goes toward negative infinity.
please helppppppppppppppppppppppppppppppppp 11/12 - 7/9
11/12 - 7/9
=>taking L.C.M of the denominator
=>11/36 - 7/36
=>4/36
=>2/18=>1/9
Answer:
it is 5 36
heres why
Step-by-step explanation:
Here's how to subtract 7/9 from 11/12:
11
12
−
7
9
Step 1
We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 11 by 9, and get 99.
Then we multiply 7 by 12, and get 84.
Next we give both terms new denominators -- 12 × 9 = 108.
So now our fractions look like this:
99
108
−
84
108
Step 2
Since our denominators match, we can subtract the numerators.
99 − 84 = 15
So the answer is:
15
108
Step 3
Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?
To find out, we try dividing it by 2...
Nope! So now we try the next greatest prime number, 3...
Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:
15
108
÷ 3 =
5
36
Let's try dividing by 3 again...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! The final answer is:
11
12
−
7
9
=
5
36
Approximately how many time greater is the amount of earth surface that is covered by water compared to the amount of earth of earth surface that is covered by land?
Answer:
The amount of the earth’s surface covered by water is 2.12*10^8 greater than the amount of the earth’s surface covered by land.
Step-by-step explanation:
(Subtraction of scientific notation)
Earth’s surface covered by water- 3.61*10^8
Earth’s surface covered by land- 1.49*10^8
(3.61*10^8) - (1.49*10^8)
(3.61-1.49) *10^8
2.12*10^8
Hope this helps you out
Three times one number minus another number equals 34. If the sum of the numbers is 22, what are the two numbers?
Answer:
8 and 14
Step-by-step explanation:
let the 2 numbers be x and y with x > y
We can model the situation using the following 2 equations
x + y = 22 → (1)
3x - y = 34 → (2)
adding the equations term by term will eliminate the term in y
(x + 3x) + (y - y) = (22 + 34)
4x = 56 ( divide both sides by 4 )
x = 14
substitute x = 14 into (1)
14 + y = 22 ⇒ y = 22 - 14 = 8