Answer: $106,700
Step-by-step explanation:
y = money amount
x = months
Slope (m) = change in y / change in x = (68000-25000) /(23-3)= 43,000/20= 2,150
Now, we have to write the equation in the form y =mx+b, using one of the points:
25000= 2,150(3) +b
25,000= 6,450+b
25,000-6,450=b
18,550=b
So, the final equation is:
y = 2,150x+18,550
So, when x=41 months
y = 2,150(41)+18,550
y= $106,700
Feel free to ask for more if needed or if you did not understand something.
Eva invested $10,000 in a savings account. If the interest rate is 3.5%, how much will be in the account in 10 years by
compounding continuously? Round to the nearest cent.
Answer:
The total in the account after 10 years would be: $14,190.68
Step-by-step explanation:
Recall the formula for continuous compounding:
[tex]A=P\,e^{r\,t}[/tex]
where "A" is the accrued value after t years (what we need to find), "P" is the principal invested (in our case $10,000), "r" is the interest rate in decimal form (in our case r = 0.035), and "t" is the time in years (in our case t = 10). Therefore the formula becomes:
[tex]A=P\,e^{r\,t}\\A=10000\,\,e^{0.035\,*\.10}\\A=14190.68[/tex]
Therefore the total in the account after 10 years would be: $14,190.68
If a person can complete a job in 8 hours and his/her friend needs 6 hours to do the same job, what portion of the job would the tow of them complete by working together
for two hours?
Both of them can complete 7/12 of the job in 2 hours.
What is rate?Rate is the mathematical term use to show how one quantity varies with a standard quantity.
Analysis:
If He can do the job in 8 hours, then he can do 1/8 of the job in 1 hour
If his friend can do the same job in 6 hours, then he can do 1/6 of that job in 1 hour.
So both of them would do the same job combine in 1 hour = 1/8 + 1/6
LCM of 6 and 8 is 24 so that 3/24 + 4/24 = 7/24
In 2 hours they would complete = 7/24 x 2 = 7/12
In conclusion, both of them can do 7/12 of that job in 2 hours.
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Mikes mother took 18 minutes to make 2 bowls of salad. How long would it take to make 7 such bowls of salad?
Answer:
63 minutes or 1 hour 3 minutes
Step-by-step explanation:
We can use ratios to solve
18 minutes x minutes
--------------- = --------------
2 bowls 7 bowls
Using cross products
18*7 = 2x
Divide by 2
18/2 *7 = x
63 minutes
Answer: 63 minutes or 1 hour and 3 minutes
Step-by-step explanation:
18 minutes is how long it takes to make 2 bowls. To find out how long it takes to make 1 bowl, divide by 2.
18 / 2 = 9
Now multiply that by 7 to find out how long it takes to make 7 bowls.
9 * 7 = 63
63 minutes
Will name brainliest please help me.
Answer:
CD = 9
Step-by-step explanation:
ΔADE is similar to ΔBCD
Such that:
AD is similar to CD
BD is similar to ED
AE is similar to BC
Taking the proportion of their sides to find the unknown sides CD
=> [tex]\frac{6}{2} = \frac{CD}{3}[/tex]
Cross Multiplying
=> 2(CD) = 3*6
=> CD = 18/2
=> CD = 9
Evaluate the following:
Answer:
[tex]3\frac{17}{24}[/tex]
Step-by-step explanation:
[tex]14\frac{1}{6}-10\frac{11}{24}=\\\\\frac{85}{6}-\frac{251}{24}=\\\\\frac{340}{24}-\frac{251}{24}=\\\\\frac{89}{24}=\\\\3\frac{17}{24}[/tex]
14x6= 84/6
84/6 +1/6 = 85/6
10 x 24= 240/24
240/24 +11/24 = 251/24
85x 4 = 340
340-251= 89/24
3 17/24
4/7 divided by 7/2?????
Answer:
8/49
Step-by-step explanation:
4/7 ÷7/2
Copy dot flip
4/7 * 2/7
Multiply the numerators
4*2 = 8
Multiply the denominators
7*7= 49
numerator over denominator
8/49
Answer: 8/49
Step-by-step explanation: When dividing by a fraction, we can change the division sign to multiplication and flip the second fraction.
So 4/7 ÷ 7/2 means the same thing as 4/7 · 2/7.
So when dividing by a fraction, we can just multiply by the
reciprocal of that fraction or that fraction flipped.
Now multiply across the numerators
and denominators to get 8/49.
Since 8/49 is in lowest terms, it's our final answer.
A tank is 2m long, 1.4m wide and 1.8m high. find the volume of water in the tank when it is half full.
Answer:
volume of water in the tank when it its half full
The capacity of the water tank = (5.04) /2 = 2.52 m³
2,520 litres
Step-by-step explanation:
Dimensions of a water tank:
Length (l) = 2.0 m,
wide (w) = 1.4 m,
Depth (h)= 1.8 m,
Volume of the tank (V)
LWH
2.0m × 1.4m × 1.8 m
= 5.04 m³
= 5.04 × 1000 litres
/* 1m³ = 1000 litres */
5,040 litres
Therefore,
The capacity of the water tank = 5.04 m³
5,040 litres
ASAPPP What is the slope of the line represented by the equation y
3?
-3
4
o
O
The slope of the line represented by this equation is 4/5.
We know this because this line is in slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept. Thus, we can conclude that the slope is 4/5, which means that for every 4 units the line moves up, it also moves 5 units over (because slope is defined as rise/run).
This equation is in slope-intercept form, or
y = mx + b where m is the slope and b is the y-intercept. The number in the m position in our equation is 4/5, so the slope is 4/5
Hope this helps!
please mark me brainliest!
Classify the following real numbers as rational or irrational:
Answer:
a. rational - It can be written as a fraction so it's rational.
b. rational - Simplified it equals to 9, a whole, therefore rational, number.
c. irrational - Even once simplified, it contains a square root, therefore it's irrational.
d. rational - It can be written as a fraction so it's rational.
e. irrational - It cannot be simplified from a square root, therefore it's irrational.
The distance between points (X7, Yı) and (4, 8) is the square root of (x7 - 8)2 +
(1-4)²
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Given
[tex]Points: (x_7 - y_i),(4,8)[/tex]
Required
Is the distance between them [tex]\sqrt{(x_7 - 8)^2 + (y_1 - 4)^2}[/tex]
Given that there are two points, the distance between them is calculated using
Distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
In this case;
[tex](x_1,y_1)= (x_7 - y_i)\\(x_2,y_2) =(4,8)[/tex]
Substitute these in the given formula
Distance = [tex]\sqrt{(4- x_7)^2 + (8 - y_1)^2}[/tex]
Comparing this with the given formula, both are not the same;
Hence, the formula is false and the correct formula is of the form [tex]\sqrt{(4- x_7)^2 + (8 - y_1)^2}[/tex]
Which coordinate pair is a solution of the linear
equation below?
5x – 3y = -21
Click on the correct answer.
(9,-8)
(-9,-8)
(-9,8)
Answer:
5x - 3y = -21
5x - 3y
= 5(-9) - 3(-8)
= -45 + 24
= -21
the answer is (-9,-8)
given
[tex] log(x) = 2 \: and \: log(y) = - 1[/tex]
prove that
[tex]xy - 100y {}^{2} = 9[/tex]
Step-by-step explanation:
[tex] log(x) = 2 \\ {10}^{2} = x \\ x = 100[/tex]
then for y:
[tex] log( y) = - 1 \\ {10}^{ - 1} = y \\ y = 0.1[/tex]
so:
[tex]xy - 100 {y}^{2} \\ = 100 \times 0.1 - 100 \times {(0.1)}^{2} \\ = 10 - 100 \times 0.01 \\ = 10 - 1 \\ = 9[/tex]
If you travel 200 miles in 300 minutes. How fast did you travel in MPH...mile per hour?
Answer: 40 miles per hour
Step-by-step explanation:
first you do 300 divided by 60 to see how many hoiurs there is in 300 min. (5)
then you devide 200 by 5 to get 40 miles per hour
What is the point-slope equation of the line with slope
3/2
that goes through the
point (-3,5)?
Answer:
y-5 = 3/2(x+3)
Step-by-step explanation:
The point slope form of the equation for a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y-5 = 3/2(x--3)
y-5 = 3/2(x+3)
Answer:
y-5 = 3/2(x+3)
Step-by-step explanation:
I did ze math
In the diagram, point P is a point of tangency. Find the radius r of circle O.
Answer:
r = 12
Step-by-step explanation:
From the figure attached,
QP is a tangent to the circle O at the point P.
Therefore, by the property of tangency,
OP ⊥ QP
By applying Pythagoras theorem In right triangle QPO,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
(OQ)² = (OP)² + (PQ)²
(25 + r)² = (35)² + r²
625 + r² + 50r = 1225 + r²
50r = 1225 - 625
50r = 600
r = 12
Therefore, r = 12 units is the answer.
Answer:
r=12
Step-by-step explanation:
The table below shows student's preferred European football clubs as indicated in a survey run by
their math teacher. If two students were selected without replacement at random, what is the
probability that the first and second students prefer Juventus?
Answer:
Option D. 91/4950
Step-by-step explanation:
The following data were obtained from the question:
Barcelona (B) = 23
Real Madrid (R) = 23
Liverpool (L) = 22
Manchester City (M) = 18
Juventus (J) = 14
Total (T) = 100
Next, we shall determine the probability of the first pick i.e probability of Juventus. This is illustrated below:
P(J1) = n(J) /n(T)
P(J1) = 14/100
Now, the picking is done without replacement. The next pick being Juventus will reduce in number and likewise the total number will also reduce i.e
Juventus = 13
Total = 99
Therefore, the probability that the 2nd pick is Juventus is given below:
P(J2) = 13/99
Now, we can obtain the probability that the 1st and 2nd student prefer Juventus as follow:
P(J1 and J2) = P(J1) x P(J2)
P(J1) = 14/100
P(J2) = 13/99
P(J1 and J2) = P(J1) x P(J2)
P(J1 and J2) = 14/100 x 13/99
P(J1 and J2) = 7/50 x 13/99
P(J1 and J2) = 91/4950
Therefore, the probability that the 1st and 2nd student prefer Juventus is 91/4950
The equation of line CD is y = −2x − 2. What is the equation of a line parallel to line CD in slope-intercept form that contains point (4, 5)?
y = −2x + 13
y = negative one halfx + 7
y = negative one halfx + 3
y = −2x − 3
Answer:
y = −2x + 13
Step-by-step explanation:
equation of line slope intercept form is y = mx +c
where m is slope and c is y intercept
when two lines are parallel then their slope are equal.
_______________________________________
Given line
CD
y = −2x − 2
it is in form of y = mx +c
thus, m = -2
Given that other line parallel to CD y = −2x − 2
Thus, its slope will be -2.
Let the equation of required line be
y = mx +c (as slope will be -2)
Then equation of line will be
y = -2x +c
Given that this line contains (4,5) it will satisfy the equation y = -2x+c
using x = 4 and y = 5
we have
y = -2x +c
5 = -2*4 + c
=> 5 = -8 + c
=> c = 5+8 = 13
Thus, equation of line parallel to y = −2x − 2 and containing point(4,5) is
y = −2x + 13
Answer:
A. y = −2x + 13
Step-by-step explanation:
Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure. answwers: A) (x, y) → (x + 4, y + 5) B) (x, y) → (x – 4, y – 5) C) (x, y) → (x – 4, y + 5) D) (x, y) → (x + 5, y – 4)
Answer:
C. (x, y) -> (x - 4, y + 5)
Step-by-step explanation:
A is at (2, -2)
A' is at (-2, 3)
To get from 2 to -2, you must subtract 4, so (x - 4)
To get from -2 to 3, you must add 5, so (y + 5)
(x - 4, y + 5)
I hope this helps :))
The algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure should be option C. (x, y) -> (x - 4, y + 5)
Algebraic description:Since
A is at (2, -2)
A' is at (-2, 3)
So,
To get from 2 to -2, you should deduct 4, so (x - 4)
And,
To get from -2 to 3, you should deduct 5, so (y + 5)
Therefore,
(x - 4, y + 5)
Learn more about algebraic here: https://brainly.com/question/24754151
Anyone help with this too?
Answer:
36
Step-by-step explanation:
I cant be asked
Answer:
the answer is x = ( 5 + r )²
Step-by-step explanation:
I hope this was helpful
A new television set was recently purchased for the common room in a Residence Hall for $ 499.20 including tax. If the tax rate is 4 %, find the price of the television set before taxes. $______(Type an integer or a decimal rounded to two decimal places.)
Answer: $479.20
Step-by-step explanation:
[tex]499.20*0.04=19.968[/tex]
[tex]round \\[/tex] [tex]19.968[/tex]
= 20
tax= $20
[tex]499.20-20=479.2[/tex]
The price of the TV before tax was $479.20
Neil is making colorful friendship bracelets for 6 of his friends. He has all of the colors of
thread he plans to use except for green. If every bracelet uses 22 inches of each color of
thread, how many feet of green thread should Neil buy from the craft store?
Answer:
11 feet(or 132 inches)
Step-by-step explanation:
Since there are 6 bracelets to make, we can multiply 22 and 6 to get 132.
The correct unit / format to answer this is in feet and all we have right now is the amount of inches we must convert.
132 inches converted into feet can be found by dividing by the amount of inches there are in a 1 foot.
Since there are 12 inches in a foot, we can divide 132 by 12 to get 11.
some steps to construct an angle MNT congruent to angle pqr
You work for a florist. Normally, it takes you 20 hours to assemble 10 flower arrangements. How long does it take you to assemble one flower arrangement?
Answer:
2 hours
Step-by-step explanation:
We want to find the unit rate, or time per flower arrangement.
To find the unit rate, divide the number of hours by the number of flower arrangements.
hours/flower arrangements
It takes 20 hours to assemble 10 flower arrangements.
20 hours/ 10 flower arrangements
Divide 20 by 10 (20/10=2)
2 hours/ flower arrangement
It take 2 hours to assemble one flower arrangment.
Rewrite in radical form PLEASE HELP
Answer:
b)7c∛d⁵
or
c) 7c∛d⁵
Both options are the same
Step-by-step explanation:
In the above diagram, we are asked to simplify this:
= ∜c × 2d⁴/³ ×1/2c¾ ×7∛d
Collect the like terms
= ∜c × 1/2c³/⁴ × 2d⁴/³ × 7∛d
= c¹/⁴ × 1/2c³/⁴ × 2d⁴/³ × 7d¹/³
= [1 × 1/2c(¹/⁴ + ³/⁴)] × [2 × 7d(⁴/³ +¹/³)
= 1/2c(¹) × 14d(⁵/³)
= 1/2c× 14d(⁵/³)
Collect the whole number together
= 1/2× 14 [C × d(⁵/³)]
= 7cd⁵/³
Writing it in a radical form
= 7c∛d⁵
The cities A, B, and C, in respective order, lie approximately in a straight line. The distance from city A to city B is 100 miles. The distance from city A to city C is 110 miles. Find the distance from city B to city C
Answer:
10 miles
Step-by-step explanation:
A & B is 100
A & C is 110
the difference is 10, Which should make B & C 10 miles
The distance from city B to city C will be 10 miles.
What are collinear points?An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.
Let A, B, C, and D be the collinear points. Then the condition of the collinear will be
AB + BC = AC
The cities A, B, and C, in respective order, lie approximately in a straight line. The distance from city A to city B is 100 miles. The distance from city A to city C is 110 miles.
The distance from city B to city C will be given as,
AB + BC = AC
100 + BC = 110
BC = 110 - 100
BC = 10 miles
The distance from city B to city C will be 10 miles.
More about the collinear points link is given below.
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What is the volume of the rectangular prism below? (Don't forget to
label your answer!)
Answer: 84 3/8 or 84.375 inches cubed
Step-by-step explanation:
4 1/2 * 5 = 22 1/2
22 1/2 * 3 3/4 = 45/2 * 15/4 = 675/8
675/8 = 84 3/8 or 84.375
If the two factors in a multiplication problem are integers with different signs how does the product compared to other number?
Answer and Step-by-step explanation:
Well, the product would not change much. If we took the problem -3*7 it has one negative number and one positive number. Now, the rule is when there is two different signs, the answer becomes negative right away. So, your answer would be -21. If the integers were the same, the equation would be 3*7=21. Therefore, there is not much change in the product only the signs.
Select the correct shapes.
Select the shapes that are similar to shaoe A
Answer:
A , B and C are similar to each other
Step-by-step explanation:
Please give me branlest
Find the exact values of the following, giving your answers as fractions.
a) 2^-3
b) 3^-2
c) 10^-4
Answer:
a) 1/8
b) 1/9
c) 1/10,000
Step-by-step explanation:
When a number is raised to a negative exponent, that means that the answer will be less than one. The format is:
x^-y = 1/x^y (i apologize, exponents on here are really messy)
Ok so for a, you get 1/2^3. 2^3 = 8, so your resulting fraction is 1/8
b). 1/3^2. 3^2 = 9, so your resulting fraction is 1/9
c). 1/10^4. 10^4 = 10,000, so your resulting fraction is 1/10,000.
Sorry fractions and exponents don't work well on my computer. Hope this helps!
It costs $38 for 2 people to go to the movie theater, 40% of the money was for snacks What was the cost of each movie ticket?
Answer:
$11.40
Step-by-step explanation:
$38 for 2 people to go to the movie theater.
38/2=19
$19 for each person to go to the movie theater.
40% of the money is for snacks, the movie ticket must be 60% of the money.
19×60%
19×60/100=11.4
The cost of each movie ticket is $11.40
Answer:
$11.4
Step-by-step explanation:
Total Cost = $38
Snacks:
=> [tex]\frac{40}{100}* 38[/tex]
=> $15.2
Left for 2 tickets:
=> $38-$15.2
=> $22.8
For 1 ticket:
=> $22.8/2
=> $11.4