Answer:
a) 20r + 20w = 500, 10r + 35w = 500
b) r = 15, w = 10
c) 900 calories
Explanation:
Let running time be r, walking time be w
a) Hence, make equation's:
20r + 20w = 500... equation 1
10r + 35w = 500... equation 2
b) Determine the value of the variables by solving simultaneously.
⇒ (500 - 20w)/20 = (500 - 35w)/10
cross multiply
⇒ 10(500 - 20w) = 20(500 - 35w)
multiply
⇒ 5000 - 200w = 10000 - 700w
shift sides
⇒ -200w + 700w = 10000 - 5000
simplify
⇒ 500w = 5000
divide both sides by 500
⇒ w = 10
Now find the value of variable r,
⇒ r = (500 - 20w)/20
insert w = 10
⇒ r = (500 - 20(10))/20
simplify
⇒ r = 15
Hence the value of r is 15 and w is 10
c) Find calories burnt after one hours of running: [1 hours = 60 minutes]
calories = 60r = 60(15) = 900 calories
Hence, he can burn 900 calories after one hours of running.
Solve the equation. Determine the solution(s) and any extraneous solution.
√2x = x - 4
I assume you mean the equation
√(2x) = x - 4
Take the square of both sides. Note that √(2x) is a non-negative number, so any solution we find must also satisfy x - 4 ≥ 0, or x ≥ 4.
(√(2x))² = (x - 4)²
2x = x² - 8x + 16
x² - 10x + 16 = 0
(x - 8) (x - 2) = 0
x - 8 = 0 or x - 2 = 0
x = 8 or x = 2
If x = 2, then x ≥ 4 is false. The only solution is then x = 8.
You deposit $800 in an account that pays 8% annual interest compounded quarterly. About how
long will it take for the balance to triple?
find the solution set of the inequality 52-3x<-14
Answer:
22<x
Step-by-step explanation:
52-3x<-14
66<3x
(we divide both sides to 3)
22<x
A couple is looking for a mortgage to purchase a house for $256,000. If the bank requires a 5% down payment, what is the amount to be mortgaged?
$128000
$12800
$243200
$25600
7cm
10cm
1 Define the perimeter of any closed two-dimensional shape.
2 Hence, calculate the perimeter of the figure above.
If m(x) = x2 3 and n(x) = 5x 9, which expression is equivalent to (mn)(x)?
These are functions inside another function. The resulting composite function is given as (5x+9)^2 + 3
Composite functionsThese are functions inside another function. Given the following functions
m(x) = x^2 +3
n(x) = 5x +9
We are to solve for the function m(n(x))
m(n(x)) = m(5x+9)
Substitute 5x +9 into m(x) to have:
m(n(x)) = (5x+9)^2 + 3
Hence the resulting composite function is given as (5x+9)^2 + 3
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The map uses a scale 1 inch = 880 ft. On the map, How many inches represent 2 miles?
PLS HURRY
Answer:
[tex]12\ inches[/tex]
Step-by-step explanation:
Step 1: Determine how many ft are in 2 miles
[tex]1\ mile = 5280\ ft[/tex]
[tex]2\ miles = 5280\ ft * 2[/tex]
[tex]2\ miles = 10560\ ft[/tex]
Step 2: Determine how many 880 ft's are in 10560 ft
[tex]10560\ ft / 880\ ft[/tex]
[tex]12[/tex]
Answer: [tex]12\ inches[/tex]
6a+6b Factorise these expressions.
find the perimeter of the figure below, in centimeters
Answer:
73
Step-by-step explanation:
(7.7 * 2) + (9.6 * 6) = 74
Which is Greater, negative 2 and 2 fifths or negative 2 and 1 forth?
Answer:
-2 and 1/4
Step-by-step explanation:
1/4 is equal to 0.25
2/5 is equal to 0.40
Because it is negative, 1/4 is considered greater.
Anna is painting the outside of cardboard box for an art project. The box is a rectangular prism that has a lenght of 24 inches, a width of 24 inches, and a height of 30 inches. Fine the Surface area of the cardboard box.
i need help on this please
Answer:
C
You have to use radius not the diameter
Kofi is 8years old and his mother is 42. In how many years will his mother's age be 3 times more than kofi's age?
Answer:
After 9 years mother's age will be 3 times more than kofi's age .
Step-by-step explanation:
Given
Age of Kofi = 8 years
Age of Mother = 42 years
According to question , 3 times more than kofi's age .
=> ( 8+ x ) 3 = 42 + x
=> 24 + 3x = 42 + x
=> 3x - x = 42 - 24
=> 2x = 18
=> x = 18/2
=> 9
After 9 years ,
Age of Kofi = 8 + 9 = 17 years Age of Mother = 42 + 9 = 51 yearsLast year, the number of skateboards produced by a skateboard company is normally distributed. The standard deviation of skateboards produced was 20 skateboards. They found they produced up to 280 skateboards on 93.32% of the days last year. Use this information to find the average number of skateboards produced per day last year.
The average number of skateboards produced per day last year is 310.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
We have:
The standard deviation of skateboards produced was 20 skateboards. They found they produced up to 280 skateboards on 93.32% of the days last year.
Z- score at 93.32% is -1.5
We know:
[tex]\rm Z = \dfrac{(x - \mu)}{\sigma}[/tex]
[tex]\rm -1.5 = \dfrac{(280 - \mu)}{20}[/tex]
μ = 280 + 30
μ = 310
Thus, the average number of skateboards produced per day last year is 310.
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A cosmetologist conducted a survey to see which color hair was most popular among her customers. She surveyed 160 people. The results are shown in this circle chart.
How many more customers chose brown than red?
24 customers
35 customers
40 customers
88 customers
Circle graph titled Hair Color showing colors by percentage. Sectors are labeled Brown, 40 percent. Red, 15 percent. Black, 25 percent. Blonde, 20 percent.
Answer:
40 customers
Step-by-step explanation:
40% brown,
25% black
20% blonde
15% red
100% = 160
(40* 160)/ 100
6400 / 100 = 64
40% = 64 customers
(15 * 160)/100
2400/100 = 24
15% = 24 customers
64 customers - 24 customers =40 customers.
For the exact binomial test, we are using the binomial distribution assuming ____________________ to compute the probability of observing the equal number of successes or more extreme number of successes.
Answer:
The proportion defined by the null hypothesis.
Step-by-step explanation:
Show how to write 3/4 with the denominator 12
Write the number shown in standard notation. 1.02 x 10 A. 1,020,000 B. 102,000,000 C. 102,000 D. 10,200,000
i think its c
Step-by-step explanation:
don't count me on this
Your answer should be A please mark brainlest
I need help asap!!!
Answer:
x-30+x+50=180(being co interior angle)
2x+20=180
2x=180-20
x=160/2
x=80
putting the value of x in x-30
80-30=50
again
y+50=180(being co interior angle)
y=180-50
y=130
Step-by-step explanation:
hope this will help you
They are same side ineterior so supplementary
x-30+x+50=1802x+20=1802x=160x=80Again
x-30+y=180x+y=21080+y=210y=1307513% [tex]\frac{5}{3x^{2} }[/tex] x³ Find the Product Show All work!
[tex]\\ \rm\Rrightarrow \dfrac{7513/100\times 5x^3}{3x^2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{75.13(5)x^3}{3x^2}[/tex]
[tex]\\ \rm\Rrightarrow {125.22x}[/tex]
The radius of a small ornament in the shape of a sphere is 2 inches. what is the approximate volume of the ornament? use 3.14 for pi. round to the nearest tenth of a cubic inch. recall the formula v = four-thirds pi r cubed. inches cubed
Answer: 33 is your answer my love.
Step-by-step explanation: Hope this helps.
Answer:
33 give the guy above me branliest
Step-by-step explanation:
Can someone help me with the steps to create the formula? It involves quadratics
The formula of the quadratic function passing through the points (-2,0), (8,0) and (2, -24) is f(x) = x² - 6x - 16
How to create the formula?The points are given as:
(-2,0) , (8,0) and (2, -24)
The points (-2,0) and (8,0) are the zeros of the function.
So, we have:
f(x) = a(x + 2)(x -8)
Substitute (2, -24) in the above equation
-24 = a(2 + 2)(2 -8)
Evaluate the sum and the difference
-24 = a(4)(-6)
Divide both sides by -24
a = 1
Substitute a = 1 in f(x) = a(x + 2)(x -8)
f(x) = (x + 2)(x -8)
Expand
f(x) = x² + 2x - 8x - 16
Evaluate the like terms
f(x) = x² - 6x - 16
Hence, the formula of the quadratic function is f(x) = x² - 6x - 16
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Solve this system of equations by
using the elimination method.
3x + 3y = 18
2x+y = 4
([?], [ ])
Answer:
solution: (x,y)=(-2,8)
Step-by-step explanation:
1) 3x+3y=18
2x+y=4
2) -x-y=-6
2x+y=4
3) x=-2
4) 2x(-2)+y=4
5) y=8
6) (x,y)=(2,8)
and that is :D
You are the manager at the town pool. You need to build a fence around the new children's pool area. The pool is 5 feet wide by 8 feet long. You want the fence to be the same distance "x ft" from all sides of the pool, except you need to put a lifeguard chair at one end of the width, so the fence should be twice as far away from the pool on that one side. How many linear feet of fencing must you buy? (Use an algebraic approach to receive credit for your solution)
The length of the fence which needs to be put around the pool will be 26 feet.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
You are the manager of the town pool.
You need to build a fence around the new children's pool area.
The pool is 5 feet wide by 8 feet long.
You want the fence to be the same distance "x ft" from all sides of the pool, except you need to put a lifeguard chair at one end of the width, so the fence should be twice as far away from the pool on that one side.
Then the length of the fence which needs to be put around the pool will be
P = 2 (5 + 8)
P = 2 x 13
P = 26 ft
Then the length of the fence which needs to be put around the pool will be 26 feet.
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Victoria had $200 in her account at the end of one year. at the first of each subsequent year she deposits $15 into the account and earns 2% interest on the new balance, compounded annually. which recursive formula represents the total amount of money in victoria’s account at the end of the nth year?
The recursive formula is; 1.02(an-1 + 15) a1=200 based on the question.
What is a recursive formula?The term recursive formula can be used to describe the derivation of a term in a sequence based on the previous term.
Given the information in the question, the recursive formula is; 1.02(an-1 + 15) a1=200.
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Billy has been on a diet for
22
weeks. He has averaged a loss of
0.73
pounds each week.
How many total pounds has Billy lost?
Answer:
16.06 lbs
Step-by-step explanation:
I believe, I did~ 0.73x22
Helppp meee please so confused
Answer:
1. Blue = 8 votes
2. Green = 4 votes
3. Yellow = 6 votes
4. Red = 2 votes the first 2 votes one
5. Pink = 2 votes the second one that says 2 votes.
Step-by-step explanation:
okay I understand this.
You just use the colors from above and fill them in in order.
Answer:
1.blue has got 8 number of votes
2.yellow has got 4 number of votes
3.green has got 6 number of votes
4.red has got 2 number of votes
and the last one is written there
Explanation:
I hope it helps
For the following sequence.
1/2 2/3 3/4 4/5 5/6
Describe the term to term rule.
...............................................
Calculate the 10th term
.............................................
Answer:
Term-to-term rule: Adding one to the numerator and the denominator
10th term: 10/11
Step-by-step explanation:
Thank you for answer, if you do
The majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.
What is the meaning of dot plot?The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.
The data given in the table is-
3.01, 3.26, 3.26, 3.79, 4.26, 4.34, 5.17, 5.94, 5.94, 5.94, 5.94, 7.14, 7.54, 7.90, 8.03, 9.15, 10.25, 11.98, 12.84, 19.86
The majority of data is between 3.01 to 7.90. The percentage of these data values to total data is 70%.
When data is represented in dot plot, then the distribution is a normal distribution. The data set has the value of median and mode equal to 5.94.
Median=5.94
Mode=5.94
Thus, the majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.
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Consider functions f and g
vvvv
Answer:
C. 77x⁷ + 78x⁶ - 27x⁵
Step-by-step explanation:
Operation of functions
f(x) g(x)
f(x) • g(x) = (11x³ - 3x²)(7x⁴ + 9x³)
Simplify or expand
(11x³ - 3x²)(7x⁴ + 9x³)
Expand the expression
11x³ × 7x⁴ + 11x³ × 9x³ - 3x² × 7x⁴ - 3x² × 9x³
Multiply
77x⁷ + 99x⁶ - 21x⁶ - 27x⁵
Combine like terms
77x⁷ + 78x⁶ - 27x⁵
Hope this helps and have a nice day