The tortoise and the hare are having a race.In this tale,the tortoise moves 50 ft per hr while the hare moves at 259ft per hour. The tortoise takes 8hrs longer than the hare to finish. a. Let t represent the unknown time in hours that it took the hare to complete the race,
Write an expression (not an equation!) representing the time it took the tortoise to finish
the race.
b. Write two equations that represent the race, one for the hare and one for the tortoise.
c. What is the distance of the race?
Answer:
Step-by-step explanation:
1). Let the distance of the race = x feet
Speed of hare = 250 feet per hour
If it takes the time to complete the race = t hours
Since, Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
250 = [tex]\frac{x}{t}[/tex]
t = [tex]\frac{x}{250}[/tex]
2). Speed of tortoise = 50 feet per hour
Time taken by the tortoise [tex]t_1=\frac{x}{50}[/tex]
So the equations will be,
t = [tex]\frac{x}{250}[/tex] -------(1)
[tex]t_1=\frac{x}{50}[/tex] -------(2)
3). Since, tortoise took 8 hours longer than hare,
[tex]t_1[/tex] - t = 8
[tex]\frac{x}{50}- \frac{x}{250}=8[/tex]
[tex]\frac{(5-1)x}{250}=8[/tex]
[tex]\frac{4x}{250}=8[/tex]
x = [tex]\frac{250\times 8}{4}[/tex]
x = 500 feet
Pls help I’ll brainlest ASAP
Answer:
He is 15 years old.
Step-by-step explanation:
I hope this helps :)
Answer:
Artaud is 15 years old
Step-by-step explanation:
Imagine Artaud is x yearrs old.
Now, turning the words in the problem into math equations, we get:
-x + 42 = 27.
Solving for x, we get:
-x = -15
x = 15.
So, Artaud is 15 years old.
If student D can solve 60% of multiple choice questions and Student B can solve 51% of the multiple choice questions and Student C can solve 57%. The students are unaware of each other.
a) At least one can be solved
b) Probability at most one of them can be solved
c) Probability that neither of them can be solved
d) Exactly two them can be solved
At a factory that produces pistons for cars, Machine 1 produced 174 satisfactory pistons and 116 unsatisfactory pistons today. Machine 2 produced 180 satisfactory pistons and 20 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory
Answer:
[tex]0.7[/tex] is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory
Step-by-step explanation:
The two events are independent of each other.
Hence the probability of choosing satisfactory piston from Machine 1 and unsatisfactory piston from Machine 2 is equal probability of choosing satisfactory piston from Machine 1 + probability of choosing unsatisfactory piston from Machine 2
Substituting the given values we get
Probability of choosing satisfactory piston from Machine 1 and unsatisfactory piston from Machine 2 =[tex]\frac{174}{174 +116} + \frac{20}{180 +20}[/tex]
=[tex]\frac{174}{174 +116} + \frac{20}{180 +20}[/tex]
=[tex]= \frac{174}{290} + \frac{20}{200}\\= 0.6 + 0.1\\= 0.7[/tex]
A company produces two types of jackets; windbreakers and rainbreakers. The company has at most 61 hours of finishing time per week and 67 hours of packaging time per week. Each windbreaker jacket takes 59 minutes of finishing time and 21 minutes of packaging time per week, whereas each rainbreaker jacket takes 58 minutes of finishing time and 34 minutes of packaging time per week. The company's profit for each windbreaker and rainbreaker jacket is 28 and 41, respectively. Let x denote the number of windbreaker jackets they should produce and y denote the number of rainbreaker jackets they should produce. The company wants to maximize profit. Set up the Linear Programming Problem for this situation.
Answer:
Max p = 28x + 41y
Subject to
59x + 58y ≤ 3660
21x + 34y ≤ 4020
x ≥ 0, y ≥ 0
Step-by-step explanation:
As given ,
Windbreakers Rain breakers Total
Finishing time 59 min 58 min 61 hr
Packaging time 21 min 34 min 68 hr
Profit 28 41
Let
The number of windbreaker jackets they should produce = x
The number of rain breaker jackets they should produce = y
As given,
The company wants to maximize profit.
⇒ Maximum Profit , p = 28x + 41 y
Now,
As 1 hour = 60 min
⇒61 hours = 61×60 = 3660 min
and 67 hours = 67×60 = 4020 min
∴ we get
The equations become
59x + 58y ≤ 3660
21x + 34y ≤ 4020
x ≥ 0, y ≥ 0
So, the Linear Programming Problem (LPP) for this problem is -
Max p = 28x + 41y
Subject to
59x + 58y ≤ 3660
21x + 34y ≤ 4020
x ≥ 0, y ≥ 0
Mid-Mod 3 Review
Name
1 Lisa used 5 orange juice containers, From the fust container, she poured out gallon of
orange juice. She then poured out 'h gallon from each of the four remaining containers,
a. How much orange juice did Lisa pour out in all? Show and label all your work.
Write a ratio, in simplest form, and a percent for the shaded area. (3x4)
3/10, 27%
1/2, 50%
1/3, 33.33%
3/10, 30%
Please help......................
18.9 or 18 9/10 or b or the second option.
Answer:
it's 18 9/10
Step-by-step explanation:
M is the midpoint of PA.
8x - 1
M
2x + 17 A
PM =
Use the given functions to set up and simplify PM
M =
PA =
8x - 1
M=
2x + 17A
PM=
If you score a 99, what percentage of the population scored above you?
Answer:
1%
Step-by-step explanation:
Answer:
1% pf the population scored above you
Step-by-step explanation:
make brainliest
Need help super fast pls help
Answer:
My answer is 8
Step-by-step explanation:
I calculate the area of all the shapes and added them together
the square comes first = the formlula = a to the power of 2 or just L x W = 2 x 2 = 4
The traingles - the formula = the height x base/2 2 x 2 /2 = 2 ( but there are two traingles so) 2 x 2 = 4
add the two shapes areas together = 4+4 = 8
12.6d07
Find the probability.
In one town, 47% of all voters are Democrats. If two voters are randomly selected for a
survey, find the probability that they are both Democrats.
Select one:
a. 0.221
b. 0.940
c. 0.470
d. 0.216
Answer:
A
Step-by-step explanation:
The fact you need to use is 47%
47/100 * 47/100 = 2209 / 10000 = 0.221
If the turning point is lower than the nearby point it's called a
Answer:
Step-by-step explanation:
Local minimum. It would be the minimum value of the function not including the end points. If you are including the end points, its an absolute minimum
Line passes through point (1, 7) and point (-2, 4). What is the slope of this line?
The slope of the line is 1.
The slope of the line is 1 because the line moves ror goes up from left to right, making it a positive. The line also moves one block over and one block up.
Answer:
1
Step-by-step explanation:
Suppose that f (x) = 1.5x2 for -1 < x < 1 and f (x) = 0 otherwise. Determine the following probabilities.
a. P(0 < X)
b. P(0.5 < X)
c. P(-0.5 = X = 0.5)
d. P(X<-2)
e. P(X < 0 or X>-0.5)
f. Determine x such that P(x < X) = 0.05.
Answer:
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Step-by-step explanation:
Given that;
f(x) = 1.5x²
Now. the probabilities would be the integral of the given function from (-1 to 1)
a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
= (1/2)x³
= 1/2 - 0
= 0.5
Therefore; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
this will also be done in the same way except that, the limits changes to { 0.5 to 1]
= (1)³/2 - (0.5)³ /2
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
= (0.5)³/2 - (-0.5)³/2
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let the value be 'a'
Then, integral from -1 to a will = 0.05
a³ - (-1)³ = 0.05 × 2
a³ + 1 = 0.10
a³ = 0.10 - 1
a³ = -0.9
a = ∛-0.9
a = -0.9654
Therefore, value of x is -0.9654
a) P(0 < X) = 0.5
b) P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5) = 0.125
d) P(X< -2) = 0
e) P(X < 0 or X>-0.5) = 1
f) value of x is -0.9654
Determine the following probabilities:a) P(0 < X)
P(X > 0)
⇒ Integral from 0 to 1 of f(x)
[tex]= (1\div 2)x^3\\\\= 1\div2 - 0[/tex]
= 0.5
So; P(0 < X) = 0.5
b) P(0.5 < X)
P(X > 0.5)
Now
[tex]= (1)^3\div 2 - (0.5)^3 \div2[/tex]
= 0.4375
Therefore; P(0.5 < X) = 0.4375
c) P(-0.5 = X = 0.5)
The limits become [-0.5 , 0.5]
[tex]= (0.5)^3\div 2 - (-0.5)^3\div 2[/tex]
= 0.125
Therefore; P(-0.5 = X = 0.5) = 0.125
d) P(X<-2)
since value of f(x) = 0 in that region
Therefore P(X< -2) = 0
e) P(X < 0 or X>-0.5)
= P(X < 0) + P(X > -0.5) - P( -0.5 < X < 0 )
= 0.5 + 0.5625 - 0.0625
= 1
Therefore; P(X < 0 or X>-0.5) = 1
f) Determine x such that P(x < X) = 0.05.
Let us assume the value be 'a'
So, integral from -1 to a will = 0.05
[tex]a^3 - (-1)^3 = 0.05 \times 2\\\\a^3 + 1 = 0.10\\\\a^3 = 0.10 - 1\\\\a^3 = -0.9\\\\a = \sqrt[3]{-0.9}[/tex]
a = -0.9654
Therefore, the value of x is -0.9654
Learn more about the probabilities here: https://brainly.com/question/24710931
if cos theta = 3/5, then tan theta =
Step-by-step explanation:
cos theta=3/5
theta=53.13°
tan theta =1.33
PLEASE HELP GEOMETRY
Answer:
2x=8
x=4
Step-by-step explanation:
The diameter of the raw cookie is 2 1 2 inches. After baking the cookie, the diameter is 5 1 2 inches. By what factor does the cookie expand?
Answer:
[tex]Factor = 220 \%[/tex]
Step-by-step explanation:
Given
[tex]Initial = 2\frac{1}{2}[/tex]
[tex]Final = 5\frac{1}{2}[/tex]
Required
Determine the factor of increment
First, we calculate the percentage increment
[tex]\% Increment = \frac{Final - Initial}{Initial} * 100\%[/tex]
Substitute values for Final and Initial
[tex]\% Increment = \frac{5\frac{1}{2} - 2\frac{1}{2}}{2\frac{1}{2}} * 100\%[/tex]
Express fractions as decimals
[tex]\% Increment = \frac{5.5 - 2.5}{2.5} * 100\%[/tex]
[tex]\% Increment = \frac{3}{2.5} * 100\%[/tex]
[tex]\% Increment = \frac{3* 100}{2.5} \%[/tex]
[tex]\% Increment = \frac{300}{2.5} \%[/tex]
[tex]\% Increment = 120 \%[/tex]
So, the factor of increment is:
[tex]Factor = 100\% + Increment[/tex]
[tex]Factor = 100\% + 120 \%[/tex]
[tex]Factor = 220 \%[/tex]
Which of these polygons is not a regular polygon?
B
С
D
А
B
A
Answer:
B. A regular polygon is a shape with sides that are all equal to each other.
We see that for shape B, the sides are not equal to each other, as some sides are longer than others.
Hope this helps!
11. There are 14 boys and 16 girls in Mr. Allen's
class. What is the ratio of girls to the total
number of students in the class? Write the
ratio in 3 ways.
Answer:
16 : 30, 16 to 30, 16/30
Step-by-step explanation:
Answer:
The ratio of boys to girls in the simplest form is 7:8
Step-by-step explanation:
There are 14 boys and 16 girls in a class. The ratio of boys to girls in the class is 14:16 or 7:8.
6 is 30% of what number
Answer:
1.8
Step-by-step explanation:
Answer:
6 is 30 percent of 20 STEP 1 6 = 30% × Y
STEP 2 6 =
30
100
× Y
Multiplying both sides by 100 and dividing both sides of the equation by 30 we will arrive at:
STEP 3 Y = 6 ×
100
30
STEP 4 Y = 6 × 100 ÷ 30
STEP 5 Y = 20
Finally, we have found the value of Y which is 20 and that is our answer.
You can easily calculate a similar type of calculation by using any regular calculator, simply enter 6 × 100 ÷ 30 and you will get your answer which is 20
Step-by-step explanation:
PLEASE HELP WILL GIVE BRAINLIST
y is directly proportional to x.
(y = 44
when
x = 4.)
Find a mathematical model that represents the statement. (Determine the constant of proportionality.)
Answer:
11
Step-by-step explanation:
Trust me
Answer:
Step-by-step explanation:
directly proportional means it is in the form
y=kx, given y=44 and x=4
44=4k
k=11
Which expression is the simplest form of 5(x-3)-3(2x+4)/9 ?
A. -x-3/9
B. -x-27/9 C.11x-27/9
D.-x-3
y=-2y-4 and y=1/2x-5
solve by systems of equations
pls help I need help ALL I NEED IS THE WORK PLSSSS HELP
Answer:
1. Y = -4/3
2. 2x = 2y + 10
Step-by-step explanation:
1. y =− 2y − 4
Step 1: Add 2y to both sides.
y + 2y = −2y − 4 + 2y
3y = −4
Step 2: Divide both sides by 3.
3y/3 = -4/3
y = -4/3
2. solve for x
y=1/2x-5
Step 1: Flip the equation.
1/2x−5=y
Step 2: Add 5 to both sides.
1/2x−5+5=y+5
1/2x=y+5
Step 3: Divide both sides by 1/2.
1/2x/1/2=y+5/1/2
x=2y+10
not sure if this will help but here you go :)
What is this fraction shown above?
Answer:
1/3 because they have only colored on out of three, so the answer will be 1/3. Hope this helped!
Step-by-step explanation:
A rectangular garden has a width of 10 feet and a length of 14 feet. A cement walkway is added around the outside of the garden. The area of the garden and the walkway together are 320 square feet. What is the width of the walkway
Answer:
The width of the walkway is of 12.86 feet.
Step-by-step explanation:
Area of a rectangle:
The area of a rectangle of length l and width w is given by:
A = lw
A rectangular garden has a width of 10 feet and a length of 14 feet.
So the area of the rectangular garden is of 10*14 = 140 square feet.
The area of the garden and the walkway together are 320 square feet.
So the area of the walkaway is of 320 - 140 = 180 square feet.
What is the width of the walkway
It has the same length of the garden, of 14. So
[tex]14w = 180[/tex]
[tex]w = \frac{180}{14}[/tex]
[tex]w = 12.86[/tex]
The width of the walkway is of 12.86 feet.
how do you solve for x? 3 + 2x = 4y
Answer:
x= 2y - 3/2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x=2y - 3/2
Step-by-step explanation:
Which expression is equivalent to 2(3 - x) - 12 + 4x
1. 3x - 6
2. 3x - 7
3. 2x - 6
4. 2x - 7
A soft drink-dispensing machine uses paper cups that hold a maximum of 12 ounces. The machine is set to dispense a mean of 10 ounces of the drink. Because of an imprecise process, the amount dispensed actually varies; it is normally distributed with a standard deviation of 1 ounce. If we simulated the filling process, and had the random number .564, how many ounces would the cup contain? Give your answer to 3 decimal places.
Answer:
The cup would contain 10.16 ounces.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Mean of 10 ounces, standard deviation of 1 ounce:
This means that [tex]\mu = 10, \sigma = 1[/tex]
If we simulated the filling process, and had the random number .564, how many ounces would the cup contain?
This means that we have to find X when Z has a pvalue of 0.564. So X when Z = 0.16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.16 = \frac{X - 10}{1}[/tex]
[tex]X - 10 = 0.16*1[/tex]
[tex]X = 10.16[/tex]
The cup would contain 10.16 ounces.