Answer: the sale price of one hammer is $6.8
the sale price of one nail is $0.16
Step-by-step explanation:
Let x represent the sale price of one hammer.
Let y represent the sale price of one nail.
His first customer bought 3 hammers and 16 nails for $22.96. It means that
3x + 16y = 22.96- - - - - - - - -1
His last customer bought 2 hammers and 20 nails for $16.80. It means that
2x + 20y = 16.8- - - - - - - - - 2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 32y = 45.92
6x + 60y = 50.4
Subtracting, it becomes
- 28y = - 4.48
y = - 4.48/- 28
y = 0.16
Substituting y = 0.16 into equation 2, it becomes
2x + 20 × 0.16 = 16.8
2x + 3.2 = 16.8
2x = 16.8 - 3.2
2x = 13.6
x = 13.6/2
x = 6.8
Which of the following equations describes the line shown below ?
Given:
Points on the line are (-2, 4) and (-4, -8).
To find:
The equation of a line.
Solution:
[tex]x_1=-2, y_1=4, x_2=-4, y_2=-8[/tex]
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points.
[tex]$m=\frac{-8-4}{-4-(-2)}[/tex]
[tex]$m=\frac{-12}{-4+2}[/tex]
[tex]$m=\frac{-12}{-2}[/tex]
m = 6
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute [tex]x_1=-2, y_1=4[/tex] and m = 6
[tex]y-4=6(x-(-2))[/tex]
y - 4 = 6(x + 2)
Substitute [tex]x_1=-4, y_1=-8[/tex] and m =6 in point-slope formula.
[tex]y-(-8)=6(x-(-4))[/tex]
y + 8 = 6(x + 4)
Option A and Option D are the correct answers.
Therefore y - 4 = 6(x + 2) and y + 8 = 6(x + 4) are the equations describes the shown line.
A sphere has a diameter of 36 meters. What its exact volume?
Answer:
V = 7776 pi m^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We need to know the radius
r = d/2 = 36/2 = 18
V = 4/3 pi (18)^3
V = 4/3 * pi *5832
V = 7776 pi
We cannot approximate pi since we want the exact answer
Answer:
7776π cubic meters.
Step-by-step explanation:
Recall the volume formula for a sphere is
V = (4/3) π r^3
r = (1/2)*diameter = (1/2)*36 m = 18 meters
V = (4/3)*π*(18)^3 = 24,429.02447 cubic meters
However the problem wants an exact answer, and not an approximation, therefore I will express the volume in terms of simplified expressions.
V = (4/3)*π*(18)^3 = (4/3)*π * (3*6)^3 = 4 *π * (1/3)*(3^3) *(6^3)
V = 4 *π * (1/3)*(3^3) *(6^3) = 4*π * 9 * 6^3 = 7776π cubic meters.
How do you find the arc length in a circle given any angle?
You find the circumference and multiply it by the central angle. If the central angle is in degrees, you divide that by 360. If the central angle is in radians, you divide by 2pi.
The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random variable ranging from 2 to 7. Find the mean and standard deviation of this random variable. (Round your answers to 2 decimal places.) Mean Standard deviation
Answer:
The mean is 4.5 and the standard deviation is 1.44.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The mean of the uniform probability distribution is:
[tex]M = \frac{(a + b)}{2}[/tex]
The standard deviation of the uniform probability distribution is:
[tex]S = \sqrt{\frac{(b-a)^{2}}{12}}[/tex]
Uniformly distributed random variable ranging from 2 to 7.
This means that [tex]a = 2, b = 7[/tex].
So
[tex]M = \frac{(2 + 7)}{2} = 4.5[/tex]
[tex]S = \sqrt{\frac{(b-a)^{2}}{12}} = \sqrt{\frac{(7 - 2)^{2}}{12}} = 1.44[/tex]
The mean is 4.5 and the standard deviation is 1.44.
The diagram shows two different buttons and their weights.
12 grams
8 grams
c)
How many of each type of button are in the box?
To solve this problem, set up a system of equations with x and y representing the number of buttons. If there are 20 Weights of buttons in total, 20 of them weigh 12 grams and none weigh 8 grams.
To solve this problem, we can set up a system of equations. Let x be the number of buttons weighing 12 grams, and y be the number of buttons weighing 8 grams.
We can then write the following equations based on the information given:
x + y = total number of buttons
12x + 8y = total weight of the buttons
Substituting the given values, we have:
x + y = total number of buttons
12x + 8y = 240
From the first equation, we can express y in terms of x:
y = total number of buttons - x
Substituting this into the second equation:
12x + 8(total number of buttons - x) = 240
Simplifying:
12x + 8total number of buttons - 8x = 240
4x + 8total number of buttons = 240
4x = 240 - 8total number of buttons
4x = 8(30 - total number of buttons)
x = 2(30 - total number of buttons)
Since x and y represent the number of buttons, they must be whole numbers.
We can test different values for the total number of buttons to find a solution that satisfies this condition.
For example, if we assume there are 20 buttons in total:
x = 2(30 - 20) = 2(10) = 20
y = 20 - 20 = 0
Therefore, if there are 20 buttons in total, 20 of them weigh 12 grams and none weigh 8 grams.
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The probable question may be:
In a box, there are two types of buttons with different weights. One type of button weighs 12 grams, and the other type weighs 8 grams. If the total weight of the buttons in the box is 240 grams, how many buttons of each type are in the box?
The bricklayer exerted 150 newtons of force as he pushed the pushcart of bricks down
an alley that is 20 meters long. When the bricklayer reached the end of the alley, how
much work had he done?
Answer:
3000 N
Step-by-step explanation:
The work done by a force on an object is given as the product of the force applied on the object and the distance moved by the object.
Mathematically:
W = F * d
The force applied by the man is 150 N and the distance moved is 20 m. Hence, the work done by the man is:
W = 150 * 20 = 3000 J
The work done by the man is 3000 Joules.
Bill's golf bag contains 9 white golf balls, 6 yellow golf balls, 1 orange golf ball, and 1 pink golf ball. Without looking, Tim is going to take 1 golf ball out of his bag to tee off with and a different golf ball out to putt with. What is the probability of Tim teeing off with a white ball and putting with an orange ball? P(white, then orange) Are the events above independent or dependent events?
Final answer:
The probability of Tim teeing off with a white ball and putting with an orange ball is 0.0331. The events are dependent.
Explanation:
To calculate the probability of Tim teeing off with a white ball and putting with an orange ball, we need to consider the total number of balls in the bag and the number of white and orange balls.
There are a total of 9 white balls, 6 yellow balls, 1 orange ball, and 1 pink ball in the bag. The probability of Tim teeing off with a white ball is 9 out of 17, since he can choose any of the 9 white balls out of the total 17 balls. After Tim tees off with a white ball, there are now 8 white balls left in the bag.
Next, Tim needs to putt with an orange ball. The probability of Tim putting with an orange ball is 1 out of 16, since there is 1 orange ball left in the bag and a total of 16 balls.
To find the probability of both events happening, we multiply the two probabilities:
P(white, then orange) = P(white) × P(orange|white) = 9/17 × 1/16 = 9/272 = 0.0331 (rounded to four decimal places).
The events of teeing off with a white ball and putting with an orange ball are dependent events, as the outcome of the first event affects the probability of the second event.
WILL MARK AS BRAINLEST!!!!!!!!
A rectangular prism is 7.8 yards long and 7.4 yards high. Its volume is 461.76 cubic yards. What is the width of the rectangular prism?
Answer:
The width is 8 yards.
Step-by-step explanation:
[tex]\frac{461.76}{7.8\cdot7.4}=8[/tex]. Hope this helps!
Find an equation for the line that passes through the points (-3,-2) and (1,4)
Answer:
y=2/3x
Step-by-step explanation:
First, we have to find the slope, which is [tex]\frac{(y_{1} -y_{2})}{(x_{1}-x_{2}}[/tex]
(-3-1)/(-2-4)
-4/-6
2/3 is slope.
y=2/3x+-___
substitute in -3 from first point
y=-2+__=-2
y=2/3x+0
y=2/3x
Answer:
y + 2 = (3/2) (x+3) (point slope form)
Step-by-step explanation:
(see attached for reference)
Given
(x₁, y₁) = (-3,-2)
(x₂, y₂) = (1,4)
Since we are given 2 points, it would be easiest to express the equation of the line in point-slope form (see attached)
(y - y₁) = m (x - x₁)
we already have the values for x₁ and y₁, hence we only need to find the slope m (see 2nd attached graphic)
m = (y₂-y₁) / (x₂ - x₁)
= [4 - (-2) ] / [1 - (-3)]
= (4+2) / (1+3)
= 6/4
= 3/2
substituting the value for m and the values for x₁ and y₁:
(y - y₁) = m (x - x₁)
[y - (-2)] = (3/2) [x - (-3)]
y + 2 = (3/2) (x+3)
A teacher randomly chooses a two-person team from a group of four students. The first person chosen will
be the presenter and the second person will be the researcher. Two of the students, Amir and Aaron, are
boys. The other two students, Caitlin and Deniz, are girls. All the possible outcomes of the team selection
are listed below.
If we take outcomes 2, 3, 5, 6, 7, 8, 10, and 11 as a subset of the sample space, which of the statements
below describe this subset?
Answer:
•The subset consists of all of the outcomes where the team is made up of one boy and one girl
• the subset consists of all of the outcomes where the team is not made up of all boys and not made up of all girls.
Answer:
A & D
Step-by-step explanation:
KHAN
The Lopez family took a taxi to there next destination. The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled.When they arrived the total cost 37 dollars how far did they go in the taxi
Answer: 8.3
Step-by-step explanation: 37 divided by=12.3 then 12.3 - 4
Answer: the taxi travelled 11 miles
Step-by-step explanation:
Let x represent the number of miles that the taxi traveled.
The cost of the taxi was 4 dollars plus 3 dollars for each mile traveled. It means that the total cost of renting and driving the taxi over x miles is
4 + 3x
The Lopez rented the taxi and when they arrived at their destination, the total cost 37 dollars. It means that
4 + 3x = 37
3x = 37 - 4
3x = 33
x = 33/3
x = 11 miles
A recent study showed that the modern working person experiences an average of 2.1 hours per day of distractions (phone calls, emails, impromptu visits, etc.). A random sample of 50 workers for a large corporation found that these workers were distracted an average of 1.8 hours per day and the population standard deviation was 20 minutes. Estimate the true mean population distraction time with 90% confidence, and compare your answer to that of the study.
Answer:
True mean population distraction time with 90% confidence is
C.I[103.34 ,112.66] at 108
Step-by-step explanation:
Given:
Study Average hrs =2.1 =2.1 *60=126 minutes
For sample mean =1.8 *60= 108 minutes
S.D=20 and n=50
To Find:
True mean population distraction time with 90% confidence,
Solution:
90% C.I. means 90 % will fall in true mean and other will not .
So for that calculating the
Standard error=S.D/Sqrt(n)
S.E=20/Sqrt(50)
S.E=2.828
For 90% Confidence interval Z=1.65
C.I= mean±Z*Standard error
C.I=108±1.65*2.828
C.I=108±4.662
Hence C.I will range from 103.34 to 112.66
Study mean =126 minutes .
Here it ranges from 103.34 to 112.66
In this exercise we have to use the knowledge of probability to calculate this we will use percentage as:
[tex]C.I= 108[/tex]
Given the following information in the text we find that:
Study Average=126 minutesFor sample mean =108 minutesS.D=20 and n=50Then calculating the probability we find that:
[tex]Standard error=S.D/\sqrt(n)\\ S.E=20/\sqrt(50)\\ S.E=2.828\\ Z=1.65\\ C.I=108+4.662 [/tex]
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There are 4 green marbles and 6 yellow marbles in a bag. You want to find the compound probability of picking a green marble and a yellow marble. However, you do not put back the marble back into the bag. Is this an example of a dependent event or independent event?
Answer:
Dependent event because the sample space depends on the first event
Step-by-step explanation:
10 marbles total
4 green
6 yellow
1st pick green: Probability= 4/10
2nd pick yellow: Probability= 6/9
Dependent event because the sample space depends on the first event
5(3x+2)=8(2x-4) solve for x
Answer:
x = 42 i hope this helps! :)
Step-by-step explanation:
given 5(3x + 2) = 8(2x - 4)
distribute the 5 to both the 3x and the 2 15x + 10 = 8(2x - 4)
now distribute the 8 to both the 2x and the -4 15x + 10= 16x - 32
subtract 15x from both sides 10 = x - 32
add 32 to both sides 42 = x
flip the equation around so the x is first x = 42
answer x = 42
Jayden’s family took a road trip to the Grand Canyon. Jayden fell asleep 15% of the way through the trip if the total length of the trip was 1000 miles, how many miles had they travelled when Jayden fell asleep?
Answer:
150 miles
Step-by-step explanation:
0.15x1000=150
A graph creates a triangle with the x-axis, the line 3x-2y=0, and the line x+2y=10. Find the area of the triangle formed in square units.
Answer:
18.75
Step-by-step explanation:
To identify the vertices of this triangle, you need to find the x intercepts of both lines, as where their solutions match. Let's start with setting them equal to each other. If you subtract 10 from both sides of the second equation, then both equations are left equaling zero. You can also multiply both sides of the equation by -1 for easier solving later Now:
3x-2y=-2y-x+10
4x=10
x=2.5
y=3.75
This shows that the height of this triangle is 3.75. Now, to find the x intercepts of both equations, we simply have to plug in the y value as 0. For the first one, 3x-0=0, so x=0 as well and the coordinates are (0,0). For the second one, x+0=10, so x=10 and the coordinates are (10,0). This shows that the base is 10-0=10 units long. The formula for the area of a triangle is [tex]\frac{bh}{2}=\frac{10\cdot3.75}{2}=18.75[/tex]. Hope this helps!
Use the law of cosines to find each missing side. Round to the nearest tenth.
(I'm doing each individual question)
Answer:
x = 9.3
Step-by-step explanation:
The Law of Cosines
[tex] c^2 = a^2 + b^2 - 2ab \cos C [/tex]
[tex] x^2 = 15^2 + 13^2 - 2(15)(13) \cos 38^\circ [/tex]
[tex] x^2 = 225 + 169 - 2(15)(13) \cos 38^\circ [/tex]
[tex] x^2 = 394 - 390(0.7880) [/tex]
[tex] x^2 = 86.6758 [/tex]
[tex] x = \sqrt{86.6758} [/tex]
[tex] x = 9.3 [/tex]
Find the area of a circle with diameter 10 cm . Use the value 3.14 for π , and do not round your answer. Be sure to include the correct unit in your answer.
Formula for the area of a circle:
A = πr² [A = area r = radius]
The radius is [tex]\frac{1}{2}[/tex] (half) the diameter. Since the diameter = 10cm, the radius = 5cm.
You know:
r = 5cm Substitute/plug this into the equation
A = πr²
A = π(5)²
A = 25π -> A = 25(3.14)
A = 78.5cm²
The area of the circle when the diameter is 10 cm should be [tex]78.5\ cm^2[/tex].
Calculation of the area of the circle:Since the diameter is 10 cm
We know that
The diameter should be
[tex]= \pi r^2\\\\= 3.14\times 5^2\\\\= 25\times 3.14\\[/tex]
= [tex]78.5\ cm^2[/tex]
Hence, The area of the circle when the diameter is 10 cm should be [tex]78.5\ cm^2[/tex].
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5-x= -(x - 5)
how many solutions does this equation have
Answer:
Infinitely many solutions
Step-by-step explanation:
5-x= -(x - 5) ➡ 5 - x = -x + 5 add x to both sides and subtract 5 from both sides
5 - x - 5 + x = -x + x - 5 + 5 ➡0 = 0 in this case we say the equation has infinitely many solutions because whatever value you give for x there will always be a solution.
Sandra biked 7 kilometers on Wednesday. She biked 3 times as many kilometers on Thursday. How many total
meters did she bike?
What do you know? What do you need to find?
What question do you need to answer first?
How many meters did Sandra bike in all?
Which of the following sentences do you know? Select all that apply.
DA. Sandra biked 7 kilometers on Wednesday
OB. She biked 3 times as many kilometers on Thursday.
OC. How many total meters did she bike?
Answer:
A and B
Step-by-step explanation:
From what we know, Sandra biked 7 kilometers on Wednesday because of the statement, followed by how she biked 3x as many miles on Thursday. We do not know how many total meters she biked because it does not give us that information. Hope this helps!
Leila, Charlie, and Joe have a total of $144 in their wallets. Joe has 4 times what Leila has. Charlie has $6 more than Leila. How much does each have?
Answer:
The amounts of money each has are:
Joe = $92
Charlie = $29
Leila = $23
Step-by-step explanation:
To solve this, we will convert the statements into an equation, and use that to solve for the unknowns, as follows:
total amount = $144
Let Leila's share be S
Joe's share = 4 times Leila's = 4S
Charlie's share = $6 + Leila's share = 6 + S
Joe's share + Charlie's Share + Leila's Share = $144
4S + (6 + S) + S = 144
4S + 6 + S + S = 144
4S + 2S + 6 = 144
6S + 6 = 144
6S = 144 - 6 = 138
S = 138 ÷ 6 = $23
Therefore Leila's share 'S' = $23
Joe share= 4S = 4 × 23 = $92
Charlie's share = 6 + 23 = $29
If (− 4, −8) and (−10, −12) are the endpoints of a diameter of a circle, what is the equation of the circle?
A) (x + 7)^2 + (y + 10)^2 = 13
B) (x + 7)^2 + (y − 10)^2 = 12
C) (x − 7)^2 + (y − 10)^2 = 169
D) (x − 13)^2 + (y − 10)^2 = 13
Answer:
Correct option: A
(x + 7)^2 + (y + 10)^2 = 13
Step-by-step explanation:
First we need to find the center of the circle. We can find it calculating the midpoint of the diameter.
the x-coordinates of the diameter are -4 and -10, so the midpoint is:
(-4 -10)/2 = -7
the y-coordinates of the diameter are --8 and -12, so the midpoint is:
(-8 -12)/2 = -10
Now we need to find the radius of the circle, so we find the diameter and then find half of it.
The lenght of the diameter is the distance of the endpoints:
D = sqrt((-4+10)^2 + (-8+12)^2) = 7.21
radius = 7.21/2 = 3.605
The generic equation of the circle is:
(x - xc)^2 + (y - yc)^2 = r^2
So we have:
(x + 7)^2 + (y + 10)^2 = 13
Correct option: A
If f(x) = -x^2 – 1, and
g(x) = x + 5, then
g(f (x)) = [? ]x^2+[ ]x + [ ]
Answer:
g(f(x)) = - x² + 4
Step-by-step explanation:
To evaluate g(f(x)), substitute x = f(x) into g(x), that is
g(f(x))
= g(- x² - 1)
= - x² - 1 + 5
= - x² + 4
Scott runs 4 sprints of 20 yards each. If he continues his routine, how many practices will it take for Scott to have sprinted a total of 2 miles combined?
Answer:
It will take 44 practices for Scott to have sprinted a total of 2 miles combined
Step-by-step explanation:
This question can be solved using rules of three.
First step:
Scott practice is measured in yards.
We want to know how many practices it will take for him to have sprinted 2 miles.
So we pass 2 miles to yards
Each mile has 1760 yards.
So 2 miles is 1760*2 = 3520 yards.
A practice:
4 sprints of 20 yards each.
So 4*20 = 80 yards.
A practice is 80 yards. How many practices for 3520 yards?
1 practice - 80 yards
x practices - 3520 yards
80x = 3520
x = 3520/80
x = 44
It will take 44 practices for Scott to have sprinted a total of 2 miles combined
Here are the numbers of times 8 people ate out last month.
5, 6, 3, 3, 4, 4, 7, 7
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, click on "No mode."
Answer: 3,4,7
Step-by-step explanation:
Jim needs to rent a car. A rental company charges $21 per day to rent a car and $0.10 for every mile driven. He will travel 250 miles and has $115 to spend. Write an inequality that can be used to determine the maximum number of DAYS that Jim can rent a car?
Final answer:
To determine the maximum number of days Jim can rent a car, set up the inequality 21d + 25 ≤ 115. Solving for 'd', Jim can rent a car for a maximum of 4 days.
Explanation:
To determine the maximum number of days that Jim can rent a car, we need to set up an inequality using the given information. Let's denote the number of days as 'd'. The rental cost per day is $21, so the total cost for 'd' days would be 21d. The cost for the miles driven is $0.10 per mile, and Jim will travel 250 miles. So the cost for the miles driven would be 0.10 * 250 = $25. Now, we can set up the inequality:
21d + 25 ≤ 115
To solve for 'd', we need to subtract 25 from both sides of the inequality:
21d ≤ 90
Now, divide both sides of the inequality by 21:
d ≤ 90/21
d ≤ 4.29 (approx)
So, Jim can rent a car for a maximum of 4 days.
Antoine wants to get a subscription to a local library. There are two libraries, each of which charges a monthly subscription free plus a fee for each book instead
Answer:
b then a
Step-by-step explanation:
Answer:
Step-by-step explanation:
find the volume of a cylinder with a height of 2 and a radius of 3. Use terms of pi
Answer:
56.55
Step-by-step explanation:
The formula to find the volume of a cylinder is V=πr2h so you would just need to plug the numbers in to get 56.55.
The total cost of attending a state university is $19,700 for the first year.
•A student’s grandparents will pay half of this cost
•An athletic scholarship will pay another $5000
Which amount is closest to the minimum that the student will need to save every month in order to pay off the remaining cost at the end of 12 months?
Answer:
$ 404.17 every month
Step-by-step explanation:
$19,700/2 =$9,850
$9,850-$5,000= $4,850
$4,850/12 = $404.1666666666667
rounds to $ 404.17
What is the volume of a sphere with a radius of 3 inches ? Use 3.14 for pi
Final answer:
The volume of the sphere is 113.04 cubic inches.
Explanation:
The volume of a sphere can be calculated using the formula V = (4/3)×πr³. In this case, the radius is given as 3 inches. Plugging in the value, we get:
( V) volume of the sphere = (4/3)×3.14×3³ = (4/3)×3.14×27 = 113.04 cubic inches.