125 liters of pure peroxide should be added to the 500 liters of the 10% solution to produce a new product that is 28% peroxide.
The concentration C of the new mixture is given by the formula:
C = (x + 0.1 * 500) / (x + 500)
We want to find out how many liters of pure peroxide (100% peroxide) should be added to produce a new product that is 28% peroxide.
In other words, we want to find the value of x that makes C equal to 0.28 (28%).
So, we set up the equation:
0.28 = (x + 0.1 * 500) / (x + 500)
Now, we can solve for x:
0.28(x + 500) = x + 0.1 * 500
Distribute 0.28 on the left side:
0.28x + 0.28 * 500 = x + 0.1 * 500
Simplify:
0.28x + 140 = x + 50
Subtract x from both sides:
0.28x - x + 140 = 50
-0.72x + 140 = 50
Subtract 140 from both sides:
-0.72x = -90
Divide by -0.72:
x = 125
So, 125 liters of pure peroxide should be added to the 500 liters of the 10% solution to produce a new product that is 28% peroxide.
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Final answer:
To achieve a 28% peroxide concentration, approximately 125 liters of pure peroxide should be added to the existing 500-liter, 10% peroxide solution.
Explanation:
The question asks how many liters of pure peroxide (x liters) must be added to a 500-liter solution with a 10% peroxide concentration to produce a new product that is 28% peroxide. To solve this, we'll set up the equation:
C = (x+0.1(500)) / (x+500) where C = 0.28 (the target concentration). So,
0.28 = (x + 50)/(x + 500)
Multiply both sides by (x + 500) to get 0.28(x + 500) = x + 50
Distribute 0.28 to get 0.28x + 140 = x + 50
Subtract 0.28x from both sides to isolate x on one side: 140 = 0.72x + 50
Subtract 50 from both sides: 90 = 0.72x
Divide both sides by 0.72 to solve for x: x ≈ 125 liters
Therefore, approximately 125 liters of pure peroxide should be added to the 500-liter solution to achieve a 28% peroxide concentration.
A clothesline is tied between two poles, 10 m apart. The line is quite taut and has negligible sag. When a wet shirt with a weight of 0.5 kg is hung at the middle of the line, the midpoint is pulled down 10 cm. Find the tension in each half of the clothesline. (Use g = 9.8 m/s2 for the acceleration due to gravity. Enter your answers from smallest to largest value of the coefficient of i.)
Answer:
Tension in each half of the clothesline is 25 kg
Step-by-step explanation:
When the middle of the line is pulled down a right triangle is formed in each half of the rope whose legs measure 0.1 m and 5 m respectively.
Since the rope has an insignificant sag, the measure of the hypotenuse of the triangle is approximately equal to that of the longer leg.
The value of the rope tension is equal to the value of the force applied divided by the sine value of the angle of the rope with the horizontal.
So,
[tex]Sin (a)=\frac{0.1}{5} = 0.02[/tex]
T=[tex]\frac{0.5 kg}{0.02}=25kg[/tex]
Isaiah helped pick 72 bananas on the weekend. There were a total of 6 people picking bananas. If they each picked an equal number of bananas, how many bananas did each person pick?
Answer:
Step-by-step explanation:
72/6=13
Answer:
Each person picked 12 bananas.
Step-by-step explanation:
Given,
Total numbers of banana = 72,
The number of persons = 6,
If each person picks equal number of bananas,
Then,
[tex]\text{Total bananas picked by each person}=\frac{\text{Total bananas}}{\text{Total persons}}[/tex]
[tex]=\frac{72}{6}[/tex]
= 12
You are choosing between two health clubs. Club A offers membership for a fee of $ 19plus a monthly fee of $ 21.  Club B offers membership for a fee of $ 23plus a monthly fee of $ 20.  After how many months will the total cost of each health club be the​ same
Answer:
For 2 months
Step-by-step explanation:
Let after x months the cost of each health club is same,
Now, In club A,
Membership fees = $ 19,
Monthly fees = $ 21,
So, the total fees for x months = membership fees + total monthly fees for x months
= 19 + 21x
In Club B,
Membership fees = $ 23,
Monthly fees = $ 20,
So, the total fees for x months = membership fees + total monthly fees for x months
= 23 + 20x
Thus, we can write,
19 + 21x = 23 + 20x
21x - 20x = 23 - 21
x = 2
Hence, for 2 months the total cost of each health club would be same.
Functions f(x) and g(x) are defined below. Determine where f(x) = g(x) by graphing.
f(x)=1/x-3+1
g(x)=2rootx-3
A. x = 1 B. x = 3 C. x = 2 D. x = 4
Answer:
Option D. x = 4
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{x-3}+1[/tex]
[tex]g(x)=2\sqrt{x-3}[/tex]
we know that
The solution of the system
f(x)=g(x)
is the x-coordinate of the intersection point both graphs
using a graphing tool
The intersection point is (4,2)
see the attached figure
therefore
The solution is x=4
Answer:
for plato its d
Step-by-step explanation:
i got it
What is the best solution for the equation -5/2=3/4+n
Answer:-13/4
Step-by-step explanation:
Move 3/4 to the left:
-2/5-3/4=-20/8-6/8
-26/8=n
-13/4=n
The first one is the answer
How can you express 20 percent as a fraction?
Answer:
20/100
Step-by-step explanation:
20 over 100 due to 100 percent is a whole and you are taking 20 percent so 20 will be ur numerator and 100 for you dominator
PLZ HELP Describe the end behavior and determine whether the graph represents an odd-degree or an even-degree polynomial function. Then state the number of real zeros. simple answer
Answer:
x=8
Step-by-step explanation:
6. an odd-degree polynomial function.
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
Step by step explanation;
6. The graph represent an odd-degree polynomial function.
The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;
f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞
Answer:
End behavior: [tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex] and [tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]
The function has odd-degree.
The number of real zeros in 5.
Step-by-step explanation:
From the given graph it is clear that the graph approaches towards negative infinite as x approaches towards negative infinite.
[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]
The graph approaches towards positive infinite as x approaches towards positive infinite.
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]
For even-degree the polynomial has same end behavior.
For odd-degree the polynomial has different end behavior.
Since the given functions has different end behavior, therefore the graph represents an odd-degree polynomial function.
If the graph of a function intersects the x-axis at a point then it is a zero of the function.
If the graph of a function touch the x-axis at a point and return then it is a zero of the function with multiplicity 2. It means, the function has 2 equal zeros.
The graph intersect the x -axis at 3 points and it touch the x-axis at origin. So, the number of zeros is
[tex]N=3+2=5[/tex]
The number of real zeros is 5.
Find the length of the diagonal Bd rectangle ABCD drawn on the coordinate plane
Answer:
The answer to your question is letter: c) √106 units
Step-by-step explanation:
data
B (5, 3)
D (-4 , -2)
Formula
d = √((x2-x1)² + (y2-y1)²)
dBD = √(-4-5)² + (-2-3)²)
dBD = √(-9)² + (-5)²
dBD = √81 +25
dBD = √106 units
Noah earned w dollars over the summer. Mai earned x dollars, which is y dollars
more than Noah did.
The question revolves around basic algebra and setting up an equality equation based on the given information. In this case, from the facts given, we can state Mai's earnings (x) in terms of Noah's earnings plus an additional amount (y), resulting in the equation x = w + y.
Explanation:The subject of this problem is algebra, specifically involving variables and the concept of equality. In this problem, Noah earned an amount we will denote as w dollars over the summer. Mai, on the other hand, earned x dollars, and it's said that this is an amount of y dollars more than Noah did.
We can express Mai's earnings in terms of Noah's earnings by adding the extra amount to what Noah earned, which gives us the following equality equation:
x = w + y
This equation means that Mai's earnings (x) are equal to the sum of Noah's earnings (w) and the additional amount (y).
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Gabriel wants to make five banners for the parade. He has 75 feet of material. The size of four of the banners are: 12 1/3 ft., 16 1/6 ft., 11 3/4 ft., and 14 1/2 ft. How much material is left for the fifth banner?
Answer:
20 1/4 ft
Step-by-step explanation:
Subtracting the four given lengths from 75 feet will tell you how much is left.
75 - (12 1/3 +16 1/6 +11 3/4 +14 1/2) = 75 -54 3/4 = 20 1/4
Gabriel has 20 1/4 ft of material left for his 5th banner.
After adding the lengths of the first four banners, we subtract that number from the total material Gabriel originally had. Gabriel has 20 13/24 feet of material left for the fifth banner.
Explanation:To determine the amount of material left for the fifth banner, we first have to add the lengths of the four banners that Gabriel has already made. These lengths are 12 1/3 ft., 16 1/6 ft., 11 3/4 ft., and 14 1/2 ft. We add these four values together:
12 1/3 + 16 1/6 + 11 3/4 + 14 1/2 = 54 11/24 ft.
Gabriel originally had 75 feet of material, so to find out how much is left for the fifth banner, we subtract the total length of the first four banners from the original amount:
75 - 54 11/24 = 20 13/24 ft.
So, Gabriel has 20 13/24 ft. of material left for the fifth banner.
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The scalar product can be described as the magnitude of B times the component of A that is parallel to B. In terms of the positive scalar quantities a, b, and d, what is the component of A that is parallel to B? Suppose that c = 0.
The component of A that is parallel to B can be found using the equation A_parallel to B = (A.B)/|B|. Therefore, the component of A parallel to B is A_parallel to B = Scalar product / |B|
Explanation:The component of A that is parallel to B can be found using the equation:
Aparallel to B = (A.B)/|B|
where A.B is the dot product of vectors A and B and |B| is the magnitude of vector B.
Since the scalar product is equal to the magnitude of B times the component of A parallel to B, we can rewrite the equation as:
Scalar product = |B| * Aparallel to B
Therefore, the component of A parallel to B is:
Aparallel to B = Scalar product / |B|
A researcher wants to test the hypothesis that college students weigh less on average than the average American (160 lbs). The sample mean of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03. This means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.True or False.
Answer: True.
Step-by-step explanation:
Let [tex]\mu[/tex] be the population mean.
Given : Null hypothesis = [tex]H_0:\mu=160[/tex]
Alternative hypothesis =[tex]H_1:\mu<160[/tex]
Since , the alternative hypothesis is left-tailed, then the test is a left-tailed test.
The sample mean ([tex]\overlien{x}[/tex]) of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03.
We know that p-value gives that probability that if the null hypothesis is true, than the sample mean ([tex]\overlien{x}[/tex]) will be at least as small as the actual mean ([tex]\mu[/tex]).
It means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.
Hence, the answer is "True".
Final answer:
The statement is true; a p-value of 0.03 indicates a 3% chance of observing a sample mean weight of 142 lbs or less if the true mean weight of all college students is 160 lbs, suggesting strong evidence against the null hypothesis.
Explanation:
The statement provided is true: if the null hypothesis is true (that college students' average weight is 160 lbs), there would only be a 3% chance that a random sample of 80 students would have a mean weight of 142 lbs or less. This small p-value (0.03) typically indicates strong evidence against the null hypothesis, suggesting that the average weight of college students is indeed less than the average American.
In other words, a p-value is the probability that we observe a sample statistic as extreme as the one measured (or more extreme) given that the null hypothesis is true. Taking another example to illustrate the concept: if the null hypothesis assumes no difference in the average height between male and female students, and we observe a sample where the difference is 4 inches with a p-value of 0.04, this means there's a 4% chance we would see at least this large a difference if in reality there was no difference at all.
which equation is the equation of the line, in point-slope form, that has a slope of -4 and passes through the point (7, -1) ?
Answer:
y - 1 = -4(x - 7).
Step-by-step explanation:
Point-slope equation is:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
Here m = -4 , x1 = 7 and y2 = 1, so:
y - 1 = -4(x - 7).
An equation of the line in point-slope form is: D. y - 1 = -4(x - 7).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.
m represent the slope.
At data point (7, 1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -4(x - 7)
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A PC that is communicating with a web server is utilizing a window size of 6,000 bytes when sending data and a packet size of 1,500 bytes. What byte of information will the web server acknowledge after it has received four packets of data from the PC?a. 5b. 1,500c. 1,501d. 6,000e. 6,001
Answer: d 6000 bytes
Step-by-step explanation: The web server will acknowledge 6000 bytes of information after receiving 4 packets of data from the PC. This is because 1 packet of data has a size of 1500 bytes. In a situation where the web server receives 4 of these, it is 1500 multiplied by 4 which is 6000 bytes. The window size of 6000 is there to try distract you from calculating the answer correctly, it serves as a misguidance.
The byte of information that the web server acknowledge is 6000 bytes.
From the information given, were told that the web server is utilizing a window size of 6,000 bytes when sending data and a packet size of 1,500 bytes.
The byte of information that'll be received will be:
= 1500 × 4
= 6000 bytes
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please help-many points
Which pair of numbers is relatively prime?
A. 68 and 119
B. 40 and 395
C. 119 and 715
D. 63 and 56
Relatively prime means there are no number greater than 1 that divides them both.
Find the GCF for each set:
A. 68 and 119
68: 1 , 2, 4, 17, 34,68
119: 1, 7, 17
Both numbers can be divided by 1 or 17 so are not relative.
B.
40 and 395
are both divisible by 1 and 5 so are not relative.
C. 119 and 715
Are both only divisible by 1, so are relative.
D. 63 and 56
Are divisible by both 1 and 7 so are not relative.
The answer is C. 119 and 715
A candy bowl contains 723 candies. Some of the candies are red, and the rest are green. There are twice as many green candies as red candies. How many red candies are in the candy bowl ?
Answer: There are 241 red candies in the bowl. 482 Green candies in bowl.
Step-by-step explanation:
241 (is the answer) x2= 482. There's TWICE as many green as there is red, since there is 241 red candies, we multply that by two (482). Now let's add to check if it is correct. 241+482= is indeed 723.
Answer:
red = 241
green = 482
Step-by-step explanation:
The total = 723
red candies = x
green candies = y
⇒ x + y =723
There are twice as many green candies as red candies.
this means: y = 2x
x + y = 723
x +2x = 723
3x = 723
x = 241
y = 723 - 241 = 482
To control this y = 2x ⇒ 482 = 2 * 241
This means that there 241 red candies and 482 green candies.
Estefani‘s house is at point E (3,-2) and Jasmin's house is at point J (-5,3). Jasmin's house is the Mid-point of Estefani's house and Preston's house. Give the y-coordinate of Preston's house.
Answer:
8
Step-by-step explanation:
The coordinates of Preston's house are ...
2J -E = P = 2(-5, 3) -(3, -2) = (-13, 8)
The y-coordinate of P is 8.
Lily's car used 2 gallons of gas to drive 52 miles. At what rate does her car use gas in miles per gallon? Express your answer in simplest form.
Question 7 options:
A)
-26 miles per gallon
B)
104 miles per gallon
C)
52 miles per gallon
D)
26 miles per gallon
Answer:
D) 26 miles per gallon
Step-by-step explanation:
To find miles per gallon, divide miles by gallons:
Lily's miles/gallon = (52 miles)/(2 gallon) = 26 miles/gallon
_____
Comment on the answer choices
Unless Lily's car manufactures gas, her mileage will not be negative miles per gallon.
point b is the midpoint of ac-. if ab= 4x+2 and ac=10x-6, find the length of ac
let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.
[tex]\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44[/tex]
This is a geometry problem, specifically involving the calculation of lengths using the properties of midpoints. A midpoint divides a line into two equal lengths. The problem is solved by equating the length of AB to half of AC to determine the value of x, which is then substituted back into the equation for AC to find its length.
Explanation:The solution to your problem involves understanding that Point B is the midpoint of AC. A midpoint essentially divides a line into two equal lengths. Therefore, AB is equal to BC which can also be referred to as (AC/2). If AB = 4x+2 and AC = 10x-6, then to solve for the value of x, you would need to equate (4x+2) to (10x-6)/2. After solving this equation, the value of x can then be substituted back into the equation of AC to get the length of AC.
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The 1992 world speed record for a bicycle (human powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 s, at which he commented, "Cogito ergo zoom!" (I think, therefore I go fast!) In 2001, Sam Whittingham beat Huber's record by 19.0 km/h. What was Whittingham's time through the 200 m?
Answer:
Whittingham's time through the 200 m was 5.55 seconds.
Step-by-step explanation:
Huber's peed = 200m / 6.509s = 30.72m/s
1 meter per second = 3.6 km per hour
30.72 m/s = [tex]30.72\times36.=110.6[/tex] km/hr
Sam's speed is 110.6 + 19 = 129.6 km/hr
1 km per hour = 0.2778 meter per second.
So, 129.6 km/hr = [tex]129.6\times0.2778[/tex]= 36m/s
So, Sam Whittingham's time through the 200 m was =
[tex]\frac{200}{36}= 5.55[/tex] seconds.
Final answer:
Chris Huber's average speed was 30.73 m/s. Sam Whittingham beat this by 19.0 km/h, or 5.28 m/s, totaling to an average speed of 35.01 m/s. Whittingham's time for the 200m stretch was thus approximately 5.71 seconds.
Explanation:
To calculate Sam Whittingham's time through the 200 m stretch, we first need to find Chris Huber's average speed during his record-setting ride. Huber's time was 6.509 seconds for a 200 meter stretch, giving us an average speed of 200 m / 6.509 s ≈ 30.73 m/s. Whittingham beat Huber's record by 19.0 km/h. Since 1 km/h is approximately 0.27778 m/s, a 19.0 km/h increase translates to 19.0 km/h * 0.27778 m/s/km/h ≈ 5.28 m/s. Therefore, Whittingham's average speed was 30.73 m/s + 5.28 m/s = 35.01 m/s.
To find Whittingham's time for the 200 m stretch, we divide the distance by his average speed.
Time = Distance / Speed
Time = 200 m / 35.01 m/s ≈ 5.71 seconds.
Therefore, Sam Whittingham's record-breaking time through the 200-meter distance was approximately 5.71 seconds.
The back of Alisha's property is a creek. Alisha would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 600 feet of fencing available, what is the maximum possible area of the pasture?
A square has all 4 sides equal, so divide the amount of fence available by 4 to get the length of one side of the square
600/4 = 150
Now since the creek is being used for one side, add one side of the square to the other side to get a rectagle 150 by 300 feet.
Area = 150 x 300 = 45,000 square feet.
The maximum possible area of the pasture is;
A_max = 45000 ft²
We are given;Available fencing; Perimeter = 600 feet
Number of sides to fence; 3 sides of rectangle
Since we are dealing with rectangle, let L be the length and W be the width.
Perimeter of rectangle; P = 2L + 2W
But we are told one of the edges is the creek.
Thus, New perimeter = L + 2W
thus, we have; L + 2W = 600
L = 600 - 2W
Formula for Area of a rectangle is; A = LW
Let's put 600 - 2W for L in the area equation to get;
A = (600 - 2W)W
A = 600W - 2W²
We can maximize this area by finding the value of W when dA/dW = 0
Thus;
dA/dW = 600 - 4W
At dA/dW = 0, we have;
600 - 4W = 0
4W = 600
W = 600/4
W = 150 ft
Let's put 150 for W in L = 600 - 2W
L = 600 - 2(150)
L = 600 - 300
L = 300 ft
Therefore, Maximum possible area of pasture = 300 × 150 = 45000 ft²
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A professional baseball team won 84 games this season.The team won 14 more games than it lost.There was no ties.How many games did the team lose? How many games did it play?
Answer:
The answer to your question is: lost 70 games; played 154 games
Step-by-step explanation:
Data
Won 84 games
Won 14 more games than it lost
There was no toes.
# of games did the team lose?
# of games did it play?
Process
games lost = games won - 14
games lost = 84 - 14
games lost = 70
# of games played = games won + games lost
# games played = 84 + 70
= 154
A crop scientist is conducting research with a drought resistant corn hybrid. She is interested in determining if using fertilizer X will increase plant height. She prepares 20 single acre plots and randomly assigns 10 to have normal soil while the other 10 are planted with fertilizer X. The resulting average height for each group of 10 plots was recorded. Select all that apply.
a. This is best described as an observational study.
b. The response variable is whether or not fertilizer X was used.
c. The explanatory variable is the average height for each group of 10 plots
d. This study is best described as an experiment.
e. The explanatory variable is whether or not fertilizer X was used.
f. The response variable is the average height for each group of 10 plots
Answer: d. This study is best described as an experiment.
e. The explanatory variable is whether or not fertilizer X was used.
f. The response variable is the average height for each group of 10 plots.
Step-by-step explanation:
Given : A crop scientist is conducting research with a drought resistant corn hybrid.
She is interested in determining if using fertilizer X will increase plant height.
She prepares 20 single acre plots and randomly assigns 10 to have normal soil while the other 10 are planted with fertilizer X.
This study is best describe as an experiment because the scientist is experimenting about the increase in plant height with an generation of 20 single acre plots not like an observational study where the observer just observe the study without any influence.
Here the fertilizer is used to see the change in the plant height.
So, the explanatory variable is whether or not fertilizer X was used and the response variable is the average height for each group of 10 plots.
Simplify the expressions by combining like terms
1. 6n^2 - 2n - 3 + 5n^2 - 9n - 6
2. 8c^2 - c + 3 + 2c^2-c + 2
Hey!
---------------------------------------------------------
Question #1:
= 6n^2 - 2n - 3 + 5n^2 - 9n - 6
= 6n^2 + (-2n) + (-3) + 5n^2 + (-9n) + (-6)
= (6n^2 + 5n^2) + (-2n + -9n) + (-3 + -6)
= (11n^2) + (-11n) + (-9)
Answer: 11n² + (-11n) + (-9)
---------------------------------------------------------
Question #2:
= 8c^2 - c + 3 + 2c^2 - c + 2
= 8c^2 + (-c) + 3 + 2c^2 + (-c) + 2
= (8c^2 + 2c^2) + (-c + -c) + (3 + 2)
= (10c^2) + (-2c) + (5)
Answer: 10c² + (-2c) + 5
---------------------------------------------------------
Hope This Helped! Good Luck!
Answer:
1. 11n^2-11n-9
2. 10c^2-2c+5
Step-by-step explanation:
1. 6n^2+5n^2 = 11n^2
-2n-9n = -11n
-3-6=-9
2. 8c^2+2c^2 = 10c^2
-c-c= -2c
3+2=5
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
(4 square root of 2, 45°), (-4 square root of 2, 225°)
(4 square root of 2, 135°), (-4 square root of 2, 315°)
(4 square root of 2, 225°), (-4 square root of 2, 45°)
(4 square root of 2, 315°), (-4 square root of 2, 135°)
Answer:
D
Step-by-step explanation:
[tex]4=r cos \theta\\-4=r sin \theta\\square ~and~add\\16+16=r^2(cos^2 \theta+sin^2\theta)\\r^2=32\\ r=4\sqrt{2} \\divide \\tan \theta=-1\\as x is positive ,y is negative ,so \theta lies in 4th quadrant.\\tan \theta=-1=-tan 45=tan(360-45)=tan 315\\\theta=315°\\\\co-ordinates~ are~(r,theta) ~or~(-r,\theta+ -180°)\\hence ~co-ordinates~are(4\sqrt{2} ,315°),(-4\sqrt{2} ,135°)[/tex]
Machine A produces bolts at a uniform rate of 120 every 40 seconds, and Machine B produces bolts at a uniform rate of 100 every 20 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 200 bolts?
Answer:
25 seconds
Step-by-step explanation:
Hi there!
In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes.
For machine A:
[tex]A = \frac{120 bolts}{40 s}= 3 \frac{bolts}{s}[/tex]
For machine B:
[tex]B = \frac{100 bolts}{20 s}= 5 \frac{bolts}{s}[/tex]
So, if the two machines run simultaneously, we will have a rate of prodcution of bolts equal to the sum of both:
[tex]A+B=(3+5)\frac{bolts}{s}=8\frac{bolts}{s}[/tex]
Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:
[tex]t = \frac{bolts}{ProductionRate}= \frac{200 bolts}{8 \frac{bolts}{s} }[/tex]
The bolts unit cancell each other and we are left with seconds
[tex]t = \frac{200}{8} s = 25 s[/tex]
So it will take 25 seconds to produce 200 bolts with machine A and B running simultaneously.
Greetings!
Answer:
25 seconds.
Step-by-step explanation:
We have been given that Machine A produces bolts at a uniform rate of 120 every 40 seconds.
Bolts made by Machine A in one second would be [tex]\frac{120}{40}=3[/tex] bolts.
Machine B produces bolts at a uniform rate of 100 every 20 seconds.
Bolts made by Machine B in one second would be [tex]\frac{100}{20}=5[/tex] bolts.
The speed of making bolts in one second of both machines running simultaneously would be [tex]3+5=8[/tex] bolts per second.
[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8\frac{\text{bolts}}{\text{Sec}}}[/tex]
[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8}*\frac{\text{Sec}}{\text{bolts}}[/tex]
[tex]\text{Time taken by both Machines to make 200 bolts}=25\text{ Sec}[/tex]
Therefore, the both machines will take 25 seconds to make 200 bolts.
URGENT!
Each day we purchase 1.7 thousand ice cream cones per minute. Use the fact that there are approximately 5.3 times 10^5 minutes in a year to approximate how many ice cream cones are purchased in one year. Write your answer in scientific notation.
Approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year, given a rate of 1.7 thousand cones per minute over [tex]\(5.3 \times 10^5\)[/tex] minutes.
To find the total number of ice cream cones purchased in one year, we can multiply the rate of purchase per minute by the total number of minutes in a year.
Given: Purchase rate = 1.7 thousand ice cream cones per minute, and there are [tex]\(5.3 \times 10^5\)[/tex] minutes in a year.
[tex]\[ \text{Total cones in one year} = \text{Rate per minute} \times \text{Minutes in a year} \][/tex]
[tex]\[ \text{Total cones} = 1.7 \times 10^3 \, \text{cones/minute} \times 5.3 \times 10^5 \, \text{minutes} \][/tex]
Now, multiply the coefficients and add the exponents:
[tex]\[ \text{Total cones} = 8.51 \times 10^8 \, \text{ice cream cones} \][/tex]
Therefore, approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year.
Final answer:
By multiplying 1.7 × 10³ cones per minute by 5.3 × 10⁵ minutes per year, the total number of cones purchased in one year is approximately 9.01 × 10⁸ cones.
Explanation:
To calculate the total number of ice cream cones purchased in one year, we can use scientific notation and multiplication. First, convert the number of ice cream cones bought per minute into scientific notation:
1.7 thousand cones per minute = 1.7 × 10³ cones/minute
Next, multiply this by the total number of minutes in a year, also given in scientific notation:
5.3 × 10⁵ minutes/year
The calculation will look like this:
(1.7 × 10³ cones/minute) × (5.3 × 10⁵ minutes/year) = (1.7 × 5.3) × (10³× 10⁵) = 9.01 × 10⁸ cones/year
The approximation for the number of cones purchased in one year is 9.01 × 10⁸ cones.
Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) ?
Answer:
Step-by-step explanation:
y - 1 = 2(x + 8)
y - 1 = 2x + 16
y = 2x + 17
An equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) is: B. y - 1 = 2(x + 8).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-8, 1) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 2(x - (-8))
y - 1 = 2(x + 8)
In slope-intercept form, the equation of the line is given by;
y - 1 = 2x + 16
y = 2x + 16 + 1
y = 2x + 17
Read more on point-slope here: brainly.com/question/24907633
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Complete Question:
Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1)?
A. y - 1 = 2(x - 8)
B. y - 1 = 2(x + 8)
C. y - 8 = 2(x + 1)
D. y - 8 = 2(x - 1)
Solve for x: 2 over 3 equals the quantity x minus 1 end quantity over 5
Question 6 options:
7 over 3
11 over 3
13 over 3
3
Answer:
13 over 3
Step-by-step explanation:
Hi Jakeyriabryant! I hope you’re fine!
I hope I have understood the problem well.
If so, what the exercise raises is the following equality:
(x-1) / 5 = 2/3
From this equation you must clear the "x".
First, we pass the 5 that is dividing on the side of the x, to the other side and passes multiplying
(X – 1) / 5 = 2/3
(X – 1) = (2/3)*5
X – 1 = 10/3
Then we pass the one that is subtracting from the side of the x, to the other side and passes adding
X = 10/3 + 1
Remember that to add or subtract fractions they must have the same denominator or a common denominator (in this case we can write 1 as fraction 3/3). Then,
X = 10/3 + 3/3
X = 13/3
I hope I've been helpful!
Regards!
The solution to the equation 2/3 = (x-1)/5 is x = 13/3. This is achieved by cross-multiplying, then isolating x.
Explanation:To solve for x in the equation 2/3 = (x-1)/5, you will need to isolate the variable 'x'. This requires you to perform the same mathematical operation on both sides of the equation in order to maintain balance. Here we have a situation that involves proportions. Solve it by cross-multiplying:
Multiply 2 by 5, the denominator on the right side of the equation; and 3, the denominator on the left, by (x-1). So, 2*5 = 3*(x-1).This simplifies to 10 = 3x -3.Add 3 to both sides to get '3x=13', then divide both sides by 3 to get x= 13/3.Learn more about Algebraic Equation here:https://brainly.com/question/32183344
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A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?A. 0.5< t < 0.75B. 1.75< t < 2.0C. 2.0 < t < 2.5D. 2.5 < t < 3.0E. 3 < t < 3.5
Answer:
Option C is the answer.
Step-by-step explanation:
Given diameter is = 2 miles
So, radius will be = 1 mile
Let t represents the number of hours it took Johanna to walk completely around the lake.
Now, the circumference is given as: [tex]2\pi r[/tex]
So, circumference = [tex]2(3.14)(1)[/tex] = 6.28 miles
Johanna's speed = 3 miles/ hour
We know the formula [tex]Time=Distance / Speed[/tex]
t = [tex]6.28/3[/tex]
t = 2.09 hours
This is greater than 2, but less than 2.5, therefore, 2.0 < t < 2.5 is the answer.