Answer: C
Step-by-step explanation:707.10-682.87= 24.23. Similar difference can also be found in only chair which is. 161.55-137.32=24.23
Answer:
The correct answer is C on edge :) i just did the test
Step-by-step explanation:
What is the solution to the following system of equations?
x − 4y = 6
2x + 2y = 12
answer choices
(0,10)
(10,0)
(6,0)
(0,6)
Answer:
The answer to your question is (6, 0)
Step-by-step explanation:
Solve the system of equations by elimination
x - 4y = 6 (I)
2x + 2y = 12 (II)
Multiply (II) by 2
x - 4y = 6
4x + 4y = 24
Simplify
5x + 0 = 30
Find x
5x = 30
x = 30/ 5
x = 6
Find "y"
6 - 4y = 6
-4y = 6 - 6
-4y = 0
y = 0/-4
y = 0
Answer:
(6,0)
Step-by-step explanation:
Given equations are:
\[x - 4y = 6\] -------------------- (1)
\[2x + 2y = 12\] -------------------- (2)
Multiplying (1) by 2 :
\[2x - 8y = 12\] -------------------- (3)
Calculating (2) - (3) :
\[2x + 2y -2x + 8y = 12 - 12\]
=> \[10y =0\]
=> \[y = 0\]
Substituting the value of y in (1):
\[ x = 6 \]
So the required solution of the system of equations is x=6,y=0. This can be alternatively expressed in coordinate notation as (6,0).
Grant thinks he has reached the point where he has maximized his profit. However, because this can be tricky to determine, he is not sure. He decides to test it by selling one more unit. If Grant is correct in his assumption,
what should happen when he sells this additional unit?
a. Grant will break even on his sales
b. Profit will increase but at a slower rate
c. Marginal revenue will exceed marginal cost
d. Marginal cost will exceed marginal revenue
e. Profits will be reduced to zero
Answer:c
Step-by-step explanation:
Profit maximization happens with marginal revenue is equal to marginal cost, so if Grant's assumption was right before selling the extra unit, when he actually sells the extra unit, this will increase his revenue
That's why the answer is c
Marginal revenue will exceed marginal cost
Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?
A. 1/24
B. 1/8
C. 1/4
D. 1/3
E. 3/8
Answer:
The probability that only 1 letter will be put into the envelope with its correct address is [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Given:
Number of Letters=4
Number of addresses= 4
To Find:
The probability that only 1 letter will be put into the envelope with its correct address=?
Solution:
Let us assume first letter goes in correct envelope and others go in wrong envelopes, then
=> Probability putting the first letter in correct envelope =[tex]\frac{1}{4}[/tex]
=> Probability putting the second letter in correct envelope =[tex]\frac{2}{3}[/tex]
=> Probability putting the third letter in correct envelope= [tex]\frac{1}{2}[/tex]
=> Probability putting the fourth letter in correct envelope = 1;
( only 1 wrong addressed envelope is left);
This event can occur with other 3 envelopes too.
Hence total prob. = [tex]4\times(\frac{1}{4}\times\frac{2}{3}\times\frac{1}{2}\times1)[/tex]
=> [tex]\frac{1}{3}[/tex]
An astronaut is returning to earth in a spacecraft. If the spcecraft is descending at a rate of 13.81 kilometers per minute, what will its change be in height after 5 1/2 minutes ?
Answer:
-75.955 kilometers
Step-by-step explanation:
multiply the speed by the time to get distance
the spacecraft is descending, so change in height will most likely be answered as a negative number
13.81 × 5.5 = 75.955
The required change in the height of the spacecraft will be 76 kilometers down.
Given that, an astronaut is returning to earth in a spacecraft. If the spacecraft is descending at a rate of 13.81 kilometers per minute, what will its change be in height after 5 1/2 minutes is to be determined.
What is Distance?Distance is defined as the object traveling at a particular speed in time from one point to another.
Here,
Speed = 13.81 km/s
Time = 5 1 /2 minute = 5+0.5 minute = 5.5 minutes
Distance traveled = speed * time
Distance traveled = 13.81 * 5.5 ≈ 76 km (down)
Thus, the required change in the height of the spacecraft will be 76 kilometers down.
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In a recent year, 32% of all college students were enrolled part-time. If 8.2 million college students were enrolled part-time that year, what was the total number of college students? Round your answer to the nearest million
Answer:
26 million
Step-by-step explanation:
8200000 / 0.32 = 25625000
25625000 rounded to nearest million = 26 million
The total number of college students is 26 million.
Given that, in a recent year, 32% of all college students were enrolled part-time and 8.2 million college students were enrolled part-time that year.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Let the total number of college students be x.
Now, 32% of x=8.2 million
⇒ 0.32 x=8200000
⇒ x = 8200000/3.2
⇒ x = 2562500
2562500 rounded to nearest million = 26 million
Therefore, the total number of college students is 26 million.
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A scientist estimates that the mean nitrogen dioxide level in a city is greater than 30 parts per billion. To test this estimate, you determine the nitrogen dioxide levels for 31 randomly selected days. The results (in parts per billion) are listed below.
Answer:
Step-by-step explanation:
incomplete. no results listed below
Derrick adds equations A and B to solve this system of equations. What makes this approach a valid method in general for solving a system of equations?
Answer:
The substitution and addition properties of equality.
Step-by-step explanation:
The substitution property tells you that equals may be substituted for each other at any time.
The addition property of equality tells you that the same quantity can be added to both sides of an equation without violating the equal sign.
So, if you start with the equation ...
a = b
and you add c to both sides (addition property), you get
a + c = b + c
and if c = d, this can become (substitution property) ...
a + c = b + d . . . . . d substituted for c
In other words, we have added the equations
a = b
c = d
to get ...
a + c = b + d
The addition and substitution properties of equality make this valid.
it is b cuz im smart and i know t
A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x^2=4y around its axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? Express your answer as a fraction or a decimal rounded to two decimal places.
Answer:
1.00 inches
Step-by-step explanation:
The distance from vertex to focus is "p" in the quadratic equation ...
x^2 = 4py
In the given equation, p=1. Since units are inches, ...
the bulb should be placed 1.00 inches from the vertex.
The probability of drawing two aces from a standard deck is 0.0059. We know this probability, but we don't know if the first card was replaced. If the two draws are defined as event A and event B, are the events dependent or independent?
A. They are dependent because, based on the probability, the first ace was replaced before drawing the second ace.
B. They are dependent because, based on the probability, the first ace was not replaced before drawing the second ace.
C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.
D. They are independent because, based on the probability, the first ace was not replaced before drawing the second ace.
Answer:
Option C is right
C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.
Step-by-step explanation:
Given that the probability of drawing two aces from a standard deck is 0.0059
If first card is drawn and replaced then this probability would change. By making draws with replacement we make each event independent of the other
Drawing ace in I draw has probability equal to 4/52, when we replace the I card again drawing age has probability equal to same 4/52
So if the two draws are defined as event A and event B, the events are independent
C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.
Add or subtract
x/x^2-4 -2/x^2-4
The top and bottom margins of a poster are 8 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area.
The top and bottom margins of a poster are 8 cm an
Width = (include units)
Height = (include units)
Final answer:
To find the dimensions of the poster with the smallest area, subtract the margins from the total dimensions of the poster. Set up an equation using the area of the printed material and find the dimensions that result in the smallest area. By substituting different values into the equation, the dimensions are approximately 30 cm by 56 cm.
Explanation:
To find the dimensions of the poster with the smallest area, we need to subtract the margins from the total dimensions of the poster and then find the dimensions that result in the smallest area. Let's assume the width of the poster is x cm and the height of the poster is y cm.
Using the information given, we can set up the following equations:
x - 2(6) = x - 12 cm (effective width)
y - 2(8) = y - 16 cm (effective height)
The area of the printed material is fixed at 390 square centimeters, so we have:
(x - 12) × (y - 16) = 390
To find the dimensions with the smallest area, we can find the derivative of the area equation with respect to either x or y, set it equal to zero, and solve for x or y. However, this is a complicated process. So, we can use a graphing calculator to find the minimum area. By substituting different values for x and y into the area equation, we can find the dimensions that result in the smallest area.
After substituting different values, we find that the dimensions of the poster with the smallest area are approximately 30 cm by 56 cm.
Let H be a subgroup of a group G. We call H characteristic in G if for any automorphism σ∈Aut(G) of G, we have σ(H)=H.
(a) Prove that if σ(H)⊂H for all σ∈Aut(G), then H is characteristic in G.
(b) Prove that the center Z(G) of G is characteristic in G.
Answer:Problem 1. Let G be a group and let H, K be two subgroups of G. Dene the set HK = {hk : h ∈ H,k ∈ K}.
a) Prove that if both H and K are normal then H ∩ K is also a normal subgroup of G.
b) Prove that if H is normal then H ∩ K is a normal subgroup of K.
c) Prove that if H is normal then HK = KH and HK is a subgroup of G.
d) Prove that if both H and K are normal then HK is a normal subgroup of G.
e) What is HK when G = D16, H = {I,S}, K = {I,T2,T4,T6}? Can you give geometric description of HK?
Solution: a) We know that H ∩ K is a subgroup (Problem 3a) of homework 33). In order to prove that it is a normal subgroup let g ∈ G and h ∈ H ∩ K. Thus h ∈ H and h ∈ K. Since both H and K are normal, we have ghg−1 ∈ H and ghg−1 ∈ K. Consequently, ghg−1 ∈ H ∩ K, which proves that H ∩ K is a normal subgroup.
b) Suppose that H G. Let K ∈ k and h ∈ H ∩ K. Then khk−1 ∈ H (since H is normal in G) and khk−1 ∈ K (since both h and k are in K), so khk−1 ∈ H ∩ K. This proves that H ∩ K K.
c) Let x ∈ HK. Then x = hk for some h ∈ H and k ∈ K. Note that x = hk = k(k−1hk). Since k ∈ K and k−1hk ∈ H (here we use the assumption that H G), we see that x ∈ KH. This shows that HK ⊆ KH. To see the opposite inclusion, consider y ∈ KH, so y = kh for some h ∈ H and k ∈ K. Thus y = (khk−1)k ∈ HK, which proves that KH ⊆ HK and therefoere HK = KH. To prove that HK is a subgroup note that e = e · e ∈ HK. If a,b ∈ HK then a = hk and b = h1k1 for some h,h1 ∈ H and k,k1 ∈ K. Thus ab = hkh1k1. Since HK = KH and kh1 ∈ KH, we have kh1 = h2k2 for some k2 ∈ K, h2 ∈ H. Consequently,
ab = h(kh1)k1 = h(h2k2)k1 = (hh2)(k2k1) ∈ HK
(since hh2 ∈ H and k2k1 ∈ K). Thus HK is closed under multiplication. Finally,
Step-by-step explanation:
A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct. 0.1492 0.3508 0.0901 0.8508 Normal approximation is not suitable.
Answer:
Option 4 - 0.8508
Step-by-step explanation:
Given : A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses.
To find : Estimate the probability of getting at least 20% correct ?
Solution :
20% correct out of 60,
i.e. [tex]20\%\times 60=\frac{20}{100}\times 60=12[/tex]
Minimum of 12 correct out of 60 i.e. x=12
Each question has 4 possible answers of which one is correct.
i.e. probability of answering question correctly is [tex]p=\frac{1}{4}=0.25[/tex]
Total question n=60.
Using a binomial distribution,
[tex]P(X\geq 12)=1-P(X\leq 11)[/tex]
[tex]P(X\geq 12)=1-[P(X=0)+P(X=1)+P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)][/tex]
[tex]P(X\geq 12)=1- [^{60}C_0(0.25)^0(1-0.25)+^{60-0}+^{60}C_1(0.25)^1(1-0.25)^{60-1}+^{60-1}+^{60}C_2(0.25)^2(1-0.25)^{60-2}+^{60}C_3(0.25)^3(1-0.25)^{60-3}+^{60}C_4(0.25)^4(1-0.25)^{60-4}+^{60}C_5(0.25)^5(1-0.25)^{60-5}+^{60}C_6(0.25)^6(1-0.25)^{60-6}+^{60}C_7(0.25)^7(1-0.25)^{60-7}+^{60}C_8(0.25)^8(1-0.25)^{60-8}+^{60}C_9(0.25)^9(1-0.25)^{60-9}+^{60}C_{10}(0.25)^{10}(1-0.25)^{60-10}+^{60}C_{11}(0.25)^{11}(1-0.25)^{60-11}][/tex]
[tex]P(X\geq 12)\approx 0.8508 [/tex]
Therefore, option 4 is correct.
Jimmy walks 9 miles West and 12 miles North. How much shorter is the diagonal distance from point A to point B than walking the distance of both sides?
Answer:
6 miles shorter
Step-by-step explanation:
Right now, Jimmy walked 21 miles. If he had gone diagonally, he would've walked only 15 miles. This is 6 miles shorter than before.
A rectangular poster is to contain 81 square inches of print. The margins at the top and bottom and on each side are to be 5 inches. Find the dimensions of the page which will minimize the amount of paper used.
To minimize the paper used for a poster with a specific print area and margin size, we derive a formula for total paper area, take its derivative with respect to the print width, solve for the width, and then find the matching height.
To find the dimensions of the page that will minimize the amount of paper used for a rectangular poster that contains 81 square inches of print with 5-inch margins on all sides, we need to set up a function to minimize. Let the width of the print area be x inches, and the height be y inches. Therefore, the total dimensions of the poster will be (x + 10) inches wide and (y + 10) inches high due to the margins on each side.
The area of print is given, so x*y = 81. We will minimize the total area of the page, A = (x+10)(y+10). Substituting the value of y from the print area equation, y =[tex]\frac{81}{x}[/tex], we get A(x) = (x+10)([tex]\frac{81}{x}[/tex]+10).
Now, to find the dimensions that minimize the paper used, we will take the derivative of A(x) with respect to x, set it to zero, and solve for x. From there, we can find the corresponding value of y to get the dimensions that will use the least amount of paper while still fitting the print area and margins.
Suppose that in a bushel of 100 apples there are 20 that have worms in them and 15 that have bruises. Only those apples with neither worms nor bruises can be sold. If there are 10 bruised apples that have worms in them, how many of the 100 apples can be sold?
To determine the number of sellable apples, we subtract the number of apples with defects from the total, but add back the ones counted twice due to having multiple defects. The calculation reveals that 75 out of 100 apples can be sold.
To calculate the number of apples that can be sold from the bushel, we need to consider those without worms or bruises. We have 20 apples with worms and 15 with bruises. However, since there are 10 apples that have both worms and bruises, these are counted twice in our total of defective apples.
First, we'll subtract the number of apples with worms (20) and those with bruises (15) from the total number of apples (100), but then we need to add back the ones we subtracted twice, those with both worms and bruises (10). Here's the calculation:
Total apples = 100
Apples with worms = 20
Apples with bruises = 15
Apples with both worms and bruises = 10
Apples that can be sold = Total apples - (Apples with worms + Apples with bruises - Apples with both worms and bruises)
Apples that can be sold = 100 - (20 + 15 - 10) = 100 - 25 = 75 apples can be sold.
75 of the 100 apples can be sold.
To find out how many apples can be sold, we need to determine the number of apples that are neither bruised nor have worms.
Given:
- Total number of apples = 100
- Number of apples with worms = 20
- Number of apples with bruises = 15
- Number of bruised apples with worms = 10
First, let's find the number of apples that have both bruises and worms. We are given that there are 10 bruised apples that have worms, so these apples are counted in both the bruised and worms categories. Therefore, we need to subtract these from the total number of bruised apples to avoid double-counting:
[tex]\[ \text{Number of apples with both bruises and worms} = 10 \][/tex]
Next, let's find the number of apples that have either bruises or worms. This can be done by adding the number of apples with bruises and the number of apples with worms and then subtracting the number of apples with both bruises and worms:
[tex]\[ \text{Number of apples with either bruises or worms} = 15 + 20 - 10 = 25 \][/tex]
Now, to find the number of apples that can be sold (i.e., the number of apples that are neither bruised nor have worms), we subtract the number of apples with either bruises or worms from the total number of apples:
[tex]\[ \text{Number of apples that can be sold} = 100 - 25 = 75 \][/tex]
So, 75 of the 100 apples can be sold.
Find the area. The figure is not drawn to scale.
Answer:
15
Step-by-step explanation:
to find area you need to do height times base and divide by 2 or multiply it by 1/2.
10 x 3 = 30
30/2 = 15
Hello, I'm posting this again because I really need help, I will give brainliest, I'm pretty desperate. ;--;
What is the inequality represented by the graph?
Thank you !!
Answer:
[tex]y < - \times + 2[/tex]
and
[tex]y \geqslant 2x + 4[/tex]
Step-by-step explanation:
Dotted line means regular < and >
Solid line mean (< or equal to) and > (or equal to)
They're asking for an equation for both lines, which you can use the formula y = mx + b, but in this case you'll be using y < or y > since it's an inequality.
The m in the equation represents the slopeThe b in the equation represents where the line intercepts on the y-axisFor the dotted line: Its dotted so you already know it's a regular sign (< and >). We have to find the slope of the dotted line, which is m. The formula for m = (y2 - y1) ÷ (x2 - x1), which means you choose two points that the dotted line intercepts with. (0, 2) and (2,0) are two points the line goes through. Now plug it into the slope formula. (0 - 2) ÷ (2 - 0) = -2/2 = -1
The line intercepts at 2 on the y-axis and the area below the dotted line is shaded. When it's shaded below, the sign is < therefore y < -1x + 2
For the solid line: Its solid so the sign in underlined indicating equal to or (</>). Do the exact same thing you did for the dotted line. Slope formula and where the line intercepts the y-axis. Let's do (-2,0) and (0,4), then (4 - 0) ÷ (0 - (-2)) = 4/2 = 2.
The line intercepts at 4 on the y-axis and the area above the solid line is shaded. When its shaded above, the sign is > therefore y > or equal to (underline it) 2x + 4
QUESTION 1 A researcher compares differences in positivity between participants in a low-, middle-, or upper-middle-class family. If she observes 15 participants in each group, then what are the degrees of freedom for the one-way between-subjects ANOVA?
Answer:
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-K=3*15-3=42[/tex].
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
If we assume that we have [tex]3[/tex] groups and on each group from [tex]j=1,\dots,15[/tex] we have [tex]15[/tex] individuals on each group we can define the following formulas of variation:
[tex]SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]
[tex]SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 [/tex]
[tex]SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]
And we have this property
[tex]SST=SS_{between}+SS_{within}[/tex]
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k-1=3-1=2[/tex] where k =3 represent the number of groups.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-K=3*15-3=42[/tex].
And the total degrees of freedom would be [tex]df=N-1=3*15 -1 =44[/tex]
And the F statistic to compare the means would have 2 degrees of freedom on the numerator and 42 for the denominator.
Find the area. The figure is not drawn to scale.
Answer:
1188 in²
Step-by-step explanation:
The area of a parallelogram is the product of its base length and height.
A = bh = (36 in)(33 in) = 1188 in²
A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 30000 feet. The pilot would like to estimate her distance from Gateway Arch. She finds that the angle of depression to a point on the ground at the arch is 23°. Find the distance between the plane and the arch. Round your answer to the nearest foot. (Do not include ft in your answer)
Answer: 70676
Step-by-step explanation:
First we draw a diagram representing the problem, which can be found in the picture uploaded,
Point a is the point of the plane, you can see where the angle of depression is imputed in the diagram, point C is the point where the gateway arch is, and drawing a vertical line to the ground from the point of the plane, point Blank is where that vertical line touches the ground
So we can tell the the angle of depression from the plane to the arch is the same as the angel of elevation from the arch to the plane
And we are to look for the distance between B and C which is labeled x in the diagram
So looking at the right angle triangle made from this question, we can see we have the opposite length which the angle of elevation from the arch is looking at, and we are looking for the adjacent length, so we use SOH, CAH, TOA, to solve
Choosing TOA which means
Tan(angle) = (opposite length)/(adjacent length)
Tan 23 = 30000/x
Multiplying both sides by x
xtan23 = 30000
Dividing both sides by tan23
x = 30000/tan23
x = 70675.57
Approximately 70676
Which number completes the inequality?
2/3 < <7/9
3/5
6/9
3/4
6/7
Answer:
3/4
Step-by-step explanation:
It can be helpful to use a common denominator for comparison. That denominator can be 100, meaning we can make them all decimal fractions. Approximate (2 digit) values are good enough for the purpose.
2/3 ≈ 0.67 . . . . left end of the range
7/9 ≈ 0.78 . . . . right end of the range
3/5 = 0.60
6/9 ≈ 0.67 . . . . = 2/3, so is not greater than 2/3
3/4 = 0.75
6/7 ≈ 0.86
The only decimal value between 0.67 and 0.78 is 0.75, corresponding to the fraction 3/4.
2/3 < 3/4 < 7/9
An adult can lose or gain two pounds of water in the course of a day. Assume that the changes in water weight are uniformly distributed between minus two and plus two pounds in a day. What is the standard deviation of your weight over a day?
Answer: 1.15 pounds
Step-by-step explanation:
For uniform distribution.
The standard deviation is :
[tex]\sigma=\sqrt{\dfrac{(b-a)^2}{12}}[/tex]
, where a = Lower limit of interval [a,b].
b = Upper limit of interval [a,b].
Given : The changes in water weight are uniformly distributed between minus two and plus two pounds in a day.
i.e. Interval = [-2 , +2]
Here , a= -2 and b= 2
Then, the standard deviation is :
[tex]\sigma=\sqrt{\dfrac{(2-(-2))^2}{12}}[/tex]
[tex]\sigma=\sqrt{\dfrac{(2+2)^2}{12}}[/tex]
[tex]\sigma=\sqrt{\dfrac{16}{12}}=\sqrt{1.3333}=1.15468610453\approx1.15[/tex]
Hence, the standard deviation of your weight over a day = 1.15 pounds
The standard deviation of the uniform distribution representing an adult's daily change in weight due to water is around 1.155 pounds.
Explanation:The question is about the standard deviation of the adult weight changes due to gain or loss in water content which is uniformly distributed between minus two and plus two pounds in a day.
To calculate the standard deviation for this uniform distribution, you need to follow these steps:
The range of the distribution is the difference between the highest and lowest values. In this case, the range is 4 pounds (2 pounds of gain - (-2 pounds of loss)). The formula of standard deviation for a uniform distribution is: sqrt((range^2) / 12). Substituting the values, the answer would be sqrt((4^2) / 12), which equals to 1.155 pounds.
So, the standard deviation of your weight changes over a day due to the water flux is approximately 1.155 pounds.
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Find an equation of the line that passes through the point (-1, 7) and is parallel to the line passing through the points (-3, -4) and (1, 4). (Let x be the independent variable and y be the dependent variable.)
To find a line parallel to another, determine the slope of the original line, which is 2 in this case, and then use the point-slope form with a given point and the same slope to find the equation, resulting in y = 2x + 9.
Explanation:To find an equation of the line that is parallel to another, we must first determine the slope of the given line. The line passing through the points (-3, -4) and (1, 4) has a slope calculated by the formula ∆y/∆x = (4 - (-4))/(1 - (-3)) = 8/4 = 2.
Since parallel lines have the same slope, our new line will also have a slope of 2. We can use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Substituting our known point (-1, 7) and the slope 2, we get y - 7 = 2(x - (-1)). Simplified, the equation of our parallel line is y = 2x + 9.
A farmer packed 3 pints of strawberries every 4 minutes. In the afternoon she packed 2 pints of strawberries every 3 minutes. What was the difference between her morning and afternoon packing rates in pints per hour?
Answer:
5 (strawberries / hours)
Step-by-step explanation:
calculation fro morning
strawberries / minutes x minutes / hours = strawberries / hours
so after adding the value in above equation
3/4* 60/1 = 45 strawberries / hours
calculation in the afternoon
strawberries / minutes x minutes / hours = strawberries / hours
2/3 x 60/1 = 40 strawberries / hours
so now by calculating difference between morning and afternoon packing rates, you can easily calculate
45-40 = 5 (strawberries / hours)
Julian walked 6/10 of a mile to his friends house and another 35/100 mile to the store. He walked 1/4 of a mile back home. Julian's sister said he walked 1/5 mile. Do you agreed. Why or why not
The statement, "Julian's sister said he walked 1/5 mile" cannot be agreed because Julian totally walked [tex]1\frac{1}{5} \text{ or } \frac{6}{5}[/tex] miles.
Solution:
Given that,
Julian walked 6/10 of a mile to his friends houseAnother 35/100 mile to the storeHe walked 1/4 of a mile back homeTo find total distance walked by Julian we have to add the above stated values. That is, [tex]\frac{6}{10} +\frac{35}{100} +\frac{1}{4}[/tex]
Factors of 10 = [tex]5\times2[/tex]
Factors of 100 = [tex]5\times2\times5\times2[/tex]
Factors of 4 = [tex]2\times2[/tex]
Therefore, the least common factor of 10, 100 and 4 is 100. With like denominators we can operate on just the numerators,
[tex]\frac{6\times10}{10\times10} +\frac{35\times1}{100\times1} +\frac{1\times25}{4\times1}\rightarrow\frac{60+35+25}{100}\rightarrow\frac{120}{100}[/tex]
[tex]\Rightarrow\frac{120}{100}\rightarrow\frac{6}{5}[/tex]
Which can also be written as [tex]1\frac{1}{5}[/tex].
So, from the above calculation it can be said that Julian walked [tex]1\frac{1}{5} \text{ miles }[/tex].
Julian did not walk 1/5 mile. He actually walked 1.2 miles.
Explanation:To determine whether Julian's sister's claim is accurate, we need to add up the distances Julian walked. He walked 6/10 mile to his friend's house, 35/100 mile to the store, and 1/4 mile back home. Using a common denominator of 100, we can add the fractions: 6/10 + 35/100 + 25/100 = 60/100 + 35/100 + 25/100 = 120/100 = 1.2 miles. Therefore, Julian walked 1.2 miles, not 1/5 mile as his sister claimed. So, I do not agree with his sister's statement.
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The half life of a certain tranquilizer in the bloodstream is 37 hours. How long will it take for the drug to decay to 86% of the original decay model,A=A
Answer:
8.1 hours
Step-by-step explanation:
A model of the fraction remaining can be ...
f = (1/2)^(t/37) . . . . t in hours
So, for the fraction remaining being 86%, we can solve for t using ...
0.86 = 0.5^(t/37)
log(0.86) = (t/37)log(0.5)
t = 37·log(0.86)/log(0.5) ≈ 8.0509 ≈ 8.1 . . . hours
It takes about 8.1 hours to decay to 86% of the original concentration.
Flying against the wind, an airplane travels 5760 kilometers in 6 hours. Flying with the wind, the same plane travels 6300 kilometers in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?
Step-by-step explanation:
Let the speed of plane be p and speed of wind be w.
Flying against the wind, an airplane travels 5760 kilometers in 6 hours.
Here
Speed = (p-w) kmph
Time = 6 hours
Distance = 5760 kmph
Distance = Speed x Time
5760 = (p-w) x 6
p-w = 960 -----eqn 1
Flying with the wind, the same plane travels 6300 kilometers in 5 hours.
Here
Speed = (p+w) kmph
Time = 5 hours
Distance = 6300 kmph
Distance = Speed x Time
6300 = (p+w) x 5
p+w = 1260 -----eqn 2
eqn 1 + eqn 2
p-w + p +w = 960 + 1260
2p = 2220
p = 1110 kmph
Substituting in eqn 2
1110 + w = 1260
w = 150 kmph
Speed of plane = 1110 kmph
Speed of wind = 150 kmph
Find the point P on the line yequals=22x that is closest to the point (10,0 )(10,0).
What is the least distance between P and (10,0 )(10,0)?
There is no Graph to go in response to this question
Identify the graph for the complex number 3 − 5i. HELP ASAP!
Answer:
Plot the point (3, -5)
Step-by-step explanation:
Recall that the general number a+bi can be plotted on a complex plane with the x axis as the real part and the y axis as the imaginary part.
In short,
a = real part = x
b = imaginary part = y
So (a,b) = (x,y)
In this case, a = 3 and b = -5 which is how I got (3, -5).
It might help to rewrite 3 - 5i into 3 + (-5)i