The equation of line passing through points (-2,7) and (3,2) is y = -x + 5. The slope, m, is -1. The y-intercept, b, is 5.
Explanation:The subject matter here is finding the equation of a line in slope-intercept form, which is expressed as y = mx + b. Here, 'm' is the slope of the line and 'b' is the y-intercept. The slope, m, can be found using the formula: m = (y2 - y1)/(x2 - x1). Applying the coordinates given, (-2,7) and (3,2), we find the slope, m = (2 - 7) / (3 - (-2)) = -5 / 5 = -1.
Then, substituting m, x, and y into the equation, we get the y-intercept. Using the point (-2,7), we have: 7 = -1*-2 + b -> 7 = 2 + b -> b = 7 - 2 = 5. So the y-intercept, b, is 5. Therefore, the equation of the line in slope-intercept form is y = -x + 5.
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Verify that the divergence theorem is true for the vector field f on the region
e. give the flux. f(x, y, z) = 3xi + xyj + 4xzk, e is the cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3.
To verify the divergence theorem, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
Explanation:To verify the divergence theorem for the given vector field f(x, y, z) = 3xi + xyj + 4xzk on the region e, which is a cube bounded by the planes x = 0, x = 3, y = 0, y = 3, z = 0, and z = 3, we need to calculate the flux of the vector field through the surface of the cube and compare it with the divergence of the vector field integrated over the volume of the cube.
The flux, Ƭ, can be calculated using the surface integral of the vector field over each face of the cube. According to the divergence theorem, this should be equal to the volume integral of the divergence of the vector field over the entire volume of the cube.
By calculating both sides of the equation, we can verify that the divergence theorem holds true for the given vector field on the specified region.
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P(1+r)t Using the expression above, choose the correct answers for the new balance and the amount of interest earned in the following compound interest problem. $950 at 7% for 8 years, compounded annually. Total Amount = $ Interest Amount = $
Final answer:
The new balance after 8 years with an initial $950 at a 7% annual interest rate compounded annually is $1632.77, and the amount of interest earned is $682.77.
Explanation:
The compounded interest formula is P(1+r)^t, where P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. To find the new balance and amount of interest earned for $950 at 7% for 8 years, compounded annually, we use the formula with P = $950, r = 0.07 (7% as a decimal), and t = 8.
First, we calculate the new balance:
Total Amount = $950(1 + 0.07)^8
Total Amount = $950(1.07)^8
Total Amount = $950 * 1.718186
Total Amount = $1632.77 (rounded to two decimal places)
Subsequently, to find the amount of interest earned, we subtract the original principal from the total amount:
Interest Amount = Total Amount - Original Principal
Interest Amount = $1632.77 - $950
Interest Amount = $682.77
Therefore, the new balance after 8 years is $1632.77, and the interest earned is $682.77.
Harland just got his second major credit card, so his credit score rose from 671 to 711. According to the following table for a $150,000 mortgage, how much less per year would Harland have to pay on a $150,000 mortgage with the new credit score?
Answer:
2004
Step-by-step explanation:
The ticket sales for Fist Bump are as follows:
On Monday 1 /7 of the tickets are sold
On Tuesday 1/3 of the tickets are sold
On Wednesday 2/7 of the tickets are sold
What fraction of tickets was sold by Thursday?
To calculate the total fraction of tickets sold for the movie Fist Bump by Thursday, we find the least common denominator for the fractions (21), convert each fraction, and then sum them up to get 16/21 of the tickets sold.
Explanation:The question is asking how much of the tickets were sold by Thursday for the movie Fist Bump. To find the total fraction of tickets sold from Monday to Wednesday, we need to add up the fractions:
Monday: 1/7 of the ticketsTuesday: 1/3 of the ticketsWednesday: 2/7 of the ticketsFirst, let's find a common denominator for the fractions. The least common multiple of 7 and 3 is 21, so we'll convert all fractions to have a denominator of 21:
1/7 = 3/211/3 = 7/212/7 = 6/21Now we can add the fractions:
3/21 + 7/21 + 6/21 = 16/21
Therefore, by Thursday, a total of 16/21 of the tickets have been sold.
arman needs 4 1/2 inches of cable to make A,3 3/4 inches to make B, and 5 1/8 inches to make C. He used a 12 inch piece of cable to make A and B.
Answer:
8 1/4
Step-by-step explanation:
Ahmed is working at the burger joint. His boss pays him $6.50 per hour and promises a raise of $0.25 per hour every 6 months. Which sequence describes Ahmed's expected hourly wages in dollars, starting with his current wage?
Answer:
Sequence will be $6.50, $6.75, $7.0, $7.25.......
Step-by-step explanation:
Ahmed is working at the burger joint and he was paid by his boss $6.50 per hour.
His boss promised him to raise $0.25 per hour every six months.
So we have to find the sequence which describes Ahmed's expected hourly wages starting with his current wage.
As at every 6 months increase in wages is $0.25 so the sequence formed will be an arithmetic sequence with common difference of 0.25 and first term 6.50
Sequence will be $6.50, $6.75, $7.0, $7.25,.........
Evaluate x 1 - x -1 + x 0 for x = 2
a) 0
b)1/2
c)1 1/2
d)2 1/2
The solution of expression is, 7/2.
What is an expression?A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
We have to give that,
An expression is,
⇒ x¹ + x⁻¹ + x⁰
Now, Substitute x = 2 in the above expression and find the value,
⇒ x¹ + x⁻¹ + x⁰
⇒ 2¹ + 2⁻¹ + 2⁰
⇒ 2 + 1/2 + 1
⇒ 3 + 1/2
⇒ (6 + 1)/2
⇒ 7/2
Therefore, The solution is, 7/2
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What is 45 ones times 10?
Choices are:
45 hundreds
45 tenths
or 45 tens.
Answer:
Option 3 - 45 tens
Step-by-step explanation:
Given : Expression 45 ones times 10.
To find : What is the expression?
Solution :
We know that,
"one" means " 1
We have 45 ones means multiply 45 by 1.
[tex]45\text{ ones}=45\times 1=45[/tex]
Now, 45 ones times 10 means
[tex]45\times 10=450[/tex]
450 means 45 tens as tens is 10.
So, The correct choice is 45 tens.
Therefore, Option 3 is correct.
A number N is multiplied by 3. The result is the same as when N is divided by 3. What is the value of N?
Answer:
[tex]N=0[/tex]
Step-by-step explanation:
We have been given that a number N is multiplied by 3. So our number would be [tex]3\cdot N[/tex].
We are also told that N is divided by 3. So our number would be [tex]\frac{N}{3}[/tex].
As we are told that the both results are same, so we can equate both expressions as:
[tex]3\cdot N=\frac{N}{3}[/tex]
[tex]3*3\cdot N=\frac{N}{3}*3[/tex]
[tex]9N=N[/tex]
[tex]9N-N=N-N[/tex]
[tex]8N=0[/tex]
[tex]\frac{8N}{N}=\frac{0}{N}[/tex]
[tex]N=0[/tex]
Therefore, the value of N is 0.
A maintenance man has 12 keys on his key ring. if he tries the keys at random on a storage room door, discarding those that do not work, what is the probability that he will get the door open on his 4th try?
Final answer:
The probability that the maintenance man will open the storage door on his fourth try with 12 keys is 1/12.
Explanation:
The question asks for the probability that the maintenance man will open a storage room door on his fourth try with 12 unique keys at his disposal. This is a classic probability problem that involves permutations.
To solve this, we consider the scenario as a sequence of independent events. He has 1 out of 12 chances to pick the correct key on the first try, 1 out of 11 on the second try (after discarding the first incorrect key), 1 out of 10 on the third try, and so on. However, we want the first three attempts to be unsuccessful and the fourth to be successful.
Thus, the probability that the first three keys are incorrect is (11/12) * (10/11) * (9/10), and the probability the fourth key is correct is 1/9. The overall probability of the desired outcome is the product of these probabilities, which simplifies to:
(11/12) * (10/11) * (9/10) * (1/9) = 1/12.
f(x)=-x^2-2x-4
Does the function have a minimum or maximum value?
Where does the minimum or maximum value occur? x = ____
What is the function's minimum or maximum value?
If one calendar year had two consecutive months with Friday the thirteenth, which months would they be?
Use the position equation
s = −16t^2 + v0t + s0
as the model for the problem.
A cargo plane flying at 6000 feet over level terrain drops a 700-pound supply package.
(a) How long will it take the package to strike the ground? (Round your answer to two decimal places.)
(b) The plane is flying at 600 miles per hour. How far will the package travel horizontally during its descent? (Round your answer to two decimal places.)
A. To solve for the time it takes for the package to strike the ground, all we have to do is to plug in the given values in to the position equation:
s = −16 t^2 + v0 t + s0
Where,
s = distance of the plane from the ground = - 6000 ft (negative since the package moves from top to bottom)
t = time for it to strike the ground = unknown
v0 = 0 since the package starts from rest
s0 = 0 since we take the plane as the reference point
Substituting the given values:
- 6000 = -16 t^2 + 0 * t + 0
16 t^2 = 6000
t^2 = 375
t = 19.36 s
B. s = v * t
where v = 600 miles / hr = 0.17 miles / s
s = (0.17 miles / s) * 19.36 s
s = 3.23 miles = 17,054 ft
Simplify: (4a + 2b)(a - b)
A) 4a^2 - 6ab - 2b^2
B) 4a^2 - 2ab - 2b^2
C) 4a^2 - 8ab - 2b^2
D) 4a^2 + 2ab - 2b^2
11 X 11= 4, 12x12=9,13x13=?
Based on the pattern observed in the given equations, 13 + 13 would equal 8.
The given equations seem to follow a pattern where the sum of two numbers is not their arithmetic sum but rather a result derived from some other relationship. Let's try to decipher the pattern:
For the equation 11 + 11 = 4:
The word "eleven" has 6 letters, so it becomes 6 + 6 = 4, which is true.
For the equation 12 + 12 = 9:
The word "twelve" has 6 letters, so it becomes 6 + 6 = 9, which is true.
Following the same pattern:
For 13 + 13:
The word "thirteen" has 8 letters, so it becomes 8 + 8 = ?
Thus, 13 + 13 = 8.
Therefore, based on the pattern observed in the given equations, 13 + 13 would equal 8.
The probable question maybe:
If 11 + 11 = 4 and 12 + 12 = 9 then what is 13 + 13 = ?
Use the distributive property to write an equivalent expression for 4(x-2)
Calculating the return on investment using financial leverage. suppose Dave invested only 20,000 of his own money and borrowed 180,000 interest-free from his rich father. what was his return on investment?
A cone shaped funnel has a radius of 3 inches and a height of 7 inches.
Betty closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 14 cubic inches per minute, how long will it take for all the liquid in the funnel to pass through the nozzle? (Use π = 3.14.)
A) 4.71 minutes
B) 3.14 minutes
C) 14.13 minutes
D) 9.42 minutes
Hence, it will take 4.71 minutes for all the liquid in the funnel to pass through the nozzle.
Step-by-step explanation:A cone shaped funnel has a radius(r) of 3 inches and a height(h) of 7 inches.
Now, the volume(V) of the cone is given as:
[tex]V=\dfrac{1}{3}\times (\pi r^2h)[/tex]
Hence, on putting the value of r and h in the formula of volume we obtain the volume of cone funnel as:
[tex]V=\dfrac{1}{3}\times (3.14\times (3)^2\times 7)\\\\\\V=\dfrac{1}{3}\times (197.82)\\\\V=65.94 \ in^3[/tex]
If the liquid drips at the rate of 14 cubic inches per minute.
i.e. for 14 cubic inches it takes 1 minutes.
Now for 1 cubic inches it will take:
[tex]\dfrac{1}{14} \ min.[/tex]
Hence, for all the liquid ( i.e. 65.94 cubic inches) to pass the nozzle is the time taken is:
[tex]\dfrac{65.94}{14}\ min.\\\\=4.71\ min.[/tex]
Hence, it will take 4.71 minutes for all the liquid in the funnel to pass through the nozzle.
Given m || n, find X....PLEASE HELP ASAP....SOS...SUCK AT MATH PLEASE HELP ME!!
EASY 5 POINTS!!!! A new park in the shape of a hexagon will have 66 sides of equal length. On a scale drawing, the coordinates of the vertices of the park are: (6.5,5)6.5,5, (18.5,0)18.5,0, (6.5,-5)6.5,-5,
(-6.5,-5)-6.5,-5, (-18.5,0)-18.5,0, and (-6.5,5)-6.5,5. How long is each side of the park?
To solve this problem, first we have to plot the vertices in a Cartesian plane to know the plot. This would also give us an idea of which points are adjacent or interconnected forming a hexagon.
The plot is shown below. Now we can see which points are adjacent to each other. Let us take points (-6.5, 5) and (6.5, 5) for our calculation.
The distance formula given two points is:
d^2 = (x2 – x1)^2 + (y^2 – y^1)^2
Now we calculate the distance between 2 points:
d^2 = (6.5 – (-6.5))^2 + (5 – 5)^2
d^2 = 169
d = 13
Therefore the length of each side of the park is 13 units.
Answer:
13 units
To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. By following the steps outlined, you can determine the length of each side of the hexagon.
Explanation:To find the length of each side of the hexagon, you can use the distance formula. The distance formula is derived from the Pythagorean theorem for finding the length of the hypotenuse of a right triangle. In this case, the coordinates of the vertices of the hexagon form a regular hexagon, meaning all sides are equal in length. Here's how you can find the length of one side:
Take the coordinates of two adjacent vertices of the hexagon.Use the distance formula, which is sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.Plug in the coordinates and calculate the distance.Repeat the process for different pairs of adjacent vertices to make sure all sides have the same length.By following these steps, you should be able to determine the length of each side of the hexagon.
The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 42 inches, how long is each spoke? Round your answer to the nearest hundredth.
Indicate in standard form the equation of the line through the given points.
P(0, -4), Q(5, 1)
lim θ→π/4 1 - tan θ / sin θ - cos θ
You are dealt one card from a standard 52-card deck find the probability of being dealt an ace or an 8
there are 4 Aces and 4 8's for a total of 8 cards
52 cards in a deck
so probability of picking an Ace or 8 = 8/52
Final answer:
The probability of being dealt an ace or an 8 from a standard 52-card deck is 2/13, which is approximately 15.38%.
Explanation:
The question asks for the probability of being dealt an ace or an 8 from a standard 52-card deck. There are 4 aces and 4 eights in a 52-card deck. To calculate the probability of getting either an ace or an 8, we add the probability of getting an ace to the probability of getting an 8. The probability of drawing an ace (P(Ace)) is 4/52 and the probability of drawing an 8 (P(8)) is also 4/52. Since these are mutually exclusive events (you cannot draw an ace and an 8 simultaneously with one card), we can simply add these probabilities together:
P(Ace or 8) = P(Ace) + P(8)
= (4/52) + (4/52)
= 8/52
= 2/13
Therefore, the probability of being dealt an ace or an 8 is 2/13, which is approximately 0.1538 or 15.38%.
Henry Devine bought a new dishwasher for$320 he paid $20 down and made 10 monthly payments of $34 what actually yearly rate did Henry pay
Tommy and Sally are arguing over the meanings of x^4 and x^-4. Tommy argues that x^4 is the reciprocal of x^-4. Sally insists that x^-4 is the reciprocal of x^4 . Who is correct? A. Tommy is correct. x^4 is the reciprocal of x^-4. B. Sally is correct. x^-4 is the reciprocal of x^4. C. Both Tommy and Sally are correct. x^-4 and x^4 are the reciprocals of each other. D. Niether Sally nor Sally is correct. Neither x^-4 nor x^4 is a reciprocal of the other.
A manufacturing machine has a 10% defect rate. if 4 items are chosen at random, what is the probability that at least one will have a defect?
The probability that at least one of the four randomly chosen items will be defective is 34.39%. This is calculated by subtracting the probability that all items are not defective from 1.
Explanation:The subject of the question relates to the field of Probability. This problem pertains to the concept known as 'probability of at least one' event. In this case, we are considering the probability that at least one item will have a defect.
To calculate this, it's easier to find the probability that none of the items have a defect and then subtract that from 1. Since the machine has a 10% defect rate, it means there's a 90% chance that any item chosen will NOT be defective. If we choose 4 items, the probability that all are good is 0.9 * 0.9 * 0.9 * 0.9 = 0.6561.
So, the probability that at least one defective item will be chosen is 1 - 0.6561 = 0.3439 or 34.39%.
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Each day a small business owner sells 200 pizza slices for $1.50 per slice and 85 sandwiches at $3.50 each. Business exspenses come to $130 per day. What is the owner's profit for a ten-day period.
Final answer:
The small business owner's profit for a ten-day period is $4,675, calculated by determining the total daily revenue from pizza slices and sandwiches, subtracting daily expenses, and then multiplying the result by ten.
Explanation:
The question pertains to calculating the profit for a small business over a ten-day period. To do this, we first calculate the daily revenue from selling pizza slices and sandwiches and then subtract the daily expenses. After that, we multiply the daily profit by ten.
Daily pizza slice revenue: 200 slices × $1.50/slice = $300Daily sandwich revenue: 85 sandwiches × $3.50/sandwich = $297.50Total daily revenue: $300 + $297.50 = $597.50Total daily expenses: $130Daily profit: $597.50 - $130 = $467.50Total 10-day profit: $467.50/day × 10 days = $4,675The owner's profit for the ten-day period would then be $4,675.
the circle is centered at the origin and the length of its radius is 4. what is
the circles equation
Answer: [tex]x^2+y^2=16[/tex]
Step-by-step explanation:
The general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given: Radius of the circle : r= 4 units
The center of the circle : (h,k)=(0,0)
Now, the equation of a circle having center at (0,0) and radius 4 units is given by :-
[tex](x-0)^2+(y-0)^2=4^2\\\\\Rightarrow\ x^2+y^2=16[/tex]
Answer:
X²+Y²=16
Step-by-step explanation:
A p e x
Which of the following shows 2.1851 rounded to the nearest tenth?
A. 2.1
B.2.185
C.2.19
D.2.2