equation of a line with slope m=−2/5 that contains the point (10,−5).
Answer:
y = (-2/5)x+b
Step-by-step explanation:
First plug these into the y=mx+b equation:
-5 = (-2/5)(10)+b.
Then solve for b:
-5 = -4+b
Add 4 to both sides:
-1 =b.
Therefore, the equation of the line is y = (-2/5)x+b. You can also double check this by plugging 10 into the equation we just obtained.
Two lines meet at a point that is also the vertex of an angle set up and solve an appropriate equation for x and y.
Both vertical angles measure 90 degrees, and the adjacent angles each measure 90 degrees as well.
When two lines intersect at a point, we can use the properties of vertical and adjacent angles to set up and solve equations relating to their measures. This can help us find missing angles or verify that two angles are congruent.
When two lines intersect at a point, they form two angles. These angles are called vertical angles, and they are always congruent. In addition, the two lines also form two pairs of adjacent angles, each pair of which adds up to 180 degrees.
Let's consider an example to understand this concept better. Suppose we have two lines AB and CD that intersect at point P. If angle APD measures x degrees, then angle BPC also measures x degrees because they are vertical angles. Similarly, angle APB and angle CPD are adjacent angles, and their sum is 180 degrees. If angle APB measures y degrees, then angle CPD also measures y degrees.
Therefore, we can set up the following equation:
x + y = 180
This equation relates the measures of the adjacent angles formed by the two lines. We can solve for one variable in terms of the other by rearranging the equation:
y = 180 - x
This equation gives us the measure of one angle in terms of the measure of the other. We can substitute this expression into the equation for the vertical angles to get:
2x = 180
Solving for x, we find that x = 90.
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PLEASE HELP!! Find the area of the figure.
The area of the trapezoid in this problem is given as follows:
15 square feet.
How to obtain the height of the trapezoid?The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:
A = 0.5 x h x (b1 + b2).
The dimensions for this problem are given as follows:
h = 3 ft, b1 = 4 ft and b2 = 6 ft.
Hence the area is given as follows:
A = 0.5 x 3 x (4 + 6)
A = 1.5 x 10
A = 15 square feet.
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The area of a square with side length s is s2. Meg crocheted a baby blanket for her new cousin. The blanket is a square with 30-inch sides. What is the area of the baby blanket? Write your answer as a whole number or decimal
The area of the baby blanket with side length of 30 inches is equal to 900 square inches.
Let 'A' represents the area of the square.
And s represents the side length of the square.
The area of a square is given by the formula
A = s^2.
For Meg's baby blanket,
The side length of the baby blanket is equal to 30 inches,
Substitute the values in the area formula we get,
A = s^2
⇒ A = 30^2
⇒ A = 900 square inches
Therefore, the area of Meg's baby blanket is equal to 900 square inches.
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Orlando wants to borrow $3,000 for the purchase of a used car. He has to pay back the loan after 4 years. The two loan options are simple interest at a rate of 5. 8% each year, or interest compounded annually at a rate of 5. 2% each year. Which method should he choose , simple or compound , and how much less will he owe using that method?
Orlando should consider using simple interest and the amount he will have to pay is $696, under the condition that he wants to borrow $3,000 for the purchase of a used car. He needs to clear the loan after 4 years.
Orlando should apply the simple interest method.
The amount of interest he will pay using simple interest is evaluated
I = P × r × t
Here
I = interest paid
P = borrowed principal amount
r = rate of annual interest
t = time
In this case,
P = $3,000
r = 5.8%
t = 4 years
Therefore,
I = $3,000 × 0.058 × 4
= $696
So Orlando will pay $696 in interest using simple interest.
The amount of interest he will pay using compound interest is calculated as follows:
[tex]A = P * (1 + r/n)^{(n*t)}[/tex]
I = A - P
Here,
A = end term amount
n = count of interest that is compounded each year
In this case,
P = $3,000
r = 5.2%
t = 4 years
Interest is compounded annually so n=1
Therefore,
A = $3,000 × (1 + 0.052/1)⁴
= $3,697.47
I = $3,697.47 - $3,000
= $697.47
So Orlando will pay $697.47 in interest using compound interest.
Therefore, Orlando should choose simple interest method and he will owe $1.47 less using that method.
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This question is kinda confusing :(
Two different furniture manufacturers produce chairs. let x represent the number of chairs produced daily at plant x, and let y represent the number of chairs produced daily at plat y
Sure, happy to help! So, we have two furniture manufacturers producing chairs, and we'll call them Plant X and Plant Y. Let x represent the number of chairs produced daily at Plant X, and let y represent the number of chairs produced daily at Plant Y.
Now, we don't know what the actual numbers are, but we can use these variables to talk about them in a general way. For example, we could say that Plant X produces 100 chairs per day (so x = 100), and Plant Y produces 200 chairs per day (so y = 200).
Does that make sense? Let me know if you have any other questions!
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Why does this limit evaluate to 0 instead of 2?
[tex]\lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right)[/tex]
You're partially correct, as if x approaches ∞ it would approach 2, as eˣ is exponentially growing if x is positive.
If x is negative, which it is in this case, eˣ would get exponentially smaller. For example, e⁻² = 1/e².
So, in this case [tex]\frac{5}{e^x}[/tex] would get exponentially larger, as it is a number over an increasingly small number, like how [tex]\frac{1}{0.001}[/tex] is larger than [tex]\frac{1}{0.1}[/tex].
Therefore the limit would be equivalent to [tex]\frac{2}{\infty}[/tex], which is equal to 0
[tex] \Large{\boxed{\sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = 0}} [/tex]
[tex] \\ [/tex]
Explanation:
We are trying the find the limit of [tex] \: \sf \dfrac{2}{1 - \dfrac{5}{ {e}^{x} } } \: [/tex] when x tends to -∞.
[tex] \\ [/tex]
Given expression:
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) [/tex]
[tex] \\ [/tex]
[tex]\blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Properties\text{:}}}} \\ \\ \sf{ \diamond \: \dfrac{c}{ + \infty} = 0^{ + } \: \: and \: \: \dfrac{c}{ - \infty} = 0^{ - } \: \: , \: where \: c \: is \: a \: positive \: number.} \\ \\ \\ \diamond \: \sf \dfrac{c}{ {0}^{ + } } = + \infty \: \: and \: \: \dfrac{c}{ {0}^{ - } } = - \infty \: \: , \: where \: c \: is \: a \: positive \: number.\\ \\ \\ \diamond \: \sf c - \infty = -\infty \: \: and \: \: c + \infty = \infty \: \: ,\: where \: c \: is \: a \: positive \: number. \\ \\ \\ \sf{ \diamond \: \green{e ^{ - \infty} = 0^{+} \: \: and \: \: e ^{ + \infty} = + \infty} } \\ \end{array}}\\\end{gathered} \end{gathered}}[/tex]
[tex] \\ [/tex]
Substitute -∞ for x[tex] \\ [/tex]
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \sf \left(\dfrac{2}{1-\frac{5}{e^{ - \infty}}}\right) [/tex]
[tex] \\ [/tex]
Simplify knowing that [tex] \sf e^{-\infty} \\ [/tex] approaches 0 but remains a positive number. This will be written as 0⁺.
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \left(\dfrac{2}{1-\frac{5}{e^{ - \infty}}}\right) = \left(\dfrac{2}{1-\frac{5 \: \: }{0^{ + } }}\right)[/tex]
[tex] \\ [/tex]
Simplify again knowing that 5/0⁺ = +∞.
[tex] \\ [/tex]
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \left(\dfrac{2}{1-\frac{5 \: \: }{0^{ + } }}\right) = \sf \left(\dfrac{2}{1 - \infty}\right) = \dfrac{2}{ - \infty} [/tex]
[tex] \\ [/tex]
Conclusion[tex] \\ [/tex]
[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \dfrac{2}{ - \infty} = 0^{-} \\ \\ \\ \implies \boxed{ \boxed{ \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) =0}}[/tex]
[tex] \\ \\ \\ [/tex]
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A skier can purchase a daily or season pass.
The daily pass costs $48 per day and included
the price of ski rentals. The season pass costs
$190 plus a daily fee of $10 to rent the skis.
How many days would a skier have to go skiing
in order for both options to cost the same?
A.
5 days
C. 240 days
D. 10 days
B.
3 days
We know that the skier would have to go skiing for 5 days in order for both options to cost the same.
To find out how many days a skier would have to go skiing for both options to cost the same, we need to set up an equation. Let's use "d" to represent the number of days the skier goes skiing.
For the daily pass option:
Total cost = $48 x d
For the season pass option:
Total cost = $190 + ($10 x d)
Now we can set up the equation:
$48 x d = $190 + ($10 x d)
Simplifying this equation, we get:
$38 x d = $190
Solving for "d", we get:
d = 5
Therefore, the skier would have to go skiing for 5 days in order for both options to cost the same.
So the answer is A. 5 days.
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(1 point) Calculate T..T,, and n(u, v) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point. (u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v) = . The tangent plane: = 92
Given points:
(u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v)
the equation of the tangent plane at the point (u, v) = (24, 9) is:-8x + z = -183T
Process of finding equation:
To start, let's find T..T,, which represents the magnitude of the tangent vector at the given point:
T..T, = ||n(u, v)|| = ||n(24, -31, 72)|| = ||<48, -62, 144>|| = sqrt(48^2 + (-62)^2 + 144^2) = sqrt(11668) ≈ 108.03
Next, let's find the normal vector n(u, v) at the given point:
n(u, v) =
where f_u and f_v are the partial derivatives of the surface equation with respect to u and v, respectively.
In this case, we have:
f(u, v) = (24 + 0,u - 40, 8u)
f_u = <0, 1, 8>
f_v = <1, 0, 0>
Therefore, at the point (u, v) = (24, 9), we have:
n(u, v) = <0, 1, 8> x <1, 0, 0> = <-8, 0, 1>
Finally, let's find the equation of the tangent plane at the point (u, v) = (24, 9). The equation of a plane can be written as:
Ax + By + Cz = D
where A, B, and C are the components of the normal vector, and D can be found by plugging in the coordinates of the point on the plane. In this case, we have:
A = -8
B = 0
C = 1
D = -8(24) + 1(9) = -183
Therefore, the equation of the tangent plane at the point (u, v) = (24, 9) is:
-8x + z = -183
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Casho signed up for a streaming music service that costs $7 per month. The service allows Casho to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1. 50 per song. How much total money would Casho have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded ss songs?
To find out how much Casho would have to pay in a month in which she downloaded 30 songs, we need to consider both the monthly subscription cost and the cost per song for offline listening.
Step 1: Determine the cost of the monthly subscription, which is $7.
Step 2: Calculate the cost of downloading 30 songs for offline listening. To do this, multiply the cost per song ($1.50) by the number of songs (30).
1.50 * 30 = $45
Step 3: Add the monthly subscription cost ($7) to the cost of downloading 30 songs ($45).
7 + 45 = $52
So, Casho would have to pay $52 a month in which she downloaded 30 songs.
Now, let's find out how much Casho would have to pay if she downloaded ss songs.
Step 1: The cost of the monthly subscription remains the same at $7.
Step 2: Calculate the cost of downloading ss songs for offline listening. Multiply the cost per song ($1.50) by the number of songs (ss).
1.50 * ss = 1.50ss
Step 3: Add the monthly subscription cost ($7) to the cost of downloading ss songs (1.50ss).
7 + 1.50ss = 7 + 1.50ss
The total amount Casho would have to pay if she downloaded ss songs is 7 + 1.50ss.
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This is absolute value so if u dont know just leave if u steal points im reporting
Answer:
k = - 1/3------------------------
We know the property of an absolute value: it is never negative.
Hence the given inequality is equivalent to below equation:
(3k + 1)/74 = 03k + 1 = 03k = - 1k = - 1/3This is the only solution.
When we solve for K in the inequality, 0 ≥ |(3K + 1) / 74|, the result obtained is -1/3
How do i solve 0 ≥ |(3K + 1) / 74|?We can solve the expression 0 ≥ |(3K + 1) / 74| as illustrated below:
0 ≥ |(3K + 1) / 74|
Remove the absolute sign
0 ≥ (3K + 1) / 74
Cross multiply
0 ≥ (3K + 1) / 74
0 × 74 ≥ 3K + 1
0 ≥ 3K + 1
Collect like terms
0 - 1 ≥ 3K
-1 ≥ 3K
Divide both sides by 3
-1/3 ≥ K
K = -1/3
Thus, we can conclude from the above calculation that the value of K in the inequality, 0 ≥ |(3K + 1) / 74| is -1/3
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The following table is based on 16 trials.
Х 15 16 17 18
frequency 2 4 8 2
Based on the table, how many 16's would you expect to get if there are 120 trials?
This means that there is a 50% chance that the outcome of a trial will be 17.
The given table represents the frequency distribution of a discrete random variable X, which has four possible outcomes: 15, 16, 17, and 18. The frequency of each outcome indicates the number of times that outcome occurs in 16 trials.
To calculate the probability of a specific outcome, we divide its frequency by the total number of trials. In this case, we want to find P(X=17), which is the probability that the outcome of a trial is 17. From the table, we see that the frequency of X=17 is 8, which means that 17 occurred 8 times out of 16 trials. Therefore,
P(X=17) = frequency of X=17 / total number of trials = 8 / 16 = 0.5
This means that there is a 50% chance that the outcome of a trial will be 17.
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Full Question: The Following Table Is Based On 16 Trials. X 15 16 17 18 Frequency 2 4 8 2 Based On The Table, What Is P(X=17)? Leave Your Answer In Decimal Form To Three Places.
The following table is based on 16 trials.
x 15 16 17 18
frequency 2 4 8 2
Based on the table, what is P(x=17)?
Leave your answer in decimal form to three places.
Find the critical value t Subscript c for the confidence level c=0.90. and sample size n=26
The critical value t Subscript c for a confidence level of 0.90 and sample size of 26 is 1.708. A t-value greater than or less than 1.708 in absolute value would lead to rejection of the null hypothesis at the 0.10 level of significance.
To find the critical value t Subscript c for the confidence level c=0.90 and sample size n=26, we can use a t-distribution table or calculator.
Since we have a sample size of n=26, we have n-1 = 25 degrees of freedom. Using a t-distribution table or calculator with 25 degrees of freedom and a confidence level of 0.90, we get
t Subscript c = 1.708
Therefore, the critical value t Subscript c for the confidence level c=0.90 and sample size n=26 is 1.708. This means that if we calculate the t-value from our sample data and it is greater than or less than 1.708 in absolute value, we can reject the null hypothesis at the 0.10 level of significance.
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An object is launched vertically in the air at 41.65 meters per second from a 7-meter-tall platform. using the projectile motion model h(t)=-4.9t^2+v0t+h0, where h(t) is the height of the projectile t seconds after it’s departure, v0 is the initial velocity in meters per second, and h0 is the initial height in meters, determine how long it will take for the object to reach its maximum height. what is the maximum height?
To find the maximum height of the object, we need to first determine when the object reaches that height. We can use the projectile motion model h(t) = -4.9t^2 + v0t + h0 to solve for the time it takes for the object to reach its maximum height.
Since the object is launched vertically, we know that its initial velocity is 41.65 m/s and its initial height is 7 meters. We can substitute these values into the projectile motion model and solve for when the object reaches its maximum height by finding the vertex of the resulting quadratic function.
h(t) = -4.9t^2 + 41.65t + 7
To find the time it takes for the object to reach its maximum height, we can use the formula t = -b/2a, where a = -4.9 and b = 41.65.
t = -(41.65)/(2(-4.9))
t = 4.25 seconds
Therefore, it takes 4.25 seconds for the object to reach its maximum height.
To find the maximum height, we can plug in this time value into the projectile motion model and solve for h(t).
h(4.25) = -4.9(4.25)^2 + 41.65(4.25) + 7
h(4.25) = 89.57 meters
The maximum height of the object is 89.57 meters.
In summary, the object launched vertically from a 7-meter-tall platform with an initial velocity of 41.65 m/s takes 4.25 seconds to reach its maximum height of 89.57 meters. This is found by using the projectile motion model h(t) = -4.9t^2 + v0t + h0 and finding the time it takes for the object to reach its maximum height, and then plugging in that time value to find the maximum height.
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PLEASE HELP ME ASAP
Can you please make a copy and put dots in eachone that goes where its supposed to go
Answer:
1
1
1
2
2
2
2
Step-by-step explanation:
Explain how you can determine if (x + 3) is a factor of the given polynomial through factoring and polynomial division:
(A-APR. 2) (A1. 26. A, A1. 26. B)
x3-x2-12x
fast with step by step explanation if possible please!
To determine whether (x + 3) is a factor of the polynomial x^3 - x^2 - 12x, we can use polynomial division.
Step 1: Write the divisor, (x + 3), on the left side of a long division symbol and the dividend, x^3 - x^2 - 12x, on the right side.
x + 3 | x^3 - x^2 - 12x
Step 2: Divide the first term of the dividend, x^3, by the first term of the divisor, x, and write the result, x^2, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the dividend.
lua
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2
Step 3: Bring down the next term of the dividend, -12x, and write it next to the remainder, -4x^2.
lua
Copy code
x^2 - 4x
___________________
x + 3 | x^3 - x^2 - 12x
- (x^3 + 3x^2)
----------
-4x^2 - 12x
Step 4: Divide the first term of the new dividend, -4x^2, by the first term of the divisor, x, and write the result, -4x, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the previous subtraction.
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Kera took out a 24-month bank loan of $13,000 at an interest rate of 5. 95%. She budgets to pay
$450 per month towards the loan. Write an equation that represents how much total interest
Kera will pay towards the remaining balance of the loan at the end of each year. Let m equal the
number of months paid and r equal the interest charged on the remaining balance
The equation that represents how much total interest Kera will pay towards the remaining balance of the loan at the end of each year is Total Interest Paid = (Remaining Balance) x (Annual Interest Rate) = $422.03.
The equation that represents how much total interest Kera will pay towards the remaining balance of the loan at the end of each year is:
Total Interest Paid = (Remaining Balance) x (Annual Interest Rate)
To calculate the remaining balance after m months, we can use the formula for the present value of an annuity:
Remaining Balance = (Payment per Month) x ((1 - (1 + r)^(-n)) / r)
where r is the monthly interest rate (0.0595 / 12 = 0.004958), n is the total number of months (24), and m is the number of months paid (12, 24, etc.).
Plugging in the given values, we get:
Remaining Balance = 450 x ((1 - (1 + 0.004958)^(-12)) / 0.004958) = $6,752.45
To calculate the annual interest rate, we can use the formula:
Annual Interest Rate = (1 + r)^12 - 1
Plugging in the monthly interest rate, we get:
Annual Interest Rate = (1 + 0.004958)^12 - 1 = 0.0625
Therefore, the equation that represents how much total interest Kera will pay towards the remaining balance of the loan at the end of each year is:
Total Interest Paid = $6,752.45 x 0.0625 = $422.03 (rounded to the nearest cent)
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A backyard is 40. 5 feet long and 25 feet wide. in order to install a pool, the yard needs to be reduced by a scale of one-third. what is the area of the reduced yard? feet2.
If A backyard is 40. 5 feet long and 25 feet wide then, the area of the reduced yard is approximately 450.09 ft².
The area of the original backyard is:
40.5 ft x 25 ft = 1012.5 ft²
To reduce the yard by a scale of one-third, we need to multiply the length and width by 2/3:
40.5 ft x 2/3 = 27 ft
25 ft x 2/3 = 16.67 ft (rounded to two decimal places)
The area of the reduced yard is:
27 ft x 16.67 ft = 450.09 ft² (rounded to two decimal places)
Therefore, the area of the reduced yard is approximately 450.09 ft².
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Patricia bought 4 apples and 9 bananas for $12. 70. Jose bought 8 apples and 11 bananas for $17. 70 at the same grocery store. What's the price of one apple?
The price of one apple is $0.70, obtained by solving the system of equations 4x + 9y = 12.70 and 8x + 11y = 17.70 using elimination.
How much would Patricia pay for each apples?Let's use a system of equations caculation the problem.
Let x be the price of one apple and y be the price of one banana.
From the first sentence, we know that:
4x + 9y = 12.70
From the second sentence, we know that:
8x + 11y = 17.70
Now we can solve for x by using either substitution or elimination.
Let's use elimination.
We can multiply the first equation by 11 and the second equation by -9, then add them together:
44x + 99y = 139.70
-72x - 99y = -159.30
-28x = -19.60
Dividing both sides by -28, we get:
x = 0.70
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Consider the vector field F(x, y, z) = (yz, -5xz, –4xy). Find the divergence and curl of F. div(F) = V.F= = curl(F) = V XF =( ). B) Consider the vector field F(x, y, z) = (-x?, -(x + y)
a) The divergence of F is -4x - 2y,
b) The curl of F is (-2(x+y), 0, -2x).
A) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:
div(F) = ∇ · F = ∂(yz)/∂x + ∂(-5xz)/∂y + ∂(-4xy)/∂z
= 0 - 5z - 4x
= -5z - 4x
To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:
curl(F) = ∇ × F = ( ∂(-4xy)/∂y - ∂(-5xz)/∂z, ∂(yz)/∂z - ∂(4xy)/∂x, ∂(-yz)/∂x - ∂(-5xz)/∂y )
= (-5z, y, -5x)
B) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:
div(F) = ∇ · F = ∂(-x²)/∂x + ∂(-(x+y)²)/∂y + ∂(0)/∂z
= -2x - 2(x+y)
= -4x - 2y
To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:
curl(F) = ∇ × F = ( ∂(0)/∂y - ∂(-(x+y)²)/∂z, ∂(0)/∂z - ∂(-x²)/∂x, ∂(-(x+y))/∂x - ∂(-x²)/∂y )
= (-2(x+y), 0, -2x)
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The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price. What was the sale price of the skateboard?
A. 66. 00
B. 68. 80
C. 67. 20
D. 28. 80
The answer is (C) 67.20.
Charlie saved 30% off of the original price, which means he paid 70% of the original price.
Let x be the sale price of the skateboard.
We have:
0.7 * 96 = x
x = 67.20
Therefore, the sale price of the skateboard was $67.20.
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The sales director noticed that sales in the Midwest and Northeast regions were not as expected. Additional field training is necessary for the sales representatives in these regions. After conducting a one-month training program, the sales director wants to determine the effectiveness of the training. After all, the company invested a significant amount of money in this program! So the sales director collects the sales data for the first month after the training. The sales director wants to compare the number of orders secured by those who attended the training program and those who didn't attend. This study will help the company to determine the effectiveness of the training. Part A What type of study is the sales director conducting—a survey, an observational study, or an experiment? Justify your answer
The type of study the sales director is conducting is an experiment to compare the number of orders secured by those who attended the training program and those who didn't attend.
The sales director conducted an experimented
The experiment is to do a test to see if something works or to try to improve it
Here the objective of the experiment was to see the effectiveness of the training by providing a one-month training program for employees. After that, the sales director collects the sales data for the first month. The sales director compared the number of orders secured by those who attended the training program and those who didn't attend. This experiment will help the company to determine the effectiveness of the training. If the experiment is effective or not.
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Elena has an empty mini fish tank. She drops her pencil in the tank and notices that it fits
just diagonally. (See the diagram.) She knows the tank has a length of 4 inches, a width of
5 inches, and a volume of 140 cubic inches. Use this information to find the length of
Elena's pencil. Explain or show your reasoning.
The length of Elena's pencil is approximately 9.49 inches.
Let's break down the problem :
We are given that Elena's mini fish tank has a length of 4 inches, a width of 5 inches, and a volume of 140 cubic inches.
To find the height of the tank, we can use the formula for the volume of a rectangular prism: volume = length * width * height.
Plugging in the given values, we have[tex]140 =4 \times 5 \times height.[/tex]
Solving for height, we get height [tex]= 140 / (4 \times 5) = 7[/tex] inches.
Now, let's move on to finding the length of Elena's pencil.
We are told that the pencil fits diagonally in the tank.
The diagonal of a rectangular prism can be found using the formula: diagonal [tex]= \sqrt{(length^2 + width^2 + height^2) }[/tex]
Plugging in the values, we have diagonal [tex]= \sqrt{(4^2 + 5^2 + 7^2) }[/tex]
[tex]= \sqrt{(16 + 25 + 49) }[/tex]
= √90
= 9.49 inches (rounded to two decimal places).
Therefore, the length of Elena's pencil is approximately 9.49 inches.
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The line plot shows the ages of participants in the middle school play
Determine the appropriate measures of center and variation
The appropriate measures of center and variation are 13 and 4.
Measures of Center:
The appropriate measure of center for this data set is the median since there is no clear outlier present in the data. Hence, the value of median here is 13
Measures of Variation:
The appropriate measure of variation for this dataset is the range, which is the difference between the largest and smallest value in the dataset, Hence the value of range is 4
Since the data is small and there is no clear outlier present, the median is the appropriate measure of center. The range, which is the difference between the largest and smallest value in the dataset, is the appropriate measure of variation
Hence, the appropriate measures of center and variation are 13 and 4.
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3. John has a bag of marbles. The ratio
of red marbles to blue marbles is 3:7.
What percent of the marbles are red?
Answer:
Step-by-step explanation:
percentage is taken as out of 100 we have to do like this for finding any percentage for any given ratio.
add the given ration 7+3=10
now as ratio is given from red to blue so we have red=3 and blue=7.
now final step is that simply do this.....
if 10(total) is equal to 100 %
then 3(for red) is equal how many percentage?
so we know that it will be (3 x 100) / 10 = 30%
so 30 percent of marbles are red.
Find the value of this expression if x=8. x^2-8/x+1
The value of the expression when x=8 is 56/9.
To find the value of an expression, follow these steps:
Replace any variables in the expression with the given values. For example, if the expression is "3x + 5" and x = 2, replace x with 2 to get "3(2) + 5".Simplify the expression using the order of operations (PEMDAS/BODMAS). Evaluate any operations inside parentheses first, then perform any multiplications or divisions from left to right, and finally perform any additions or subtractions from left to right.Continue simplifying the expression until you reach a single value.To find the value of the expression when x=8, we substitute 8 for x in the expression:
(8^2 - 8) / (8+1)
= (64 - 8) / 9
= 56/9
Therefore, the value of the expression when x=8 is 56/9.
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PLEASE HELP ME IMMEDIATELY!!!!!
The intervals where f is decreasing are given as follows:
None of the above.
When a function is increasing and when it is decreasing, looking at it's graph?Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.Hence the decreasing intervals of the function are given as follows:
-3.5 < x < -1.x > 2.5.Which are none of the options given in the problem.
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The probability that Mr Smith will have coffee with his breakfast is 0. 35. Find the probability that in the next 25 mornings, Mr Smith will have coffee on exactly 8 mornings
The probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is 0.142, or 14.2%.
This scenario can be modeled by a binomial distribution, where:
The probability of success (having coffee) on any given morning is p = 0.35
The number of trials (mornings) is n = 25
The number of successes (mornings with coffee) we want to find the probability for is k = 8.
The probability mass function for a binomial distribution is given by:
[tex]P(X = k) = (n \: choose \: k) \times p^k \times (1-p)^{(n-k)},[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n. It can be calculated as:
(n choose k) = n! / (k! × (n-k)!)
Using this formula and putting in the values we have,
[tex]P(X = 8) = (25 \: choose \: 8) \times 0.35^8 \times (1-0.35)^{(25-8)} [/tex]
[tex]P(X = 8) ≈ 0.142[/tex]
Therefore, the probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is approximately 0.142, or 14.2%.
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Tabitha bought a new SUV and obtained a loan for $29,000. The annual interest
rate is 4. 3% for 7 years. If Tabitha takes the loan for 5 years instead of 7, she will
save. 5% on the interest rate. How much less will Tabitha pay for her SUV if she
takes the loan for 5 years? *
Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.
To calculate the total amount Tabitha might pay for the SUV with a 7-year loan, we are able to use the compound interest formula for calculating the total amount of a loan, that is:
[tex]total amount = principal x (1 + interest charge)^{time}[/tex]
Wherein:
principal is the amount of the loaninterest charge is the annual interest rate Time is the length of the loan in yearsWith a 7-year loan, the full amount Tabitha could pay is:
[tex]total amount = $29,000 x (1 + 0.043)^{7} = $37,501.76[/tex]
To calculate the overall amount she could pay with a 5-year loan and a 5% decrease interest rate, we first need to calculate the new interest price. A 5% discount inside the interest price of 4.3% is:
New interest price = 4.3% - 5% = 3.3%
Then we can use the equal formula as before to calculate the total amount with the 5-year mortgage:
[tex]total amount = $29,000 x (1 + 0.033)^{5} = $33,093.47[/tex]
The difference in the overall amount among the two loans is:
$37,501.76 - $33,093.47 = $4,408.29
Therefore, Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.
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