The management fee Mike must pay this year is $84.
To calculate the management fee Mathew must pay this year, we need to find 0.50 percent of $16,800.
First, let's convert the percentage to a decimal by dividing it by 100. So, 0.50 percent is equal to 0.50/100 = 0.005.
Now, multiply the total investment amount by the management fee rate:
Management fee = $16,800 x 0.005 = $84.
Therefore, Mathew must pay $84.00 as the management fee this year for his investment in the New Colony Pacific Region mutual fund (rounded to 2 decimal places).
In summary, management fees are a percentage of the total asset value invested in a mutual fund, which goes toward compensating the fund managers for their services. In this case, Mathew's management fee is 0.50 percent, which equals $84.00 for the year.
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Find parametric equations for the line that is tangent to the given curve at the given parameter value.
r(t) = 3t^2 i +(4t-1)j + t^3 k t = T_o = 4
what is the standard parameterization for the tangent line. (type expressions using t as the variable)
x =
y=
z=
The standard parametric equations for the tangent line to the curve r(t) at t = T₀ = 4 are: x = 24(t-4) + 48, y = 15(t-4) - 3, z = 64(t-4) + 64
To find the parametric equations for the tangent line to the curve r(t) at t = T₀ = 4, we can follow these steps:
Step 1: Find the point on the curve at t = T₀.
To find the point on the curve at t = T₀ = 4, we simply evaluate r(4):
r(4) = 3(4²)i + (4(4)-1)j + 4³k
= 48i + 15j + 64k
So the point on the curve at t = 4 is (48, 15, 64).
Step 2: Find the direction of the tangent line at t = T₀.
To find the direction of the tangent line, we need to take the derivative of r(t) and evaluate it at t = 4. So we first find r'(t):
r'(t) = 6ti + 4j + 3t²k
Then we evaluate r'(t) at t = 4:
r'(4) = 6(4)i + 4j + 3(4²)k
= 24i + 4j + 48k
So the direction of the tangent line at t = 4 is the vector <24, 4, 48>.
Step 3: Write the parametric equations for the tangent line.
To write the parametric equations for the tangent line, we use the point and direction found in steps 1 and 2. We can write the parametric equations as:
x = 48 + 24(t-4)
y = 15 + 4(t-4)
z = 64 + 48(t-4)
Simplifying these equations gives us:
x = 24t + 48
y = 4t - 3
z = 48t + 64
These are the standard parametric equations for the tangent line to the curve r(t) at t = 4.
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Rob bought a 1965 Fender Jazzmaster vintage electric guitar in 1980 for a price of $150. In 2010 it was appraised for $4,200. Suppose $150 was deposited in a variable-rate certifi cate of deposit for 30 years with interest compounded daily. A. If the CD paid 12. 3% interest for the fi rst 7 years, what would the balance be after the fi rst 7 years? Round to the nearest cent. B. If the CD paid 6% interest for the next 10 years, what would the balance be after the fi rst 17 years? Round to the nearest cent. C. If the CD paid 4. 1% interest for the remaining 13 years, what would the balance be after 30 years? Round to the nearest cent. D. What is the difference between the appraised value of the guitar and the amount the original $150 would have earned in the CD?
a. If the CD paid 12. 3% interest for the first 7 years, he balance be after the first 7 years will be $492.89.
b. If the CD paid 6% interest for the next 10 years, the balance be after the first 17 years would be $784.98.
c. If the CD paid 4. 1% interest for the remaining 13 years, the balance be after 30 years would be $1,265.59.
d. The difference between the appraised value of the guitar and the amount the original $150 would have earned in the CD is $2,784.41.
A. The annual interest rate for a CD that pays 12.3% interest compounded daily is 12.3%/365 ≈ 0.0337% per day. The balance after 7 years can be calculated using the formula:
Balance = $150 x (1 + 0.000337)^((365 x 7) / 365) ≈ $492.89
Rounding to the nearest cent, the balance after 7 years is $492.89.
B. After 7 years, the remaining term of the CD is 30 - 7 = 23 years. The annual interest rate for a CD that pays 6% interest compounded daily is 6%/365 ≈ 0.0164% per day. The balance after 17 years can be calculated using the formula:
Balance = $492.89 x (1 + 0.000164)^((365 x 10) / 365) ≈ $784.98
Rounding to the nearest cent, the balance after 17 years is $784.98.
C. After 17 years, the remaining term of the CD is 30 - 17 = 13 years. The annual interest rate for a CD that pays 4.1% interest compounded daily is 4.1%/365 ≈ 0.0112% per day. The balance after 30 years can be calculated using the formula:
Balance = $784.98 x (1 + 0.000112)^((365 x 13) / 365) ≈ $1,265.59
Rounding to the nearest cent, the balance after 30 years is $1,265.59.
D. The difference between the appraised value of the guitar and the amount the original $150 would have earned in the CD is:
$4,200 - $1,265.59 - $150 ≈ $2,784.41
Rounding to the nearest cent, the difference is $2,784.41.
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Please help with this math problem!
The equation of the ellipse is x^2/9 + y^2/6.75 = 1
Finding the equation of the ellipseTo find the equation of an ellipse, we need to know the center, the major and minor axis, and the foci.
Since we are given the eccentricity and foci, we can use the following formula:
c = (1/2)a
Since the foci are (0, +/-3), the center is at (0, 0). We know that c = 3/2, so we can find a:
c = (1/2)a
3/2 = (1/2)a
a = 3
The distance from the center to the end of the minor axis is b, which can be found using the formula:
b = √(a^2 - c^2)
b = √(3^2 - (3/2)^2)
b = √6.75
So the equation of the ellipse is:
x^2/a^2 + y^2/b^2 = 1
Plugging in the values we found, we get:
x^2/3^2 + y^2/6.75 = 1
Simplifying:
x^2/9 + y^2/6.75 = 1
Therefore, the equation of the ellipse is x^2/9 + y^2/6.75 = 1
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What is the interquartile range of 58,55,54,61,56,54,61,55,53,53?
The interquartile range of 58,55,54,61,56,54,61,55,53,53 is 6.
To find the interquartile range (IQR), we first need to find the first and third quartiles of the data set. The first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half of the data set. The IQR is then the difference between Q3 and Q1.
To find Q1 and Q3, we first need to put the data set in order from lowest to highest:
53, 53, 54, 54, 55, 55, 56, 58, 61, 61
The median of the entire data set is the average of the two middle numbers, which in this case is (55 + 56) / 2 = 55.5.
To find Q1, we need to find the median of the lower half of the data set, which includes the numbers 53, 53, 54, 54, 55. The median of this lower half is the average of the two middle numbers, which is (53 + 54) / 2 = 53.5.
To find Q3, we need to find the median of the upper half of the data set, which includes the numbers 56, 58, 61, 61. The median of this upper half is the average of the two middle numbers, which is (58 + 61) / 2 = 59.5.
Now that we have Q1 and Q3, we can calculate the IQR as:
IQR = Q3 - Q1 = 59.5 - 53.5 = 6
Therefore, the interquartile range of the given data set is 6.
The IQR is a useful measure of variability because it is not influenced by outliers or extreme values in the data set, unlike the range or standard deviation. The IQR gives us an idea of the spread of the "middle" 50% of the data, which can help us understand the distribution of the data and identify any potential skewness or outliers.
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THIS IS DUE TONIGHT! PLEASE HELP ME! :c
USE STRUCTURE Complete the table to show the effect that the transformation has on the table of the parent function f(x)=x2.
g(x)is a reflection of f(x)across the x-axis.
x f(x) g(x)
-2 4
-1 1
0 0
1 1
2 4
The table of values to show the effect of the transformation is
x f(x) g(x)
-2 4 -4
-1 1 -1
0 0 0
1 1 -1
2 4 -4
Completing the table of values to show the effectFrom the question, we have the following parameters that can be used in our computation:
f(x) = x²
Also, we have
g(x) is a reflection of f(x)across the x-axis
This means that
g(x) = -f(x)
So, we have
g(x) = -x²
Using the above as a guide, we have the following:
x f(x) g(x)
-2 4 -4
-1 1 -1
0 0 0
1 1 -1
2 4 -4
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Write the standard form of the equation of the circle with the given characteristics. Endpoints of a diameter: (0, 0), (8, 6)
The standard form of the equation of the circle with the given characteristics is[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
To get the equation of the circle using the endpoints of a diameter, we have to use the standard form :
[tex](x - h) ^{2} + (y - k)^{2} = {r}^{2} [/tex]
In which (h, k) represents the middle point of the circle and r as the radius. so, we need to find the midpoint of the diameter using the endpoints (0, 0) and (8, 6).
Midpoint = ((0+8)/2, (0+6)/2) = (4, 3)
Next, we need to calculate the radius by using the distance formula to calculate the distance between the center and one of the diameter endpoints.
[tex] {r}^{2} = {(8 - 4)}^{2} + {(6 - 3)}^{2} = {4}^{2} + {3}^{2} = 16 + 9 = 25[/tex]
Now, substituting the values of (h, k) and
[tex] {r}^{2} [/tex] into the standard form equation to get the equation:
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
Therefore, the standard form equation of the circle with the given characteristics is
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
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The standard form of the given question is (x - 4)² + (y - 3)² = 25, under the condition endpoints of a diameter: (0, 0), (8, 6).
In order To write the standard form of the equation of a circle with endpoints of a diameter (0, 0), (8, 6), we first need to find the center and radius of the circle.
The diameter comprises the midpoints of the center of the circle. The midpoint of (0, 0) and (8, 6) is ((0+8)/2, (0+6)/2) = (4,3). Center point of the circle is (4,3).
Diameter = 2× radius
. The distance between (0, 0) and (8, 6) is √((8-0)² + (6-0)²)
= √(64+36)
= √100
= 10.
Then, the radius of the circle is 10/2 = 5.
Then,
(x - h)² + (y - k)² = r²
here
(h,k) = center of the circle
r = radius.
Staging in this equation
h=4,
k=3
r=5
(x - 4)²+ (y - 3)² = 25
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Javier's deli packs lunches for a school field trip by randomly selecting sandwich, side, and drink options. each lunch includes a sandwich (pb&j, turkey or ham and cheese), a side (cheese stick or chips), and a drink (water or apple juice)
1. what is the probability that a student gets a lunch that includes chips and apple juice?
2. what is the probability that a student gets a lunch that does not include chips?
Answer is: Probability of a student getting a lunch that does not include chips is 6/12 or 0.5.
1. To find the probability of a student getting a lunch that includes chips and apple juice, we need to first find the total number of possible lunch combinations. There are 3 options for sandwiches, 2 options for sides, and 2 options for drinks, so there are a total of 3 x 2 x 2 = 12 possible lunch combinations.
Out of those 12 combinations, there is only 1 combination that includes chips and apple juice: ham and cheese sandwich, chips, and apple juice.
Therefore, the probability of a student getting a lunch that includes chips and apple juice is 1/12 or approximately 0.083.
2. To find the probability of a student getting a lunch that does not include chips, we can count the number of possible lunch combinations that do not include chips and divide by the total number of lunch combinations.
There are 3 sandwich options and 2 drink options, so there are a total of 3 x 2 = 6 possible lunch combinations without chips.
Out of the total of 12 possible lunch combinations, 6 do not include chips, so the probability of a student getting a lunch that does not include chips is 6/12 or 0.5.
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Shea wrote the expression 5(y + 2) + 2 to show the amount of money five friends paid for snacks at a basketball game. Which expression is equivalent to the one Shea wrote?
a 5 + y + 5 + 2 + 4
b 5 x y x 5 x 2 +4
c 5 x y x 4 + 5 x 2 x 4
d 5 x y + 5 x 2 + 4
The expression that is equivalent to the one Shea wrote is b 5 x y x 5 x 2 +4
Which expression is equivalent to the one Shea wrote?From the question, we have the following parameters that can be used in our computation:
5(y + 2) + 2 shows the amount of money five friends paid for snacks at a basketball game
This means that
Amount = 5(y + 2) + 2
When expanded, we have
Amount = 5 * y + 5 * 2 + 2
Using the above as a guide, we have the following:
The expression that is equivalent to the one Shea wrote is b 5 x y x 5 x 2 +4
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Find all solutions of the equation in the interval [0, 2π). Show formula and steps used, not a calculator problem. (8 csc x - 16)(4 cos x - 4) = 0
The solutions for the equation in the interval [0, 2π) are x = 0, x = π/6, and x = 5π/6.
To find all solutions of the equation (8 csc x - 16)(4 cos x - 4) = 0 in the interval [0, 2π), we can set each factor equal to zero and solve for x separately.
1) 8 csc x - 16 = 0
8 csc x = 16
csc x = 2
Recall that csc x = 1/sin x, so:
1/sin x = 2
sin x = 1/2
In the interval [0, 2π), sin x = 1/2 at x = π/6 and x = 5π/6. So, the solutions for this part are x = π/6 and x = 5π/6.
2) 4 cos x - 4 = 0
4 cos x = 4
cos x = 1
In the interval [0, 2π), cos x = 1 at x = 0 and x = 2π. However, since 2π is not included in the interval, we only have x = 0 as a solution for this part.
Combining both parts, the solutions for the equation in the interval [0, 2π) are x = 0, x = π/6, and x = 5π/6.
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Please help I need it ASAP, also needs to be rounded to the nearest 10th
The length of segment BC is given as follows:
BC = 47.2 km.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:
c² = a² + b² - 2ab cos(C)
The parameters for this problem are given as follows:
a = 27.8, b = 24.7, C = 129.1
Hence the length of segment BC is given as follows:
(BC)² = 27.8² + 24.7² - 2 x 27.8 x 24.7 x cosine of 129.1 degrees
(BC)² = 2249.0497
[tex]BC = \sqrt{2249.0497}[/tex]
BC = 47.2 km.
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Pls help I really need help on this
The operations that results in a rational numbers are C + D, A · B and C · D.
How to obtain a rational number from combining irrational numbersIn this problem we must determine what operations between irrational numbers are equivalent to a rational number. Real numbers are result of the union between rational and irrational numbers. We need to check if each operation is equivalent to a rational number:
Case 1: A + B
A + B = √3 + 2√3 = 3√3 (Irrational)
Case 2: C + D
C + D = √25 + √16 = 5 + 4 = 9 (Rational)
Case 3: A + D
A + D = √3 + √16 = √3 + 4 (Irrational)
Case 4: A · B
A · B = √3 · 2√3 = 2 · 3 = 6 (Rational)
Case 5: B · D
B · D = 2√3 · √16 = 2√3 · 4 = 8√3 (Irrational)
Case 6: C · D
C · D = √25 · √16 = 5 · 4 = 20 (Rational)
Case 7: A · A
A · A = √3 · √3
A · A = 3 (Rational)
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A 5 m long car is overtaking a 19 m long bus. The bus is travelling at a constant speed of 25 m/s. The car takes 3 s to overtake the bus. We assume that overtaking starts when the frontmost part of the car crosses the backmost part of the bus and ends when the backmost part of the car crosses the frontmost part of the bus. So at what constant speed (in m/s) is the car driving?
Answer:
Length of a car is 5m
Length of bus is 19m
Velocity of bus is 25ms-¹
Step-by-step explanation:
Assuming that overtaking start from front most part to back most part
Distance travel by car is 19m+5m=24m
Let velocity of bus be Vc and of car be Vb
Now
Velocity of car is 32ms-¹
How can I get the answer for
A=
Vertex for y=
Answer:
1) a = 14
2) -4 (x - 2)² - 5
Step-by-step explanation:
To obtain a vertex, you take h and k in a equation.
So a(x-h)²+k = a(x-2)² -5
For the point (1, - 9),
a[(1)-2]² - 5 = - 9
a(1) = -9+5
a = -4
so the final equation is
-4(x-2)² - 5
I'm not 100% sure about this but I tried. Let me know if it makes sense
A $70,000 mortgage is $629. 81 per month. What was the percent and for how many years?
9%, 20 years
9%, 25 years
7%, 20 years
9%, 30 years
The closest answer is 9% interest rate and 25 years term of the loan.
Assuming the $70,000 mortgage is a fixed-rate mortgage, we can use the formula for the monthly payment of a mortgage to solve for the interest rate and the term of the loan.
The formula is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where:
M = monthly payment
P = principal (amount borrowed)
i = interest rate (per month)
n = number of months
Substituting the given values, we get:
$629.81 = $70,000 [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Using a mortgage calculator or by trial and error, we can find that the closest answer is 9% interest rate and 25 years term of the loan.
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Sort each set of triangle measurements into the appropriate category for number of possible triangles. No Triangles One Triangle Many Triangles 5, 15", 160 45°, 45°, 90° 2.8. 10 7, 24, 25 30", 85°, 60° 5 of 5 Done
Walmart is contacting all of the manufacturers that supply its more than 4,000 u. s. stores with a logistics proposition: the world’s largest retailer wants to use its own fleet of trucks to pick up products directly from manufacturers and deliver the merchandise to walmart’s stores. in short, walmart’s truck fleet would replace manufacturers’ or common carriers’ trucks. by doing so, walmart believes it will enjoy substantial cost savings while allowing manufacturers to concentrate on what they do best—making products rather than managing logistical systems. walmart, with about 6,500 trucks and over 50,000 trailers, believes it has the capacity to implement this new logistical program
Walmart's decision to use its own fleet of trucks to pick up products directly from manufacturers and deliver them to its stores is a strategic move that has the potential to benefit both Walmart and manufacturers.
By using its own fleet, Walmart will be able to cut down on transportation costs and gain more control over the supply chain, which can lead to better efficiency and cost savings. This is especially important given Walmart's massive scale, with over 4,000 stores in the US alone.
For manufacturers, this move by Walmart could be a relief as they can focus on their core competency of making products rather than managing logistics. With Walmart taking over the transportation aspect, manufacturers can rest assured that their products will be delivered on time and in the right condition.
The fact that Walmart already has a large fleet of trucks and trailers means that it has the capacity to implement this new program without too much additional investment. However, it remains to be seen how manufacturers will respond to this proposal, as they may have existing contracts with other carriers or may be hesitant to rely too heavily on Walmart for their transportation needs.
Overall, Walmart's move towards using its own fleet of trucks is a smart one that has the potential to benefit both the retailer and its suppliers.
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suppose you own a restaurant and have a cook whose ability and attitude you are suspicious of. one of the dishes on the menu is duck cassoulet, which uses duck legs that have been slow fried over a couple of hours in oil that does not exceed a temperature of 175 degrees. this is a time consuming and monotonous process, but one that results in excellent meat that you sell for a large mark-up. you suspect your cook is lazy and doesn't properly monitor and maintain the oil temperature. you take a random sample of 12 duck legs and take them to a forensics lab where you are able to discover the maximum temperature the meat has reached. within your sample the mean maximum temperature of the duck legs is 182 degrees with a standard deviation of 5 degrees. meat cooked precisely to 175 degrees is what your cook is supposed to do. test the claim that your employee is capable (meaning he doesn't over-fry the meat) at the 90% confidence level. what is your conclusion? group of answer choices reject the null hypothesis, accept the alternative hypothesis fail to reject the null hypothesis reject the null hypothesis, reject the alternative hypothesis fail to reject the null hypothesis, fail to reject the null hypothesis fail to reject the null hypothesis, reject the alternative hypothesis
The claim of cooking duck legs at given temperature with mean , standard deviation represents reject the null hypothesis, accept the alternative hypothesis.
Confidence level = 90%
Sample mean maximum temperature x = 182 degrees
Hypothesized population mean μ =175 degrees
Sample standard deviation s = 5 degrees)
Sample size n =12
To test the claim that employee is capable of cooking the duck legs within the required temperature range.
Set up the following hypotheses,
Null hypothesis,
The mean maximum temperature of the duck legs is equal to or greater than 175 degrees (μ ≥ 175).
Alternative hypothesis,
The mean maximum temperature of the duck legs is less than 175 degrees (μ < 175).
Testing whether the mean is less than a specific value (175 degrees), this is a one-tailed test.
To reject or fail to reject the null hypothesis,
Use a one-sample t-test with a significance level of 0.1 .
T-test statistic is ,
t = (x - μ) / (s / √n)
Plugging in the values, we get,
t = (182 - 175) / (5 / √(12))
= 4.85
The degrees of freedom for this test is n-1 = 11.
Using a t-distribution table ( attached table) ,
Critical value for a one-tailed test with 11 degrees of freedom and a significance level of 0.1.
The critical value is 1.363.
Since the calculated t-value 4.85 is greater than the critical value (1.363).
Reject the null hypothesis at the 90% confidence level.
⇒Sufficient evidence to conclude that the mean maximum temperature of the duck legs cooked by your cook is less than 175 degrees.
Employee is not capable of cooking the duck legs within the required temperature range.
Therefore, for the given situation of confidence level of 90% reject the null hypothesis, accept the alternative hypothesis.
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QUESTION 3 2 - 1 Let () . Find the interval (a,b) where y increases. As your answer please input a+b QUESTION 4 Let(x) = xº - 6x3 - 60x2 + 5x + 3. Find all solutions to the equation f'(x) = 0. As your answer please enter the sum of values of x for which f() -
The interval where y increases for the function f(x) = (4x² - 1)/(x² + 1) is (-∞, -0.5) U (0.5, ∞) is 0.5-(-∞) = ∞.
To find the intervals where the function f(x) = (4x² - 1)/(x² + 1) increases, we need to find its derivative and determine its sign. The derivative of f(x) can be found using the quotient rule:
f'(x) = [(8x)(x² + 1) - (4x² - 1)(2x)]/(x² + 1)²
Simplifying this expression, we get:
f'(x) = (12x - 4x³)/(x² + 1)²
To find the critical points, we need to solve the equation f'(x) = 0:
12x - 4x³ = 0
4x(3 - x²) = 0
This gives us the critical points x = 0 and x = ±√3. We can now test the intervals between these critical points to determine the sign of f'(x) in each interval.
Testing x < -√3, we choose x = -4, and we get f'(-4) = (-224)/(17²) < 0. Therefore, f(x) is decreasing on this interval.
Testing -√3 < x < 0, we choose x = -1, and we get f'(-1) = (16)/(2²) > 0. Therefore, f(x) is increasing on this interval.
Testing 0 < x < √3, we choose x = 1, and we get f'(1) = (16)/(2²) > 0. Therefore, f(x) is increasing on this interval.
Testing x > √3, we choose x = 4, and we get f'(4) = (-224)/(17²) < 0. Therefore, f(x) is decreasing on this interval.
Hence, the interval where f(x) increases is (-∞, -0.5) U (0.5, ∞). Therefore, the answer is 0.5 - (-∞) = ∞.
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Pls help me with this! I need to finish today
Answer:
T=64
Step-by-step explanation:
Multiply both sides by 4
t/4=16
t/4×4=16×4 Cancel out the 4
t=64
Goldilocks walked into her kitchen to find that a bear had eaten her tasty can of soup. All that was left was the label below that used to completely cover the sides of the can (without any overlap). What was the volume of the can of soup that the bear ate? The label is 22 in. (top) by 9 in. (side).
The volume of the can of soup that the bear ate was approximately 4644.64 cubic inches.
To solve this problem, we need to make some assumptions about the can of soup. Let's assume that the can is cylindrical and that it is completely filled with soup. We also need to assume that the label covered the entire surface area of the can without any overlap.
The label is 22 inches tall and 9 inches wide, so it covered a total surface area of 22 x 9 = 198 square inches. Since the label completely covered the sides of the can without any overlap, we can use this surface area to find the surface area of the can itself.
The surface area of a cylinder is given by the formula A = 2πrh + 2πr², where r is the radius of the base of the cylinder, and h is the height of the cylinder. In this case, we know that the height of the cylinder is 22 inches (the height of the label), and the circumference of the base of the cylinder is 9 inches (the width of the label).
Using these values, we can solve for the radius of the cylinder:
9 = 2πr
r = 4.53 inches
Now we can use the formula for the surface area of a cylinder to solve for the volume of the can:
A = 2πrh + 2πr²
198 = 2π(22)(4.53) + 2π(4.53)²
198 = 634.26
A = πr²h
V = A x h/3
V = 634.26 x 22/3
V ≈ 4644.64 cubic inches
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Cam put 4 12/25 pounds of rice in bags that each weigh 7/25 pound. She uses 1/8 of the bags of rice. How many bags of rice are left?
Answer:
14
Step-by-step explanation:
Cam put a total of 4 12/25 pounds of rice in bags, which is equivalent to 112/25 pounds of rice.
Each bag weighs 7/25 pound, so the total number of bags of rice is:
(112/25) ÷ (7/25) = 16
Cam uses 1/8 of the bags of rice, which is:
(1/8) x 16 = 2
So Cam uses 2 bags of rice.
The number of bags of rice left is the total number of bags (16) minus the number of bags used (2):
16 - 2 = 14
Therefore, 14 bags of rice are left.
An architect needs to design a new light house. an average-man (6 ft tall) can see 1 mile
into the horizon with binoculars. if the company building the light house would like for
their guests to be able to see 20 miles out from the top of the light house with binoculars,
then how tall does the building need to be?
The lighthouse needs to be at least 270.7 feet tall to allow guests to see 20 miles out with binoculars.
Assuming the Earth is a perfect sphere, the distance a person can see to the horizon is given by: d = 1.22 * sqrt(h)
Where d is the distance in miles, h is the height of the observer in feet, and 1.22 is a constant based on the radius of the Earth.
Using this formula, we can solve for the required height of the lighthouse: 20 = 1.22 * sqrt(h), 20/1.22 = sqrt(h), h = (20/1.22)^2, h ≈ 270.7 feet
Therefore, the lighthouse needs to be at least 270.7 feet tall to allow guests to see 20 miles out with binoculars.
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ignore the 94 don’t really understand this problem pls help (giving brainliest)
Answer:
measure of angle GHJ = 1/2 the measure of arc GJ = (1/2)(86°) = 43°
measure of angle JIG = 1/2 the measure of arc GJ = (1/2)(86°) = 43°
Given that MNPQ is a rectangle with vertices M(3, 4), N(1, -6), and P(6, -7), find the coordinates Q that makes this a rectangle
Given that MNPQ is a rectangle with verticles M(3, 4), N(1, -6), and P(6, -7), to find the coordinates of point Q, we can use the fact that opposite sides of a rectangle are parallel and have equal lengths.
First, let's find the vector MN and MP:
MN = N - M = (1 - 3, -6 - 4) = (-2, -10)
MP = P - M = (6 - 3, -7 - 4) = (3, -11)
Now, let's add the vector MN to point P:
Q = P + MN = (6 + (-2), -7 + (-10)) = (4, -17)
Therefore, the coordinates of point Q that make MNPQ a rectangle are Q(4, -17).
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A sector with a central angle measure of 4/ 7π(in radians) has a radius of 16 cm. what is the area of the sector.
The area of the sector is approximately 73.14 square centimeters.
The formula to calculate the area of a sector is given by A = (θ/2) × r^2, where θ is the central angle measure in radians, and r is the radius of the circle.
Substituting the given values in the formula, we get A = (4/7π/2) × 16^2
Simplifying this expression, we get A = (8/7) × 16^2 × π/2
A = 128π square centimeters/7
Using the approximation π ≈ 3.14, we can calculate the value of A as follows:
A ≈ (128 × 3.14) square centimeters/7 ≈ 573.44 square centimeters/7 ≈ 73.14 square centimeters (rounded to two decimal places)
Therefore, the area of the sector is approximately 73.14 square centimeters.
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O is the centre of the given circle. if OX⊥PQ, OY⊥RS and PQ=RS, write down the relation between OX and OY.
Since OX is perpendicular to PQ, and OY is perpendicular to RS, we know that OX and OY are both radii of the circle. Therefore, we can write:
OX = OY
This is because all radii of a circle are equal in length. Alternatively, we could also say that OX and OY are both the distance from the center O to the respective lines PQ and RS. Since PQ=RS, OX and OY are equal in length.
What is the circle about?In a circle, the center is the point from which all points on the circumference are equidistant. This means that any line segment from the center to a point on the circle is a radius of the circle.
In this problem, we have two lines PQ and RS, both of which are tangent to the circle at points P and R respectively. We also have two lines OX and OY, each of which is perpendicular to one of the tangent lines.
Because the tangent lines are perpendicular to their respective radii (PQ is perpendicular to OX, and RS is perpendicular to OY), we can conclude that OX and OY are both radii of the circle, and therefore, they have the same length.
Note that both are still angles at 90 degrees.
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Analyze the diagram below and answer the questions that follow.
F
G
t
How many different ways can the line above be named? What are those names?
A. 2 ways; FG, GF
B. 3 ways; t, FG, GF
C. 4 ways; t, FG, FG, GF
D. 5 ways; t, FG, GF, FG GF
Answer: A. 2 ways; FG, GF
Step-by-step explanation: There are only two ways to name a line, and they are interchangeable: starting from one endpoint and naming the other endpoint second, or starting from the second endpoint and naming the first endpoint second.
the figure above, AB is parallel to DE; (ABC = 800 and (CDE = 280. Find (DCB.(3mks)
Answer:
Step-by-step explanation:
Since AB is parallel to DE, we know that:
(ABC + BCD) = (CDE + EDC)
Substituting the given values, we get:
800 + BCD = 280 + EDC
Simplifying, we get:
BCD = EDC - 520
We also know that:
(BCD + CDE + DCE) = 180
Substituting BCD = EDC - 520 and CDE = 280, we get:
(EDC - 520 + 280 + DCE) = 180
Simplifying, we get:
EDC + DCE - 240 = 0
EDC + DCE = 240
Now we can solve for DCE in terms of BCD:
DCE = 240 - EDC
DCE = 240 - (BCD + 520)
DCE = 760 - BCD
Substituting this expression for DCE into the equation (BCD + CDE + DCE) = 180, we get:
BCD + 280 + (760 - BCD) = 180
Simplifying, we get:
1040 - BCD = 180
BCD = 860
Therefore, (DCB) = 180 - (BCD + CDE) = 180 - (860 + 280) = -960. However, since angles cannot be negative, we can add 360 degrees to this value to get:
(DCB) = -960 + 360 = -600
Therefore, (DCB) = -600 degrees.
what is the sampling distribution of the sample mean? group of answer choices in practice, to estimate the mean values of a varibale in a large population, we only get to observe a sample, and we can only plot the distribution of this sample, not the distribution of the whole population. the distribution of the sample we have have observed is called the sampling distribution of the sample mean. if we hypothetically had a large number of samples taken from the same population, the distribution of the means of those individual samples is called the sampling distribution of the sample mean
The sampling distribution of the sample mean is the distribution of the means of all the individual samples that were hypothetically drawn from the same population.
A sampling distribution refers to the probability distribution of a statistic that is obtained from a large number of random samples drawn from a population. The sampling distribution is important because it enables us to make statistical inferences about the population based on the sample data.
This makes the sampling distribution a valuable tool for making statistical inferences about population parameters. We could randomly select a sample of students and compute their mean height. If we repeat this process many times and compute the mean height for each sample, we would obtain a sampling distribution of means. This distribution would provide information about the range of possible mean heights we might expect to see if we were to repeat the sampling process many times.
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3/4+(1/3 divided by 1/6) - (-1/2)
3/4 + (1/3 divided by 1/6) - (-1/2) when simplified give 3 1/4
How to determine this
3/4 + (1/3 divided by 1/6) - (-1/2)
3/4 + (1/3 ÷ 1/6) - (-1/2)
Using the rule of BODMAS
Whee B = Bracket
O = Order
D = Division
M = Multiplication
A = Addition
S = Subtraction
By removing the bracket
3/4 + 1/3 ÷ 1/6 + 1/2
By dividing
3/4 + 1/3 * 6/1 + 1/2
3/4 + 6/3 + 1/2
3/4 +2 + 1/2
By finding the LCM
The LCM is lowest common factor of the denominator which is 4
= [tex]\frac{3+8+2}{4}[/tex]
= 13/4
= 3 1/4
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