The maximum concentration of the antibiotic between hours 1 and 7 is 1.03 mg/ug, which occurs at t = 1/39 hours.
To find the maximum concentration of the antibiotic between hours 1 and 7, we need to find the maximum value of the function C(t) on the interval [1, 7]. We can do this by taking the derivative of C(t), setting it equal to zero, and solving for t.
C(t) = 4te^{-39t}
C'(t) = 4e^{-39t} - 156te^{-39t}
Setting C'(t) equal to zero, we get:
4e^{-39t} - 156te^{-39t} = 0
4e^{-39t}(1 - 39t) = 0
1 - 39t = 0
t = 1/39
We can now evaluate C(t) at t = 1/39 and the endpoints of the interval [1, 7] to determine the maximum concentration:
C(1) = 4e^{-39} ≈ 0.00011 mg/ug
C(7) = 28e^{-273} ≈ 0.000000003 mg/ug
C(1/39) = 1.0256 mg/ug
Therefore, the maximum concentration of the antibiotic between hours 1 and 7 is 1.03 mg/ug, which occurs at t = 1/39 hours.
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work out minimum and maximum number of hikers who could have walked between 7 miles and 18 miles
(a) The minimum number of hikers who could have walked between 7 miles and 18 miles: at least 5 hikers and at most 13 hikers.
(b) The maximum number of hikers who could have walked between 7 miles and 18 miles: at most 15 hikers.
According to the question and given conditions, we need to find the cumulative frequency of the distance intervals that fall within the range of 7 miles and 18 miles, to find the minimum number of hikers and the maximum number of hikers who could have walked between 7 miles and 18 miles.
The sum of the frequencies up to a certain point in the data is the cumulative frequency. By adding the frequency of the current interval to the frequency of the previous interval, we can calculate the cumulative frequency.
a) To find the minimum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 5 miles to 10 miles and then from 10 miles to 15 miles.
Cumulative frequency for 5 < x <= 10: 2 + 3 = 5
Cumulative frequency for 10 < x <= 15: 5 + 8 = 13
Therefore, we find that at least 5 hikers and at most 13 hikers could have walked between 7 miles and 18 miles.
b) To find the maximum number of hikers who could have walked between 7 miles and 18 miles, we will find the cumulative frequency of the intervals from 10 miles to 15 miles and from 15 miles to 20 miles.
Cumulative frequency for 10 < x <= 15: 8
Cumulative frequency for 15 < x <= 20: 8 + 7 = 15
Therefore, we can conclude that at most 15 hikers could have walked between 7 miles and 18 miles.
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The complete question is "a) work out the minimum number of hikers who could have walked between 7 miles and 18 miles b) work out the maximum number of hikers who could have walked between 7 miles and 18 miles."
What is the missing step in solving the inequality 4(x – 3) 4 < 10 6x? 1. the distributive property: 4x – 12 4 < 10 6x 2. combine like terms: 4x – 8 < 10 6x 3. the addition property of inequality: 4x < 18 6x 4. the subtraction property of inequality: –2x < 18 5. the division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative startfraction 1 over 9 endfraction. x > –x is greater than or equal to negative startfraction 1 over 9 endfraction.
The missing step in solving the inequality 4(x – 3) /4 < 10/6x is to divide both sides by 2.
Apply the distributive property to get 4x - 12 /4 < 10/6x.
Combine like terms to obtain 4x - 3 < 5/3x.
Add 3/3x to both sides to get 4x < 8/3x + 3.
Subtract 8/3x from both sides to get 4/3x < 3.
Divide both sides by 4/3 to get x < -9/4.
Simplify the result by dividing both sides by 2 to get x < -9/2 or x > -4/3.
Therefore, the missing step is to divide both sides by 2, which gives x < -9/2 or x > -4/3.
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Third-, fourth-, and fifth-grade students collected food items to be sent to 2 different food pantries. The third-grade students collected 35 items and the fourth-grade students collected 25 items. each food pantry was given 50 items. write and solve an equation to find how many items fifth-grade collected
Answer: 35 + 25 + 50 / 2 = 85
Step-by-step explanation: You would have to add them all together and then divide them by 2.
Scientists estimate that the mass of the sun is 1. 9891 x 10 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
There are 26 zeros in this number when it is written in standard notation. The correct answer is option (A). The mass of the sun is estimated to be 1.9891 x 10³⁰kg. To determine the number of zeros in this number when written in standard notation, we need to first convert it to standard form.
In standard form, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. To convert the given number to standard form, we move the decimal point 30 places to the right because the exponent is positive 30. This gives us 1989100000000000000000000000000. As we can see, there are 27 digits in this number. Therefore, there are 27-1=26 zeros in this number when it is written in standard notation.
In conclusion, the answer is A, 26. This type of question is commonly asked in science and engineering, where large or small numbers are expressed in scientific notation for convenience. Understanding how to convert between scientific notation and standard form is important for anyone studying or working in these fields.
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Taylor is making a large banner that
measures 6 yards in length. He split the
banner into 18 sections for him and
some of his friends to work on. How
many inches long is each section?
Answer:
12 is the answer
Step-by-step explanation:
6 y = 6 × 36 in. ( y = yards, in = inches )
do the math:
6(36) ÷ 18 = 12 ( for 18 sections of course )
12 × 18 = 6 × 36
becuase;
12 × 18 = 216 \
——- They are the same
6 × 36 = 216 /
= 216
Divide
216 ÷ 18 = 12
12 being the answer
Answer:
12 inches long
Step-by-step explanation:
One yard is equal to 36 inches, so 6 yards is equal to:
[tex]\sf:\implies 6 \times 36 = 216\: inches[/tex]
To find the length of each section, we need to divide the total length of the banner (216 inches) by the number of sections (18):
[tex]\sf:\implies 216 \div 18 = \boxed{\bold{\:\:12\:\:}}\:\:\:\green{\checkmark} [/tex]
Therefore, each section is 12 inches long.
The area of triangle ABC is 4 root 2. Work out the value of x
Question is from mathswatch
Find dy/dt given that x^2+y^2 = 2x+4y, x = 3, y = 1 and dx/dt = 7
To find dy/dt, we need to use implicit differentiation.
First, we differentiate both sides of the equation with respect to t:
2x(dx/dt) + 2y(dy/dt) = 2(dx/dt) + 4(dy/dt)
Next, we plug in the given values for x, y, and dx/dt:
2(3)(7) + 2(1)(dy/dt) = 2(7) + 4(dy/dt)
Simplifying, we get:
42 + 2(dy/dt) = 14 + 4(dy/dt)
Subtracting 2(dy/dt) and 14 from both sides:
28 = 2(dy/dt)
Finally, we divide both sides by 2 to solve for dy/dt:
dy/dt = 14
To find dy/dt, first differentiate the given equation x^2+y^2=2x+4y with respect to time t. Use the chain rule:
2x(dx/dt) + 2y(dy/dt) = 2(dx/dt) + 4(dy/dt).
Now substitute the given values, x = 3, y = 1, and dx/dt = 7:
2(3)(7) + 2(1)(dy/dt) = 2(7) + 4(dy/dt).
Solve for dy/dt:
42 + 2(dy/dt) = 14 + 4(dy/dt).
Rearrange and solve:
2(dy/dt) - 4(dy/dt) = 14 - 42,
-2(dy/dt) = -28.
Finally, divide by -2:
dy/dt = 14.
So the value of dy/dt is 14 when x = 3, y = 1, and dx/dt = 7.
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Write two numbers that multiply to the value on top and add to the value on bottom.
Answer:
-17 and -5
Step-by-step explanation:
-5 x -17 = 85
-5 + -17 = -22
Just-in-time (JIT) delivery: Increases physical distribution costs for business customers. Requires that a supplier be able to respond to the customer's production schedule. Usually does not require e-commerce order systems and computer networks. Means that deliveries are larger and less frequent. Shifts greater responsibility for physical distribution activities from the supplier to the business customer
Just-in-time (JIT) delivery is a supply chain management strategy that aims to improve efficiency and reduce inventory costs by having materials and goods delivered exactly when they are needed in the production process.
This approach requires suppliers to be able to respond to the customer's production schedule, ensuring timely deliveries to prevent disruptions. As a result, JIT delivery shifts greater responsibility for physical distribution activities from the supplier to the business customer, who needs to closely monitor inventory levels and maintain efficient communication with suppliers.
However, JIT delivery does not typically lead to larger, less frequent deliveries, nor does it inherently increase physical distribution costs. In fact, it may reduce costs by minimizing inventory storage expenses. Additionally, e-commerce order systems and computer networks are often utilized to facilitate the communication and coordination required for effective JIT delivery.
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true or false, Inflation occurs in an economy when there's a reduction in the total amount of money.
Answer:
False.
Inflation occurs in an economy when there is an increase in the overall price level of goods and services over time. It is usually caused by factors such as an increase in the money supply, higher demand for goods and services, or a decrease in the supply of goods and services. Therefore, a reduction in the total amount of money in an economy would generally lead to deflation, which is the opposite of inflation.
A hummingbird flaps its wings 80 times in one second. A bumblebee flutters its wings 7,800 times in 1 minute. Which animal flutters its wings more times in 1 minute?
Answer:
Step-by-step explanation:
The bumblebee flutters its wings more times in 1 minute, as it flutters its wings 7,800 times in one minute, whereas the hummingbird flaps its wings 80 times in one second, which translates to 4,800 times in one minute.
To understand this calculation in more detail, we can use unit conversions and multiplication. Since the hummingbird's wing flaps are given in seconds and the bumblebee's wing flutters are given in minutes,
we convert the hummingbird's wing flaps from seconds to minutes by multiplying by 60. We then compare the total number of wing flaps for each animal and find that the bumblebee flutters its wings more times in one minute than the hummingbird flaps its wings.
This is due to the bumblebee's higher frequency of wing movement, which enables it to achieve more wing flutters in a given amount of time.
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Use the image below to find x: Show your steps and identify the TRIG RATIO that you used to find x.
The measure of the angle x in the circle is 65 degrees
Solving for x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
On the circle, we have the angle at the vertex of the triangle to be
Angle = 100/2
Angle = 50
The sum of angles in a triangle is 180
So, we have
x + x + 50 = 180
Evaluate the like terms,
2x = 130
So, we have
x = 65
Hence, the angle is 65 degrees
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What capital letter that has more than two right angles.
Answer:
E,F,H
Step-by-step explanation:
Answer:
B = 2 (could be 4, like with this font)
E = 4
F = 3
H = 4
P = 0 (could be 3, like this this font)
R = 0 (could be 3, like with this font)
X = (could be 4)
Other right angles:
D = 0 (could be 2, like with this font)
L = 1
T = 2
Y = (could be 1)
The circumference of a wheel is 320.28 centimeters.
a) Determine the radius of the wheel.
b) Determine the area of the wheel.
Answer:
radius is 50.95
area is 8158.55
Step-by-step explanation:
cirumference = 2pi×r
or,320.28=2×(22/7)×r
or, r=320.28/(2×(22/7))
r=50.95 cm
area=(22/7)r^2
=8158.55
In a school of 580 students, one class was asked which hand they write with.
• “L” means they use their left hand.
• “R” means they use their right hand.
Here are the results:
L, R, R, R, R, R, R, R, R, L, R, R, R, R, R
1) Based on this sample, estimate the proportion of students at the school who write with their left hand.
2) Estimate the number of students at the school who write with their left hand.
3) A different class of `18` students is surveyed. Estimate how many write with their left hand.
1. The proportion of students at the school who write with their left hand is 2/15 OR 13.3%
2. The estimated number of students who write with their left hand is 77 students
3. The estimated number of students in the different class of 18 students who write with their left hand is 2
Estimating the number of students that write with their left handFrom the question, we are to estimate the proportion of students who write with their left hand
To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.
From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:
2/15 = 0.133
OR
13.3%
2.
To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school
That is,
2/15 x 580 = 77.33
Thus, about 77 students write with their left hand
3.
To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:
2/15x 18 = 2.4
Hence, about 2 students in the different class write with their left hand.
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Micayla wants the print shop to reduce the size of there painting but keep the same ratio of length to width so that it will fit into her frame. Study the scale drawings to determine the proportional relationship between her painting and the frame she wants to use. What is the width of Micayla's frame?
The width of Micayla's frame is Wf = (Lf x Wp) / Lp
Let's say that the painting has a length of Lp and a width of Wp, and the frame has a length of Lf and a width of Wf. We want to find the width of the frame, which we can call x. We know that Micayla wants to keep the same ratio of length to width between the painting and the frame, so we can set up the following equation:
Lp/Wp = Lf/Wf
This equation states that the ratio of the length to the width of the painting is equal to the ratio of the length to the width of the frame. We can use this equation to solve for x, the width of the frame. First, we can cross-multiply to get:
Lp x Wf = Lf x Wp
Then, we can solve for x by isolating it on one side of the equation:
Wf = (Lf x Wp) / Lp
This equation tells us that the width of the frame is proportional to the length of the frame and the width of the painting, divided by the length of the painting. By plugging in the appropriate values for Lp, Wp, and Lf, we can solve for x and determine the width of the frame.
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The graph represents the distance the Pennsylvania Train traveled over 8 hours.
The Baltimore Train traveled 1,020 miles in 12 hours. Both trains traveled at a constant rate. Which sentence is true?
A. The Baltimore Train was faster by 10 miles per hour.
B. The Baltimore Train was faster by 15 miles per hour.
C. The Pennsylvania Train was faster by 10 miles per hour.
D. The Pennsylvania Train was faster by 15 miles per hour.
Answer:
Baltimore Train: 1,020 mi/12 hr = 85 mph
Pennsylvania Train: 75 mph
So the correct answer is A.
In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day
was 153 bottles with a standard deviation of 22 bottles. assuming the survey represented a normal distribution,
what is the range of the number of bottled waters that approximately 68.2% of the students drink?
68.2% confidence of the students drink between: 131 and 175 bottles of water per day.
We can use the empirical rule, also known as the 68-95-99.7 rule, to determine the range of values that contain 68.2% of the data in a normal distribution. According to the rule, approximately 68.2% of the data falls within one standard deviation of the mean.
We know that the mean amount of bottled water consumed is 153 bottles, with a standard deviation of 22 bottles. Therefore, one standard deviation below the mean is 153 - 22 = 131 bottles, and one standard deviation above the mean is 153 + 22 = 175 bottles.
Thus, we can say with 68.2% confidence that the number of bottled water consumed by students each day falls between 131 and 175 bottles.
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A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5. 623 to 6. 377) was established based on these results. True or False: Of all possible samples of 100 stores taken from the population of 1,000 stores, 95% of the confidence intervals developed will contain the true population mean within the interval
The statement is True.
The statement "95% confidence interval (5.623 to 6.377)" means that if we were to repeat this process of taking 100 samples from the population and constructing a confidence interval for each sample, then about 95% of those intervals would contain the true population mean.
This is the definition of a confidence interval at a certain level of confidence (in this case, 95%). Therefore, the statement is true.
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A town’s population doubles in 23 years. Its percentage growth rate is approximately *
23% per year.
70/23 per year
23/70 per year
The answer is that the town's percentage growth rate is approximately 3% per year.
What is the approximate percentage growth rate per year of a town whose population doubles in 23 years?To find the town's percentage growth rate, we can use the formula:
growth rate = (final population - initial population) / initial population * 100%
Let P be the initial population of the town, and let t be the time it takes for the population to double, which is 23 years in this case. We know that:
final population = 2P (since the population doubles)
t = 23 years
Substituting these values into the formula, we get:
growth rate = (2P - P) / P * 100% / 23
= P / P * 100% / 23
= 100% / 23
≈ 4.35%
However, this is the annual growth rate that would result in a doubling of the population in exactly 23 years. Since the question asks for the approximate percentage growth rate per year.
We need to find the equivalent annual growth rate that would result in a doubling time of approximately 23 years.
One way to do this is to use the rule of 70, which states that the doubling time (t) of a quantity growing at a constant percentage rate (r) is approximately equal to 70 divided by the growth rate:
t ≈ 70 / r
In this case, we want t to be approximately 23 years, so we can solve for r:
23 ≈ 70 / r
r ≈ 70 / 23
r ≈ 3.04%
Therefore, the town's percentage growth rate is approximately 3% per year.
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PLEASEEE SHOW ALL WORK THANK
YOUUUUUUUUUUUUUUUUUUUUU!!!!!!!!!!!!!!!!!!!!!!!!!!!!
LQ - 10.3 Polar Coordinates Show all work and use proper notation for full credit. Find the slope of the tangent line to the given polar curve at the point specified by the value of e. TT r = 1-2sine,
To find the slope of the tangent line to the polar curve, we need to find the derivative of the equation with respect to θ.
First, we can convert the polar equation into rectangular coordinates using the conversions rcos(θ) = x and rsin(θ) = y:
rcos(θ) = (1-2sin(θ))cos(θ)
r = x/cos(θ)
x/cos(θ) = 1 - 2sin(θ)
x = cos(θ) - 2sin(θ)cos(θ)
y = sin(θ) - 2sin^2(θ)
Next, we can find the derivative of y with respect to x using the chain rule:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dθ = cos(θ) - 4sin(θ)cos(θ)
dx/dθ = -sin(θ) - 2cos^2(θ)
Plugging in the value of e for θ, we get:
dy/dθ = cos(e) - 4sin(e)cos(e)
dx/dθ = -sin(e) - 2cos^2(e)
Finally, we can find the slope of the tangent line by taking the ratio of dy/dθ to dx/dθ:
slope = (cos(e) - 4sin(e)cos(e)) / (-sin(e) - 2cos^2(e))
This is the slope of the tangent line to the polar curve at the point specified by the value of e.
Hi! I'd be happy to help you with your question. To find the slope of the tangent line to the polar curve r = 1 - 2sin(θ) at a specific value of θ, we'll first need to convert the polar equation into Cartesian coordinates.
Let's recall the conversion formulas:
x = r*cos(θ)
y = r*sin(θ)
Now, substitute the polar curve equation into these formulas:
x = (1 - 2sin(θ))*cos(θ)
y = (1 - 2sin(θ))*sin(θ)
To find the slope, we need the derivative of y with respect to x, which is dy/dx. To do this, we'll first find dy/dθ and dx/dθ.
Differentiating both x and y with respect to θ:
dx/dθ = -2cos(θ)^2 + 2sin(θ)cos(θ)
dy/dθ = -2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)
Now, we find the derivative of y with respect to x:
dy/dx = (dy/dθ) / (dx/dθ)
dy/dx = (-2sin(θ)^2 + 2sin(θ) - 2sin(θ)cos(θ)) / (-2cos(θ)^2 + 2sin(θ)cos(θ))
Now, you can plug in the specific value of θ for which you want to find the slope of the tangent line to the polar curve, and simplify the expression to obtain the final answer.
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For the given cost and demand functions, find the production level that will maximize profit. (Round your answer to the nearest whole number.)C(q) = 660 + 5q + 0.03q^2, p = 10 − q/400
The production level that will maximize profit is 80 units
To find the production level that will maximize profit given the cost function C(q) = 660 + 5q + 0.03q^2 and demand function p = 10 - q/400, follow these steps:
1. Write down the revenue function: Revenue (R) is the product of price (p) and quantity (q). So, R(q) = p * q.
2. Substitute the demand function into the revenue function: R(q) = (10 - q/400) * q
3. Simplify the revenue function: R(q) = 10q - q^2/400
4. Write down the profit function: Profit (P) is the difference between revenue and cost. So, P(q) = R(q) - C(q).
5. Substitute the revenue and cost functions into the profit function: P(q) = (10q - q^2/400) - (660 + 5q + 0.03q^2)
6. Simplify the profit function: P(q) = 10q - q^2/400 - 660 - 5q - 0.03q^2
7. Combine like terms: P(q) = 5q - q^2/400 - 0.03q^2 - 660
8. Differentiate the profit function with respect to q to find the first derivative: P'(q) = 5 - q/200 - 0.06q
9. Set the first derivative equal to 0 and solve for q: 5 - q/200 - 0.06q = 0
10. Solve for q: q ≈ 80
The production level that will maximize profit is approximately 80 units (rounded to the nearest whole number).
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A poll used a sample of randomly selected car owners. Within the sample, the mean time of ownership for a single car was years with a standard deviation of years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than years. Use a 0. 05 significance level
If t is less than -1.699, we reject the null hypothesis.
To test the claim by the owner of the large dealership, we will use a one-sample t-test with the following hypotheses:
Null Hypothesis: H0: µ >= µ0 (The population mean time of ownership is greater than or equal to µ0)
Alternative Hypothesis: Ha: µ < µ0 (The population mean time of ownership is less than µ0)
where µ is the population mean time of ownership, µ0 is the claimed mean time of ownership by the owner of the dealership.
The significance level is α = 0.05.
We can calculate the t-value as:
t = ([tex]\bar{x}[/tex] - µ0) / (s / √n)
where [tex]\bar{x}[/tex] is the sample mean time of ownership, s is the sample standard deviation, n is the sample size.
Plugging in the values given in the problem, we get:
t = ([tex]\bar{x}[/tex] - µ0) / (s / √n) = (5.7 - µ0) / (1.8 / √n)
Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value from the t-distribution table with n-1 degrees of freedom and a significance level of 0.05. For a sample size of n = 30 (assuming it is large enough), the critical t-value is -1.699.
If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.
If the calculated t-value is greater than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.
So, if we assume that the sample is representative of the population and meets the assumptions of the t-test, we can calculate the t-value as:
t = (5.7 - µ0) / (1.8 / √30)
If t is less than -1.699, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Note that we don't have any information about the claimed mean time of ownership by the owner of the dealership, so we cannot calculate the t-value or make any conclusions.
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Find the indicated length
Answer:
y = 32/3 or 10.67 units------------------------------
The two smaller right triangles are similar by AA property.
Use ratios of corresponding sides to get:
8/y = 6/8Simplify and solve for y:
8/y = 3/4y = 8*4/3y = 32/3 ≈ 10.67In my class, everyone studies French or German, but not both languages.
One third of the girls and the same number of boys study German.
Twice as many boys as girls study French.
Which of these could be the total number of boys and girls in my class?
The possible total number of boys and girls in the class is 21, and
the answer is b).
Let's denote the number of girls in the class as 'g' and the number of
boys as 'b'.
We know that all students in the class study either French or German,
but not both.
Therefore, the total number of students in the class is equal to the sum
of the number of students who study French and the number of students
who study German
From the given information, we can write the following equations:
g + b = total number of students(1/3)g = (1/3)b (one third of the girls and the same number of boysstudy German
2(1/3)g = b (twice as many boys as girls study French)We can simplify the second equation by multiplying both sides by 3:g = bSubstituting this into the first equation, we get:
2g = total number of studentsSubstituting the second equation into the third equation, we get:2g = b (twice as many boys as girls study French)Substituting this into the first equation, we get:
3g = total number of studentsTherefore, the total number of students in the class must be a multiple
of 3.
Let's try the answer choices:
a) 15 students (total number of students is not a multiple of 3)
b) 21 students (total number of students is a multiple of 3 and the
number of girls is a multiple of 3, so this is a possible solution)
c) 24 students (total number of students is a multiple of 3 and the
number of girls is not a multiple of 3)
d) 30 students (total number of students is a multiple of 3 but the
number of girls is not a multiple of 3)
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Question 6 of 20 :
Select the best answer for ige question. 6. Simplify (4x 4)-3. O B. 2
O C. -8x12
0D. -64x9
The correct answer is (C) -8x12.
To simplify (4x^4)^-3, we use the power of a power rule which states that (a^m)^n = a^(mn), where a is a non-negative number and m and n are integers. Applying this rule, we get:
(4x^4)^-3 = 4^(-3) x^(4 x -3) = (1/64)x^(-12) = -8x^12 (using the negative exponent rule, which states that a^(-n) = 1/a^n)
Therefore, the simplified form of (4x^4)^-3 is -8x^12.
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HELP!! 50 points !!
13. An online job - seeking service allows job - seekers to post their resumés for free. The service charges employers looking for applicants a fee to look through the resumés. The fee is based on how long the employer wants the employer wants to consider. The fees are $585 for a 100 - mile radius for access to the resumés , and how many miles from the workplace address 3 weeks and $675 for a 150-mile radius for 3 weeks. A If there are 98 resumés within a 100 - mile radius , what is the average cost to b. If there are 208 resumés within a 150 - mile radius , what is the average cost. Under the 150 - mile radius option , an employer would see the same 98 resumés from part a that he would have seen under the 100 - mile radius option. What is the average cost to the employer for looking at the extra resumés he would see if he opted for the more expensive plan ? Explain. The nearest cent to the employer for looking at each resume ? to the employer for looking at each resumé? d. Give an advantage and a disadvantage of opting for the more expensive plan.
a. The cost for a 100-mile radius for 3 weeks is $585, and there are 98 resumes within this radius, so the average cost per resume would be:
$585 / 98 = $5.96 per resume
b. The cost for a 150-mile radius for 3 weeks is $675, and there are 208 resumes within this radius, so the average cost per resume would be:
$675 / 208 = $3.25 per resume
c. If an employer opts for the 150-mile radius option instead of the 100-mile radius option, they would pay an extra $90 ($675 - $585) to see an additional 110 resumes (208 - 98).
The average cost to the employer for looking at each extra resume would be:
$90 / 110 = $0.82 per resume
d. An advantage of opting for the more expensive plan is that the employer would have access to a larger pool of potential candidates, which could increase the likelihood of finding a qualified applicant.
A disadvantage is that the employer would have to pay more money, which could be a significant expense for smaller businesses or those with limited budgets.
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Susan’s weekly earnings were proportional to the number of hours she worked. this table shows
the number of hours susan worked and the amount she earned. how much money did susan
earn per hour?
hours earnings ($)
5 $47.50
7 $66.50
9 $85.50
11 $104.50
Susan earns $9.50 per hour. This is found by dividing her earnings by the number of hours worked for each corresponding row in the table.
To find how much money Susan earned per hour, we need to divide the total earnings by the total number of hours worked. For finding the Total earnings we need to add the money earned in every hour,
Total earnings = $47.50 + $66.50 + $85.50 + $104.50 = $304
Total hours worked = 5 + 7 + 9 + 11 = 32
Money earned per hour = Total earnings / Total hours worked
= $304 / 32
= $9.50
Therefore, Susan earned money of $9.50 per hour.
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Answer quickly please
Given that A is a constant, the general solution to the differential equation dy dt -5y is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y=est +A The solution to the exact differential equati
The general solution to the differential equation dy/dt - 5y = A is y = Ce^(5t) + A/5, where C is a constant of integration. The general solution is y = (A/5) + Ce^(5t). so, the correct answer is D).
The general solution to the differential equation dy/dt - 5y = A, where A is a constant, is
y = Ce^(5t) + A/5
where C is an arbitrary constant determined by any initial or boundary conditions given.
The general solution is a combination of the homogeneous solution y_h = Ce^(5t) (which satisfies the differential equation without the constant term A) and the particular solution y_p = A/5 (which satisfies the differential equation with A but without any initial or boundary conditions).
so, the correct option is D).
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--The given question is incomplete, the complete question is given
" Answer quickly please
Given that A is a constant, the general solution to the differential equation dy/dt -5y = A is Select one O a. 3t2 2 Ob. 3= Ae-56 Ос. y = Aest Od y = Ce^(5t) +A/5 The solution to the exact differential equation"--
help me with pythagorean therom pleaseeeeeeeeeeeee i will legit do anything if someone can help i will give brainliest just help me pleaseeeeeeeeeeee
6.6,your answer is correct.
As the theorem is a^2+b^2=c^2 you first must assign the proper components to each variable. Since 12 is the longest since it is the hypotenuse that means it is c so in this case 144. And since 10 is the leg it is a.
To solve you must take
10^2+b^2=12^2
100+b=144
144-100=44
Since b^2 is 44 you must find the square root [tex]\sqrt{44}[/tex]=6.6
