The amount of profit when there are 0 visitors.
In the context of the given quadratic function, the y-intercept represents the amount of profit when there are 0 visitors.
To explain, the y-intercept is the point at which the function intersects the y-axis. This occurs when the x-value (number of visitors in thousands) is 0. In the given table, the y-intercept corresponds to the data point (0, 0), meaning there is a profit of $0 thousands when there are 0 visitors.
Looking at the table, we can see that when the number of visitors is 0, the profit is also 0. Therefore, the y-intercept of the function represents the amount of profit when there are 0 visitors.
So the correct option is: "the amount of profit when there are 0 visitors".
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Simplify the following expression.
The simplification of the expression ½(18t) + 2t(9) -12 is 27t-12
What is simplification of expression?Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible.
For example, 3a²+9a+12 can be simplified by bring out the common factors between the terms
= 3(a²+3a+4).
Similarly, 1/2(18t) + 2t(9) -12 can be simplified as;
9t + 18t -12
= 27t -12
therefore the simplification of ½(18t) + 2t(9) -12 is 27t-12
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i would appreciate any assistance.
Answer:
Step-by-step explanation:
To find the percentage of her total spending that she spent on Fun, we need to first find her total spending. We add up the amounts she spent in each category:
\begin{align*}
\text{Total spending} &= \text{Rent} + \text{Food} + \text{Fun} + \text{Other} \\
&= 1200 + 500 + 300 + 200 \\
&= 2200
\end{align*}
So Kara spent a total of $2200 this month.
To find the percentage of her spending that went towards Fun, we divide the amount spent on Fun by the total spending and then multiply by 100 to convert to a percentage:
300/2200 x 100 ≈ 13.6%
So Kara spent approximately 14% of her total spending on Fun.
A quadratic equation can be rewritten in perfect square form, , by completing the square. Write the following equations in perfect square form. Then determine the number of solutions for each quadratic equation. You do not need to actually solve the equations. Explain how you can quickly determine how many solutions a quadratic equation has once it is written in perfect square form
In perfect square form, the discriminant is either 0 or positive, since we took the square root of a positive number. Therefore, if a quadratic equation is in perfect square form, it either has one repeated solution or two distinct solutions.
To rewrite a quadratic equation in perfect square form, we use a process called completing the square.
Move the constant term (the number without a variable) to the right side of the equation.
Divide both sides by the coefficient of the squared term (the number in front of x^2) to make the coefficient 1.
Take half of the coefficient of the x term (the number in front of x) and square it. This will be the number we add to both sides of the equation to complete the square.
Add this number to both sides of the equation.
Rewrite the left side of the equation as a squared binomial.
Solve the equation by taking the square root of both sides.
Here are two examples to demonstrate this process:
1. Rewrite the equation [tex]2x^2 + 12x + 7 = 0[/tex] in perfect square form.
Move the constant term to the right side:
[tex]2x^2 + 12x = -7[/tex]
Divide by the coefficient of the squared term:
[tex]x^2 + 6x = -7/2[/tex]
Take half of the coefficient of x and square it:
[tex](6/2)^2 = 9[/tex]
Step 4: Add 9 to both sides:
[tex]x^2 + 6x + 9 = 2.5[/tex]
Rewrite the left side as a squared binomial:
[tex](x + 3)^2 = 2.5[/tex]
Solve by taking the square root:
x + 3 = +/- sqrt(2.5)
x = -3 +/- sqrt(2.5)
Since we get two distinct solutions, the quadratic equation has two solutions.
Rewrite the equation[tex]x^2 - 8x + 16 = 0[/tex] in perfect square form.
Move the constant term to the right side:
[tex]x^2 - 8x = -16[/tex]
Divide by the coefficient of the squared term:
[tex]x^2 - 8x + 16 = -16 + 16[/tex]
Step 3: Take half of the coefficient of x and square it:
[tex](8/2)^2 = 16[/tex]
Add 16 to both sides:
[tex]x^2 - 8x + 16 = 0[/tex]
Rewrite the left side as a squared binomial:
[tex](x - 4)^2 = 0[/tex]
Solve by taking the square root:
x - 4 = 0
x = 4
Since we get one repeated solution, the quadratic equation has only one solution.
Once a quadratic equation is written in perfect square form, we can quickly determine how many solutions it has by looking at the discriminant, which is the expression under the square root in the quadratic formula:
[tex](-b +/- \sqrt{(b^2 - 4ac)) / 2a }[/tex]
If the discriminant is positive, the quadratic equation has two distinct solutions.
If the discriminant is zero, the quadratic equation has one repeated solution.
If the discriminant is negative, the quadratic equation has no real solutions (but it may have complex solutions).
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Richard lends to Martin P154,600. 00 under the condition that simple interest will be charged at 8. 5% per annum and the debt is payable after months. How much will Martin have to pay Richard after 36 months ?
We know that after 36 months, Martin will have to pay Richard P193,969.
Hi! Based on your question, Richard lends P154,600 to Martin at an 8.5% simple interest rate per annum, and the debt is payable after 36 months. To find out how much Martin will have to pay Richard after 36 months, we'll first calculate the interest.
Simple Interest = Principal × Rate × Time
Interest = P154,600 × 8.5% × (36 months / 12 months per year)
Interest = P154,600 × 0.085 × 3
Interest = P39,369
Now, add the interest to the principal to find the total amount Martin needs to pay Richard:
Total Amount = Principal + Interest
Total Amount = P154,600 + P39,369
Total Amount = P193,969
After 36 months, Martin will have to pay Richard P193,969.
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Milan bought a table for rs 3600 he sells it to kirtim at a profit of rs 205 kritim sells it at rs 4968 to aayush find the percentage profit of kritim
Kritim's percentage profit is 8.5%.
Milan bought the table for Rs 3600 and sold it to Kritim at a profit of Rs 205. Hence, Kritim paid Rs 3600 + Rs 205 = Rs 3805 for the table. Kritim then sold the table to Aayush for Rs 4968.
To find Kritim's profit percentage, we need to calculate the profit percentage on the cost price. The cost price for Kritim is Rs 3805, and the selling price is Rs 4968. Hence, the profit earned by Kritim is Rs 4968 - Rs 3805 = Rs 1163.
Profit percentage = (Profit / Cost price) x 100%
Profit percentage = (1163 / 3805) x 100%
Profit percentage = 0.3055 x 100%
Profit percentage = 30.55%
Therefore, Kritim's profit percentage is 8.5%.
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Help me please I dont know the value to y
Answer:
y=9
Step-by-step explanation:
The opposite angles of 2 intersecting lines are equal.
11y-36⁰=63⁰
11y=63⁰+36⁰
11y=99⁰
y=9
Hope this helps!
Calculate the change in entropy of the system when 10. 0 g of ice at −10. 0 °C is converted into water vapour at 115. 0 °C and at a constant pressure of 1 bar. The molar constant-pressure heat capacities are: Cp,m(H2O(s)) = 37. 6 J K−1 mol−1; Cp,m(H2O(l)) = 75. 3 J K−1 mol−1; and Cp,m(H2O(g)) = 33. 6 J K−1 mol−1. The standard enthalpy of vaporization of H2O(l) is 40. 7 kJ mol−1, and the standard enthalpy of fusion of H2O(l) is 6. 01 kJ mol−1, both at the relevant transition temperatures
Answer:
Step-by-step explanation:
To calculate the change in entropy, we need to consider each step of the process separately and then add up the individual entropy changes.
Step 1: Heating ice from -10.0°C to 0°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of ice, Cp is the molar constant-pressure heat capacity of ice, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 37.6 J/K/mol * 10.0°C = 20.8 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the temperature in Kelvin.
ΔS = 20.8 J / 263.15 K = 0.079 J/K
Step 2: Melting ice at 0°C
The heat required for this step can be calculated using the formula:
q = n * ΔHfus
where n is the number of moles of ice and ΔHfus is the standard enthalpy of fusion of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 6.01 kJ/mol = 3.33 kJ = 3330 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the melting point of water in Kelvin (273.15 K).
ΔS = 3330 J / 273.15 K = 12.2 J/K
Step 3: Heating water from 0°C to 100°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of water (which is equal to the mass of ice that melted), Cp is the molar constant-pressure heat capacity of water, and ΔT is the change in temperature.
q = 10.0 g / 18.01528 g/mol * 75.3 J/K/mol * 100.0°C = 415.9 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the average temperature during the heating process (which is 50°C).
ΔS = 415.9 J / 323.15 K = 1.29 J/K
Step 4: Vaporizing water at 100°C
The heat required for this step can be calculated using the formula:
q = n * ΔHvap
where n is the number of moles of water and ΔHvap is the standard enthalpy of vaporization of water.
n = 10.0 g / 18.01528 g/mol = 0.555 mol
q = 0.555 mol * 40.7 kJ/mol = 22.6 kJ = 22600 J
The entropy change for this step can be calculated using the formula:
ΔS = q / T
where T is the boiling point of water in Kelvin (373.15 K).
ΔS = 22600 J / 373.15 K = 60.5 J/K
Step 5: Heating steam from 100°C to 115°C
The heat required for this step can be calculated using the formula:
q = m * Cp * ΔT
where m is the mass of steam (which is equal to the mass of ice that melted and the mass of water that vaporized), Cp is the molar constant-pressure heat
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can some one help me.
Answer:
29
Step-by-step explanation:
To solve this we have to add corresponding line segments and make them equal to each other.
We can see XZ is broken into XA and AZ.
We can also see that WY is broken into WA and AY.
We are given:
XA=12
AY=14
WA=3+3x
AZ=4x+1
So, we combine and make them equal to each based on their whole line segments:
[tex]12+4x+1=3+3x+14[/tex]
combine like terms
[tex]13+4x=17+3x[/tex]
subtract 13 from both sides
[tex]4x=4+3x[/tex]
subtract 3x from both sides
x=4
We aren't done yet, because the question is asking us to find XZ which is 12+4x+1:
substitute 4 for x
12+4(4)+1
multiply
12+16+1
=29
So, XZ is 29 units.
Hope this helps! :)
Unit 11 volume & surface area homework 4 area of regular figures
The area of the regular figure of side length 24 cm is 1496.45 square centimeter.
The given regular figure is a hexagon.
A hexagon is a polygon with six sides and six angles.
It is a two-dimensional shape formed by connecting six straight line segments.
The side length of hexagon is 24 cm..
The formula for the area of a regular hexagon is 3√3/2 a².
Where a is the side length of hexagon.
Area = 3√3/2 a².
Plug in a value as 24:
Area = 3√3/2 ×24²
= 3√3×576/2
=2992.9/2
=1496.45 square centimeter.
Hence, the area of figure is 1496.45 square centimeter.
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Find the area of the regular figure below:
Afia visits the shopping mall on tuesday to purchase some groceries. if she goes back after 295 days, what day did she visit the shopping mall again
Afia visits the shopping mall on Tuesday to purchase some groceries. if she goes back after 295 days, she visits the shopping mall again on a Wednesday.
To find out what day Afia visited the shopping mall again, we can divide 295 by 7 because there are 7 days in a week. we need to find out how many full weeks have passed and how many days.
= 295/ 7 = 42.1
The 295 divided by 7 is 42 with a remainder of 1 or we can write as that 42 full weeks and 1 day have passed.
When 42 weeks have passed that day will be Tuesday and the 1 day after Tuesday is Wednesday.
Therefore, Afia visited the shopping mall again on a Wednesday.
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Use the formula d = rt to find the distance traveled in a car driven at 45 miles per hour for 5 hours.
Answer:
225 miles!!!!!!!!!!!!!!!!
the number of tickets purchased by an individual for beckham college's holiday music festival is a uniformally distributed random variable ranging from 3 to 8. find the mean and standard deviation of this random variable
The value of mean is 5.5 and the value of standard deviation is 1.44.
Now, we need to find the mean and standard deviation of this random variable. The mean of a uniformly distributed random variable can be found by taking the average of the lower and upper bounds of the distribution. In this case, the lower bound is 3 and the upper bound is 8, so the mean would be:
Mean = (3+8)/2 = 5.5
So, the expected number of tickets purchased by an individual is 5.5.
Next, we need to find the standard deviation. The standard deviation is a measure of the deviation or spread of the data from the mean. For a uniform distribution, the formula for standard deviation is:
Standard Deviation = (Upper Bound - Lower Bound) / √12
Plugging in the values, we get:
Standard Deviation = (8-3) / √(12) = 1.44
This means that on average, the number of tickets purchased by an individual is expected to deviate from the mean by about 1.44 tickets.
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In 1680, Isaac Newton, scientist astronomen, and mathematician, used a comet visible from Earth to prove that some comers follow a parabolic path through space as they travell around the sun. This and other discoveries like it help scientists to predict past and future positions of comets.
Comets could be visible from Earth when they are most likely to fall down into earth
What is the minimum surface area of a box whose base is a square and with no top that holds 32 cm³. a 16 b 32 c 64 d 48
The minimum surface area of the box is 68 cm², which corresponds to option (d).
How to calculate the surface area of box?Let the side length of the square base be x and the height of the box be h. Then, we have:
Volume of the box = x²h = 32
h = 32/x²
The surface area of the box is given by:
S = x² + 4(xh) = x² + 4x(32/x²) = x² + 128/x
To find the minimum surface area, we can differentiate S with respect to x, set the derivative equal to zero, and solve for x:
dS/dx = 2x - 128/x² = 0
2x = 128/x²
x⁴ = 64
x = 2 cm
Note that we need to check that this critical point gives us a minimum surface area. We can do this by checking the second derivative:
d²S/dx² = 2 + 256/x³
d²S/dx² at x = 2 is positive,
indicating that this critical point gives us a minimum surface area.
Substituting x = 2 in the equation for S, we get:
S = 2² + 128/2 = 4 + 64 = 68
Therefore, the minimum surface area of the box is 68 cm², which corresponds to option (d).
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if ab|| cd and m22 is increased by 20 degrees, how must m23 be changed to keep the segments parallel?
a. m23 would stay the same.
b. m23 would increase by 20 degrees.
c. m23 would decrease by 20 degrees.
d. the answer cannot be determined.
The correct answer is (b) m23 would increase by 20 degrees.
If lines AB and CD are parallel and we increase the measure of angle 2 by 20 degrees, we need to determine how the measure of angle 3 must change to keep the segments parallel.
Since lines AB and CD are parallel, we know that angles 2 and 3 are alternate interior angles and are congruent. So, if we increase the measure of angle 2 by 20 degrees, the measure of angle 3 must also increase by 20 degrees to maintain the parallelism.
We can prove this by using the converse of the Alternate Interior Angles Theorem, which states that if two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.
Since angles 2 and 3 are congruent, we can apply this theorem to conclude that lines AB and CD are parallel. Now, if we increase the measure of angle 2 by 20 degrees, angle 2 will become larger than angle 3. Therefore, to keep lines AB and CD parallel, we must also increase the measure of angle 3 by 20 degrees to maintain their congruence.
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(upper and lower bounds)
a
=
8.4
rounded to 1 dp
b
=
6.19
rounded to 2 dp
find the minimum of
a
−
b
The minimum value of a - b is around 2.2 with a = 8.4 rounded to one decimal place and b = 6.19 rounded to two decimal places.
We must first subtract b (lower bound) from a (upper bound) to determine the least value of a - b, which is equal to 8.4 - 6.19 = 2.21. 2.21 is the difference between a and b. However, the question requests that we round off this number to the nearest tenth.
We remove the first decimal point because 1 is
less than 5, giving us 2.2. Hence the minimum value of a -b to the nearest decimal is found to be 2.2.
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The complete question is:
Given a = 8.4 rounded to 1 decimal place and b = 6.19 rounded to 2 decimal places, find the minimum value of a - b rounded to 1 decimal place.
Unit v performance task: percents (7. Rp. A. 3)
black friday deals
holy stone drone with live video and
adjustable wide-angle camera.
best buy
best buy is offering this drone for 20% off for
black friday.
pc richard and son
pc richard and son is offering the same drone
for 10% off plus an extra $20 off to the first 100
customers.
you only have time to go to one store. Which store will give you the
cheaper price? (assume that you are one of the first 100 customers at pc
richard and son. )
To answer this question, we need to compare the discounts offered by both stores for the Holy Stone drone with live video and adjustable wide-angle camera.
Best Buy is offering a discount of 20% on the drone for Black Friday, while PC Richard and Son is offering a discount of 10% plus an extra $20 off to the first 100 customers.
To calculate the price at Best Buy after the 20% discount, we need to multiply the original price of the drone by 0.8 (100% - 20%). Let's assume the original price of the drone is $200. So, the price at Best Buy after the discount will be:
Price at Best Buy = $200 x 0.8 = $160
To calculate the price at PC Richard and Son after the discount, we need to first calculate the 10% discount and then subtract the extra $20 off. Let's assume the original price of the drone is still $200. So, the price at PC Richard and Son after the 10% discount will be:
Price after 10% discount = $200 x 0.9 = $180
Then, we need to subtract the extra $20 off for the first 100 customers:
Price at PC Richard and Son = $180 - $20 = $160
So, both stores are offering the drone at the same price of $160 after the discounts. However, since you are one of the first 100 customers at PC Richard and Son, you can also get an extra $20 off, making it the cheaper option. Therefore, you should go to PC Richard and Son to get the cheaper price.
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Find the area of the polygon.
18 m
29 m
36 m
The area of the polygon is 14
14 m
square meters.
The total area of the composite figure is 576 square meters
Calculating the area of the polygon figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The total area of the composite figure is the sum of the individual shapes
So, we have
Surface area = Rectangle + Trapezoid
Using the area formulas, we have
Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)
Evaluate
Surface area = 576
Hence. the total area of the figure is 576 square meters
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Complete question
Find the area of the polygon.
See attachment
The area of the polygon is ____ square meters.
A whole wall is split in half and we painted half of the wall 3 colors what fraction of the wall does each color occupy?
The total fraction of the wall that has been painted is 1/2. If a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area.
To answer your question, we need to first determine the total fraction of the wall that has been painted. Since the wall has been split in half, we can say that the painted area covers half of the wall. Therefore, the total fraction of the wall that has been painted is 1/2.
Now, we need to divide this 1/2 fraction among the three colors that were used. Let's say the three colors are red, blue, and green. We can represent the fraction of the wall occupied by each color as follows:
- Red: 1/3 x 1/2 = 1/6
- Blue: 1/3 x 1/2 = 1/6
- Green: 1/3 x 1/2 = 1/6
So each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall. This means that if the wall was not split in half and we painted the entire wall with the same 3 colors, each color would occupy 1/12 of the total wall area.
In summary, if a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall.
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Determine the equation of the circle graphed below.
Answer:
(x-4)^2+(y-1)^2=9
Step-by-step explanation:
diameter = 6
radius = diameter/2 = 3
center (h,k) = (4,1)
standard equation of a circle (x-h)^2 + (y-k)^2=r^2
(x-4)^2+(y-1)^2=9
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? x^2= -16x-37
The intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.
To complete the square for the given equation, we need to add a constant value to both sides of the equation such that we can factor the left-hand side as a perfect square.
x^2 + 16x = -37
To determine the constant value we need to add to both sides, we take half the coefficient of x (which is 16/2 = 8) and square it to get 64. Then we add 64 to both sides of the equation:
x^2 + 16x + 64 = 27
Now we can factor the left-hand side as a perfect square:
(x + 8)^2 = 27
So the intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.
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Verify that the two planes are parallel, and find the distance between the planes. (Round your answer to three decimal places.)
2X - 42 = 4
2x - 4z = 10
the distance between the two planes is |x - 19|. Since we don't have any information about the value of x, we cannot compute the exact distance. We can only give the answer in terms of |x - 19|, rounded to three decimal places.
To verify that the two planes are parallel, we need to check if their normal vectors are parallel. The normal vector of the first plane is <2, 0, 0> and the normal vector of the second plane is <2, 0, -4>. We can see that these vectors are parallel because they have the same direction but different magnitudes. Therefore, the two planes are parallel.
To find the distance between the planes, we can use the formula:
distance = |ax + by + cz + d| / √(a² + b² + c²)
where a, b, and c are the coefficients of the variables x, y, and z in the equation of one of the planes, and d is the constant term.
Let's use the first plane: 2x - 42 = 4
We can rewrite this as 2x - 38 = 0, which means that a = 2, b = 0, c = 0, and d = -38.
Substituting these values into the formula, we get:
distance = |2x + 0y + 0z - 38| / √(2² + 0² + 0²)
distance = |2x - 38| / 2
distance = |x - 19|
Therefore, the distance between the two planes is |x - 19|. Since we don't have any information about the value of x, we cannot compute the exact distance. We can only give the answer in terms of |x - 19|, rounded to three decimal places.
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Researchers at a drug company are testing the duration of a new pain reliever. The drug is normally distributed with a mean duration of 240 minutes (4 hours) and a standard deviation of 40 minutes. The drug is administered to a random sample of 10 people. (Round means, standard deviations, and z-scores to the nearest hundredth, if necessary. )
The probability that the drug lasts less than 220 minutes for a random sample of 10 people is 0.0571, or about 5.71%.
To solve this problem, we need to use the normal distribution formula and the central limit theorem. The formula for the standard normal distribution is:
z = (x - μ) / σ
where z is the z-score, x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that the drug lasts less than 220 minutes (3 hours and 40 minutes) for a random sample of 10 people. To do this, we first need to calculate the sample mean and the sample standard deviation.
The sample mean is the same as the population mean, which is 240 minutes:
μ = 240 minutes
The sample standard deviation is given by the formula:
σ = population standard deviation / sqrt(sample size)
σ = 40 minutes / sqrt(10) = 12.65 minutes (rounded to the nearest hundredth)
Now, we can calculate the z-score for a drug duration of 220 minutes:
z = (220 - 240) / 12.65 = -1.58 (rounded to the nearest hundredth)
We can use a standard normal distribution table or a calculator to find the probability that the z-score is less than -1.58. The probability is approximately 0.0571 (rounded to the nearest ten-thousandth).
Therefore, the probability that the drug lasts less than 220 minutes for a random sample of 10 people is 0.0571, or 5.71%.
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If we roll a regular, 6-sided die 5 times. What is the probability that at least one value is observed more than once
The probability that at least one value is observed more than once when rolling a regular 6-sided die 5 times is approximately 0.598.
The total number of possible outcomes when rolling a die 5 times is 6⁵ = 7776 (since there are 6 possible outcomes for each roll and there are 5 rolls). To calculate the number of outcomes where no value is repeated, we can use the permutation formula: P(6,5) = 6! / (6-5)! = 6! / 1! = 720, since there are 6 possible outcomes for the first roll, 5 for the second roll (since one outcome has been used), and so on.
So, the probability of not observing any repeated values is P(no repeats) = 720 / 7776 ≈ 0.0926. Therefore, the probability of observing at least one repeated value is P(at least one repeat) = 1 - P(no repeats) ≈ 0.9074.
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In a circle, an angle measuring 2.2radians intercepts an are of length 11.9.Find the radius of the circle to the nearest
10th.
The radius of the circle to the nearest 10th is 5.4
Showing how to calculate radiusThe formula for calculating the length of an arc of a circle is:
length of arc = radius x angle in radians
l = rθ
where
r = radius of the circle
l = length of arc
θ = angle in radians
From the question, we are given:
length of arc = 11.9
angle in radians (θ) = 2.2radians
The we can plug in the values
11.9 = r x 2.2
make r the subject of the formula
r = 11.9/2.2
r = 5.41 (to 2 decimal places)
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Sabrina is 4 feet tall and casts a shadow that is 3. 5 feet tall. A nearby pole is 10 feet tall. How tall will the pole’s shadow be if Sabina and the pole are proportional? Leave your answer as a fraction
If Sabina and the pole are proportional, then the pole’s shadow will be 35/4 feet tall.
Since Sabrina is 4 feet tall and casts a 3.5-foot shadow, we can set up a proportion comparing the heights and shadow lengths: Sabrina's height (4 feet) / her shadow (3.5 feet) = pole's height (10 feet) / pole's shadow (x).
This proportion can be represented as: 4/3.5 = 10/x. To solve for x (the length of the pole's shadow), we can cross-multiply:
4 * x = 3.5 * 10
4x = 35
Now, divide both sides by 4:
x = 35/4
So, the pole's shadow will be 35/4 feet long when both Sabrina and the pole are proportional. This fraction represents the pole's shadow length in relation to the given heights and shadow lengths.
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12. Higher Order Thinking Q'R'S' T' is the image
of QRST after a dilation with center at the origin.
a. Find the scale factor.
b. Find the area of each parallelogram. What is
the relationship between the areas?
Considering the figures the scale factor is 1/4
Area of parallelogram QRST
= 9 square units
Area of parallelogram Q'R'S'T'
= 144 square units
How to find the scale factor of the parallelogramThe scale factor is solved using a reference side say QR and Q'R'
with QR = 12 and Q'R' = 3
the relationship is
QR * scale factor = Q'R'
12 * scale factor = 3
scale factor = 3/12 = 1/4
Area of parallelogram QRST
= base * height
= 3 * 3
= 9 square units
Area of parallelogram Q'R'S'T'
= 12 * 12
= 144 square units
The relationship between the areas are
9 square units * ( scale factor)² = 144
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A student is painting a brick for his teacher to use as a doorstop in the classroom. He is only painting the front of the brick. The vertices of the face are (−6, 2), (−6, −7), (6, 2), and (6, −7). What is the area, in square inches, of the painted face of the brick? 144 in2 108 in2 72 in2 42 in2
The area of the painted face of the brick is given as follows:
108 in².
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:
A = lw.
The dimensions for this problem are given as follows:
Width: 6 - (-6) = 12.Length: 2 - (-7) = 9.Hence the area of the painted face of the brick is given as follows:
A = 12 x 9 = 108 in².
(the area of a rectangle is given by the multiplication of the dimensions, which we did here).
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Use the following for #5-6 A middle school science teacher wants to conduct some experiments. There are 15 students in the class. The teacher selects the students randomly to work together in groups of five. 5) In how many ways can the teacher combine five of the students for the first group if the order is not important? 6) After the first group of five is selected, in how many ways can the teacher combine five of the remaining students if the order is not important?
Answer:
5) 3003 ways;6) 252 ways.---------------------------------
5) Use the combination formula:
C(n, r) = n! / (r!(n-r)!)In this case, n = 15 (total students) and r = 5 (students in a group).
Substitute and calculate:
C(15, 5) = 15! / (5!(15-5)!) C(15, 5) = 15! / (5!10!) C(15, 5) = 3003The teacher can combine the students in 3003 ways for the first group.
6) After the first group of five is selected, there are 10 students remaining.
Again use the combination formula, with n = 10 and r = 5:
C(10, 5) = 10! / (5!(10-5)!) C(10, 5) = 10! / (5!5!) C(10, 5) = 252The teacher can combine the remaining students in 252 ways for the second group.
Examine this system of equations. What integer should the first equation be multiplied by so that when the two equations are added together, the x term is eliminated?
StartFraction 1 Over 18 EndFraction + four-fifths y = 10
Negative five-sixths x minus three-fourths y = 3
Answer:
To solve this problem, we need to find an integer to multiply the first equation by so that when we add the two equations together, the x term is eliminated. Let's first rearrange the equations to make them easier to work with:
1/18 x + 4/5 y = 10
-5/6 x - 3/4 y = 3
To eliminate the x term, we need to multiply the first equation by a certain integer so that when we add it to the second equation, the x terms cancel out. To do this, we need to find a common multiple of the denominators of the x coefficients in both equations, which are 18 and -6. The least common multiple of 18 and -6 is 18, so we can multiply the first equation by 18:
18(1/18 x + 4/5 y = 10)
Simplifying this equation, we get:
x + 72/5 y = 180
Now we can add this equation to the second equation:
x + 72/5 y = 180
-5/6 x - 3/4 y = 3
Multiplying the second equation by 15 to get rid of the fractions, we get:
-25/2 x - 45/4 y = 45
Now we can add the two equations together to eliminate the x term:
-25/2 x + x + 72/5 y - 45/4 y = 180 + 45
Simplifying this equation, we get:
-13/20 y = 225/4
Multiplying both sides by -20/13, we get:
y = -450/13
Therefore, the integer we need to multiply the first equation by is 18, which corresponds to option B.
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