So the area of the rectangle (or lane) whose length is 19 feet and whose width is the free throw line, together with the two circles at each end of the court that surround the free throw line, is approximately 450.39 square feet.
What is the length of the rectangle and how many free throw line square feet?Since the circle at each end of the court that surrounds the free throw line is the same size as the jump ball circle, they both have the same radius. Let's call this radius "r".
The diameter of the circle is equal to the width of the lane, which is the same as the width of the free throw line. Therefore, the diameter of the circle is also 12 feet (the width of the free throw line is always 12 feet).
We know that the area of a circle is given by the formula A = πr^2, so the area of each circle is πr^2.
The rectangle (or lane) has a length of 19 feet and a width of 12 feet. Therefore, its area is simply the product of its length and width, which is:
A = 19 feet * 12 feet
A = 228 square feet
Since there are two circles, the total area of the circles is 2πr^2.
We know that the diameter of the circle is equal to the width of the lane, which is 12 feet. Therefore, the radius is half of the diameter, or:
r = 12 feet / 2
r = 6 feet
Now we can calculate the area of the circles:
A = 2πr^2
A = 2π(6 feet)^2
A = 72π square feet
Therefore, the total area of the rectangle and circles (or lane and circles) is:
A_total = A_rectangle + A_circles
A_total = 228 square feet + 72π square feet
A_total ≈ 450.39 square feet
So the area of the rectangle (or lane) whose length is 19 feet and whose width is the free throw line, together with the two circles at each end of the court that surround the free throw line, is approximately 450.39 square feet.
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Practice writing and solving equations to solve number problems.
assessment started: undefined.
item 1
question 1
ansley’s age is 5 years younger than 3 times her cousin’s age. ansley is 31 years old.
let c represent ansley’s cousin’s age. what expression, using c, represents ansley’s age?
enter your response in the box.
Ansley's cousin is 12 years old, and Ansley's age can be found by plugging in 12 for Cousin's age.
How can we know that Ansley's age is 5 years less than 3 times her cousin's age?The problem tells us that Ansley's age is 5 years less than 3 times her cousin's age. We can write this as an equation:
Ansley's age = 3 × Cousin's age - 5
We also know that Ansley is 31 years old. So we can substitute 31 for Ansley's age in the equation:
31 = 3 × Cousin's age - 5
Now we solve for Cousin's age. First, we add 5 to both sides of the equation:
31 + 5 = 3 × Cousin's age
Simplifying:
36 = 3 × Cousin's age
Finally, we divide both sides by 3:
Cousin's age = 12
So Ansley's cousin is 12 years old, and Ansley's age can be found by plugging in 12 for Cousin's age in the expression we found earlier:
Ansley's age = 3 × Cousin's age - 5 = 3 × 12 - 5 = 31
So Ansley is indeed 31 years old.
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How to get the centre of the circle when the circumference is not given
To find the center of a circle when the circumference is not given, you still find it.
1. Determine the coordinates of at least three non-collinear points on the circle. Non-collinear points are points that do not lie on a straight line.
2. Using these points, create two line segments that are chords of the circle. A chord is a line segment connecting two points on the circle.
3. Find the midpoints of each chord. The midpoint formula is given as: Midpoint (M) = ((x1 + x2) / 2, (y1 + y2) / 2).
4. Calculate the slope of each chord using the slope formula: Slope (m) = (y2 - y1) / (x2 - x1).
5. Calculate the slope of the perpendicular bisectors of each chord. Since these lines are perpendicular to the chords, their slopes are the negative reciprocal of the chord slopes: m_perpendicular = -1 / m_chord.
6. Write the equation of each perpendicular bisector using the point-slope formula: y - y_midpoint = m_perpendicular * (x - x_midpoint).
7. Solve the system of equations formed by the two perpendicular bisectors. The solution is the coordinates of the center of the circle.
By following these steps, you can find the center of the circle even when the circumference is not given.
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FILL IN THE BLANK. Find the indefinite integral ∫ sin²(x)- cos²(x)/cos(x) dx =_______ Note: Use an upper-case "C" for the constant of integration.
The final result is ∫ sin²(x)- cos²(x)/cos(x) dx = -3cos²(x)/2 + 2ln|cos(x)| + C.
To solve the indefinite integral ∫ sin²(x)- cos²(x)/cos(x) dx, we need to use trigonometric identities to simplify the integrand.
First, we use the identity sin²(x) + cos²(x) = 1 to write:
sin²(x) - cos²(x) = sin²(x) + cos²(x) - 2cos²(x) = 2sin²(x) - cos²(x)
Next, we use the identity sin²(x) = 1 - cos²(x) to write:
2sin²(x) - cos²(x) = 2(1-cos²(x)) - cos²(x) = 2 - 3cos²(x)
Substituting this into the original integral, we get:
∫ sin²(x)- cos²(x)/cos(x) dx = ∫ (2 - 3cos²(x))/cos(x) dx
Now, we use the substitution u = cos(x) and du/dx = -sin(x) dx to transform the integral into a simpler form:
∫ (2 - 3cos²(x))/cos(x) dx = ∫ (2 - 3u²)/u (-du/sin(x))
= -∫ (3u² - 2)/u du
= -3∫ u du + 2∫ du/u
= -3u²/2 + 2ln|u| + C
= -3cos²(x)/2 + 2ln|cos(x)| + C
where C is the constant of integration.
Substituting back u = cos(x), we obtain the final result
∫ sin²(x)- cos²(x)/cos(x) dx = -3cos²(x)/2 + 2ln|cos(x)| + C
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QUESTION 4
This spinner is divided into eight equal-sized sections. Each section is labeled with a number.
Write the events below in the correct
order from least likely to most likely.
A) Arrow lands on a section labeled with an odd number.
B) Arrow lands on a section labeled
with the number 1.
C) Arrow lands on a section labeled
with a number less than 4.
Ranking of the events below in the correct order from least likely to most likely are:
Event B
Event A
Event C
What is the probability of Occurrence?The probability of an event is defined as a number that describes the chance that the event will eventually happen. An event that is sure to happen has a probability of 1. An event that can never possibly happen has a probability of zero. Finally, If there is a chance that an event will happen, then it will have a probability that is between zero and 1.
i) Arrow lands on a section labeled with an odd number: The odd numbers here are 1 and 3.
There are a total of four 1's, and two 3's. This tells us that there are 6 odd numbers on the spinner.
There are 8 numbers in total on the spinner. Thus, 6 out of the 8 numbers are seen as odd numbers. Therefore, the probability that the arrow lands on an odd number would be:
P(odd number) = 6/8 = 75%
ii) Arrow lands on a section labeled with the number 1: There are four 1's on the spinner, and there are seen to be 8 numbers in total on the spinner. Thus, the probability of the arrow landing on a 1 is:
P(Number 1) = 4/8 = 50%.
iii) Arrow lands on a section labeled with a number less than 4:
The numbers that are less than 4 are 3, 2, and 1.
There are two 3's.
There is one 2.
There are four 1's.
2 + 1 + 4 = 7.
The probability of the arrow landing on a number less than 4 is 7/8, which is 88.5%.
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Triangle XYZ has coordinates X(-2,2), Y(-3,-4). And Z(1,-2). The triangle is reflected across the x-axis. What are the coordinates of triangle X'Y'Z'?
The coordinates of triangle X'Y'Z' is X'(-2,-2), Y'(-3,4), Z'(1,2).
What are the coordinates of the triangle?
The triangle's vertices have the coordinates (x1,y1), (x2,y2), and (x3,y3). The line that connects the first two is split in the ratio l:k, and the line that runs from the division point to the opposing angular point is divided in the ratio m:k+l.
Here, we have
Given: Triangle XYZ has coordinates X(-2,2), Y(-3,-4). And Z(1,-2).
The triangle is reflected across the x-axis and we have to find the coordinates of triangle X'Y'Z'.
X(-2,2), Y(-3,-4) and Z(1,-2).
While reflecting any points across the x-axis with coordinates as (x, y) becomes, (x, -y). i.e. sign of y-coordinate changes.
The rule is (x, y) → (x, -y)
After applying the rule, we get
X(-2,2) ⇒ X'(-2,-2)
Y(-3,-4) ⇒ Y'(-3,4)
Z(1,-2) ⇒ Z'(1,2)
Hence, the coordinates of triangle X'Y'Z' is X'(-2,-2), Y'(-3,4), Z'(1,2).
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You babysat your neighbor's children and they paid you $45 for 6 hours. Fill in the t-table for hours (x) and money (y)
you got $45 for 6hours.
one hour=$7.5
two hours=$15
three hours=$7.5*3
calculation=$45/6
find the missing no 3,4,13,?,8,168
Answer:
I believe it is 38
Step-by-step explanation:
A survey of 61 randomly selected homeowners finds that they spend a mean of $62 per month on home maintenance. construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. assume that the population standard deviation is $13 per month. round to the nearest cent.
The 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is $58.06 to $65.94.
To construct a confidence interval for the mean amount of money spent per month on home maintenance by all homeowners, we can use the formula:
CI = [tex]\bar{X}[/tex] ± Zα/2 * (σ/√n)
where [tex]\bar{X}[/tex] is the sample mean, Zα/2 is the critical value from the standard normal distribution corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
In this case, we have:
[tex]\bar{X}[/tex] = $62 (the sample mean)
α = 0.02 (since we want a 98% confidence interval, which means α/2 = 0.01)
Zα/2 = 2.33 (from the standard normal distribution table)
σ = $13 (the population standard deviation)
n = 61 (the sample size)
Substituting these values into the formula, we get:
CI = $62 ± 2.33 * ($13/√61)
Simplifying this expression, we get:
CI = $62 ± $3.94
Therefore, the 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is $58.06 to $65.94.
This means that we can be 98% confident that the true population mean falls within this range. In other words, if we were to repeat the survey many times and construct confidence intervals in the same way, about 98% of the intervals would contain the true population mean.
It's important to note that this assumes that the sample is representative of the population, and that the population standard deviation is known. If these assumptions are not met, then the confidence interval may not be accurate.
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If f(9) = 9, f'(9) = 4, limit x→9√(f(x))-3/√(x)-3 =
A. 1
B. 1/4
C. 1/2
D. -1/2
The answer is A. 1. We can use L'Hopital's rule to evaluate the limit:
limit x→9√(f(x))-3/√(x)-3 = limit x→9 (f(x)-9)/(x-9) / (√(f(x))-3)/(√(x)-3)
Now, we know that f(9) = 9 and f'(9) = 4, so we can use the definition of the derivative to write:
f(x) - f(9) = f'(9)(x-9) + o(x-9)
where o(x-9) represents a term that goes to 0 faster than x-9 as x approaches 9. Plugging this into the numerator, we get:
f(x) - 9 = 4(x-9) + o(x-9)
Plugging this into the denominator, we get:
√(f(x)) - 3 = √(4(x-9) + o(x-9)) = 2√(x-9) + o(1)
√(x) - 3 = √(x-9) + o(1)
Therefore, the limit becomes:
limit x→9 (4(x-9) + o(x-9))/(√(x-9) + o(1)) / (2√(x-9) + o(1))/(√(x-9) + o(1))
Simplifying this expression, we get:
limit x→9 2(4(x-9) + o(x-9))/(√(x-9) + o(1))^2
limit x→9 8 + 2o(1)/(x-9)
As x approaches 9, the o(1) term goes to 0, so the limit becomes:
8 + 2*0/0 = 8
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If the team takes on two additional players, one at 5 feet 5 inches and the other at 6 feet 7 inches, how is the median of the data set affected? A. The effect on the median of the players' heights cannot be determined. B. The median of the players' heights is decreased. C. The median of the players' heights is increased. D. The median of the players' heights is not affected
Answer: The median of the players' heights is not affected.
Step-by-step explanation: B
The median of the players' heights is increased.
we need to consider the current arrangement of heights and the positions
of the new players in relation to the existing players' heights.
If we assume that the heights of the players are sorted in ascending order,
adding two additional players can affect the median in the following ways:
If both new players have heights lower than the current median:
In this case, adding the new players would not change the median.
The median would remain the same because the new players would be
added below the existing median, and the position of the median would
not shift.
If one new player has a height lower than the current median and the other
has a height higher than the current median:
In this case, the median would be increased.
Adding a taller player would shift the median towards the higher end of the data set.
If both new players have heights higher than the current median:
In this case, the would be increased.
Both new players would be taller than the current median, causing the
median to shift towards the higher end of the data set.
Based on these possibilities, the answer is C.
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A rectangular patio is 10 feet by 13 feet. what is the length of the diagonal of the patio? (use pythagorean theorem: a² + b ²= c²)
The length of the diagonal is c = √269 feet.
To get the length of the diagonal of a rectangular patio, we can use the Pythagorean theorem, which states that for a right triangle with legs of length a and b, and hypotenuse of length c, a² + b² = c². In this case, the legs of the right triangle are the length and width of the rectangular patio, which are 10 feet and 13 feet, respectively. Let's use a and b to represent these lengths.
a = 10 feet
b = 13 feet
We want to find the length of the diagonal, which is the hypotenuse of the right triangle. Let's use c to represent this length.
a² + b² = c²
10² + 13² = c²
100 + 169 = c²
269 = c²
Now we need to find the square root of 269 to get the length of the diagonal.
c = √269
c ≈ 16.4 feet
So the length of the diagonal of the rectangular patio is approximately 16.4 feet. We can also find the ratio of the length, width, and diagonal of the rectangular patio.
length:width = 10:13
width:length = 13:10
length:diagonal = 10:√269
width:diagonal = 13:√269
diagonal:length = √269:10
diagonal:width = √269:13
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Verónica jogged 10 3/16 miles in a one week, the next week she jogged 8 7/16 miles. how many more miles did she jog the first week? pls answer
Verónica jogged 7/4 or 1 and 3/4 more miles in the first week than in the second week.
Verónica jogged 10 3/16 miles in one week, next week she jogged 8 7/16 miles. how many miles did she jog the first week?Verónica jogged 10 3/16 miles in the first week and 8 7/16 miles in the second week. To find how many more miles she jogged in the first week, we need to subtract the distance she jogged in the second week from the distance she jogged in the first week:
10 3/16 miles - 8 7/16 miles
We need to first convert both mixed numbers to improper fractions:
10 3/16 = (10 x 16 + 3) / 16 = 163 / 16
8 7/16 = (8 x 16 + 7) / 16 = 135 / 16
Now we can subtract the two fractions:
163 / 16 - 135 / 16 = (163 - 135) / 16 = 28 / 16
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor (GCF), which is 4:
28 / 16 = (4 x 7) / (4 x 4) = 7 / 4
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Garden plots in the Portland Community Garden are rectangles
limited to 45 square meters. Christopher and his friends want a plot
that has a width of 7.5 meters. What length will give a plot that has
the maximum area allowed?
The length should be less than or equal to 6 meters in order to have a plot with the maximum area allowed (45 square meters) when the width is 7.5 meters.
To find the length that will give a plot with the maximum area allowed, we can use the formula for the area of a rectangle:
Area = Length × Width
The width is given as 7.5 meters, and the area should not exceed 45 square meters.
Let's denote the length as L.
We want to maximize the area, so we need to find the value of L that satisfies the condition Area ≤ 45 and gives the largest possible area.
Substituting the given values into the area formula, we have:
Area = L × 7.5
Since the area should not exceed 45 square meters, we can write the inequality:
L × 7.5 ≤ 45
To find the maximum value of L, we can divide both sides of the inequality by 7.5:
L ≤ 45 / 7.5
Simplifying the right side:
L ≤ 6
Therefore, the length should be less than or equal to 6 meters in order to have a plot with the maximum area allowed (45 square meters) when the width is 7.5 meters.
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Three years agoJerry purchased a condo This year his monthly maintenance fee is \$1,397 Twenty percent of this fee is for Jerry's property taxes. How much will Jerry pay this year in property taxes ?
Jerry pays $279.40 this year in property taxes.
To calculate Jerry's property taxes for the year, we need to first decide how many of his month-to-month maintenance fee is going toward property taxes.
The problem states that 20% of the price is for Jerry's assets taxes, which means we will calculate the amount of his belongings taxes with the aid of finding 20% of his monthly charge.
To do this, we multiply the price through 0.20 such as this:
20% of $1,397 = 0.20 x $1,397 = $279.40
Therefore, Jerry pays $279.40 this year in property taxes.
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if you roll two fair six-sided dice, what is the probability that the sum is 4 44 or higher?
The probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 11/12
To calculate the probability of rolling two fair six-sided dice and getting a sum of 4 or higher, we first need to calculate the total number of possible outcomes.
The number of possible outcomes when rolling two dice is 6 × 6 = 36, since each die has 6 possible outcomes.
Now, let's find the number of outcomes that result in a sum of 4 or higher. We can do this by listing all the possible outcomes:
Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes
Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes
Sum of 10: (4, 6), (5, 5), (6, 4) = 3 outcomes
Sum of 11: (5, 6), (6, 5) = 2 outcomes
Sum of 12: (6, 6) = 1 outcome
Therefore, the number of outcomes that result in a sum of 4 or higher is 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.
Therefore, the probability of rolling two fair six-sided dice and getting a sum of 4 or higher is 33/36 = 11/12.
To find the probability of getting a sum of 44 or higher, we need to subtract the probability of getting a sum of 43 or lower from 1:
Sum of 2: (1, 1) = 1 outcome
Sum of 3: (1, 2), (2, 1) = 2 outcomes
Sum of 4: (1, 3), (2, 2), (3, 1) = 3 outcomes
Sum of 5: (1, 4), (2, 3), (3, 2), (4, 1) = 4 outcomes
Sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) = 5 outcomes
Sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6 outcomes
Sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) = 5 outcomes
Sum of 9: (3, 6), (4, 5), (5, 4), (6, 3) = 4 outcomes
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Paige walks to the park 2/3 mile away it takes her 16 minutes to get there how many miles per minutes
The Paige walks at a speed of approximately 0.04167 miles per minute to get to the park.
How we find the miles per minutes?To calculate Paige's speed, we used the formula:
Speed = Distance / Time
Given that Paige walks to the park 2/3 mile away, we substitute Distance with 2/3 mile and Time with 16 minutes. We get:
Speed = 2/3 mile / 16 minutes
Simplifying the expression by converting minutes to hours, we get:
Speed = 2/3 mile / (16/60) hours
Simplifying further by multiplying both the numerator and denominator by 60, we get:
Speed = [tex](2/3) * (60/1)[/tex] mile/hour / (16/1) minutes
Speed = 0.04167 mile/minute (rounded to 5 decimal places)
"Paige walks to the park 2/3 mile away it takes her 16 minutes to get there how many miles per minutes" is that Paige walks at a speed of approximately 0.04167 miles per minute.
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Alan buys a bag of cookies that contains 5 chocolate chip cookies, 5 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies. What is the probability that Alan randomly selects a chocolate chip cookie from the bag, eats it, then randomly selects a peanut butter cookie? Express you answer as a reduced fraction
PLEASE HELPPPP!!!!
The base of a right octagonal prism has eight sides equal in length. One side of the base measures 2. 3 cm, and the area of the base is 25. 76 cm². The surface area of the prism is 223. 56 cm².
Whats the height of the prism?
The height of the right octagonal prism is approximately 10.75 cm.
The given information states that the base of the prism is a regular octagon with each side measuring 2.3 cm, and the area of the base is 25.76 cm². Additionally, the surface area of the prism is 223.56 cm².
First, let's calculate the area of the eight lateral faces. We can do this by subtracting the base's area from the total surface area:
223.56 cm² (total surface area) - 25.76 cm² (base area) = 197.8 cm² (lateral area)
Now, we know that the lateral area is the sum of the areas of all eight rectangular faces. Each rectangle has a base of 2.3 cm (the same as the sides of the octagonal base) and a height equal to the height of the prism (h). Since there are eight faces, the combined area of these rectangles is 8 x 2.3 x h:
8 x 2.3 x h = 197.8 cm²
18.4 x h = 197.8 cm²
To find the height of the prism (h), we can divide both sides of the equation by 18.4:
h = 197.8 cm² / 18.4
h ≈ 10.75 cm
So, the height of the right octagonal prism is approximately 10.75 cm.
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Prepare the operating activities section of the statement of cash flows for peach computer using the indirect method. (list cash outflows and any decrease in cash as negative amounts.)
Cash outflows and decreases in cash are reported as negative amounts in the operating activities section of the statement of cash flows for Peach Computer using the indirect method.
How to prepare the operating activities section of the statement of cash flows for Peach Computer using the indirect method?The operating activities section of the statement of cash flows for Peach Computer using the indirect method would include the following cash inflows and outflows:
Cash inflows:
Sales revenue from the sale of computersCash received from customers for computer repairs and servicesInterest received on loans or investmentsCash outflows:
Payments to suppliers for inventory purchasesPayments to employees for salaries and wagesPayments for operating expenses such as rent, utilities, and advertisingPayments of income taxesPayments of interest on loansPayments to creditors for accounts payableAny decrease in cash would be represented as negative amounts in this section.
It's important to note that the specific amounts and details would vary based on Peach Computer's individual financial transactions and operations. The operating activities section provides a summary of the cash inflows and outflows directly related to the company's core business operations during the specified period.
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a specific combination lock has 3 numbers chosen out of 40 possible numbers (0-39). assuming that all lock combinations are possible (including repeated numbers) find the number of possible lock combinations.
The total number of possible lock combination using the 40 possible numbers for making lock of 3 numbers is equal to 64,000.
Possible number used for lock combination are 40.
Range is 0 - 39.
Total number chosen for lock combination is equal to 3.
Since there are 40 possible numbers to choose from for each of the three positions on the combination lock.
The total number of possible combinations is equal to ,
40 x 40 x 40
= 40^3
= 64,000
Therefore, there are 64,000 possible lock combinations when choosing 3 numbers out of 40 possible numbers, assuming repeated numbers are allowed.
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Jenny is planning an extended trip to russia.the table below shows a list of cities which she would like to visit during her stay, along with the amount of money she anticipates needing to spend on travel, lodging, and similar expenses in each city. all costs are given in russian rubles (rub). city cost (rub) izhevsk 4,721 novosibirsk 4,870 nizhny novgorod 6,920 moscow 5,485 chelyabinsk 5,217 saint petersburg 5,960 tolyatti 5,598 yaroslavl 4,901 even though jenny wants to go to each of these cities, her budget is only rub 33,000, so she recognizes that she must change her itinerary and choose not to visit some cities. which of the following pairs of cities will not put jenny back under budget if she drops them? a. moscow and chelyabinsk b. izhevsk and nizhny novgorod c. novosibirsk and saint petersburg d. yaroslavl and tolyatti
The pairs of cities that will not put Jenny back under budget if she drops them are:
a. Moscow and Chelyabinsk
b. Izhevsk and Nizhny Novgorod
To determine which pair of cities Jenny can drop without going over budget, we need to find the total cost of each pair and see if it exceeds her budget of rub 33,000.
a. Moscow and Chelyabinsk:
Total cost = 5,485 + 5,217 = 10,702 rubles
This pair of cities is over budget, so Jenny cannot drop any other cities if she wants to visit both Moscow and Chelyabinsk.
b. Izhevsk and Nizhny Novgorod:
Total cost = 4,721 + 6,920 = 11,641 rubles
This pair of cities is over budget, so Jenny cannot drop any other cities if she wants to visit both Izhevsk and Nizhny Novgorod.
c. Novosibirsk and Saint Petersburg:
Total cost = 4,870 + 5,960 = 10,830 rubles
This pair of cities is under budget, so Jenny can drop this pair without going over budget.
d. Yaroslavl and Tolyatti:
Total cost = 4,901 + 5,598 = 10,499 rubles
This pair of cities is under budget, so Jenny can drop this pair without going over budget.
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On a baseball diamond, home plate and second base lie on the perpendicular bisector of the line segment that joins first and third base. First base is 90 feet from home plate. How far is it from third base to home plate? Sketch a baseball diamond on a separate sheet of paper, labeling home plate as point A
, first base as B
, second base as C
, and third base as D. Label the intersection of AC⎯⎯⎯⎯⎯
and BD⎯⎯⎯⎯⎯
as E. Using the Perpendicular Bisector Theorem, determine how far it is from third base to home plate. Describe your conclusion in the context of the situation
Using the Perpendicular Bisector Theorem, the distance from third base to home plate is 90 feet. This means that all the bases are equidistant from home plate, which is a fundamental property of a baseball diamond.
To find the distance from third base to home plate, we need to use the Perpendicular Bisector Theorem, which states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
First, we draw a baseball diamond with points A, B, C, and D labeled as described in the problem.
Next, we draw the line segment that joins first base (B) and third base (D), and we construct the perpendicular bisector of this segment by drawing a line through the midpoint of BD and perpendicular to BD. Let's label the point where the perpendicular bisector intersects the line that connects home plate (A) and second base (C) as E.
Since E lies on the perpendicular bisector of BD, it is equidistant from B and D. We know that first base (B) is 90 feet from home plate (A), so the distance from home plate to E must also be 90 feet. Therefore, the distance from third base (D) to home plate (A) is also 90 feet.
In conclusion, using the Perpendicular Bisector Theorem, we determined that the distance from third base to home plate is 90 feet.
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1. Use integration in cylindrical coordinates in order to compute the vol- ume of: U = {(x,y,z):05:36 - 12 - y}
The volume of the region U is 16π cubic units.
To find the volume of the region U, we can use cylindrical coordinates. In cylindrical coordinates, a point in space is represented by the coordinates (r, θ, z), where r is the distance from the z-axis, θ is the angle between the x-axis and the projection of the point onto the xy-plane, and z is the height above the xy-plane.
In this case, the region U is defined by 0 ≤ r ≤ 2, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 12 - r sin(θ).
To find the volume of U, we can integrate over the cylindrical coordinates. The volume of U is given by the integral:
V = ∫∫∫_U dV
where dV = r dz dr dθ is the volume element in cylindrical coordinates.
Substituting in the limits of integration, we have:
V = ∫₀²π ∫₀² ∫₀^(12-rsinθ) r dz dr dθ
Integrating with respect to z, we get:
V = ∫₀²π ∫₀² r(12-rsinθ) dr dθ
Integrating with respect to r, we get:
V = ∫₀²π [(6r² - (1/3)r³sinθ)] from r=0 to r=2 dθ
Simplifying, we get:
V = ∫₀²π [(24 - 16/3 sinθ)] dθ
Integrating, we get:
V = [24θ + 16/3 cosθ] from θ=0 to θ=2π
Simplifying, we get:
V = 48π/3 = 16π
Therefore, the volume of the region U is 16π cubic units.
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ALGEBRA
Farha Gadhia has applied for a $100,000 mortgage loan
at an annual interest rate of 6%. The loan is for a period of 30 years
and will be paid in equal monthly payments that include interest.
Use the monthly payment formula to find the payment.
Find the new coordinates for the image under the given translation. Square RSTU with vertices R(-2, 1), S(3, 4), T(6, -1), and U(1, -4): (x, y) → (x-4, y − 1) - -9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 R' (, ) S' (, ) T'(,0) U'(,) 3 4 LO 5 6 7 8 9
Thus, the new coordinates for the image of translated Vertices of Square RSTU are- R'(-6, 0), S'(-1, 3), T'(2, -2) and U'(-3, -5).
Define about the translations:In mathematics, a translation moves an object throughout the coordinate plane while preserving its dimensions and shape. After a translation, its area and orientation remain unchanged.
The vertical shift, horizontal shift, or perhaps a combination of the two can be referred to as a translation in mathematics.
Given that:
Vertices of Square RSTU.
R(-2, 1), S(3, 4), T(6, -1), and U(1, -4):
translation: (x, y) → (x-4, y − 1)
New vertices:
R(-2-4, 1 − 1) --> R'(-6, 0)
S(3-4, 4 − 1), ---> S'(-1, 3)
T(6-4, -1 − 1), -> T'(2, -2)
U(1-4, -4 − 1) --> U'(-3, -5)
Thus, the new coordinates for the image of translated Vertices of Square RSTU are- R'(-6, 0), S'(-1, 3), T'(2, -2) and U'(-3, -5).
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The triangle above has the following measures.
a=9cm
b=9√3cm
Use the 30-60-90 Thangle Theorem to find the
length of the hypotenuse Include correct units
Show all your work
Answer:
Step-by-step explanation:
The length of the hypotenuse is approximately 4.95 cm.
We have,
Since triangle ABC is a 45-45-90 triangle, we know that the measure of angle B is also 45 degrees.
Therefore, we can use the 45-45-90 Triangle Theorem, which states that in a 45-45-90 triangle,
the length of the hypotenuse is √2 times the length of either leg.
In this case,
We know that leg a = 3.5 cm, so we can find the length of the hypotenuse c using the formula:
c = a√2
Substituting the value of a, we get:
c = 3.5√2 ≈ 4.95 cm
Therefore,
The length of the hypotenuse is approximately 4.95 cm.
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complete question:
The triangle above has the following measures. mzC = 45° a = 3.5 cm Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units. Show all your work.
PLEASE HELP!!!!!!! Two lines, E and F, are represented by the equations given below. Line E: 5x + 5y = 40 Line F: x + y = 8 Which statement is true about the solution to the set of equations? (4 points) Question 2 options: 1) It is (40, 8). 2) It is (8, 40). 3) There is no solution. 4) There are infinitely many solutions.
Answer: (4)
Step-by-step explanation:
Two lines E and F are same.
5x + 5y = 40
x + y = 8
Deviding both hands of E by 5,
we get F's equation.
So every single point on the line x+y=8
represents the solution of the given system.
topic 3 providing lines are parallel
21
21. in the figure, provided line n and line m are parallel the values of x and y are
x = 7
y = 24
How to find x and y21. When line m and line n are parallel then using corresponding angle theorem we have that:
7y - 23 + 8x - 21 = 180
7y - 8x = 180 + 23 - 21
7x - 8x = 182
Also
8x - 21 + 23x - 16 = 180
8x + 23x = 180 + 21 + 16
31x = 217
x = 217 / 31
x = 7
using vertical angle theorem we have:
7y - 23 = 23x - 16
plugging in the value of x
7y - 23 = 23 * 7 - 16
7y - 23 = 145
7y = 145 + 23
7y = 168
y = 24
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answer questions 2-20 please 1 and 5-7 are already answered no need to correct them does not need to be correct but please have relistic answers : )
The Pythagorean Theorem with regards to the relationships between the lengths of the sides of a right triangle indicates that we get;
2. x = 51
3. x = 50
4. x = 82
8. x = 2·√(77)
9. x = √(39)
10. x = 2·√(19)
11. x = 2·√(154)
12. x = 3·√3
13. x = 6·√(13)
16. A right triangle
17. A right triangle
18. The triangle is not a right triangle
19. An obtuse triangle
20. An obtuse triangle
What is the Pythagorean Theorem?The Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the lengths of the other two sides.
2. x² = 45² + 24² = 2601
x = √(2601) = 51
3. x² = 30² + 40² = 2500
x = √(2500) = 50
x = 50
4. x² = 80² + 18² = 6724
x = √(6724) = 82
x = 82
8. According to the Pythagorean Theorem, in the right triangle we get;
x² = 18² - 4² = 308
x = 2·√(77)
9. x² = 8² - 5² = 39
x = √(39)
10. x² = 20² - 18²
x² = 76
x = √(76) = 2·√(19)
x = 2·√(19)
11. x² = 25² - 3² = 616
x = √(616) = 2·√(154)
x = 2·√(154)
12. x² = 6² - 3² = 27
x = √(27)
x = 3·√3
13. x² = 22² - 4² = 468
x = √(468) = 6·√(13)
x = 6·√(13)
16. A triangle is a right triangle if the square of the side that is the longest is equivalent to the square of the other two sides, therefore;
17² = 289
15² + 8² = 289
Therefore, the triangle is a right triangle
17. 45² = 2025
27² + 36² = 2025
Therefore, the triangle is a right triangle
18. 11² = 121
9² + 4² = 97
Therefore, the triangle is not a right triangle
19. 6² = 36
4² + 3² = 25
The square of the side that is longest is larger than the sum of the squares of the other two sides, which indicates that the angle facing the longest side is lar1ger than 90°, and the triangle is an obtuse triangle.
20. 16² = 256
9² + 11² = 202
16² > 9² + 11²; Therefore, the triangle is an obtuse triangle
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Algebra please help
Your school newspaper has an editor-in-chief and an assistant editor-in-chief. The newspaper staff
has 5 students. How many different ways can students be chosen for these positions?
There are 20 different ways the students can be chosen for the positions of editor-in-chief and assistant editor-in-chief.
There are 5 students in the newspaper staff, and two positions to fill i.e. editor-in-chief and assistant editor-in-chief. We need to find the number of different ways the students can be chosen for these positions.
To solve this problem, we can use the formula for permutation
We know the formula for Permutation is
[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]
Here, n=5 and r=2
So, P(5,2) = 5!/(5-2)!
= 5!/3!
= 120/6
= 20
Therefore, there are 20 different ways the students can be chosen for the positions of editor-in-chief and assistant editor-in-chief.
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