We can use the formula for the area of a sector to find the area of sector $LMN$
How to find the area of a sector with central angle $\theta$ in a circle with radius $r$?The area of a sector with central angle $\theta$ in a circle with radius $r$ is given by:
$A = \frac{\theta}{360^\circ} \pi r^2$
In this case, we know that $m\angle LMN = 66^\circ$ and $LM = 19$ units, so the radius of circle M is half of the diagonal of the rectangle formed by $LM$ and $MN$. Using the Pythagorean theorem, we can find the length of $MN$:
$MN^2 = LM^2 + LN^2 = LM^2 + LM^2 = 2LM^2$
$MN = \sqrt{2} LM = \sqrt{2} \cdot 19$
So the radius of circle M is $r = \frac{1}{2}MN = \frac{1}{2}\sqrt{2} \cdot 19$
Now we can use the formula for the area of a sector to find the area of sector $LMN$:
$A = \frac{m\angle LMN}{360^\circ} \pi r^2 = \frac{66^\circ}{360^\circ} \pi \left(\frac{1}{2}\sqrt{2} \cdot 19\right)^2 \approx \boxed{90.89}$ square units (rounded to the nearest hundredth).
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I need help. What would be the answer?
Answer:
Step-by-step explanation:
DE/EC.
A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 3 cm and segment BE = 3. 5 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth. Quadrilateral BCDE inscribed within circle A a 3. 91 cm b 4. 24 cm c 4. 61 cm d 4. 95 cm
Using the Pythagorean theorem, the smallest diameter of the pipe that will fit the fiber optic line is approximately 4.61 cm (Option C).
To determine the smallest diameter of the pipe that will fit the fiber optic line in rectangular casing BCDE, we need to find the diagonal AC of the rectangle. Since the rectangle is inscribed within circle A, the diameter of the circle will be equal to the diagonal of the rectangle.
Using the Pythagorean theorem, we can find the length of AC:
AC^2 = DE^2 + BE^2
AC^2 = (3 cm)^2 + (3.5 cm)^2
AC^2 = 9 + 12.25
AC^2 = 21.25
AC = √21.25 ≈ 4.61 cm
Therefore, the smallest diameter of the pipe that will fit the fiber optic line is approximately 4.61 cm (Option C).
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Start at 7 and count up 2 times by hundreds
Answer:
1,400
Step-by-step explanation:
its the same thing as 7 times 200
Which shows 71. 38 in word form? O A seventy-one thirty-eighths O B. Seventy-one and thirty eighths O c. Seventy-one and thirty-eight tenths D. Seventy-one and thirty-eight hundredths E seventy-one and thirty-eight thousands
71.38 in word form is Seventy-one and thirty-eight hundredths.
What is the decimal number?
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.
To write decimals in word form, you can read the whole number part, write "and," and then read the decimal part according to place value.
For example: 0.25 can be written as "zero and twenty-five hundredths"
Hence, the correct answer is 'D. Seventy-one and thirty-eight hundredths'.
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Let g(x) be continuous with g(0) = 3. g(1)
8, g(2) = 4. Use the Intermediate Value Theorem to ex-
plain why s(x) is not invertible.
The Intermediate Value Theorem states that if a function f(x) is continuous on a closed interval [a,b], and if M is any number between f(a) and f(b), then there exists at least one number c in the interval [a,b] such that f(c) = M.
In this case, we are given a continuous function g(x) with g(0) = 3, g(1) = 8, and g(2) = 4. Let s(x) be the inverse of g(x), which means that s(g(x)) = x for all x in the domain of g(x).
Suppose s(x) is invertible. Then for any y in the range of g(x), there exists a unique x such that g(x) = y, and therefore s(y) = x. In particular, let y = 5, which is between g(1) = 8 and g(2) = 4. By the Intermediate Value Theorem, there exists a number c in the interval [1,2] such that g(c) = 5.
However, this means that s(5) is not well-defined, since there are two values of x (namely c and s(5)) that satisfy g(x) = 5. Therefore, s(x) is not invertible.
The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], and k is any number between f(a) and f(b), then there exists a number c in the interval [a, b] such that f(c) = k.
Let g(x) be continuous with g(0) = 3, g(1) = 8, and g(2) = 4. Since g(x) is continuous, the Intermediate Value Theorem applies. However, to show that s(x) is not invertible, we need to show that g(x) is not one-to-one.
Notice that g(0) = 3 and g(2) = 4, with g(1) = 8 in between. This means that there must exist a point c1 in the interval (0, 1) such that g(c1) = 4, and another point c2 in the interval (1, 2) such that g(c2) = 3, due to the Intermediate Value Theorem.
Since g(c1) = g(c2) = 4 and c1 ≠ c2, g(x) is not one-to-one. Therefore, its inverse function s(x) does not exist, and s(x) is not invertible.
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A museum charges 12. 50 admission Each special  sip it cost extra 2. 00 Write an expression that represents the cost in dollars of admission to the museum including admittance to n special exhibits.
The expression that represents the cost, in dollars, of admission to the museum including admittance to n special exhibits can be written as 12.50 + 2n
Here, 12.50 is the base admission cost without any special exhibit, and 2n represents the cost of n special exhibits, where each exhibit costs an extra $2.00.
By multiplying the number of special exhibits, n, by $2.00, we get the total cost of special exhibits, which we can then add to the base admission cost to get the total cost of admission to the museum including admittance to n special exhibits.
For example, if someone wants to visit the museum and see 3 special exhibits, the cost of admission would be:
12.50 + 2(3) = 12.50 + 6 = $18.50
Therefore, the expression 12.50 + 2n represents the total cost of admission to the museum including admittance to n special exhibits.
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Complete question is:
A museum charges $12.50 for admission. Each special exhibit costs an extra $2.00. Part A Write an expression that represents the cost, in dollars, of admission to the museum including admittance to n special exhibits
A young doctor is working at night in an emergency room. Emergencies come in at times of a Poisson process with rate 0. 5 per hour. The doctor can only get to sleep when it has been 36 minutes (6 hours) since the last emergency. For example, if there is an emergency at 1:00 and a second one at 1:17 then she will not be able to get to sleep until at least 1:53, and it will be even later if there is another emergency before that time.
(a) Compute the long-run fraction of time she spends sleeping, by formulating a renewal reward process in which the reward in the ith interval is the amount of time she gets to sleep in that interval.
(b) The doctor alternates between sleeping for an amount of time si and being awake for an amount of time u. Use the result from (a) to compute Eui
The probability of getting to sleep in an interval is 0.0903.
The expected time the doctor spends awake in each interval is 1.8648 hours.
(a) To compute the long-run fraction of time the doctor spends sleeping, we can formulate a renewal reward process. In this process, each interval represents the time between consecutive emergencies.
Let T be the inter-arrival time between emergencies, which follows an exponential distribution with a rate of λ = 0.5 per hour. The average inter-arrival time is given by E(T) = 1/λ = 1/0.5 = 2 hours.
In each interval, the doctor can only get to sleep if it has been 36 minutes (6 hours) since the last emergency. Otherwise, she remains awake.
Let R be the reward obtained in each interval, which is the amount of time the doctor gets to sleep. If the doctor gets to sleep in an interval, the reward is (T - 0.6) since she has already waited for 0.6 hours (36 minutes). Otherwise, the reward is zero.
The long-run fraction of time spent sleeping, denoted by ρ, can be calculated as the expected reward per unit time:
ρ = E(R)/E(T)
To compute E(R), we need to consider the conditional probability that the doctor gets to sleep in an interval.
Given an interval length T, the probability that T > 0.1 (36 minutes) is given by P(T > 0.1) = 1 - P(T ≤ 0.1). This probability is equal to the cumulative distribution function (CDF) of the exponential distribution with rate λ evaluated at 0.1.
P(T > 0.1) = 1 - F(0.1) = 1 - (1 - exp(-λ * 0.1))
Substituting the value of λ = 0.5, we get:
P(T > 0.1) = 1 - (1 - exp(-0.5 * 0.1)) ≈ 0.0903
Therefore, the probability of getting to sleep in an interval is approximately 0.0903.
E(R) = (T - 0.6) * P(T > 0.1) + 0 * (1 - P(T > 0.1))
= (T - 0.6) * 0.0903
Substituting the average inter-arrival time E(T) = 2 hours:
E(R) = (2 - 0.6) * 0.0903 ≈ 0.1352 hours
Finally, we can compute ρ:
ρ = E(R)/E(T) = 0.1352/2 ≈ 0.0676
Therefore, the long-run fraction of time the doctor spends sleeping is approximately 0.0676.
(b) To compute E(ui), the expected time the doctor spends awake in each interval, we can use the fact that the total time spent in each interval is T, and the time spent sleeping is (T - R), where R is the reward obtained in each interval.
E(ui) = E(T - R)
= E(T) - E(R)
= 2 - 0.1352
≈ 1.8648 hours
Therefore, the expected time the doctor spends awake in each interval is approximately 1.8648 hours.
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Consider the function f(x) = 7(x-2)^{2/3}. For this function there are two important intervals: (-[infinity], A) and (A, [infinity]) where A is a critical number.
A is
The critical number A is 2
To find the critical number A for the function f(x) = 7(x-2)^(2/3):
We need to first find the derivative of the function and then set it equal to zero or identify where it is undefined.
Step 1: Find the derivative of f(x).
f'(x) = d/dx[7(x-2)^(2/3)]
Using the chain rule, we get:
f'(x) = (2/3) * 7(x-2)^(-1/3) * (1)
= (14/3)(x-2)^(-1/3)
Step 2: Set the derivative equal to zero or identify where it is undefined.
The derivative will never be zero since (14/3) is a constant and (x-2)^(-1/3) will never equal zero.
However, the derivative is undefined when the exponent -1/3 leads to a division by zero in the denominator.
This occurs when (x-2) = 0.
Solving for x, we get:
x-2 = 0
x = 2
Therefore, the critical number A is 2. The two important intervals for the function f(x) = 7(x-2)^(2/3) are (-∞, 2) and (2, ∞).
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The base of a solid is the region in the first quadrant between the graph of y=x2
and the x
-axis for 0≤x≤1
. For the solid, each cross section perpendicular to the x
-axis is a quarter circle with the corresponding circle’s center on the x
-axis and one radius in the xy
-plane. What is the volume of the solid?
A. pi/20
B. 1/5
C. pi/12
D. 1/3
The volume of the solid is π/20,
option (A). is correct.
What is volume?Volume is described as a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units.
we have that the limits of integration for x are 0 and 1, because the solid lies in the region between x = 0 and x = 1.
Hence, we can say that the volume of the solid is given by:
V = ∫[0,1] (1/4)πx^4 dx
V = (1/4)π ∫[0,1] x^4 dx
V = (1/4)π (1/5) [x^5]0^1
V = (1/20)π
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Which equation has a focus at (–6, 12) and directrix of x = –12?
1. ) ( y - 12)^2 = 1/12 ( x + 9 )
2. ) ( y - 12 )^2 = -1/12 ( x + 9 )
3. ) ( y - 12)^2 = 12 ( x+9 )
4. ) ( y - 12)62 = -12 (x + 9 )
Answer: C
None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.
To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:
(y - k)^2 = 4p(x - h)
where (h, k) is the focus and x = h - p is the directrix.
Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:
p = h - (-12) = -6 - (-12) = 6
Now, we can plug in the values of h, k, and p into the equation:
(y - 12)^2 = 4(6)(x + 6)
Simplify the equation:
(y - 12)^2 = 24(x + 6)
Now, let's compare this equation to the given options:
1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)
None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12
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brandy has a rectangular wooden deck that measures 7 feet by 12 feet she builds an addition to the deck that is 4 feet longer. what is the perimeter of the deck now
Answer:
new perimeter of Brandy deck is 46 feet .
Step-by-step explanation:
The new perimeter of Brandy deck is 46 feet.
Perimeter of a rectangleThe entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.
How can we find new perimeter of a deck?Using the given information,
Width = 7 Feet
Length = 12 feet
Perimeter = 2 (Width + Length)
[tex]= 2(7+12)[/tex]
[tex]=2(19)[/tex]
[tex]=38[/tex]
Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet
Hence, the new perimeter of a deck is 46 feet.
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what is the area of each student's photo?
The area of students photo with sides 10cm by 8cm is 80cm².
How to calculate the areaOn order to calculate the area of a student's photo, one can use the formula for the area of a rectangle, which is:
Area = length x width. You can simply multiply the two numbers together to get the area of the photo in that unit squared (e.g. square centimeters).
If a student's photo has a length of 10 centimeters and a width of 8 centimeters, the area of the photo would be:
Area = 10 cm x 8 cm = 80 cm²
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What is the area of students photo with sides 10cm by 8cm
Mandy bought a desktop computer system to start her business from home for $4,995. It is expected to depreciate at a rate of 10% per year. How much will her home computer system be worth after 9 years? Round to the nearest hundredth
Mandy's home computer system is expected to be worth $1,576.11.
Mandy's home computer system is expected to depreciate at a rate of 10% per year. After 1 year, the value of the computer system will be 90% of its original value.
After 2 years, it will be worth 90% of that value, or 0.9 × 0.9 = 0.81 times the original value. Continuing in this way, we can write the value of the computer system after n years as [tex]0.9^n[/tex] times its original value. Thus, after 9 years, the computer system will be worth [tex]0.9^n[/tex] times its original value:
Value after 9 years = 4995 × [tex]0.9^n[/tex]
Using a calculator, we find that the value is approximately $1,576.11 when rounded to the nearest hundredth. Therefore, after 9 years, Mandy's home computer system is expected to be worth $1,576.11.
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Algebra 2 question need help.
Answer:
c
Step-by-step explanation:
What kind of triangle is this?
The triangle is a right triangle.
What is a right triangle?Any given triangle in which one of its internal angles measures 90^o is said to be a right angle. Thus there is a common relations among the three sides of the triangle which is shown by the Pythagorean theorem.
The Pythagorean theorem states that;
For a right triangle, this relation holds among its three sides;
/Hyp/^2 = /Adj/^2 + /Opp/^2
Considering the given diagram, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
= 4^2 + 3^2
= 16 + 9
= 25
so that;
Hyp = 25^1/2
= 5
Therefore the given triangle is a right triangle.
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2x/3+x/5=13 pls help me solve it I am going to 8th this year
Thank you
Answer:
x = 15
I think thats what u wanted me to do- I hope it helps though. Middle school is hard.
Step-by-step explanation:
2x/3 + x/5 = 13
Here, we have to two different denominators in the LHS. So in order to solve the equation, we need to have like denominators and hence we find the Least Common Multiple (LCM).
The LCM of the denominators 3 and 5 is 15. Hence, we multiply each term to bring the denominator to 15.
5.(2x/3) + 3.(x/5) = 13
Now we combine the fractions with common denominator.
10x/15 + 3x/15 = 13
(10x + 3x)/15 =13
13x/15 = 13
Now, multiply the numbers and solve
13x = 13 . 15
x = 15 (cancelling 13 from both LHS and RHS)
And number d -
is q(x) the equation of a line?
Justify your answer.
Answer: for d the answer is yes
Step-by-step explanation:
a line is in the form of y=mx+c or y=mx+b, as p(x)=3x+5 then the equation passes by being compatible with the general equation of a line
Step-by-step explanation:
1d.
yes.
f(x) = 2x + 3
g(x) = x + 2
p(x) = f(x) + g(x) = (2x + 3) + (x + 2) = 3x + 5
p(x) is still a linear function (highest exponent of x is 1). therefore it is a line.
If x = -3, then which inequality is true?
The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 1
If x = -3, then which inequality is true?From the question, we have the following parameters that can be used in our computation:
The statement that x = -3
The above value implies that we substitute -3 for x in an inequality and solve for the variable y
Take for instance, we have
y < x + 4
Substitute the known values in the above equation, so, we have the following representation
y < -3 + 4
Evaluate
y < 1
This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 1
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Please Help I cant figure this out
The value of angle Y in the pentagon is 139°.
How to find the value of angle Y in the pentagon?
The sum of the interior angles of a polygon can be found using the formula:
sum of interior angles = (n - 2) * 180
where n is the number of sides of the polygon
A polygon with 5 sides is called pentagon. Thus, n = 5.
sum of interior angles = (5 - 2)*180 = 540°
Thus,
∠U + ∠W + ∠X + ∠Y + ∠Z = 540°
90 + 108 + 121 + ∠Y + 82 = 540
401 + ∠Y = 540
∠Y = 540 - 401
∠Y = 139°
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The seventh- and eighth-grade classes surveyed 180 of their classmates to help decide which of three options is best to raise money for school activities. Some results of the survey are given here:
66 participants preferred having a car wash.
50 participants preferred having a bake sale.
64 participants preferred having a talent show.
98 participants were seventh graders.
16 seventh-grade participants preferred having a talent show.
15 eighth-grade participants preferred having a bake sale.
a. Complete the two-way frequency table that summarizes the data on grade level and options to raise money.
Car Wash Bake Sale Talent Show Total
Seventh Graders
Eighth Graders
Total
b. Calculate the row relative frequencies. Round to the nearest thousandth.
Car Wash Bake Sale Talent Show
Seventh Graders
Eighth Graders
Question 2
c. Is there evidence of an association between grade level and preferred option to raise money?
Explain your answer
c. Yes, there is evidence of an association between grade level and preferred option to raise money.
How is the association between grade level and the preferred option to raise money determined?a. The completed two-way frequency table summarizing the data on grade level and options to raise money is as follows:
Car Wash | Bake Sale | Talent Show | Total
Seventh Graders[tex]| 66 | 15 | 16 | 98[/tex]
Eighth Graders [tex]| - | 50 | - | 50[/tex]
Total [tex]| 66 | 65 | 16 | 148[/tex]
Note: The "-" indicates that no data is available for those specific combinations.
b. To calculate the row relative frequencies, we divide each cell value by the corresponding row total and round to the nearest thousandth:
Car Wash | Bake Sale | Talent Show
Seventh Graders [tex]| 0.673 | 0.153 | 0.163[/tex]
Eighth Graders [tex]| - | 1.000 | -[/tex]
Total [tex]| 0.446 | 0.439 | 0.115[/tex]
c. To determine if there is evidence of an association between grade level and preferred option to raise money, we can observe the row relative frequencies. If the relative frequencies differ substantially between the rows, it suggests an association. In this case, since the row relative frequencies for each option vary between the seventh and eighth graders, there is evidence of an association between grade level and the preferred option to raise money.
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Amelia is making bags of snack mix for a class party. The snack mix includes dried fruit, cashews, and peanuts. Amelia buys 2 more pounds of peanuts than she does cashews and 1 pound of dried fruit. If her total bill is $41. 11, complete the table to show how many pounds of each ingredient Amelia buys
The table attached represents the pounds of each ingredient Amelia buys.
What is the number of pounds?Let's denote the number of pounds of cashews that Amelia buys by "c", and the number of pounds of peanuts that she buys by "p".
According to the problem, Amelia buys 2 more pounds of peanuts than cashews. So, we have:
p = c + 2
Also, she buys 1 pound of dried fruit, which we can simply denote as "1".
The total bill for the snack mix is $41.11, so we can write:
0.5c + 0.75p + 1.5(1) = 41.11
where;
0.5 represents the cost per pound of cashews, 0.75 represents the cost per pound of peanuts, and 1.5 represents the cost per pound of dried fruit.Simplifying the equation, we get:
0.5c + 0.75(c + 2) + 1.5 = 41.11
0.5c + 0.75c + 1.5 + 1.5 = 41.11
1.25c = 38.11
c = 30.488
Since we know that p = c + 2, we have:
p = 30.488 + 2 = 32.488
Now we can complete the table to show how many pounds of each ingredient Amelia buys:
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The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 925 among its requirements, what percentage of females do not satisfy that requirement?
The percentage of females who do not satisfy the minimum score requirement of 925 on the SAT-I test is 35.9%.
Calculating the z-score for the minimum score requirement:
z = (X - Mean) / Standard Deviation
z = (925 - 998) / 202
z = -73 / 202 ≈ -0.361
Now, using the z-score to find the percentage of females below the minimum score:
Since the z-score is -0.361, we can use a z-table (or an online calculator) to find the area to the left of this z-score, which represents the percentage of females who scored below 925. The area to the left of -0.361 is approximately 0.359.
3. Convert the area to a percentage:
Percentage = Area * 100
Percentage = 0.359 * 100 ≈ 35.9%
So, approximately 35.9% of females do not satisfy the minimum score requirement of 925 on the SAT-I test.
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Can someone explain ._.
The mark-up value percentage is 25 %
Given data ,
The markup amount is the selling price minus the cost price, so:
Markup = $8630 - $6900 = $1730
The markup percentage is the markup amount divided by the cost price, expressed as a percentage:
Markup percentage = (Markup / Cost price) x 100%
Markup percentage = ($1730 / $6900) x 100%
Markup percentage = 0.25 x 100%
Markup percentage = 25%
Hence , the markup percentage is 25%
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Please help!!! 10 points
The solution is, Options 1, 3, and, 5 are true.
The statements given are,
1.) The product of reciprocals is 1.
Let the fraction be a/b , and reciprocal be b/a ,
The product of the two will be 1.
Hence, the statement is true.
2.) To divide fractions, multiply the divisor by the reciprocal of the dividend.
Let the fraction be a/b , now,
a/b*1/a = a^2/b,
Hence, the statement is false.
3.) The reciprocal of a whole number is 1 over the number.
Let the number be 3, now,
The reciprocal of number 3 is 1/3 .
Hence, the statement is true.
4.) Reciprocals are used to multiply fractions.
The statement is false, Reciprocals are not used to multiply fractions.
5.) To find the reciprocal of a fraction, switch the numerator and denominator.
Let the fraction be a/b , then the reciprocal will be b/a .
Hence, the statement is true.
Therefore, Options 1, 3, and, 5 are true.
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complete question:
Select all that apply. Determine which of the following statements are true of reciprocals. Select all that apply. The product of reciprocals is 1 To divide fractions, multiply the divisor by the reciprocal of the dividend The reciprocal of a whole number is 1 over the number Reciprocals are used to multiply fractions To find the reciprocal of a fraction, switch the numerator and denominator
Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years, and A is account balance. P r compounded t $ % Daily
The account balance after 2 years is approximately $107.15.
What is the formula calculating account balance A, given the principal P, interest rate r, number of compounding periods per year n, time t in years, and A is account balance when interest is compounded daily?The compound interest formula is given by:
A = P * [tex](1 + r/n)^(^n^*^t^)[/tex]
Where:
P = Principal
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
A = Final account balance
In this problem, we are given:
P = $100
r = 3.5% per year = 0.035 per year
n = 365 (since interest is compounded daily)
t = 2 years
Substituting these values in the formula, we get:
A = [tex]100 * (1 + 0.035/365)^(^3^6^5^*^2^)[/tex]
A ≈ $107.15
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Olivia and her friends went to a movie at 1:50 P.M. The movie ended at 4:10 P.M. How long was the movie?
Answer: The movie was 2 hours and 20 minutes long.
Step-by-step explanation:
basic adding + subtracting
If you spin a spinner 75 times, how many multiples of 2?
If you spin a spinner 75 times, the number of multiples of 2 could be either 7 or 38.
Assuming the spinner has an equal chance of landing on any number from 1 to 6, we can find the probability of landing on a multiple of 2 (2, 4, or 6) by dividing the number of multiples of 2 by the total number of possible outcomes:
Number of multiples of 2 = 3
Total number of possible outcomes = 6
So the probability of landing on a multiple of 2 is:
P(multiple of 2) = 3/6 = 1/2
This means that out of 75 spins, we can expect to land on a multiple of 2 about half the time. To find the exact number, we multiply the probability by the number of spins:
Number of multiples of 2 = P(multiple of 2) x Number of spins
Number of multiples of 2 = (1/2) x 75 = 37.5
Since we can't have a fraction of a spin, we need to round to the nearest whole number. In this case, we can round up or down depending on how we interpret the question. I
f we want to know how many times we can expect to land on a multiple of 2 on average, we should round down to 37.
If we want to know the closest integer to the expected value, we should round up to 38.
So depending on the context of the question, the answer could be either 37 or 38.
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100-3(4.25)-13-4(2.99) SOMEONE PLSS HELP MEE THIS IS DIE TMRW!!
Answer:
62.29
Step-by-step explanation:
100 - 3(4.25) - 13 - 4(2.99)
= 100 - 12.75 - 13 - 11.96
= 62.29
explanation in the picture
the answer is
62,29
If a sample of 32 runners is taken from a population of 201 people what if the means of how many runners times
201 could refer to the mean of how many runners' times. The Option C is correct.
Could sample refer to the mean of runner times?The sample of 32 runners, as given, does not refer to the mean of how many runners' times. The sample size refers to the number of individuals selected from the population while population size refers to the total number of individuals in the population.
Data:
The population of 201 people is given.
The sample of 32 runners is taken from the population.
So, the mean of the runners' times would be calculated using all 201 runners in the population, not just the 32 in the sample. Therefore, the Option C is correct.
Full question "If a sample of 32 runners were taken from a population of 201 runners, could refer to the mean of how many runners' times ? A. Both 32 and 201 B. Neither 32 nor 201 C. 201 D. 32"
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Find the new coordinates for the image under the given dilation. Rhombus WXYZ with vertices W(1, 0), X (4,-1), Y(5,-4), and Z(2, -3): k = 3. W' (.) x' (,) X' Y'(,) Z' (
the new coordinates of the rhombus W'X'Y'Z' after a dilation with scale factor k=3 are: [tex]W'(3,0), X'(12,-3), Y'(15,-12), Z'(6,-9)[/tex]
What are the coordinates?To find the new coordinates of the image after dilation, we need to multiply the coordinates of each vertex by the scale factor k = 3.
Let's start with vertex W(1,0):
Multiply the x-coordinate by [tex]3: 1 *\times 3 = 3[/tex]
Multiply the y-coordinate by [tex]3: 0 \times 3 = 0[/tex]
So the new coordinates of W' are [tex](3,0).[/tex]
Next, let's look at vertex X(4,-1):
Multiply the x-coordinate by [tex]3: 4 \times 3 = 12[/tex]
Multiply the y-coordinate by [tex]3: -1 \times 3 = -3[/tex]
So the new coordinates of X' are [tex](12,-3).[/tex]
Now for vertex Y(5,-4):
Multiply the x-coordinate by [tex]3: 5 \times 3 = 15[/tex]
Multiply the y-coordinate by [tex]3: -4 \times3 = -12[/tex]
So the new coordinates of Y' are [tex](15,-12).[/tex]
Finally, let's consider vertex Z(2,-3):
Multiply the x-coordinate by [tex]3: 2 \times 3 = 6[/tex]
Multiply the y-coordinate by [tex]3: -3 \times3 = -9[/tex]
So the new coordinates of Z' are [tex](6,-9)[/tex] .
Therefore, the new coordinates of the rhombus [tex]W'X'Y'Z'[/tex] after a dilation with scale factor k=3 are:
[tex]W'(3,0)[/tex]
[tex]X'(12,-3)[/tex]
[tex]Y'(15,-12)[/tex]
[tex]Z'(6,-9)[/tex]
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