The probability of winning the jackpot with one ticket is P ( A ) = 1/34
Given data ,
To calculate the probability of winning the jackpot in the lottery, we need to determine the total number of possible outcomes (the sample space) and the number of favorable outcomes (winning outcomes).
Total number of possible outcomes:
For the white balls, there are 43 numbers to choose from, and we need to select 5 distinct numbers in any order. This can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of options and r is the number of selections. In this case, we have 43 white balls and need to choose 5, so the number of possible outcomes for the white balls is:
C(43, 5) = 43! / (5! * (43 - 5)!) = 43! / (5! * 38!) = 43 * 42 * 41 * 40 * 39
For the gold ball, there are 34 numbers to choose from, and we need to select 1 number. So the number of possible outcomes for the gold ball is simply 34.
Therefore, the total number of possible outcomes is:
Total outcomes = (43 * 42 * 41 * 40 * 39) * 34
Number of favorable outcomes (winning outcomes):
To win the jackpot, we need to match all 5 distinct numbers from the white balls and the number on the gold ball. Since order doesn't matter for the white balls, we can use the combination formula again:
C(n, r) = n! / (r! * (n - r)!)
In this case, we have 43 white balls and need to choose 5, so the number of favorable outcomes for the white balls is:
C(43, 5) = 43! / (5! * (43 - 5)!) = 43 * 42 * 41 * 40 * 39
For the gold ball, there is only 1 winning number.
Therefore, the number of favorable outcomes is:
Favorable outcomes = (43 * 42 * 41 * 40 * 39) * 1
Probability of winning the jackpot:
The probability of winning the jackpot is the ratio of the number of favorable outcomes to the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Plugging in the values, we get:
Probability = [(43 * 42 * 41 * 40 * 39) * 1] / [(43 * 42 * 41 * 40 * 39) * 34]
Simplifying, we find:
Probability = 1 / 34
Hence , the probability of winning the jackpot with one ticket in this lottery is 1 in 34.
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The graph shows the number of weeks of practice () and the number of
shote missed in a free throw drill (). The equation of the trend line that best
fits the data is y- +6. Predict the number of missed shots after 8
weeks of practice.
A.3
B.2
C.4
D.5
Answer:
B. 2
Step-by-step explanation:
You want the predicted number of missed shots after 8 weeks if the trend line equation is ...
y = -1/2x +6
PredictionUsing x=8 in the given equation, we find the prediction to be ...
y = -1/2(8) +6 = -4 +6 = 2
The number of missed shots is predicted to be 2.
__
Additional comment
We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.
<95141404393>
Warm-Up
Jug
Use the diagram below to answer the questions.
Intro
K
P
M
Which are shown on the diagram? Check all that apply.
O
OKM
Ojk
OPK
OLJK
COM
Dong
KM, JK, PK, and MJ are shown on the diagram.
Then the correct options are B, C, D, and F.
Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
A line segment in mathematics has two different points on it that define its boundaries.
All the line segments will be
JK, JM, KM, MP, PK, and KL
The triangle KPM.
And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.
Then the correct options are B, C, D, and F.
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Brynen is driving to a new job five days this week. He drives 27 miles each way. His car gets 35 miles per gallon of gas. How many gallons of gas will he use driving to and from work this week? Round to the nearest tenth.
Brynen will use 7.71 gallons of gas driving to and from work this week.
To calculate the gallons of gas Brynen will use driving to and from work this week, we need to consider the round trip distance and the car's fuel efficiency.
Given:
Brynen drives 27 miles each way to work.
His car gets 35 miles per gallon of gas.
To find the total distance Brynen will travel in a week, we need to calculate the round trip distance for each workday and multiply it by the number of workdays (five days).
Round trip distance = 27 miles (one-way distance) * 2 = 54 miles (round trip distance)
Total distance traveled in a week = 54 miles (round trip distance) * 5 days = 270 miles
Next, we can determine the total gallons of gas Brynen will use using his car's fuel efficiency.
Gallons of gas used = Total distance / Fuel efficiency
Gallons of gas used = 270 miles / 35 miles per gallon
Gallons of gas used ≈ 7.71 gallons (rounded to the nearest tenth)
Therefore, Brynen will use approximately 7.71 gallons of gas driving to and from work this week.
It's important to note that this calculation assumes that Brynen's car maintains a consistent fuel efficiency of 35 miles per gallon throughout the entire week and that no additional driving outside of the work commute is considered. Factors such as traffic, variations in fuel efficiency, or additional trips would affect the actual gas consumption.
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From the observation deck of a skyscraper, Brandon measures a 45
angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship is 1140 m
What is the angle of depression?
Under the horizontal line, the angle of depression is measured, typically in degrees. It aids in figuring out how steep or incline the line of sight is in relation to the horizontal plane. The line of sight is steeply directed downward and increases with the angle of depression.
In many different disciplines, such as surveying, navigation, engineering, and physics, the angle of depression is frequently utilized.
We know that;
Tan 45 = x/1140
x = 1140 Tan 45
= 1140 m
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Segment RT has endpoints R(1,1) and T (-7, -2) what are the coordinates of the midpoint of RT?
Question 9 of 10
Which is the standard equation for a circle centered at the origin with radius
12
O A. x²2² +²2² = r
OB.x2²=2² +2²
XA
O c. x+y=r
OD. x² +2²=2²
Which is the standard equation for a circle centered at the origin with radius r be,
⇒ x² + y² = r²
Hence option D is correct.
We have to find the standard equation of circle,
Given that,
Center of circle is at (0, 0)
And radius is r
Let a point (x, y) on the circle.
We know that,
The distance between the point (x, y) and origin is also known as radius of the circle,
Since we know that,
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Therefore distance between (0, 0) and (x, y),
⇒ √[ (x - 0)² + (y - 0)²] = r
Squaring both sides we get,
⇒ (x - 0)² + (y - 0)² = r²
⇒ x² + y² = r²
This is the standard equation of circle.
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William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols. What are they?
The two mathematical symbols that William Oughtred introduced are "×" for multiplication and "::" for proportion.
Given is a statement about William Oughtred.
William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols.
We have to find those symbols.
William Oughtred is actually an English priest who basically teaches the students in mathematics subject.
He did invent other famous things like slide rule.
But the most famous invention of him is two mathematical symbols which are "×" for multiplication and "::" for proportion which are still widely used symbols.
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help solve and explain
Answer:
6
Step-by-step explanation:
(3√3)^2/3 = (∛3)² X ∛(√3)²
= 3
27^2/3 = (∛27)²
= 3² = 9
9^-1/2 = 1/√9
= 1/3
so the answer is 3 + (9 X 1/3)
= 3 + 3
= 6
A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.15, how many dimes and how many
Answer:
9 dimes and 5 quarters----------------------
Let d be the number of dimes and q be the number of quarters.
We can set up two equations based on the information given:
d + q = 14 (14 coins in total) 0.10d + 0.25q = 2.15 (total value of his change is $2.15)Use substitution here:
d = 14 - q (from the first equation) 0.10(14 - q) + 0.25q = 2.15 (substituting into the second equation) 1.40 - 0.10q + 0.25q = 2.15 0.15q = 0.75 q = 5So he has 5 quarters.
We can plug that back into either equation to find the number of dimes:
d + 5 = 14 d = 9So he has 9 dimes and 5 quarters.
Non Shaded Shaded
Area
Area
8
Find the radius
of the small circle
Answer:
The answer is 16pi or 50.3cm² to 1 d.p
Step-by-step explanation:
The non shaded=area of shaded
d=8
r=d/2=4
A=pir³
A=p1×4²
A=pi×16
A=16picm² or 50.3cm² to 1d.p
Answer:
3.45 cm (3 s.f.)
Step-by-step explanation:
We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.
To find the radius of a regular polygon given its side length, we can use this formula:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):
[tex]\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}[/tex]
The formulas for the area of a regular polygon and the area of a circle given their radii are:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Therefore, the area of the regular pentagon is:
[tex]\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}[/tex]
The area of the circumcircle is:
[tex]\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}[/tex]
The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.
The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.
Given the shaded area is equal to the unshaded area:
[tex]\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}[/tex]
[tex]\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}[/tex]
Therefore, the radius of the small circle is 3.45 cm (3 s.f.).
Find the area of a circle with radius,
r
= 42cm.
Give your answer rounded to 3 SF.
Answer:
5541.77 cm^2
Step-by-step explanation:
Warm-Up
What is the approximate area of the shaded region?
Select the correct answer.
O 15.45 cm²
O69.53 cm²
128.54 cm²
18 cm
182.47 cm²
4
Answer:
The answer is 69.63cm²
Step-by-step explanation:
d=18
r=d/2=18/2=9cm
Area of shaded portion =Area of square -Area of circle
A=18²-pi×9²
A=69.53cm²
Answer:
69.53 centimeters squared.
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To solve for the area of the shaded region, we must figure out what the length and width is. Assuming this is a square, the length and width of the shape are 18cm. To solve for the area of a square, we can use the formula:
Area = [tex]side^{2}[/tex]Inserting 18 as our side length:
Area = [tex]18^{2}[/tex] = 324Therefore, the area of the square without the circular gap is 324 [tex]cm^{2}[/tex].
To solve for the area of a circle, we can use the formula:
Area = π[tex]r^{2}[/tex]But wait, we are given the diameter, not the radius!
No worries, the radius is simply half the size of the diameter, so we can just divide 18 by 2.
18 ÷ 2 = 9Inserting 9 into the formula for the radius:
Area = π × [tex]9^{2}[/tex] = 81π = 254.47 (Rounded to 2 decimal points)Now we can subtract this from the squares area.
324 - 254.47 = 69.53The closest to match this approximation is [tex]69.53cm^{2}[/tex].
Find the volume of the solid generated by rotating the figure around the given axis. If
necessary, use 3.14 for and round your answer to the nearest hundredth.
TU
2
5
The volume of the solid generated by rotating the figure is 62.8 cubic units
How to find the volume of the solid generated by rotating the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
The figure is a rectangle with the following dimensions
Length = 5
Width = 2
When rotated around the given axis, we have a cylinder with the following dimensions
Height = 5
Radius = 2
So, we have
Volume = πr²h
This gives
Volume = 3.14 * 2² * 5
Evaluate
Volume = 62.8
Hence, the volume of the solid generated by rotating the figure is 62.8 cubic units
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Draw a box plot for each set of data. {65,92,74,61,55,35,88,99,97,100,96} Cost of MP3 Players ($)
A construction of the box-and-whisker plot representing the data set is shown below.
What is a box-and-whisker plot?In Mathematics and Statistics, a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the data (information) provided above, the five-number summary for the given data set include the following:
Minimum (Min) = 35.First quartile (Q₁) = 61.Median (Med) = 88.Third quartile (Q₃) = 97.Maximum (Max) = 100.In conclusion, we can logically deduce that the maximum number is 100 while the minimum number is 35, and the median is equal to 88.
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Use Juliana's text message data to answer the questions.
What was the mean number of text messages that Julianna sent per day
The mean number of text messages that Julianna sent per day is 7.
To calculate the mean number of text messages that Julianna sent per day, we need to sum up the number of text messages she sent each day and divide it by the total number of days.
Total number of text messages sent:
13 + 0 + 4 + 4 + 5 + 6 + 17 = 49
Total number of days: 7
Mean = Sum of all observations/number of observations
Mean =Total number of text messages sent/Total number of days
Mean number of text messages per day: 49 / 7
= 7
Therefore, 7 is the mean number of text messages that Julianna sent per day.
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Use julianna’s text message data to answer the questions.
Text messages sent:
Sun: 13 Mon: 0 tues: 4 wed: 4 thurs: 5 fri: 6 sat: 17
1. What was the mean number of text messages that julianna sent per day ?
A. 4
B.6
C.8
D.7
Gift Wrapping A gift box has the shape of a rectangular prism. How much wrapping
paper do you need to cover the box?
You need
in.2 of paper to cover the box.
C
16 in
12 in
Answer:
608 in²
Step-by-step explanation:
To figure out how much wrapping paper we need to cover the box, we can find its surface area.
The surface area of a rectangular prism (a box) is defined as:
[tex]SA = 2A + (P \cdot d)[/tex]
where [tex]A[/tex] is the area of the base, [tex]P[/tex] is the perimeter of the base, and [tex]d[/tex] is the prism's depth.
From the diagram, we can identify the following values for these variables:
[tex]A=16\cdot 12 = 192 \text{ in}^2[/tex]
[tex]P = 16 + 12 + 16 + 12 = 56 \text{ in}[/tex]
[tex]d = 4\text{ in}[/tex]
Now, we can plug these values in for the variables in the above formula and solve for the prism's surface area.
[tex]SA = 2A + (P \cdot d)[/tex]
[tex]SA = 2(192) + (56 \cdot 4)[/tex]
[tex]SA = 384 + 224[/tex]
[tex]SA = 608 \text{ in}^2[/tex]
So, we need 608 in² of paper to cover the box.
Music students and art students at a middle school were surveyed to choose a cardiovascular activity: playing sports or dancing.
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Music students 32 15 47
Art students 31 22 53
Column totals 63 37 100
What is the marginal frequency of students who chose dancing?
15
22
37
53
The marginal frequency of students who chose dancing is 37.
The correct answer to the given question is option 3.
The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.
Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.
It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.
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The next model of a sports car will cost 14.7% more than the current model. The current model costs $34,000. How much will the price increase in dollars?
What will be the price of the next model?
Increase in price:
Price of next model:
Answer: $4,998
Step-by-step explanation:
34000*1.147
38998-34000=4998
Find the value of x and y in simplified radical form.
x and y have the values 7 and 7√2, respectively.
The sides of a right triangle with 45-degree acute angles have a unique ratio of 1:1:2.
We can use this information to determine the values of x and y because the base is specified as being 7.
Let's give the perpendicular side the value of x, and the hypotenuse the value of y.
The perpendicular side (x) and the base (7) have the same length because the acute angles are both 45 degrees.
Consequently, x = 7.
We can determine that x:y:2x using the ratio of 1:1:2.
When we enter the value of x, we may calculate y:
7:y:√2(7)
Simplifying even more
7:y:7√2
Given that the hypotenuse (y) equals 72, we can write:
y = 7√2
Thus, x and y have the values 7 and 7√2, respectively.
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1. Calculate GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion
The GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion is: Rs. 1,800 billion.
What is GDP?Using this formula to determine the GDP at FC
GDP at FC = GDP at MP - Indirect taxes + Subsidies
Where:
GDP at MP (Market Price) = Rs. 2,000 billion
Indirect taxes = Rs. 300 billion
Subsidies = Rs. 100 billion
Let plug in the formula
GDP at FC = 2,000 billion - 300 billion + 100 billion
GDP at FC = 1,800 billion
Therefore the GDP at factor cost (FC) is Rs. 1,800 billion.
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En el negocio familiar los hermanos Jaziel Elisa y Sofía deben ayudar a atender así el acude cada cuatro días Elisa cada cinco días y Sofía que a las seis si los tres han coincidido el 4 de marzo después de cuantos días se volverán a coincidir
Based on the LCM, Jaziel, Elisa, and Sofía will coincide again after 60 days.
How to calculate the valueFrom the information, in the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock.
In order to determine when Jaziel, Elisa, and Sofía will coincide again, we need to find the least common multiple (LCM) of their visit intervals.
The intervals for Jaziel, Elisa, and Sofía are 4 days, 5 days, and 6 days, respectively. We need to find the smallest number that is divisible by all three of these intervals.
The LCM of 4, 5, and 6 is 60. Therefore, Jaziel, Elisa, and Sofía will coincide again after 60 days.
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In the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock if the three have coincided on March 4 after how many days will they coincide again
The patient is to receive 250ml of D5W with 10 units of oxytocin (Pictocin) IV at the rate of 0.002 units/min. How many ml per hour.
Answer:
0.5ml/hr
Step-by-step explanation:
Given:
Infusion rate: 0.002 units/min
To convert the infusion rate from units/min to ml/hr, we need to know the flow rate conversion factor specific to the medication and solution being administered.
In this case, we have the information that the patient is receiving 10 units of oxytocin (Pictocin) in 250 ml of D5W solution.
To calculate the ml/hr rate, we can use the following formula:
ml/hr = (Infusion rate in units/min * Volume in ml) / Time in min
ml/hr = (0.002 units/min * 250 ml) / 1 min
ml/hr = 0.5 ml/min
Therefore, the infusion rate of 0.002 units/min is equivalent to 0.5 ml/hr.
Function c
is defined by the equation c(n)=50+4n
. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n
.
True or False? The inverse function is as follows:
n=(c(n) − 50)×4
Responses
Answer:
False
Step-by-step explanation:
1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4
Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2
There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.
Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.
Denote this path as P. Let x be the vertex on path P that is closest to v.
By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.
Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.
Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
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Hello i need help please
[tex]2\cdot20\text{ m}\cdot n+2\cdot20\text{ m}\cdot 5\text{ m}+2\cdot 5\text{ m}\cdot n=1100\text{ m}^2\\40n\text{ m}+200\text{ m}^2+10n\text{ m}=1100\text{ m}^2\\50n\text{ m}=900\text{ m}^2\\n=18\text{ m}[/tex]
HELP SOMEONE EXPLAIN THIS PLEASE
Answer:
Entrance fee for children: $1.92
Entrance fee for adults: $3.92
Step-by-step explanation:
Total expenses for this year: $214.00
The child fee will be: $x
and the adult fee will be $(x+2)
Last year the number of children was 44
and the number of adults was 33
this year also has the same number of children and adults.
which means the entrance fee total for children will be $44x and for adults will be $33(x+2).
44x + 33(x+2) = 214
--> 44x + 33x + 66 = 214
--> 77x = 214 - 66 = 148
--> x = 148/77 = 1.92
So children's price is $1.92 and adults price is $1.92 + 2
hence:
Entrance fee for children: $1.92
Entrance fee for adults: $3.92
solve for C, 11 = c - 8
c = ?
Answer:
c=19
Step-by-step explanation:
11=c-8
+8 +8
19=c
11=c-8
move the variable to the left - hand side and change it sign: 11-c= -8
move the constant to the right-hand side and change its sign: -c= -8-11
calculate the difference: -c = -19
change the signs on each side c=19
Jane, John, and Joey are standing apart in such a way that they form a triangle.
The distance between Jane and John is 31 feet. The distance between John and Joey is 42 feet and the distance between Joey and Jane is 53 feet. What is the angle formed where Joey is standing?
Angle =
Did you use Law of Sine or Law of Cosine to solve for the angle?
The angle formed is 91.84° which can be obtained using Cosine Rule since all the three sides are given.
Using the Cosine Rule :CosC = (a²+b²-c²) /2(ab)
a = 31
b = 42
c = 53
Substituting the values into the relation
CosC = (31² + 42² - 53²) / 2(31×42)
CosC = - 84 / 2604
CosC = −0.032258
C =
[tex]C = {cos}^{ - 1} (- 0.03225)[/tex]
C = 91.84°
Hence, the angle formed is 91.84°
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For the following exercises, find (f x g)(x) and (g x f)(x) for each pair of functions.
f(x)=√x+2, g(x)=1/x
(f x g)(x) = √(1/x + 2)
(g x f)(x) = 1/(√(x + 2))
To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).
Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).
Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:
1. (f x g)(x):
We start by substituting g(x) into f(x) wherever we see an x in f(x):
(f x g)(x) = f(g(x)) = f(1/x)
Substitute 1/x into f(x):
(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)
2. (g x f)(x):
We start by substituting f(x) into g(x) wherever we see an x in g(x):
(g x f)(x) = g(f(x)) = g(√(x + 2))
Substitute √(x + 2) into g(x):
(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))
Therefore, we have:
(f x g)(x) = √(1/x + 2)
(g x f)(x) = 1/(√(x + 2))
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Carl's class is collecting canned food for a
food drive. If the class collects 33 pounds
on the first day and 41 pounds on the
second day, how many pounds of food
have they collected so far?
Give your answer as a mixed number in simplest form.
Enter the number that belongs in the green box.
[2] pounds
The class has collected a total of 74 pounds of food so far.
The class collected 33 pounds on the first day and 41 pounds on the second day.
To find the total pounds of food collected, we add these two amounts together:
33 pounds + 41 pounds = 74 pounds
On the first day, the students gathered 33 pounds, and on the second day, they collected 41 pounds.
We combine these two figures together to get the total number of pounds of food collected:
33 lbs. plus 41 lbs. equals 74 lbs.
On the first day, the class brought in 33 pounds, and on the second, 41 pounds.
We combine these two figures to get the total weight in pounds of food collected:
44 pounds plus 33 pounds equals 74 pounds.
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