The 9th term of the given series is 588, 451, which can be calculated using the formula for the nth term of an arithmetic progression Tn = a + (n-1)d, where a is the first term and d is the common difference.
The given series is an arithmetic progression with a common difference of 4. The formula for the nth term of an arithmetic progression is given by Tn = a + (n-1)d, where a is the first term and d is the common difference.
Therefore, for the given series, a = 1 and d = 4.
Substituting these values in the above formula, we get
T9 = 1 + (9-1)4
= 1 + 32
= 33
Now, adding 33 to each of the terms of the given series, we get
1 + 33 = 34
5 + 33 = 38
25 + 33 = 58
125 + 33 = 158
Therefore, the required 9th term of the series is 588, 451.
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X-intercept:
y-intercept:
y
1
9
8
7
6
5
NO 10
4
3
2-
1
x
-9-8-7 -6 -5 -4 -3 -2
1
2 3 4 5 6 7 8 9
CON
-2
-3
-4
-5
-6
-7
-8
-9
Answer: diffrent form so i can help you better
Step-by-step explanation:
The first three questions refer to the following information: Suppose a basketball team had a season of games with the following characteristics: 60% of all the games were at-home games. Denote this by H (the remaining were away games). 25% of all games were wins. Denote this by W (the remaining were losses). 20% of all games were at-home wins.
Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places.)
.12
.15
.20
.33
.80
Answer:
25 I am not sure
Step-by-step explanation:
The proportion of at-home games that were wins is 0.33, or 33%.
The proportion of at-home games that were wins can be found by dividing the number of at-home wins by the number of at-home games. This can be represented as a fraction:
At-home wins / At-home games
Using the information given in the question, we can plug in the values for at-home wins and at-home games:
0.20 / 0.60
Simplifying the fraction gives us:
1/3
Converting this to a decimal gives us:
0.33
Therefore, the proportion of at-home games that were wins is 0.33, or 33%.
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Your mom wants to replace the window shutters on your house for the farmhouse shutters like the picture. Each window takes two shutters. The shutters measure 18 inches times 36 inches. Both shutters need diagonal piece of wood cut to fit. What is the total amount we needed for each of the two diagonal pieces ?
14 by 16
I just know it :DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
A bicycle shop equips 60% of their bikes with a water bottle holder. 55% of the bikes they sell have a kickstand attached to the bike. 34% of the bikes sold have both
features. What is the probability that a randomly selected bicycle will have a kickstand or a water bottle holder?
Hurry
The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%, calculated by adding the probabilities of each component being present and subtracting the probability of both being present.
The probability that a randomly selected bicycle from a bicycle shop will have either a water bottle holder or a kickstand is 95%. To calculate this, we first need to consider the probability that a bicycle has a water bottle holder, which is 60%. The probability that the bicycle has a kickstand is 55%. Then, the probability of a bicycle having both a kickstand and a water bottle holder together is the product of the individual probabilities, which is 34%. Thus, the probability that a randomly selected bicycle will have either a water bottle holder or a kickstand is 60% + 55% - 34% = 95%.
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Find the smallest value of n such that Sn lies within the distance 70 x 10^-6 of the true sum
Answer:
0.00007
Step-by-step explanation:
J(7,2)k(-4,9),l(-3,-1)
Classify triangle
The triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.
What is scalene οbtuse triangle?A triangle is said tο be οbtuse scalene in geοmetry if οne οf its angles is larger than 90 degrees but less than 180 degrees, while the οther twο angles are bοth less than 90 degrees. Measurements fοr the three sides and angles vary.
Tο classify the triangle fοrmed by the pοints J(7,2), K(-4,9), and L(-3,-1), we need tο find the lengths οf its sides and apply the triangle classificatiοn criteria.
Using the distance fοrmula, we can find the lengths οf the sides:
[tex]JK = \sqrt{[(7 - (-4))^2 + (2 - 9)^2]} \\JK =\sqrt{ (11^2 + (-7)^2)} \\ JK =\sqrt{170} \\KL = \sqrt{[(-4 - (-3))^2 + (9 - (-1))^2]} \\KL =\sqrt{ (1^2 + 10^2) } \\KL = \sqrt{101} \\LJ = \sqrt{[(-3 - 7))^2 + ((-1) - 2)^2]} \\LJ=\sqrt{ (10^2 + (-3)^2)} \\LJ = \sqrt{109}[/tex]
Since all three sides have different lengths, the triangle is scalene.
Therefοre, the triangle fοrmed by J(7,2), K(-4,9), and L(-3,-1) is a scalene οbtuse triangle.
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35 of the students in the band play the flute, and another 15 play the clarinet. What fraction of the students in the band plays either the flute or the clarinet? Responses
As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
We must first ascertain the total number of students in the band in order to calculate the percentage of those who play the flute or clarinet. Let's assume that N kids make up the entire band.
The total number of pupils who play either the clarinet or the flute is then calculated as follows: 35 + 15 - x
The percentage of band students who play either the flute or the clarinet is now (35 + 15 - x) / N, and we need to know what x's value is. Nevertheless, the problem does not provide this information. As a result, we are unable to further simplify the phrase. The final solution is (35 + 15 - x) / N, where x is the proportion of students who are proficient in both instruments.
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Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
Answer: 32.2 cubic inches
Step-by-step explanation:
The volume of one coin can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = π(1.4)^2(0.0625)
V ≈ 0.14 cubic inches (rounded to the nearest hundredth)
To find the total volume of all the coins, we can multiply the volume of one coin by the number of coins:
Total volume = 230 × 0.14
Total volume ≈ 32.2 cubic inches (rounded to the nearest hundredth)
Therefore, the coins take up approximately 32.2 cubic inches of the treasure chest.
Calculate the area of the region defined by the simultaneous inequalities y ≥ x-4,
y ≤ 10, and 5 ≤ x+y.
Answer: To solve this problem, we need to graph the three inequalities and find the overlapping region.
First, let's graph the inequality y ≥ x - 4. We can start by graphing the line y = x - 4, which has a y-intercept of -4 and a slope of 1.
|
10| + +
| + +
| +
|+
|
|
| +
| +
| +
| +
0|-----------------
0 1 2 3 4 5
Since we want the region where y is greater than or equal to x - 4, we shade the area above the line.
Next, let's graph the inequality y ≤ 10. This is a horizontal line passing through y = 10.
|
10| +----+
| + +
| +
|+
|
|
|
|
|
|
0|-----------------
0 1 2 3 4 5
Since we want the region where y is less than or equal to 10, we shade the area below the line.
Finally, let's graph the inequality 5 ≤ x + y. This is a line with a y-intercept of 5 and a slope of -1.
|
10| +----+
| + | +
| + |
|+ |
| |
| |
| |
| |
| |
| +
0|-----------------
0 1 2 3 4 5
Since we want the region where x + y is greater than or equal to 5, we shade the area above the line.
Now we can find the overlapping region of the three shaded areas:
|
10| +----+
| + | +
| + |
|+ |
| |
| |
| +
| +
| +
|+
0|-----------------
0 1 2 3 4 5
The region is a triangle with vertices at (0, 4), (1, 5), and (5, 0).
To find the area of the triangle, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
The base of the triangle is the distance between the points (0, 4) and (5, 0), which is 5.
The height of the triangle is the distance between the point (1, 5) and the line 5 = x + y. We can find the equation of the line perpendicular to 5 = x + y and passing through (1, 5). This line has a slope of 1 and passes through (1, 5), so its equation is y = x + 4. We can find the intersection of this line and the line 5 = x + y by solving the system of equations:
y = x + 4
y = 5 - x
Substituting y = x + 4 into the second equation, we get:
x + 4 = 5 - x
Solving for x, we get:
x = 1
Step-by-step explanation:
i put $1000 in an account from high school graduation gifts, and $2000 into the same account after my college graduation 4 years later. five years after i started my first job how much is in the account if it earns 4% per year?
By using the concept of compound interest, the total amount is $4063.27.
We have,
The amount that was deposited during high school graduation = $1000
The amount that was deposited during college graduation after 4 years = $2000
The total number of years elapsed = 5 years
The interest rate per annum (p.a.) = 4%
The simple Interest (SI) formula is given by,
SI = P × r × t
where, P = Principal amount
r = Rate of interest
t = Time period
Compound Interest (CI) formula is given by,
CI = P (1 + (r/n))^(nt)
Where P = Principal amount
r = Rate of interest
t = Time period
n = Number of times interest is compounded
For the total amount using compound interest.
Total amount (A) = Principal + Compound interest
A = P + CI
Implying it to our data, we get the following.
For $1000 that was deposited during high school graduation,
For 5 years, n = 1, t = 5 years, r = 4% p.a.
CI = 1000[1+(4/100)]^(1×5)
CI = 1000[1+(1/25)]^5
CI = 1000×(26/25)^5
CI = 1000×1.21665
CI = $1216.65
For $2000 that was deposited during college graduation after 4 years,
The total number of years elapsed = 5 years + 4 years = 9 years
n = 1, t = 9 years, r = 4% p.a.
CI = 2000[1+(4/100)]^(1×9)
CI = 2000[1+(1/25)]^9
CI = 2000×(26/25)^9
CI = 2000×1.4233
CI = $2846.62
Therefore, the total amount (A) is $1216.65 + $2846.62 ⇒ $4063.27.
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3.6 Triathlon times, Part II: The distribution for triathlon time varies depending on the population you are describing. The distribution for men ages30−34isN(μ=4370,σ=585). The distribution for women ages25−29isN(μ=5296,σ=826). Note, these distributions list the triathlon times in seconds. Use this information to compute each of the following. Report your answer to 2 decimal places. a) The cutoff time for the fastest5%of athletes in the men's group, i.e. those who took the shortest5%of time to finish. b) The cutoff time for the slowest10%of athletes in the women's group.
a: The cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b: The cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
What is the nοrmal distributiοn?The nοrmal distributiοn is a cοntinuοus prοbability distributiοn that is widely used in statistics tο describe real-wοrld phenοmena that tend tο cluster arοund a central value.
a) Tο find the cutοff time fοr the fastest 5% οf athletes in the men's grοup, we need tο find the value οf x such that P(X < x) = 0.05, where X is a nοrmally distributed randοm variable with mean μ = 4370 and standard deviatiοn σ = 585.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 5th percentile is apprοximately -1.645. Therefοre, we can write:
(x - μ) / σ = -1.645
Substituting the given values, we get:
(x - 4370) / 585 = -1.645
Sοlving fοr x, we get:
x = 4370 + (-1.645) * 585
x ≈ 3447.68 secοnds
Hence, the cutοff time fοr the fastest 5% οf athletes in the men's grοup is apprοximately 3447.68 secοnds.
b) Tο find the cutοff time fοr the slοwest 10% οf athletes in the wοmen's grοup, we need tο find the value οf x such that P(X > x) = 0.1, where X is a nοrmally distributed randοm variable with mean μ = 5296 and standard deviatiοn σ = 826.
Using a standard nοrmal distributiοn table οr a calculatοr, we can find that the z-scοre cοrrespοnding tο the 10th percentile is apprοximately -1.28. Therefοre, we can write:
(x - μ) / σ = -1.28
Substituting the given values, we get:
(x - 5296) / 826 = -1.28
Sοlving fοr x, we get:
x = 5296 + (-1.28) * 826
x ≈ 4253.68 secοnds
Hence, the cutοff time fοr the slοwest 10% οf athletes in the grοup apprοximately 4253.68 secοnds.
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Ballet is one of the most widely performed types of concert dance. Each year, thousands of people flood t
Choreographers plan each movement and step the dancers make. Countless hours of preparation go into pra
Classical ballet is a very difficult dance style to master. It strictly follows traditional ballet technique. Dancer
and artistically express routines. Good technique requires that dancers have proper alignment. Dancers' head
perfectly. Ballet places a lot of emphasis on the lines of the body. "Good lines" are a combination of the body a
from training.
The proper positioning of the feet is especially important to ballet dancing. Turnout is the basis for all ballet
outward from the hips down, and the knee and foot are turned away from the center of the body. A perfect turnc
feet when the dancer is in first position with his or her heels touching. The knees are also supposed to touch, a
One of the most recognizable classical ballet techniques is en pointe dancing. This skill requires that dancer
the tips of their toes for extended periods of time. It takes a lot of training and strength to dance en pointe. The e
abdominal muscles-is used for this technique. Dancers can injure themselves or permanently damage their fee
What does the word lines most likely mean as it is used in this passage?
A. use of abdominal muscles
OB. ability to follow routines
OC.
arrangement of the body
avoiding injury to the body
D.
The correct option for this question is C. arrangement of the body.
Why it is?
Based on the given passage, the word "lines" most likely refers to the arrangement of the body in ballet dancing. The passage states that "Ballet places a lot of emphasis on the lines of the body" and that "Good lines" in ballet are a combination of the body alignment and artistic expression.
It also mentions that proper positioning of the feet is important for achieving good lines and that turnout, which is the outward rotation of the hips and knees, is the basis for all ballet movements.
Therefore, "lines" in this context is referring to the visual lines created by the dancer's body and limbs in ballet dance, which are essential to proper technique and artistic expression.
Therefore, the correct answer is C. arrangement of the body.
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Productivity for a small country was 25 units per worker hour in 2011. Productivity increased 20 percent between 2011 and 2016. What was the productivity figure for 2016? If the rate of increase is maintained, what will the figure be in 2021? In 2026?
Answer:
525 units
Step-by-step explanation:
firsat find a 1% increase
25/100 = 0.25
multiply this by 20 (per 5 years) and add to the original amount
0.25 x 20 = 500
500+25 = 525
This is your answer, and you just repeat this process for each year
Create two dot plots so that:
• They have at least 5 points each.
• Their centers are around 7.
• Dot Plot A has a larger spread than Dot Plot B.
According to the information, the graphics would remain as seen in the attached images. In them, graph A has a greater dispersion than graph B because it integrates a greater number of values.
What is a dot plot?A dot plot is a term for a type of graph used to display data by locating points on a number line. This graph is used to graphically represent certain trends or groupings of data.
According to the above, if we want to graph the information in the statement we must include at least 5 points in each graph. Additionally, we must put at least 7 points in the central value of the graph. Finally, we must have a greater dispersion of data in graph A than in graph B.
According to the above, the graphics would remain as shown in the image.
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I have 1,792 Pokémon cards, I also have 7 friends. I want to split the cards between me and the 7 of them. How many cards should each person get? Does the answer of this question has a remainder? Solve and Explain how you got your answer
We can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.
To split the 1,792 Pokémon cards equally between 8 people, including yourself and your 7 friends, you need to divide the total number of cards by the number of people:
1,792 cards ÷ 8 people = 224 cards per person.
So each person should get 224 Pokémon cards.
However, we should also check if there is a remainder after the division. To do that, we can multiply the number of cards each person is getting by the number of people and subtract it from the total number of cards:
224 cards/person x 8 people = 1,792 cards
1,792 cards - 1,792 cards = 0 remainder
Since there is no remainder, we can confirm that each person should receive exactly 224 Pokémon cards, and there won't be any cards left over.
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Please Show All Work!!
1.)You are going to eat a slice of pizza, where the central angle of your slice is 34° and the radius of your slice is 8".
What is the angle in radians? Use 3.14 for pi
A.) .72 radians
B.) 2.3 radians
C.) .59 radians
D.) .48 radians
2.) Calculate the area of the sector (the slice you eat). Round your answer to the nearest tenth. Use 3.14 for pi.
Area = n/360 * π r^2
n is your central angle in degrees.
3.) Calculate the arc length of the pizza you have eaten. Use 3.14 for pi. Ø is the angle in degrees
Arc Length = 2πr * Ø/360
To find the angle in radians, we need to convert the given angle from degrees to radians. We know that 180 degrees = π radians.
So,
34 degrees = (34/180) * π radians
= 0.1885 * 3.14
= 0.591 radians
Therefore, the answer is (C) 0.59 radians.
The area of the sector (the slice you eat) can be calculated using the formula:
Area = (n/360) * πr^2
where n is the central angle in degrees, and r is the radius of the slice.
Plugging in the given values, we get:
Area = (34/360) * 3.14 * 8^2
= 0.1 * 3.14 * 64
= 20.096 square inches
Rounding to the nearest tenth, the answer is 20.1 square inches.
The arc length of the pizza you have eaten can be calculated using the formula:
Arc Length = (2πr * Ø)/360
where Ø is the angle in degrees, and r is the radius of the slice.
Plugging in the given values, we get:
Arc Length = (2 * 3.14 * 8 * 34)/360
= 4.776 inches
Therefore, the answer is 4.776 inches.
Rewrite cos (x+5π/4) in terms of sin x and/or cos x
If c is 6x6 and the equation cx = v is consistent for every v in r^6, is it possible that for some v, the equation cx = v has more than one solution?
It is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.
What is the inverse?Inverse οperatiοns are οppοsite οperatiοns that undο each οther. Fοr example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse οperatiοns.
If the equatiοn cx = v is cοnsistent fοr every v in R⁶, it means that the matrix c is invertible, οr has a unique sοlutiοn fοr every v.
This is because if c is nοt invertible, then there exist sοme vectοrs v in R⁶ fοr which the equatiοn cx = v has nο sοlutiοn οr has infinitely many sοlutiοns.
If c is invertible, then fοr any vectοr v in R⁶, the equatiοn cx = v has a unique sοlutiοn given by
[tex]x = c^{( 1 )} v[/tex], where [tex]c^{(1)}v[/tex]
is the inverse οf c.
Therefοre, it is nοt pοssible that fοr sοme v, the equatiοn cx = v has mοre than οne sοlutiοn if c is invertible.
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4. Divide N275.00 among Eno and Musa so that for every N2.00 Eno gets, Musa gets N3.00. What are their shares? bags in such a way that one bag is twice as heavy
The shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.
Explain about the ratios of the number?A/B would be your formula if you were making comparisons one data point (A) to this other data point (B). This indicates that you are multiplying knowledge A by data B. For instance, your ratio will just be 5/10 if A is 5 and B is 10. Make the equation work. To calculate your ratio, divide data It by a data B.Total amount : R 275.00
Ratio of Eno to Musa = R 2.00 / R3.00
So,
Total ratio: 2 + 3 = 5
Then,
Eno's share = 2/5*275
Eno's share = R 110
Similarly,
Musa's share = 3/5*275
Musa's share = R 165
Thus, the shares of Eno and Musa in gained dividends are: R 110 and R 165 respectively.
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A company has two manufacturing plants with daily production levels of 8x+15 items and 3x-7 items, respectively. The first plant produces how many more items daily than the second plant?
Therefore , the solution of the given problem of equation comes out to be the first plant makes 5x + 22 more items per day.
How do equations work?
Mathematical formulas frequently employ same variable word to guarantee agreement between two claims. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. In this case, the normalise method adds b + 6 to employ the example of y + 6 rather than splitting 12 into two parts. It is possible to determine the length of the line and the quantity of connections between each sign's constituents. The significance of a symbol usually contradicts itself.
Here,
The first plant cranks out 8x + 15 items every day, while the second cranks out 3x - 7 items every day. By deducting the daily output of the second plant from the daily output of the first plant, we can determine how many more items the first plant creates than the second plant:
=> (8x + 15) - (3x - 7) (3x - 7)
If we condense this phrase, we get:
=> 8x + 15 - 3x + 7
Combining related words gives us:
=> 5x + 22
Therefore, compared to the second plant, the first plant makes 5x + 22 more items per day.
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Simplify: 2x^3+3y^3+5x^3+4y
The simplified fοrm οf the expressiοn [tex]2x^3 + 3y^3 + 5x^3 + 4y is 7x^3 + 3y^3 + 4y.[/tex]
What is an expressiοn?Mathematical statements knοwn as expressiοns in mathematics are thοse with at least twο terms cοnnected by a separatοr and cοntaining either numbers, variables, οr bοth. It is pοssible tο add, subtract, multiply, οr divide using the mathematical οperatοrs.
Fοr instance, the expressiοn "x + y" is οne where "x" and "y" are terms with a separatοr added between them. There are twο different types οf expressiοns in mathematics: numerical and algebraic. Numerical expressiοns οnly cοntain numbers, while algebraic expressiοns alsο include variables.
Tο simplify the expressiοn [tex]2x^3 + 3y^3 + 5x^3 + 4y,[/tex] we can cοmbine the like terms:
[tex]2x^3 + 5x^3 + 3y^3 + 4y[/tex]
[tex]= (2 + 5)x^3 + (3)y^3 + (4)y[/tex]
[tex]= 7x^3 + 3y^3 + 4y[/tex]
Therefοre, the simplified fοrm οf the expressiοn
[tex]2x^3 + 3y^3 + 5x^3 + 4y is 7x^3 + 3y^3 + 4y[/tex].
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A person tosses a coin 9 times. In how many ways can he get 6 heads?
If a person tosses a coin 9 times, there are 84 ways in which a person can get 6 heads in 9 coin tosses.
When a person tosses a coin 9 times, there are two possible outcomes for each toss - either heads or tails. Hence, there are a total of 2^9 = 512 possible outcomes for 9 coin tosses.
To find the number of ways in which a person can get 6 heads, we need to consider the number of ways in which 6 heads can occur in the 9 coin tosses, while the remaining 3 tosses can result in tails. The number of ways in which 6 heads can occur in 9 tosses is given by the binomial coefficient C(9,6), which is equal to 84.
Hence, there are 84 ways in which a person can get 6 heads in 9 coin tosses. This can be calculated using the formula for binomial coefficients:
C(9,6) = 9!/(6!3!) = (987)/(321) = 84
Alternatively, we can also calculate this using a combination of multiplication and addition. We can choose any 6 out of the 9 coin tosses to result in heads, which can be done in C(9,6) ways.
For each of these ways, the remaining 3 coin tosses will result in tails, which can occur in only one way. Hence, the total number of ways in which a person can get 6 heads in 9 coin tosses is given by:
Number of ways = C(9,6) * 1 = 84 * 1 = 84
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You take a package to the local shipping company. They charge a fixed base cost of $3 per package plus an additional $0. 63 per pound. If P represents the number of pounds of your package, and C is the total cost of shipping your package, write an equation that represents the relationship between P and C
If P represents the number of pounds of your package, and C is the total cost of shipping your package, the equation that represents the relationship between P and C is C = 3 + 0.63P.
To write an equation that represents the relationship between the weight of the package (P) and the total cost of shipping (C), we need to use the information given in the problem. The shipping company charges a fixed base cost of $3 per package plus an additional $0.63 per pound.
We can represent the additional cost per pound as 0.63P, since the cost increases by $0.63 for every additional pound. Therefore, the equation that represents the relationship between P and C is:
C = 3 + 0.63P
This equation gives us the total cost of shipping a package based on its weight. We can use this equation to calculate the cost of shipping a package of any weight by simply plugging in the weight (in pounds) for P and then solving for C.
For example, if a package weighs 5 pounds, we can substitute P = 5 into the equation to get:
C = 3 + 0.63(5)
C = 3 + 3.15
C = 6.15
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on a scale drawing, 1/4 in =2 foot. what are the dimensions on the scale for a room that is 27 ft by 20 ft
i cant fully answer it but i know the steps,
(the link is how you would set it up)
you can replace x with 20 or 27, i would start 20
Martha likes to knit hats and mittens for friends and family. Last fall, she knitted 3 hats and 3
pairs of mittens, which took a total of 51 hours. This fall, she knitted 3 hats and 5 pairs of
mittens, which took a total of 77 hours. If each hat takes the same amount of time and each
pair of mittens takes the same time, how long does it take Martha to knit each item?
hours to knit a pair of mittens.
It takes Martha
hours to knit a hat and
It takes Martha `4` hours to knit each hat and `13` hours to knit each pair of mittens.
What is meant by hours?
Hours are a unit of time used to measure the duration of an event or activity. An hour is equal to 60 minutes or 3,600 seconds. It is often used to indicate the time of day or to schedule appointments or events.
What is a pair?
A pair is a set of two things that go together or belong together, like a pair of shoes, socks, or gloves. It can also refer to a pair, a duo, or a twosome.
According to the given question
Let's assume that each hat takes `h` hours to knit and each pair of mittens takes `m` hours to knit.
From the given information, we know that:
- 3 hats and 3 pairs of mittens took a total of 51 hours. This means that 3h + 3m = 51.
- 3 hats and 5 pairs of mittens took a total of 77 hours. This means that 3h + 5m = 77.
We can use these two equations to solve for `h` and `m`.
First, let's solve for `h` by multiplying the first equation by 5 and the second equation by 3, and then subtracting the second equation from the first:
15h + 15m = 255
9h + 15m = 231
-----------------
6h = 24
h = 4
So each hat takes Martha `4` hours to knit.
Now we can use either of the original equations to solve for `m`. Let's use the first one:
3h + 3m = 51
3(4) + 3m = 51
12 + 3m = 51
3m = 39
m = 13
So each pair of mittens takes Martha `13` hours to knit.
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Sketch the graph of 2x²+4x
We can sketch the graph of 2x²+4x.
We can start by dissecting the equation and identifying its main components before drawing the graph of 2x²+4x.
The formula reads as y = ax² + bx + c, where a = 2, b = 4, and c = 0. It is a quadratic function.
The upward opening of the graph is indicated by the positive coefficient of x2 (a). By applying the formula -b/2a, which in this case equals -4/4 = -1, one can determine the vertex of the parabola.
Hence, the parabola's vertex is located at (-1,0).
By setting y = 0 and solving for x, we may get the graph's x-intercepts:
0 = 2x² + 4x
0 = 2x(x + 2)
Hence the x-intercepts are at x = 0 and x = -2.
We can set x = 0 to determine the graph's y-intercept:
y = 2(0)² + 4(0) = 0
The y-intercept is therefore at (0,0).
Using this knowledge, we can draw the 2x²+4x graph as follows:
Vertex located at (-1,0).
x = 0 and x = -2 are the two x-intercepts.
Y-intercept is located at (0,0).
The graph has a "U"-shaped opening that faces upward.
The graph's basic drawing is shown below:
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|
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| * *
| |
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_____|______________
-2 0 2
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a person is selected at random during the republican national convention. suppose the probability that the person selected is a woman is 38%, the probability that the person selected is tall is 54%, and the probability that the person selected is left-handed is 11%. assume that being female, tall, and left-handed are independent of each other. what is the probability that the person selected is a tall, left-handed woman?
The probability that the person selected is a tall, left-handed woman is 0.02.
Given that, The probability that the person selected is a woman is P(W) = 38% = 0.38
The probability that the person selected is tall is P(T) = 54% = 0.54
The probability that the person selected is left-handed is P(L) = 11% = 0.11
It is given that the events W, T, and L are independent of each other. Therefore, their joint probability is given by:
P(W ∩ T ∩ L) = P(W) × P(T) × P(L) = 0.38 × 0.54 × 0.11 = 0.02292
Now, the probability that the person selected is a tall, left-handed woman is given by:
P(T ∩ L ∩ W) = P(W ∩ T ∩ L) = 0.02292 = 0.02
Therefore, the probability that the person selected is a tall, left-handed woman is 0.02.
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The cooler at a picnic contained 4 apple juice boxes, 8 orange juice boxes, and 6 fruit punch juice boxes. a juice box is selected at random. what is the probability of the complement of choosing an orange juice box?
a. startfraction 1 over 18 endfraction
b. startfraction 4 over 9 endfraction
c. startfraction 5 over 9 endfraction
d. startfraction 17 over 18 endfraction
The probability of the complement of choosing an orange juice box is 17/18. (option d)
The complement of an event is the probability of that event not occurring. In this case, the event is choosing an orange juice box, so the complement is choosing any other juice box (i.e., an apple juice box or a fruit punch juice box).
The total number of juice boxes in the cooler is:
4 + 8 + 6 = 18
The number of juice boxes that are not orange juice boxes is:
4 + 6 = 10
Therefore, the probability of choosing a juice box that is not an orange juice box (i.e., the complement of choosing an orange juice box) is:
10/18 = 5/9
But the question asks for the probability of the complement, which is the probability of not choosing a juice box that is not an orange juice box. This is simply:
1 - 5/9 = 4/9
However, the question asks for the probability of the complement of choosing an orange juice box, not the complement of not choosing an orange juice box. These two probabilities are equal, since the event and its complement always add up to 1. Therefore, the probability of the complement of choosing an orange juice box is:
1 - 8/18 = 10/18 = 17/18
Therefore, the probability of the complement of choosing an orange juice box is 17/18.
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Make x the subject of the formula a/b = 2x/x+5
When x is the subject of the formula a/b = 2x/x+5, the value of x = 5a/(2b - a).
What are variables?The alphabetic letter that conveys a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
Any alphabet from a to z can be used for these variables. Most frequently, the variables "a," "b," "c," "x," "y," and "z" are utilised in equations. By performing mathematical operations on variables as if they were express numbers, one is able to handle a variety of problems in a single computation. A quadratic recipe is a common example that demonstrates how to explain each quadratic condition by simply substituting the numerical estimates of the condition's coefficients for the variables that correspond to it.
The given formula is:
a/b = 2x/x+5
To make x the subject of the formula we have to isolate the value of x.
Using cross multiplication we have:
a(x + 5) = b(2x)
ax + 5a = 2bx
5a = 2bx - ax
5a = x (2b - a)
5a/(2b - a) = x
Hence, when x is the subject of the formula a/b = 2x/x+5, the value of x = 5a/(2b - a).
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نے
A pilot is preparing to land her plane and is descending at a rate of 750 feet for every 3 miles
that she flies horizontally. If the she begins her descent at an altitude of 32,000 ft., how many
miles will she have travelled (m) when she is 16,000 ft. above the ground?
A. 21-1/2
B. 48
C. 52
D. 64
Answer:
the answer is (A) 21-1/2.
Step-by-step explanation:
First, we need to calculate the rate of descent in feet per mile:
750 ft / 3 miles = 250 ft/mile
Next, we can set up a proportion to solve for the distance traveled:
(distance traveled) / (total altitude change) = (distance traveled) / (altitude change due to descent) + (altitude at which descent begins)
Let m be the distance traveled:
m / (32000 ft - 16000 ft) = m / (250 ft/mile * x miles) + 16000 ft
where x is the number of miles traveled when the pilot is 16000 ft above the ground.
Simplifying:
m / 16000 ft = m / (250 ft/mile * x miles) + 1
Multiplying both sides by 16000 ft:
m = m / (250 ft/mile * x miles) * 16000 ft + 16000 ft * 16000 ft
Multiplying both sides by (250 ft/mile * x miles):
m * (250 ft/mile * x miles) = m * 16000 ft + 16000 ft * (250 ft/mile * x miles)
Simplifying:
250 * x * m = 16000 * m + 4000 * x * m
Dividing both sides by m:
250 * x = 16000 + 4000 * x
Subtracting 4000 * x from both sides:
-3750 * x = -16000
Dividing both sides by -3750:
x = 4.266666... miles
Rounding to the nearest half mile gives us:
x ≈ 4.5 miles
Therefore, the answer is (A) 21-1/2.