When comparing the values of f(4) and g(4), we need to take into account the fact that f(x) is exponential and g(x) is linear. Exponential functions grow at an increasing rate as x increases, while linear functions grow at a constant rate. Therefore, as x gets larger, the difference between f(x) and g(x) will become greater.
To find out how much greater f(4) is than g(4), we first need to calculate the values of f(4) and g(4). Let's say that f(x) = 2^x and g(x) = 3x + 1. Plugging in x = 4, we get:
f(4) = 2^4 = 16
g(4) = 3(4) + 1 = 13
So, f(4) is greater than g(4) by a difference of 3. However, this does not take into account the fact that f(x) is exponential and g(x) is linear.
To see the impact of the different growth rates, let's compare the values of f(x) and g(x) for a range of values of x. We can create a table to compare the two functions:
x f(x) g(x)
0 1 1
1 2 4
2 4 7
3 8 10
4 16 13
5 32 16
From this table, we can see that as x increases, the difference between f(x) and g(x) grows at an increasing rate. This is because f(x) is growing exponentially, while g(x) is growing linearly.
In summary, f(4) is 16 and g(4) is 13, so f(4) is greater than g(4) by a difference of 3. However, we also need to take into account the fact that f(x) is exponential and g(x) is linear. As x increases, the difference between f(x) and g(x) will grow at an increasing rate. Therefore, the difference between f(4) and g(4) is not only 3, but also growing exponentially.
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Which polynomial does the model represent? The model shows 1 black square block, 2 white thin blocks, 1 black thin block, 1 white small square block, 3 black small blocks
The polynomial represented by the model is [tex]]x^2 - x + 2[/tex]
Based on the provided model, the polynomial represented is:
1 black square block: x^2
2 white thin blocks: -2x
1 black thin block: x
1 white small square block: -1
3 black small blocks: +3
The polynomial that the model represents is:
[tex]x^2 - 2x + x - 1 + 3[/tex]
Combining like terms, we get:
[tex]x^2 - x + 2[/tex]
So, the polynomial represented by the model is [tex]x^2 - x + 2[/tex].
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A cylinder has volume 108 cm? What is the volume of a cone with the same
radius and height? Use 3. 14 for it and be sure to add units to your answer.
The volume of the cone with the same radius and height as the cylinder is 36 cm³.
To find the volume of a cone with the same radius and height as the cylinder, we first need to find the radius and height of the cylinder.
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
We are given that the volume of the cylinder is 108 cm^3.
So, 108 = πr^2h
To solve for r and h, we need more information. However, we can use the fact that the cone has the same radius and height as the cylinder to our advantage.
The formula for the volume of a cone is V = (1/3)πr^2h.
Since the cone has the same radius and height as the cylinder, we can substitute the values of r and h from the cylinder into the cone formula.
V = (1/3)π( r^2 )(h)
V = (1/3)π( r^2 )(108/π)
V = (1/3)( r^2 )(108)
V = 36( r^2 )
Therefore, the volume of the cone with the same radius and height as the cylinder is 36 cm³
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Ranjan is driving to Salt Lake City. His car gets 35. 5 miles per gallon of gasoline. Ranjan starts with his tank full. So far he has made two stops. Each time he stops, ranjan adds gas until his car is full again. At the first stop ranjan adds 6. 7 gallons of gas. At he second stop he adds 3. 4 gallons of gas. How many miles has ranjas drivin so far
After calculating the distance, Ranjan has driven 358.55 miles so far.
To solve this problem, we need to use the formula:
distance = fuel efficiency x fuel consumed
Let's start by calculating the total fuel consumed. At the first stop, Ranjan adds 6.7 gallons of gas, which means he consumed 6.7 gallons of gas since his tank was full at the beginning of the trip. At the second stop, he adds 3.4 gallons of gas, which means he consumed 3.4 gallons of gas between the first and second stops. Therefore, the total fuel consumed is:
6.7 + 3.4 = 10.1 gallons
Now we can calculate the distance driven using the fuel efficiency of 35.5 miles per gallon:
distance = 35.5 miles/gallon x 10.1 gallons = 358.55 miles
Therefore, Ranjan has driven 358.55 miles so far.
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The holiday health club has reduced its annual membership by 10%. if jorge sanchez purchases a years membership and pays $270, what is the regular membership fee?
The regular membership fee of the Holiday Health Club is $300.
Let the regular membership fee be x. According to the problem, the club has reduced its annual membership by 10%, so the discounted membership fee is 0.9x. We know that Jorge Sanchez has purchased a year's membership for $270, which is the discounted membership fee. Therefore, we can set up an equation as follows:
0.9x = 270
Solving for x, we get:
x = 270/0.9
x = 300
Hence, the regular membership fee of the Holiday Health Club is $300.
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Which expressions are equivalent to 2(2x + 4y + x − 2y)? (1 point)
Answer:
6x + 4y
Step-by-step explanation:
2(2x + 4y + x − 2y)
= 4x + 8y + 2x - 4y
= 6x + 4y
A t test for a mean uses a sample of 24 observations. Find the t test statistic value that has a P-value of 0. 10 when the alternative hypothesis is (a) Ha Subscript a Ha: μ ≠0, (b) Ha: μ greater than >0, (c) Ha: mu μ<0. Find the t test statistic value when Ha: μ≠0
The t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is
(a) Ha: μ ≠ 0 is ±1.711.
(b) Ha: μ > 0 is 1.319.
(c) Ha: μ < 0 is -1.319.
(d) Ha: μ ≠ 0 is ±1.711.
To find the t-test statistic value for a given P-value and alternative hypothesis, we need to use a t-distribution table or a statistical software program. Here, we will use a t-distribution table to find the t-test statistic value for a sample of 24 observations and a P-value of 0.10 for each alternative hypothesis.
(a) Ha: μ ≠ 0 (two-tailed test)
The critical t-value for a two-tailed test with a P-value of 0.10 and degrees of freedom (df) of 23 (sample size - 1) is:
t = ±1.711
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.
(b) Ha: μ > 0 (one-tailed test)
The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:
t = 1.319
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ > 0 is 1.319.
(c) Ha: μ < 0 (one-tailed test)
The critical t-value for a one-tailed test with a P-value of 0.10 and df of 23 is:
t = -1.319
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ < 0 is -1.319.
(d) Ha: μ ≠ 0 (two-tailed test)
To find the t-test statistic value when Ha: μ ≠ 0, we can use the inverse t-distribution function in a statistical software program or a calculator. The t-test statistic value that corresponds to a P-value of 0.10 with 23 degrees of freedom is:
t = ±1.711
Therefore, the t-test statistic value that has a P-value of 0.10 when the alternative hypothesis is Ha: μ ≠ 0 is ±1.711.
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30. Mean IQ of Attorneys See the preceding exercise, in which we can assume that o = 15
for the IQ scores. Attorneys are a group with IQ scores that vary less than the IQ scores of the
general population. Find the sample size needed to estimate the mean IQ of attorneys, given that
we want 98% confidence that the sample mean is within 3 IQ points of the population mean.
Does the sample size appear to be practical?
A sample size of 40 attorneys is needed to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.
To find the sample size, we use the formula:
n = (z*σ/E)²
where n is the sample size, z is the z-score for the desired level of confidence given as 98% , σ is the population standard deviation given as 15, and E is the margin of error given as 3 IQ points.
using the above values, we get:
n = (2.33*15/3)²
n = 39.05
Therefore, we need a sample size of at least 40 attorneys to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.
Whether this sample size is practical or not depends on various factors, such as the availability of attorneys with the desired characteristics, the cost and time required to collect the data, and the resources available for analysis. In general, a sample size of 40 is considered moderate to large for many applications, and it may be feasible depending on the specific context.
A sample size of 40 attorneys is needed to estimate the mean IQ with 98% confidence and a margin of error of 3 IQ points.
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5. Yelina surveyed people to find their favorite flower. She made a circle graph of the data. The central angle for the portion of the graph that represents tulips measures 54°. If 75 people chose tulips as their favorite flower, how many people did Yelina survey?
If 75 people chose tulips as their favourite flower then Yelina surveyed 500 people.
What is surveying?
Surveying is a branch of mathematics that deals with the measurement, analysis, and representation of physical features on land or in space. It uses geometry, trigonometry, and infinitesimal calculus to accurately measure distances, angles, elevations, and positions. Surveying is used in various fields such as civil engineering, construction, mapping, and geology to obtain valuable information about the earth's surface and to create maps and plans for various purposes.
According to the given information
Since the central angle for tulips is 54°, we can set up a proportion:
54/360 = 75/x
Simplifying this proportion, we get:
0.15 = 75/x
Multiplying both sides by x, we get:
x * 0.15 = 75
Dividing both sides by 0.15, we get:
x = 500
Therefore, Yelina surveyed 500 people.
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During the basketball game, you record the number of rebounds from missed shots for each team. (a) describe the likelihood that your team rebounds the next missed shot. (B) how many rebounds should ur team expect to have in 15 missed shots
In the event of describing the likelihood that the team rebounds the next missed shot is likely, and the number of rebounds that the team should expect to have missed in 15 shots is 10.5 rebounds.
Given
Number of shots missed by the given team is 7
Total number of shots fired is 10
a) Then, moving on to the first part of the question
Here we have to apply probability to evaluate the likelihood of the given team rebounds the next missed shot.
Then,
Probability = no of shots attended / total number of shots fired
Probability = 7 /10
Then the event is likely
b) Now the second part
Then the number of rebounds the given team expect to have in the next 15 missed shots
= 7/10 ×15
= 105/10
= 10.5 rebounds
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The box-and-whisker plot shows the heights (in inches) of the players on a soccer team. What fraction of the heights are at least 68 inches?
How much of the heights are at least 68 inches?
IF the median height is exactly 68 inches, then exactly 50% of the heights are at least 68 inches.
Find out that how of the heights are at least 68 inches?Without seeing the box-and-whisker plot, it is difficult to determine the exact fraction of heights that are at least 68 inches. However, we can make an estimate based on the general characteristics of a box-and-whisker plot.
In a box-and-whisker plot, the "box" represents the middle 50% of the data, with the median (50th percentile) marked by a line inside the box. The "whiskers" represent the minimum and maximum values within 1.5 times the interquartile range (IQR) of the data. Any points outside the whiskers are considered outliers.
Assuming that there are no outliers in the data, we can estimate that at least 50% of the heights are above the median, which is marked by the line inside the box. If the median height is at least 68 inches, then at least 50% of the heights are at least 68 inches.
If we assume that the median height is exactly 68 inches, then exactly 50% of the heights are at least 68 inches.
If the median height is less than 68 inches, then we can estimate that slightly less than 50% of the heights are at least 68 inches.
In summary, without more information about the box-and-whisker plot or the data it represents, we can estimate that at least 50% of the heights are at least 68 inches.
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Consider a roulette wheel. Roulette wheel has 2 green slots, 18 red slots, and 18 black slots. The wheel is spun and we are interested in the number of spins before the Rth success. : Let success be landing in a green slot. Find the following probabilities. A) identity the distribution with the parameters B) the 8th success occurs on the 17th spin. C) the 13th success occurs between the 31st and the 34th spin. PLEASE SOMEONE HELP <3
A) The distribution is a negative binomial distribution with parameters r and p.
B) The probability that the 8th success occurs on the 17th spin is approximately 0.8%.
C) The probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.
A) The distribution is a negative binomial distribution with parameters r = number of successes (in this case, r = 1 since we are only interested in the first success), and p = probability of success (landing in a green slot).
B) To find the probability that the 8th success occurs on the 17th spin, we use the formula for the negative binomial distribution:
P(X = k) = (k-1)C(r-1) * [tex]p^r[/tex] * [tex](1-p)^{(k-r)[/tex]
where X is the number of spins until the Rth success, k is the number of spins, and C(n,r) is the binomial coefficient (n choose r).
In this case, we want to find P(X = 17) when r = 8 and p = 2/38 (since there are 2 green slots out of 38 total slots):
P(X = 17) = (16 C 7) * (2/38)⁸ * (36/38)⁹
≈ 0.008 or 0.8%
So the probability that the 8th success occurs on the 17th spin is approximately 0.8%.
C) To find the probability that the 13th success occurs between the 31st and 34th spin, we need to find the probability of getting exactly 12 successes in the first 30 spins, followed by a success on one of the next 4 spins (31st, 32nd, 33rd, or 34th).
P(31 ≤ X ≤ 34) = P(X ≤ 34) - P(X ≤ 30)
= ∑[k=13 to 34] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex] - ∑[k=1 to 30] (k-1 C 12-1) * (2/38)¹² * [tex](36/38)^{(k-12)[/tex]
≈ 0.006 or 0.6%
So the probability that the 13th success occurs between the 31st and 34th spin is approximately 0.6%.
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Jose reads his book at an average rate of
2. 5
2. 5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read
20
20 pages?
To determine how long it would take Jose to read 20 pages at his average rate, you can use a proportion.
Let x be the time in minutes it would take Jose to read 20 pages.
Then, you can set up the following proportion:
2.5 pages / 4 minutes = 20 pages / x minutes
To solve for x, you can cross-multiply:
2.5 pages * x minutes = 4 minutes * 20 pages
2.5x = 80
Finally, divide both sides by 2.5 to isolate x:
x = 32
Therefore, it would take Jose 32 minutes to read 20 pages at his average rate.
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A study of the demand for air travel between two cities depends on the airfare according to the following demand equation. q=55.1−0.023p
The demand equation can be used to estimate the demand for air travel at different price levels, and can help airlines make pricing decisions based on the expected demand.
The demand equation is given as:
q = 55.1 - 0.023p
where q is the quantity demanded and p is the price of the airfare.
This equation shows an inverse relationship between price and quantity demanded. As the price of the airfare increases, the quantity demanded decreases, and vice versa.
For example, if the airfare price is $100, we can calculate the quantity demanded as:
q = 55.1 - 0.023(100) = 52.8
This means that at a price of $100, the quantity demanded is approximately 52.8 units.
Similarly, if the airfare price is $200, we can calculate the quantity demanded as:
q = 55.1 - 0.023(200) = 50.4
This means that at a price of $200, the quantity demanded is approximately 50.4 units.
So, demand equation can be used to estimate the demand for air travel at different price levels, and can help airlines make pricing decisions based on the expected demand.
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One bag of dichondra lawn food contains 30 pounds of fertilizer and its recommended coverage is 4000 square feet. if you want to cover a rectangular lawn that is 160 feet by 160 feet, how many pounds of fertilizer do you need?
To cover a rectangular lawn of 160 feet by 160 feet with dichondra lawn food, you would need 210 pounds of fertilizer.
To find the area of the rectangular lawn
Area = Length x Width
Area = 160 ft x 160 ft
Area = 25,600 sq ft
Since one bag of lawn food can cover 4000 square feet, we need to divide the total area of the lawn by the coverage of one bag
Number of bags = Total area ÷ Coverage of one bag
Number of bags = 25,600 sq ft ÷ 4000 sq ft
Number of bags = 6.4
Since we cannot buy a fraction of a bag, we need to round up to the nearest whole number of bags, which is 7.
Therefore, we need 7 bags of lawn food to cover the rectangular lawn. To find the total weight of fertilizer needed, we multiply the number of bags by the weight of one bag
Total weight of fertilizer = Number of bags x Weight of one bag
Total weight of fertilizer = 7 bags x 30 pounds/bag
Total weight of fertilizer = 210 pounds
Thus, we need 210 pounds of fertilizer to cover the rectangular lawn.
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Jill is starting her own business called Fuzzy Socks Box, where she'll knit and sell gift boxes of fuzzy socks online. She conducted a survey to predict how the price she charges per gift box will affect how many gift boxes she'll sell. She concluded that if she charges x dollars per gift box, she'll sell – 10x+350 gift boxes in her first month. It will cost Jill $2 to create each gift box. So, she will earn x–2 dollars in profit per gift box. What is the lowest price Jill can charge per gift box to earn $2,000 in profit in her first month?
The lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.
Jill is starting her own business called Fuzzy Socks Box, where she'll knit and sell gift boxes of fuzzy socks online.
Jill's profit per gift box is x - 2 dollars. To earn $2,000 in profit in her first month, she needs to sell
2000 / (x - 2) gift boxes.
According to her survey, the number of gift boxes she'll sell is
-10x + 350
Setting these two expressions equal to each other, we can find the lowest price Jill can charge per gift box to earn $2,000 in profit
-10x + 350 = 2000 / (x - 2)
Multiplying both sides by (x - 2), we get
-10[tex]x^{2}[/tex] + 12x - 470 = 0
Solving this quadratic equation, we find that
x = (6 +[tex]\sqrt{196[/tex] )/5 ≈ 3.2
or
x = (6 -[tex]\sqrt{196[/tex] )/5 ≈ 0.7
Since Jill cannot charge a negative price for her gift boxes, the lowest price she can charge per gift box to earn $2,000 in profit in her first month is approximately $3.2.
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15√2 = x√2please help me, how do i solve this? i'm in 9th grade and i completely forgot how to do this.
The equation 15√2 = x√2 can be solved, the value of x that satisfies the equation is 15.
To solve the equation 15√2 = x√2, you can divide both sides by √2 since the square root of 2 is a common factor on both sides of the equation. This gives:
15√2 / √2 = x√2 / √2
On the left side of the equation, the √2 and the denominator cancel out, leaving:
15
On the right side of the equation, the √2 and the denominator also cancel out, leaving:
x
So the solution to the equation is:
x = 15
Therefore, the value of x that satisfies the equation is 15.
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please help ASAP (can give brainliest)
Answer:
134° + (2x)° = 180°
(2x)° = 46°
x = 23
So angles 1, 2, 3, and 4 all measure 23°.
The distance between the two points M(15, a) and N(a,-5) is 20. Find the value of a.
Answer: 10
Step-by-step explanation:
just trust me
ET Previous Problem S NOX (1 point) According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not exceed 10 inches, where by "girth" we mean the perimeter of the smallest end. What is the largest possible volume of a rectangular parcel with a square end that can be sent by mait? Such a package is shown below. Assume 7 What are the dimensions of the package of largest volume? Х х Find a formula for the volume of the parcel in terms of x and y Volume The problem statement tells us that the parcel's girth plus longth may not exceed 108 inches. In order to maximize volume, we assume that we will actually need the girth plus longth to equal 108 inches. What equation does this produce involving randy Equation: It Solve this equation for y in terms of an Find a formula for the volume V (w) in terms of e. V(x) HH What is the domain of the function V7 Note that both and y must be positive consider how the constraint that girth plus length is 10 inches limit the possible values for Give your answer using interval notation Domain Find the absolute maximum of the volume of the parcel on the domain you established above and hence also determine the dimensions of the box of greatest volume Maximum Volume II Optimal dimensions = !!! andy 11
The dimensions of the package of largest volume are 18 inches by 18 inches by 36 inches. The largest possible volume is 11664 cubic inches.
How we find dimension?To find the dimensions of the package of largest volume. Let the dimensions of the square end be x, and the length of the rectangular end be y. The girth of the package is 4x, and the length is y. According to the problem statement, the girth plus length may not exceed 108 inches, so we have:
4x + y = 108We want to maximize the volume V(x,y) of the package, which is given by:
[tex]V(x,y) = x^2y[/tex]We can use the equation 4x + y = 108 to express y in terms of x:
y = 108 - 4xSubstituting this into the formula for V(x,y), we get:
[tex]V(x) = x^2(108 - 4x) = 108x^2 - 4x^3[/tex]The domain of V(x) is determined by the constraints that x and y must be positive and the girth plus length may not exceed 10 inches. Since the girth is 4x, we have:
4x + y = 108 - 3x ≤ 10Solving for x, we get:
x ≤ 32/3Since x must be positive, the domain of V(x) is:
0 < x ≤ 32/3The maximum volume and the optimal dimensions
To find the absolute maximum of V(x) on the domain 0 < x ≤ 32/3, we take the derivative of V(x) with respect to x and set it equal to zero:
[tex]V'(x) = 216x - 12x^2 = 0[/tex]
Solving for x, we get:
x = 18To confirm that this is a maximum, we take the second derivative of V(x) with respect to x:
V''(x) = 216 - 24xAt x = 18, we have V''(18) = 0, which means that the second derivative test is inconclusive. However, we can see that V(x) is increasing on the interval 0 < x < 18 and decreasing on the interval 18 < x ≤ 32/3, which means that x = 18 is indeed the absolute maximum of V(x) on the domain.
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Billy has $80 to spend. He spent $54.50 on Bruno Mars Tickets. If Stickers cost $1.34 each, what is the maximum number of Stickers he can buy? Define a variable then write and solve an inequality. Write your answer using a complete sentence.
Answer:
Billy can buy 19 or less than 19 stickers.
Step-by-step explanation:
Solving inequality:Let the unknown variable - number of stickers be 'x'.
Cost of one sticker = $1.34
Cost of 'x' stickers = 1.34 * x = 1.34x
Maximum amount that can be spent for buying stickers = 80 - 54.50
= $25.50
Inequality:
1.34x ≤ 25.50
Solving:
Divide both sides by 1.34,
[tex]\sf x \leq \dfrac{25.50}{1.34}[/tex]
x ≤ 19.03
x ≤ 19
Billy can buy 19 or less than 19 stickers.
A circle is growing, its radius increasing by 5 mm per second. Find the rate at which the area is changing at the moment when the radius is 28 mm. When the radius is 28 mm, the area is changing at approximately _____.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
We are given that the radius is increasing at a rate of 5 mm per second. This means that the rate of change of the radius with respect to time is dr/dt = 5 mm/s.
To find the rate at which the area is changing, we need to find dA/dt, the derivative of the area with respect to time. We can use the chain rule to find this derivative:
dA/dt = dA/dr * dr/dt
We can find dA/dr by taking the derivative of the area formula with respect to r:
dA/dr = 2πr
Now we can substitute the values we know into the chain rule formula:
dA/dt = dA/dr * dr/dt = 2πr * 5
When the radius is 28 mm, the rate of change of the area is:
dA/dt = 2π(28) * 5 = 280π ≈ 879.64 mm^2/s
Therefore, the area is changing at a rate of approximately 879.64 mm^2/s when the radius is 28 mm.
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Qn in attachment. ..
Answer:
pls mrk me brainliest (・(ｪ)・）
Solve the system of equations. 2x + 3y = 18 3x + y = 6 (9, 0) (3, 4) (1, 3) (0, 6)
X = 0 and Y = 6 are the answers to the equation system. The system's two equations are satisfied at the location (0, 6). Choice D
To solve the system of equations:
2x + 3y = 18
3x + y = 6
We can employ the substitution or elimination strategy. Let's solve this system via the process of elimination:
To make the coefficients of x in both equations equal, multiply the second equation by two:
2(3x + y) = 2(6)
6x + 2y = 12
Now we have the system of equations:
2x + 3y = 18
6x + 2y = 12
Next, by deducting the first equation from the second equation, we can remove the y term:
(6x + 2y) - (2x + 3y) = 12 - 18
6x + 2y - 2x - 3y = -6
4x - y = -6
4x - y = -6
y = 4x + 6
At this point, we can add this expression for y to one of the initial equations. Let's employ the first equation:
2x + 3(4x + 6) = 18
2x + 12x + 18 = 18
14x + 18 = 18
14x = 0
x = 0
Replacing x = 0 in the equation y = 4x + 6 now:
y = 4(0) + 6
y = 6
Thus, x = 0 and y = 6 are the answers to the system of equations. The system's two equations are satisfied at the location (0, 6). Basketball or baseball in option D is 5/6, or approximately 0.8333.
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Answer:
Option D, (0,6)
Step-by-step explanation:
took the test xx
What is question asking??? All I need is one example and I get the rest I just don’t understand the assignment
It's actually asking you to find the angles within the circles and match it with the angles it's supposed to be. For example if angle COE is 90° (im taking a fake angle value), you should put arc CE <——> 90
If you are still confused and need me to do it so that you can understand what I mean, reply and I'll help you!
Answer:
See below
Step-by-step explanation:
The objective of the question has been well explained by user vaishub1101.
I am just adding an additional hint and one answer to get you going
Since you just needed one example, I am providing just that
One thing to note in the figure is that segments DEF, ACD and ABF are all tangents to the circle. This fact is important since at the point of tangency (where the tangent touches the circle), the tangent to a circle is always perpendicular to the radius.
Using this knowledge and the given angles we can compute all the other angles but not the arc length [tex]\frown \atop {CE}[/tex] since to find arc length we need the value of the radius
As an example to help you get going,
[tex]\angle{DFA} \longleftrightarrow 58^\circ[/tex]
You would drag the tile with ∠DFA to the top left box and the tile with 58° to the top right box
I am sure you can figure out the rest or else user vaishub1101 can help you out with the rest
A convention center is hosting a home show where different businesses provide information and examples for improvements that can be made to homes. The sponsors are also holding a lottery to give away $10,000 in home improvements. In a giant bin, 20 balls numbered 1 - 20 are mixed together. Then , 3 balls are selected from the bin, without replacement For $5. 00a customer can try to predict the 3 numbers that will be selected. If the order in which the numbers are selected does not matter , how many different predictions are possible for this game of chance ?
There are 1140 different predictions possible for this game of chance.
In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.
To solve this problem, we can use the formula for combinations, which is
=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]
where n is the total number of items, and x is the number of items to be selected.
In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes
=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]
Using a calculator or simplifying the equation, we get:
[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]
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i need help fast look at photo
Step-by-step explanation:
B
26 = 13.5 + m/2.5; m = 31.25
26 = 13.5 + 31.25/2.5
26 = 13.5 + 12.5
26 = 26
What is the approximate area of the figure?
20 square meters
40 square meters
80 square meters
100 square meters
The approximate area of the figure is 40 square meters. So, the correct answer is B).
Recall the formula for the area of a kite, which is
Area = (1/2) x Base x Height
where "Base" is the length of one of the diagonals and "Height" is the length of the other diagonal.
Identify the base and height of the given kite from the problem statement. Here, it is given that the height is 10 meters and the base is 8 meters.
Substitute the values of the base and height into the formula for the area of a kite
Area = (1/2) x 8 meters x 10 meters
Simplify the expression by multiplying the base and height together and dividing by 2
Area = 40 square meters
Round the answer to the nearest whole number or keep the answer as a decimal, depending on the instructions of the problem.
Therefore, the approximate area of the given kite is 40 square meters. So, the correct answer is B).
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Find the exact solutions of the equation in the interval (0, 2). (Enter your answers as a comma-separated list) 4 tan 2x - 4 cot x = 0 x= π/6 , π/2, 5π/6, 7π/6, 3π/2, 11π/6
Therefore, the solutions of tan x = -1/2 in the interval (0, 2) are:
x ≈ 2.034, 5.176
We can simplify the given equation as follows:
4 tan 2x - 4 cot x = 0
4(tan 2x - cot x) = 0
4[(2tan x)/(1 - tan^2 x) - (1)/(tan x)] = 0
Multiplying both sides by (1 - tan^2 x) * (tan x), we get:
8tan^3 x - 4tan^2 x - 8tan x + 4 = 0
Dividing both sides by 4 and rearranging, we get:
2tan^3 x - tan^2 x - 2tan x + 1 = 0
Factorizing, we get:
(tan x - 1)(2tan^2 x - tan x - 1) = 0
Using the quadratic formula to solve for the roots of 2tan^2 x - tan x - 1 = 0, we get:
tan x = [1 ± sqrt(1 + 8)] / 4 = [1 ± sqrt(9)] / 4 = 1, -1/2
Therefore, the solutions of the given equation in the interval (0, 2) are the values of x such that tan x = 1 or tan x = -1/2.
We know that tan (π/4) = 1 and tan (-π/4) = -1, so the solutions of tan x = 1 in the interval (0, 2) are:
x = π/4, 5π/4
We can find the solutions of tan x = -1/2 in the interval (0, 2) by finding the reference angle and using the signs of sine and cosine in the corresponding quadrants. We have:
tan x = -1/2
Let θ be the reference angle such that tan θ = 1/2. We know that θ is in the second or fourth quadrant.
In the second quadrant, sine is positive and cosine is negative, so we have:
sin θ = sqrt(1/(1 + tan^2 θ)) = sqrt(1/5)
cos θ = -tan θ = -1/2
Therefore, we get:
x = π - θ = π + arctan(1/2) ≈ 2.034
In the fourth quadrant, both sine and cosine are negative, so we have:
sin θ = -sqrt(1/(1 + tan^2 θ)) = -sqrt(1/5)
cos θ = -tan θ = -1/2
Therefore, we get:
x = 2π - θ = 2π + arctan(1/2) ≈ 5.176
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Examples of geometric transformations can be found throughout the real world. Think about some places where you might use or se transformations. Give at least three examples for each type of transformation. Make use of the Internet, books, magazines, newspapers, and everyday life experiences to come up with your examples.
Geometric transformations can be found in everyday life, such as moving furniture (translation), opening a door (rotation), using mirrors (reflection), zooming in and out of maps (scaling), skewing images in Photoshop (shearing), and stretching a rubber band (stretching).
Here are some examples of different types of transformations and their applications:
Translation:
Moving furniture in a room
Moving a vehicle on a map
Shifting a picture on a wall
Rotation:
Swinging a pendulum
Turning a key in a lock
Opening a door
Reflection:
Mirrors reflecting images
Water reflections of a landscape
Reflective surfaces on cars and buildings
Scaling:
Enlarging or reducing a picture on a screen
Adjusting the size of a printout
Shearing:
Skewing an image in Photoshop
Tilting a picture frame on a wall
Slanting the roof of a building for better drainage
Stretching:
Stretching a rubber band
Stretching a balloon before inflating it
Stretching a canvas for painting
These are just a few examples of the many ways geometric transformations are used in our everyday lives. By understanding these concepts, we can appreciate the beauty and functionality of the world around us.
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Simplify and evaluate
Answer:
In simplified form: 1/27
Evaluated: 0.037
Step-by-step explanation:
To simplify and evaluate 81^(-3/4), we use the rule that (a^m)^n = a^(mn) and rewrite the expression as (3^4)^(-3/4). Then, we use the rule that a^(-n) = 1/(a^n) to get:
81^(-3/4) = (3^4)^(-3/4) = 3^(-3) = 1/(3^3) = 1/27
Therefore, 81^(-3/4) simplifies to 1/27 and evaluates to 0.037