Yes, we can determine the sampling distribution of the sample mean.
The name of the distribution is the Student's t-distribution. The mean of the sampling distribution is the same as the mean of the population, which is $51000. The standard error of the sampling distribution is calculated by dividing the standard deviation of the population by the square root of the sample size. So, the standard error is $5500 / sqrt(18) = $1296.56.
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Yes, we can determine the sampling distribution of the sample mean. The name of the distribution is the Student's t-distribution.
The mean of the sampling distribution is the same as the mean of the population, which is $51000. The standard error of the sampling distribution is calculated by dividing the standard deviation of the population by the square root of the sample size. So, the standard error is $5500 / sqrt(18) = $1296.56.
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a 20
b 15
c 5
d 10
i need sum help on this real quick
Answer:
C
Step-by-step explanation:
6x° and 60° form a right angle and sum to 90° , that is
6x + 60 = 90 ( subtract 60 from both sides )
6x = 30 ( divide both sides by 6 )
x = 5
If the intrinsic rate of increase, r, is 0 for a population, what is the expected lifetime reproductive value for an individual in that population?A. 1
B. 2
C. 3
D. 4
The expected lifetime reproductive value for an individual in a population with an intrinsic rate of increase (r) of 0 is 1, the correct option is A.
The calculation for the expected lifetime reproductive value can be expressed as:
R₀ = ∑ lxmx
In a stable population with an intrinsic rate of increase of 0, the survival probability (lx) is constant across all age classes, and the average number of offspring produced by an individual (mx) is also constant.
R₀ = lxm
where l is the survival probability and m is the average number of offspring per individual.
Since the population is stable, each individual replaces itself with one offspring, so m = 1.
Therefore, the calculation for the expected lifetime reproductive value in a population with an intrinsic rate of increase of 0 is:
R₀ = lxm = 1 x 1 = 1, the correct option is A.
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Is the equation, y = 9x + 3 a proportional or non-proportional linear relationship?
Point X is located at (3, 2). Point Y is located at (3, -8). What is the distance form point X to point Y.
In response to the aforementioned query, we may say that D is equal to equation sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10. As a result, it takes 10 units to get from position X to point Y.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The distance formula may be used to determine the separation between two points:
Sqrt((x2 - x1) + (y2 - y1)) = sqrt(d)
where d is the distance between the two locations, and (x1, y1) and (x2, y2) are the coordinates of the two points.
We may get the separation between points X at (3, 2) and Y at (3, -8), using the following formula:
D is equal to sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10.
As a result, it takes 10 units to get from position X to point Y.
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The angles of a triangle are 5a/2, 3a/4, 7a/4. Find the value of the largest and smallest angle
The largest angle is [tex]\frac{7a}{4}[/tex] and the smallest angle is [tex]\frac{3a}{4}[/tex].
In this case, we have the angles [tex]\frac{5a}{2}, \frac{3a}{4}, and \frac{7a}{4}[/tex]. So we can set up the equation:
[tex]\frac{5a}{2} + \frac{3a}{4} + \frac{7a}{4} = 180[/tex]
To solve for "a", we can simplify the left side of the equation by finding a common denominator:
[tex]\frac{(10a + 3a + 7a)}{4} = 180[/tex]
Simplifying the left side gives:
[tex]\frac{20a}{4} = 180[/tex]
And further simplifying gives:
5a = 180
Dividing both sides by 5 gives:
a = 36
Now that we know the value of "a", we can substitute it back into each angle expression to find their actual values:
[tex]\frac{5a}{2} = \frac{5(36)}{2} = \frac{903a}{4} = \frac{3(36)}{4} = \frac{277a}{4} = \frac{7(36)}{4} = 63[/tex]
Therefore, [tex]\frac{7a}{4} = 63[/tex] is the largest angle and [tex]\frac{3a}{4} = 27[/tex] is the smallest angle.
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HELP ASAP ON TIME LIMIT
How many yards are in two and three-fourths miles?
5,280 yards
4,840 yards
3,520 yards
2,640 yards
Answer: 2,640 yards
Step-by-step explanation:
2,640 yards. Two and three-fourths miles is equal to 14,400 yards. 14,400 yards divided by 5, which is the number of yards in a mile, is equal to 2,640 yards.
Answer: 4,840 yards
Step-by-step explanation:
What is the 5th term in the sequence of square numbers?
Natural numbers are squared to get the succession of square numbers. These sequence's initial terms includes 1, 4, 9,16, 25, so on and so forth.
We must square the fifth natural integer, which is five, in order to determine the fifth term in this series. As a result, 25 is the fifth term in the square number series.
In a more general sense, n2 represents the nth phrase in the series of square numbers. This is so that the nth term, which is n, equals the rectangle of the nth arbitrary integer.
Tn = n2 is the formulae for the nth term. The chain of square integers is a direct example of the more generic order of degrees.
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1/2 + 3y = y/5 what number is y in this equation
The solution to the equation 1/2 + 3y = y/5 is y = -3/14.
What is the linear equation in one variable?
A linear equation in one variable is an equation that can be written in the form:
ax + b = 0
where x is the variable, a and b are constants, and a is not equal to zero. The solution to the equation is the value of x that makes the equation true.
To solve for y in the equation 1/2 + 3y = y/5, we need to isolate y on one side of the equation.
First, we can simplify the left side of the equation by combining the like terms:
1/2 + 3y = (6/10) + (30y/10) = (6 + 30y)/10
Now we can rewrite the equation as:
(6 + 30y)/10 = y/5
To solve for y, we can start by multiplying both sides of the equation by 10, to eliminate the denominators:
6 + 30y = 2y
Next, we can simplify by subtracting 2y from both sides:
6 + 28y = 0
Finally, we can solve for y by subtracting 6 from both sides and then dividing by 28:
28y = -6
y = -6/28
Simplifying the fraction, we get:
y = -3/14
Therefore, the solution to the equation 1/2 + 3y = y/5 is y = -3/14.
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Sandy decided to do an experiment with a sandwich she left in her locker. She found it 4 days after she had put it there, took it to the lab, and counted 71 bacteria. 3 days later she counted 185 bacteria.
Write the exponential equation that represents this problem.
She estimates that it will take 500 bacteria to completely cover her sandwich. How many days would it take this to happen, starting from the day she first put her sandwich in her locker?
The answer tο the pοsed questiοn using equatiοns is that hence, it will take 500 bacteria apprοximately 9.7 days frοm the day Sandy put her sandwich in her lοcker tο thοrοughly cοver it.
Describe an equatiοn?The equals sign (=) denοtes equality when twο statements are jοined by a mathematical equatiοn. A mathematical statement that establishes the equality οf twο mathematical expressiοns is knοwn as an equatiοn in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign divides the numbers. A mathematical fοrmula can be used tο identify the link between the twο sentences οn either side οf a letter.
The expοnential equatiοn fοr this prοblem is as fοllοws:
[tex]N(t) = e(kt) \times N_0 (kt)[/tex]
The data mentiοned above can be used to calculate the values of [tex]N_0[/tex] and k:
=>[tex]N (4) = \frac{71}{sN(7)} = 185[/tex]
These numbers are entered intο the formula as follows:
[tex]71 = N_0\times e^{(4k) (4k) (4k)}\\185 = N_0 \times e^{(7k) (7k) (7k)}\\185/71 = e^{(3k) (3k) (3k)}[/tex]
Hence, the equation for this prοblem is:
[tex]N(t) = 23.77 \times e^ {(0.3056t) (0.3056t) (0.3056t)}[/tex]
To determine hοw many days, it will take for 500 germs to prοliferate, we can set N(t) equal to 500 and solve for t:
[tex]500 = 23.77 \times e^ {(0.3056t) (0.3056t) (0.3056t)}[/tex]
Based οn t = ln (500/23.77) / 0.3056, 9.7 days.
Hence, it will take 500 bacteria rοughly 9.7 days from the day Sandy put her sandwich in her lοcker to thoroughly cοver it.
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Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.
S:{11}
S:{14}
S:{30}
S:{42}
Answer:
6(n − 5) < 3(n + 4)
6n - 30 < 3n + 12 // Distribute the 6 and 3
3n < 42 // Add 30 to both sides
n < 14 // Divide both sides by 3
So the inequality is true for n < 14. This means that the only integer in the set S that satisfies the inequality is 11. Therefore, the solution is S:{11}.
Kendra’s water bottle contains 2 quarts of water.she wants to add drink mix to it, but he directions for the drink mix give the amount of water in fluid ounces.how many fluid ounces are in her bottle
By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:
64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.
So Kendra's water bottle holds 64 fluid ounces.
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State your yes/no research question. Do you play sports? No Make a frequency table with the headings: Frequency Percent Male Female Yes Yes No 16 9 7 14 Is it better to use frequencies or percentages to compare groups when you make your graph? Percentages are better to use when comparing the groups. Gramm: Please relo for Gramme Construct a side by side bar graph showing the men's and women's responses to your question. What do your graphs indicate about students? 5 points
Yes, it is better to use percentages to compare groups when making a graph. This is because percentages allow for a more accurate comparison of the data, as they take into account the relative size of each group. If we only use frequencies, we may get a skewed view of the data, as one group may be much larger than the other.
Here is the side by side bar graph showing the men's and women's responses to the question "Do you play sports?":
Gender Yes No
Male 9 7
Female 7 14
The graph indicates that a higher percentage of males play sports compared to females. However, it also shows that there are more females who do not play sports compared to males. This suggests that there may be a gender difference in the participation of sports among students.
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You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. Thus you are performing a two-tailed test. Your sample data produce the test statistic z=2.517z=2.517. Find the p-value accurate to 4 decimal places.
p-value =
The p-value for our test is 0.0120, accurate to 4 decimal places.
We are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. We are performing a two-tailed test and our sample data produce the test statistic z=2.517.
To find the p-value, we need to use a standard normal distribution table or calculator. We will use the table for this answer.
The first step is to find the area to the left of the test statistic z=2.517 in the standard normal distribution table. This gives us the probability of obtaining a z-score less than or equal to 2.517. The closest value in the table is 2.51, which gives us an area of 0.9940.
Since we are conducting a two-tailed test, we need to find the area in both tails of the distribution. To do this, we subtract the area to the left of the test statistic from 1: 1-0.9940 = 0.0060. This gives us the area in the right tail of the distribution.
Finally, we multiply this value by 2 to get the p-value for our two-tailed test: 0.0060 * 2 = 0.0120.
Therefore, the p-value for our test is 0.0120, accurate to 4 decimal places.
p-value = 0.0120
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A coin with P[H]=0. 3 is flipped 3 times. Define N to be the total number of heads. Find the CDF FN(n), the cumulative distribution function for N. (please provide an explanation for the answer)
The cumulative distribution function for N when a coin is flipped 3 times with P[H]=0. 3 is given by ,
F(N≤ 0) = 0.343 , F(N≤1) = 0.784 , F(N≤2) = 0.973 , F(N≤3) = 1.000.
Cumulative distribution function (CDF) of N,
Probability of getting n or fewer heads in three coin flips,
(All values of n from 0 to 3)
Probability of getting exactly n heads in three flips.
Apply binomial distribution,
P(N = n) = ³Cₙ ×(0.3)ⁿ × (0.7)³⁻ⁿ
For cumulative distribution function, add up the probabilities of getting 0, 1, 2, or 3 heads in three flips,
F(N≤ 0)
=P(N=0)
=³C₀ × (0.3)⁰ × (0.7)³
= 1 × 1 × 0.343
= 0.343
For F(N≤1) is equal to,
⇒F(N≤1)
= P(N=0) + P(N=1)
= ³C₀ × (0.3)⁰ × (0.7)³ + ³C₁ × (0.3)¹ × (0.7)²
= 0.343 + 0.441
= 0.784
F(N ≤ 2)
= P(N=0) + P(N=1) + P(N=2)
= ³C₀ × (0.3)⁰ × (0.7)³
+ ³C₁ × (0.3)¹ × (0.7)²
+³C₂ × (0.3)² × (0.7)¹
= 0.343 + 0.441 + 0.189
= 0.973
This implies CDF for N is equal to,
F(N ≤n) = [tex]\sum_{0}^{x}[/tex]³Cₓ × (0.3)ˣ × (0.7)³⁻ˣ
And F(N≤3) is equal to,
⇒F(N≤3)
= P(N=0) + P(N=1) + P(N=2) + P(N=3)
= ³C₀ × (0.3)⁰ × (0.7)³
+ ³C₁ × (0.3)¹ × (0.7)²
+ ³C₂ × (0.3)² × (0.7)¹
+ ³C₃× (0.3)³ × (0.7)⁰
= 0.343 + 0.441 + 0.189 + 0.027
= 1.000
Therefore, the cumulative distribution function for N is equal to,
F(N≤ 0) = 0.343
F(N≤1) = 0.784
F(N≤2) = 0.973
F(N≤3) = 1.000
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A circle has a radius of \( 11 \mathrm{in} \). Find the length \( s \) of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians. Do not round any intermediate computations, and round y
The length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).
To find the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \), we can use the formula for arc length: \( s = r\theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.
Plugging in the given values, we get:
\( s = (11 \mathrm{in})(\frac{\pi}{2}) \)
Simplifying, we get:
\( s = \frac{11\pi}{2} \mathrm{in} \)
Therefore, the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).
Note: If the question asks for the answer to be rounded, you can use a calculator to find the approximate value of \( \frac{11\pi}{2} \) and round to the desired number of decimal places. For example, if the question asks for the answer to be rounded to the nearest tenth, the answer would be \( 17.3 \mathrm{in} \).
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If I know that 40% of a number is 100 and I multiply that number by 2, what's 40% of that new number?
Answer: 200
Step-by-step explanation:
40% of y = 100
40/100 of y = 100
40y/100 = 100
40y = 100 multiplied by 100
40y/40 = 10000
y = 250.
40% of 2 multiplied by 250
40/100 of 500
40 multiplied by 5
answer = 200.
A contractor bids a job at $680 for materials plus $42 per hour
for labor. The total cost for the job can be modeled by: C = 42H +
680.
Find the number of hours that he has for the job if the owner wo
The contractor has 5.95 hours for the job if $930 is spent by him.
The total cost for the job can be modeled by C = 42H + 680, where C is the total cost of the job, H is the number of hours of labor, and 680 is the cost of materials.
If the owner wants to spend $930 for the job, then the number of hours that the contractor has for the job can be found by solving the equation C = 42H + 680 for H.
Thus, 42H + 680 = 930. Subtracting 680 from both sides gives 42H = 250. Dividing both sides by 42 gives H = 250/42 = 5.95 hours.
Therefore, the contractor has 5.95 hours for the job if the owner wants to spend $930.
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Use the image to determine the line of reflection. Graph of polygon ABCDE with point E at negative 6 comma 3. A second polygon A prime B prime C prime D prime E prime with E prime at negative 6 comma negative 1. Reflection across x = −6 Reflection across y = 1 Reflection across the x-axis Reflection across the y-axis
The point E' will have a y-value of -1 instead of 3 and x-value of 6 instead of -6.
What is a polygon?A polygon is a two-dimensional shape composed of straight line segments that close in a loop to form a single shape. Generally, polygons have three or more sides and angles. Depending on the number of sides, polygons can be classified as triangles, quadrilaterals, pentagons, hexagons, and so on.
A reflection across the x-axis of the graph of polygon ABCDE with point E at (-6,3) would result in the creation of a second polygon A'B'C'D'E' with E' at (-6,-1). This is because the reflection flips the points across the x-axis, meaning all of the y-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have a y-value of -1 instead of 3. This is because the reflection across the x-axis will cause the y-values of each point to flip signs, with the y-value of E increasing from -3 to -1.
Similarly, a reflection across the y-axis of polygon ABCDE with point E at (-6,3) would result in the creation of polygon A'B'C'D'E' with E' at (6,1). This is because the reflection flips the points across the y-axis, meaning all of the x-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have an x-value of 6 instead of -6. This is because the reflection across the y-axis will cause the x-values of each point to flip signs, with the x-value of E increasing from -6 to 6.
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Answer:
Reflection across y = 1
Step-by-step explanation:
i got this right on the flvs test!
The average rate of change of f(x) = x² = x + 4 from x= 2 to x = 4 is
A)2
B)10
C)5
D)3
Answer: 7
Step-by-step explanation: The average rate of change of a function f(x) over an interval [a,b] is defined as the ratio of “change in the function values” to the "change in the endpoints of the interval"1. In other words, it is the slope of the line that passes through two points on the graph of f(x)2.
To find the average rate of change of f(x) = x² + x + 4 from x = 2 to x = 4, we can use this formula:
Average rate of change = [f(4) - f(2)] / (4 - 2)
First, we need to plug in x = 4 and x = 2 into f(x) and simplify:
f(4) = (4)² + (4) + 4 f(4) = 16 + 8 f(4) = 24
f(2) = (2)² + (2) + 4 f(2) = 4 + 6 f(2) = 10
Next, we need to subtract f(2) from f(4), and divide by (4 - 2):
Average rate of change = [24 - 10] / (4 - 2) Average rate of change = 14 / 2 Average rate of change = 7
Michael, a farmer, wants to buy a new tractor using the US$ he received from his daughter in America for his birthday. The price of the tractor is R160 000, VAT excluded. b) If the exchange rate is US$1 = R17.96, calculate how much USS Michel must change for him to pay cash for the tractor. Round off your answer to the nearest USS.
For Michael to pay cash for the tractor priced at R160,000 with the exchange rate as US$1 = R17.96, the amount he must change is US$8,908. 69.
What is an exchange rate?An exchange rate is the unit rate at which one country's currency is exchanged for another.
Exchange rates are based on a country's economic performance or indices in comparison to other countries.
The price of the tractor = R160,000
Exchange Rate: US$ = R17.96
R160,000 = US$8,908. 69 (R160,000/R17.96)
Thus, Michael needs to exchange US$8,908. 69 to purchase the tractor costing R160,000.
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5. Write an expression for the area of a rectangle with length & and width w.
6. Imagine dilating the rectangle with length & and width w by a factor of k.
7. Write an expression for the area of the dilated rectangle.
8. Use your work to draw a conclusion about what happens to the area of a rectangle when it's dilated by a scale factor of k.
5. The expression fοr the area of a rectangle with length l and width w is l × w.
What is a rectangle?
In Euclidean plane geοmetry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all οf its angles are equal.
5. The area of a rectangle is given by the prοduct of its length and width. Therefore, the expressiοn for the area of a rectangle with length l and width w is:
Area = l x w
6. Imagine dilating the rectangle with length & and width w by a factοr of k.
⇒ (l × k) × (w × k)
7. An expression fοr the area of the dilated rectangle.
⇒ l × w × k²
⇒ k²lw
8. Vοlume = l × w
Volume' = k²lw
Then we have
Volume/Volume' = (l × w)/k²lw
Vk²lw = V'lw
Divide bοth sides by lw
Vk² = V'
Thus, The area ο a rectangle when it's dilated by a scale factor of k will be dilated k² times
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PLEASE EXPLAIN AND SHOW WORK
Correct statements are m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z
What are similar triangles?Similar triangles are triangles that have the same shape but can be of different sizes. All equilateral triangles and squares of any length are examples of similar objects. That is, if two triangles are similar, their corresponding angles are congruent and their corresponding sides have the same proportions. Here, triangle similarity is indicated by the symbol '~'.
Given,
two triangles ABC and DEF
m∠A = m∠D = 40°
m∠B = m∠E = 60°
Sum of all interior angles of a triangle is equal to 180°
m∠A + m∠B + m∠C = m∠D + m∠E + m∠F = 180°
40 + 60 + m∠C = 40 + 60 + m∠F
m∠C = m∠F
All three angles are congruent
By A-A-A rule
ΔABC ~ ΔDEF
ratio of corresponding sides will be equal
6/10 = y/z
3/5 = y/z
Hence, m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z are the correct statement.
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If <1 = <2, can you conclude that any of the lines are parallel?
The correct statement regarding whether there are two parallel lines is given as follows:
C. Yes, lines n and p are parallel because corresponding angles are congruent.
What are corresponding angles?When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and the transversal. Corresponding angles are always congruent, which means that they have the same measure.
The angles in the same position for this problem are given as follows:
1 and 2.
The parallel lines relative to which these two angles are at the same position are given as follows:
n and p.
Hence the correct option is given by option c.
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Help needed, findingin the side lengths of a triangle! ASAP
Answer:
BD = 5√3
AD = 10
CD = 10√3
Step-by-step explanation:
You want the missing side lengths in a right-triangle geometry that shows the hypotenuse divided into lengths 5 and 15 by the altitude.
Geometric mean relationsIn this geometry, all of the right triangles are similar. The similarity proportions can be solved to give three geometric mean relationships:
BD = √(AB·CB) = √(5·15) = 5√3
AD = √(AB·AC) = √(5·20) = 10
CD = √(CB·CA) = √(15·20) = 10√3
__
Additional comment
It can be handy to remember the geometric mean relations. They can be thought of as "each side is equal to the geometric mean of the hypotenuse segments it touches." (Note that touching the end is interpreted as touching the nearest part and the whole.)
For example, the similarity proportion for AD is ...
hypotenuse/(short side)
AD/AB = AC/AD ⇒ AD² = AB·AC ⇒ AD = √(AB·AC)
These are called "geometric mean" relations because the geometric mean of two numbers is the square root of their product.
How do I do this I’ve tried so many times please help
Answer:
100°
Step-by-step explanation:
∠A and ∠B are supplementary angles, which means:
∠A° + ∠B° = 180°
[tex](2x) + (2x + 20) = 180[/tex]
Expand the parenthesis and solve for x:
[tex]2x + 2x + 20 = 180[/tex]
[tex]4x + 20 = 180[/tex]
[tex]4x = 180 - 20[/tex]
[tex]4x = 160[/tex]
[tex]x = \frac{160}{40}[/tex]
∴[tex]x = 40[/tex]
Substitute the value of x to determine the measurement of ∠B:
[tex]2(40) + 20[/tex]
[tex]80 + 20[/tex]
= 100°
Please hurry 20 points and mark brainly.
Answer:
The answer is c 180 miles
Step-by-step explanation:
the exact is 179.8 miles rounded up is 180 mark brainliest pls and your welcome
Suppose that f ( x ) = 7 x − 7 . Complete the following
statements.
As x → 7 − , f ( x ) →
As x → 7 + , f ( x ) →
Based on the calculation we know that
The value of x as 7− is 35.
The value of x as 7+ is 35.
Suppose that f( x ) = 7 x − 7. We can complete the following statements by plugging in the values of x and evaluating the function.
As x → 7 − , f ( x ) → 42 − 7 = 35
As x approaches 7 from the left, the function f(x) approaches 35.
As x → 7 + , f ( x ) → 42 − 7 = 35
As x approaches 7 from the right, the function f(x) also approaches 35.
Therefore, the function f(x) = 7x - 7 has a horizontal asymptote at y = 35 as x approaches 7 from both the left and the right.
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The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
Is the relation a function? Explain.
A. No, because for each input there is not exactly one output
B. No, because for each output there is not exactly one input
C. Yes, because for each input there is exactly one output
D. Yes, because for each output there is exactly one input
No function exists in this relation. No, since there isn't always a single output for every input.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Here, we have
Given: The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
We have to show the relation between a function.
The x-values are entered into the function machine. The function machine generates the y-values after its operations are complete. Any internal function is possible.
A mapping diagram with arrows pointing from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5, as well as two circles with the numbers 0, and labels for the x and y values, respectively
but according to the definition of y, it should give only one value
Hence, it is not a function.
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lify (x3y3)31(32x13y18)312xy32xy2xy32x2x3y534xy2x3y534x
The simplified expression is x^(454)y^(584) * 2^(109).
To simplify the given expression, we need to use the laws of exponents. The laws of exponents are:
- (a^m)^n = a^(mn)
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)
Using these laws, we can simplify the given expression as follows:
(x^3y^3)^31 * (32x^13y^18)^31 / (2xy^3)^2 * (2xy^3)^2 * (2x)^2 * (2x^3y^5)^3 * (4xy)^5 * (2x^3y^5)^3 * (4x)^5
= x^(3*31)y^(3*31) * 32^31x^(13*31)y^(18*31) / 2^2x^2y^(3*2) * 2^2x^2y^(3*2) * 2^2x^2 * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5y^(5*5) * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5
= x^(93)y^(93) * 32^31x^(403)y^(558) / 2^6x^6y^6 * 2^6x^6y^6 * 2^2x^2 * 2^6x^9y^15 * 4^5x^5y^25 * 2^6x^9y^15 * 4^5x^5
= x^(93+403)y^(93+558) * 32^31 / 2^6 * 2^6 * 2^2 * 2^6 * 4^5 * 2^6 * 4^5 * x^(6+6+2+9+5+9+5) * y^(6+6+15+25+15)
= x^(496)y^(651) * 32^31 / 2^(6+6+2+6+6) * 4^(5+5) * x^42 * y^67
= x^(496-42)y^(651-67) * 32^31 / 2^26 * 4^10
= x^(454)y^(584) * 32^31 / 2^26 * 4^10
= x^(454)y^(584) * 2^(5*31) / 2^26 * 2^(2*10)
= x^(454)y^(584) * 2^(155) / 2^(26+20)
= x^(454)y^(584) * 2^(155-46)
= x^(454)y^(584) * 2^(109)
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If the quadrilateral below is a rhombus, find the missing measures. BC=28 BD=32
Find Ef and EC
The measures of EF and EC in the rhombus is as follows:
EC = 8√33 and EF = 4√33.
What do you mean by rhombus?Given that it meets the criteria for a parallelogram—a quadrilateral with two sets of parallel sides—a rhombus can be described as a special parallelogram. A rhombus also has four equal sides, much like a square, which is another feature. For this reason, it is often referred to as a tilted square.
We know that diagonals bisect each other perpendicularly, from the right triangle FED,
we have that:
x² + 16² = 28²
⇒ x² = 784-256
⇒ x = 4√33
Therefore, EF = x = 4√33
Since EC is twice EF, then, EC = 2 × 4√33
= 8√33
Therefore, EC = 8√33 and EF = 4√33.
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The complete question is:
If the quadrilateral below is a rhombus, find the missing measures. BC=28 BD=32
Find Ef and EC