The probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
What is probability ?
Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to happen.
To calculate probability, we usually take the number of favorable outcomes and divide it by the total number of possible outcomes. For example, if we flip a coin, the probability of getting heads is 1/2 because there is only one favorable outcome (heads) out of two possible outcomes (heads or tails).
According to the question:
Let's use Bayes' theorem to find the probability that the ball transferred was red:
Let R be the event that a red ball is drawn from urn B, and T be the event that the transferred ball was red.
Then we want to find P(T = red | R = red).
By Bayes' theorem, we have:
P(T = red | R = red) = P(R = red | T = red) * P(T = red) / P(R = red)
We can calculate each of these probabilities as follows:
P(R = red | T = red): The probability of drawing a red ball from urn B, given that a red ball was transferred from urn A to urn B, is 1/4, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we added one more red ball to it.
P(T = red): The probability that a red ball was transferred from urn A to urn B is 3/10, since urn A originally contained 3 red balls out of 10 total balls and we transferred one ball at random.
P(R = red): The overall probability of drawing a red ball from urn B is:
P(R = red) = P(R = red | T = black) * P(T = black) + P(R = red | T = red) * P(T = red)
where T = black means that a black ball was transferred from urn A to urn B. We can calculate each of these conditional probabilities as follows:
P(R = red | T = black): The probability of drawing a red ball from urn B, given that a black ball was transferred from urn A to urn B, is 1/7, since urn B originally contained 1 red ball out of 7 total balls (3 black, 3 white, and 1 red) and we did not add any more red balls to it.
P(T = black): The probability that a black ball was transferred from urn A to urn B is 4/10, since urn A originally contained 4 black balls out of 10 total balls and we transferred one ball at random.
Therefore, we have:
P(R = red) = 1/7 * 4/10 + 1/4 * 3/10 = 1/35 + 3/40 = 11/140
Putting it all together:
P(T = red | R = red) = (1/4) * (3/10) / (11/140) = 21/55
So the probability that the ball transferred was red, given that a red ball was drawn from urn B, is 21/55, or about 0.382.
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find the t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (d f).
The t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (df) is 1.753050356.
We have to determine the t-value.
The area in the right tail is 0.10 with 32 degrees of freedom(df).
The t-test is a test that is used as an alternative to the z-test in statistics. If the data are normally distributed but the sample size is small and the population standard deviation is unknown, the t-test is utilized.
A value that appears on the t distribution is the critical t value. The area under the curve and the degrees of freedom can be used to determine the t statistic value.
Using Excel Formula,
The t-value = (=TINV(0.1,15))
The t-value = 1.753050356
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given the following two point find the the length distance of ab round your asnwer to the nearrest tenth (-4,-6) and b (3,2)
The length distance of ab between the points (-4,-6) and b (3,2) is 10.6 units.
Now to find the distance between points A(-4,6) and B(3,2), we can use the distance formula which is :
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁)=(-4,-6) and (x₂,y₂)=(3,2), now we substituting the values into the formula after which we get :
d = sqrt((3 - (-4))² + (2 - (-6))²) = sqrt((7)² + (8)²) = sqrt(49 + 64) = sqrt(113) ≈ 10.6
it comes out that the distance between points A and B is approximately 10.6 units which are rounded to the nearest tenth.
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is 2x^2+4=9x real rational and equal
Answer:
76(/783/)-468
Step-by-step explanation:
what percentage of the area under the normal curve lies (a) to the left of m? (b) between m s and m 1 s? (c) between m 3s and m 1 3s
The percentages of the area under curve are 50%, 68%, and 99.7%.
Assuming a standard normal distribution with mean m = 0 and standard deviation s = 1, the percentage of the area under the curve can be determined as follows
To the left of m: This is equivalent to finding the area to the left of the z-score corresponding to m = 0. This is 50%, as the normal distribution is symmetric around the mean.
Between m s and m 1 s: This is equivalent to finding the area between the z-scores corresponding to z = -1 and z = 1. Using a standard normal distribution table or calculator, this is approximately 68% (which is also known as the 68-95-99.7 rule).
Between m 3s and m 1 3s: This is equivalent to finding the area between the z-scores corresponding to z = -3 and z = 3. Using a standard normal distribution table or calculator, this is approximately 99.7% (which is also known as the 68-95-99.7 rule).
Therefore, the percentages of the area under the normal curve are: (a) 50%, (b) 68%, and (c) 99.7%.
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how do you solve this? (-3a+56)+(5a+40)
Answer:To simplify the expression, you need to combine the like terms, which are the terms that have the same variable and power. In this case, the like terms are -3a and 5a:
(-3a + 56) + (5a + 40)
= (-3a + 5a) + (56 + 40)
= 2a + 96
Therefore, the simplified expression is 2a + 96.
Enjoy (:
Step-by-step explanation:
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table.
In response to the stated question, we may state that As a result, the overall probability of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
What is probability?Probability theory is an area of mathematics that calculates the likelihood of an occurrence or a proposition being true. A risk is a number in the range of 0 and 1, whereas 1 implies certainty and a probability of roughly 0 indicates how likely an event seems to be to occur. Probability is a mathematical expression of the chance or chances that a given event will occur. Probabilities can alternatively be stated as integers between 0 and 1 or as % from 0% to 100%. the ratio of occurrences among equally likely choices that result in a certain event in comparison to all other outcomes.
Using the data in the table, we can compute the likelihood of a correct drive-thru order for each fast food chain, as well as the overall chance of an accurate order across all chains.
Divide the number of accurate orders by the total number of orders to find the chance of a randomly picked order being accurate at each chain:
P(accurate order) = 1246 / 1300 = 0.958 for McDonald's
P(accurate order) = 1020 / 1100 = 0.927 Taco Bell
P(accurate order) = 708 / 800 = 0.885 for Burger King
P(accurate order) = 940 / 1000 = 0.94 for Wendy's
P(adequate overall order) = 0.3 * 0.958 + 0.25 * 0.927 + 0.2 * 0.885 + 0.25 * 0.94 = 0.929
As a result, the overall likelihood of an accurately picked drive-thru order across all chains is roughly 0.929, or 92.9%.
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2.5 Hence determine the total area of all the faces in mm²
2.6 Hence, determine the volume of the container in m³
Hint: The volume of the is container is determined by multiplying the area of
the base of the container by the height of the container.
Answer:
Step-by-step explanation:
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A person invests 5500 dollars in a bank. The bank pays 4.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 6700 dollars?
Answer:
Step-by-step explanation:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
In this case, we know that P = $5500, r = 4.5% = 0.045, and we want to find t when A = $6700. We also know that the interest is compounded annually, so n = 1.
Substituting these values into the formula, we get:
$6700 = $5500(1 + 0.045/1)^(1t)
Dividing both sides by $5500, we get:
1.218181818 = (1.045)^t
Taking the natural logarithm of both sides, we get:
ln(1.218181818) = ln(1.045)^t
Using the property of logarithms that ln(a^b) = b ln(a), we can rewrite the right side as:
ln(1.218181818) = t ln(1.045)
Dividing both sides by ln(1.045), we get:
t = ln(1.218181818)/ln(1.045) ≈ 4.2
Therefore, the person must leave the money in the bank for about 4.2 years to reach $6700. To the nearest tenth of a year, the answer is 4.2 years.
FILL IN THE BLANK the probability of one event given the known outcome of a (possibly) related event is known as __probability.
The probability of one event given the known outcome of a (possibly) related event is known as conditional probability.
Conditional probability is the measure of the probability of an event occurring given that the another event will already occurred. It is denoted by P(A | B), which represents the probability of event A given that event B has occurred. The conditional probability of A given B can be calculated using the formula:
P(A | B)=P(A and B)/P(B)
where P(A and B) represents the probability of both events A and B occurring, and P(B) represents the probability of event B occurring.
For example, consider a deck of 52 playing cards. The probability of drawing a king from the deck is 4/52, or 1/13. If one card is drawn from the deck and it is revealed to be a heart, then the probability of drawing a king from the remaining cards in the deck that are not hearts is:
P(king | heart) = P(king and heart) / P(heart)
P(king and heart) = 1/52 (there is only one king of hearts in the deck)
P(heart) = 13/52 (there are 13 hearts in the deck)
P(king | heart) = (1/52) / (13/52) = 1/13
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Increase R68 in the ratio of 7:4
I need someone to help me find the h of the parallelogram.
The value of height (h) will be 6 cm.
What is Parallelogram?
A parallelogram is a four-sided polygon in which both pairs of opposite sides are parallel and equal in length. It is a special case of a quadrilateral, which means a polygon with four sides. The opposite angles in a parallelogram are also equal in measure, and the adjacent angles are supplementary, which means they add up to 180 degrees.
Given : height (H) = 5 cm
base (B) = 12 cm
Similarly, height (h) = 5 cm
base (h) = 12 cm
Now, we know that area of parallelogram will be same whether we use different method.
So, area of given parallelogram = base × height
B × H = b × h
12 × 5 = 10 × h
60 = 10 h
So, h = 60/10 = 6 cm.
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Mrs Devi bought banana cakes and marble cakes for a party. She spent $112 on the cakes. Each
piece of banana cakes cost $2.50 and the cost of each piece of marble cake was 7/5 the cost of
each piece of banana cake. 30% of what she bought were marble cakes. How many pieces of
cake did Mrs Devi buy?
In linear equation, 28 pieces of cake did Mrs Devi buy.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Cost of M cake = $3.5
For every 3 M cakes she bought 7 B cakes.
Let 1 unit be 3 M cakes and 7 B cakes. 1 unit costs= 3(3.5) + 7(2.5)= $28
She bought $112 / $28 = 4 units of cakes.
Which means 12 M cakes and 28 B cakes.
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Express using algebra:
Z increased by 16%
Answer:
Let's start by expressing "Z increased by 16%" using algebra.
Let Z be the original value of some quantity.
To increase Z by 16%, we need to add 16% of Z to Z:
Z + 0.16Z
Simplifying this expression by factoring out Z, we get:
Z(1 + 0.16)
Combining like terms, we have:
Z(1.16)
Therefore, "Z increased by 16%" can be expressed algebraically as:
Z increased by 16% = Z(1.16)
Answer:
z(1.16)
Step-by-step explanation:
I cannot figure out these angles. help please
The angles for the given parallel lines are estimated.
m(∠DGF ) = 92; m(∠HGF ) = 88; m(∠AGD ) = 88; m(∠BDG ) = 92; m(∠BDC ) = 88; m(∠CDE ) = 92 ; m(∠EDG ) = 88.
Explain about the transversal?A line that cuts over two parallel lines is referred to as a transversal line.
Each pair of internal angles located on the exact side of a transversal that meets two parallel lines is supplementary, or they add up to 180°.
The opposing angles created by the junction of two lines are known as vertical angles but rather vertically opposite angles.
m(∠AGH ) = m(∠BDG ) (corresponding angles)
3x + 2 = 2x + 32
x = 30
m(∠AGH ) = 3(30) + 2 = 92
m(∠BDG ) = 2(30) + 32 = 92
m(∠DGF ) = m(∠AGH ) = 92 (vertically opposite angles)
m(∠HGF ) = 180 - m(∠AGH ) = 180 - 92 = 88 (linear pair).
m(∠AGD ) = m(∠HGF ) = 88 (vertically opposite angles)
m(∠BDG ) = 92 (calculated earlier)
m(∠BDC ) = m(∠AGD ) = 88 (corresponding angles)
m(∠CDE ) = m(∠BDG ) = 92 (vertically opposite angles)
m(∠EDG ) = m(∠BDC ) = 88 (vertically opposite angles).
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You are playing a game with a friend. It costs you $2 to play. If you roll a 1 on a 6-sided die you win $4. If you roll a 2, 3, 4, 5, or 6 you win nothing and lose $2 the cost to play. Calculate the expected value for this game. How much should the player be willing to to pay to play this game and not lose money in the long run?
The player should be willing to pay up to $12 to play this game and not lose money in the long run.
How to calculate the expected value for this game.
First we need to multiply the probability of winning by the amount won and subtract the probability of losing by the amount lost.
The probability of rolling a 1 on a 6-sided die is 1/6, and the probability of rolling any other number is 5/6.
So, the expected value of the game is:
(1/6) x $4 - (5/6) x $2
= ($4/6) - ($10/6)
= -$1/3
This means that on average, for every game played, the player can expect to lose $1/3.
To find out how much the player should be willing to pay to play this game and not lose money in the long run, we can set the expected value equal to zero:
(1/6) x $4 - (5/6) x $2 = $0
Simplifying the equation, we get:
$4/6 = $10/6
Multiplying both sides by x, we get:
(1/6) x - $2 = 0
Solving for x, we get:
x = $12
Therefore, the player should be willing to pay up to $12 to play this game and not lose money in the long run.
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Determine the equation of the ellipse with foci (-8,14) and (-8,-16), and co-vertices (0,-1) and (-16,-1).
According to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
What is co-ordinate geometry ?Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric shapes using algebraic principles. It involves the use of coordinates to represent points, lines, curves, and other geometric figures on a plane or in space.
According to the given information:we need to know the coordinates of its foci, co-vertices, and the center. We can start by finding the center of the ellipse, which is the midpoint of the line segment joining the foci:
Center = ( (-8 + (-8))/2 , (14 + (-16))/2 ) = (-8,-1)
Next, we can find the distance between the foci, which is given by:
[tex]distance between foci = 2c = sqrt[(14 - (-16))^2 + (-8 - (-8))^2] = 30[/tex]
where c is the distance from the center to either focus.
We also know that the distance between the co-vertices is given by:
distance between co-vertices = 2a = |-16 - 0| = 16
where a is the distance from the center to either co-vertex.
Finally, we can use the standard form equation for an ellipse centered at the origin:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
where b is the distance from the center to either vertex.
To find b, we can use the Pythagorean theorem:
[tex]b^2 = c^2 - a^2 \\b^2 = 30^2 - 16^2\\b^2 = 784\\b = 28[/tex]
Now we have all the information we need to write the equation of the ellipse:
[tex](x+8)^2/16^2 + (y+1)^2/28^2 = 1[/tex]
Therefore, according to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
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A scale drawing of a building needs to be made using the scale 1 in = 170 ft How tall will the building in the scale drawing be if the building is 850 ft tall?
The height of the building in the scale drawing will be 5 inches.
The scale ratio must be used to determine the height of the building in the scale drawing.
The scale ratio is:
1 inch = 170 feet
We can devise a ratio:
1 inch / 170 feet = x inches / 850 feet
In the scale drawing, x represents the height of the building in inches.
To find x, we can cross-multiply and simplify:
1 inch * 850 feet = 170 feet * x inches
850 inches = 170 feet * x
Dividing both sides by 170 yields:
x = 850 inches / 170 = 5 inches
As a result, the building's height will be 5 inches in the scale drawing.
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PLEASE HELP ! I NEED THIS ANSWER! DUE TODAY!!
Use the figure below to answer the questions
From the figure 1. Two line segments are LA and EP. 2. Two rays are EC and AH. 3. Two lines are b and AP.
What are rays, line segment and line?A ray is a segment of a line with a single endpoint and unlimited length in a single direction. A ray cannot be measured in terms of length.
The ends of a line segment are two. These endpoints are included, along with every point on the line that connects them. A segment's length can be measured, while a line's length cannot.
A line is a collection of points that extends in two opposing directions and is endlessly long and thin.
From the given figure we observe that,
1. Two line segments are LA and EP.
2. Two rays are EC and AH.
3. Two lines are b and AP.
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Question about equations, please help!
Answer:
(a) y = 0.80x + 50
(b) Plugging x = 5 into the equation from part (a), we get y = 0.80(5) + 50 = 54, so the ordered pair associated with x = 5 is (5, 54). This means that if the car is driven for 5 miles, the total charge to the renter is $54.
(c) Let y be the total charge and solve for x:
y = 0.80x + 50
187.60 = 0.80x + 50
137.60 = 0.80x
x ≈ 172
Therefore, the car must have been driven approximately 172 miles
Answer:
(a) y = 0.8x + 50
(b) D. The ordered pair associated with the equation x = 5 is (5, 54) and it means that the charge for driving the car for 5 miles is $54.
(c) If the renter paid $187.60, the car must have been driven for 172 miles.
Step-by-step explanation:
Part (a)In the given problem, we are told that the rental car costs a flat fee of $50 plus an additional charge of $0.80 per mile driven.
Let x be the number of miles driven.
Let y be the total charge to the renter (in dollars).
We know that the total charge y will depend on the number of miles driven x, and we can express this relationship using a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the value of y when x = 0).
In this case, we know that the cost per mile is $0.80 so the slope of the line is m = 0.8, and the flat fee is $50 so the y-intercept is b = 50.
Substitute these values into the equation to get:
[tex]y = 0.8x + 50[/tex]
[tex]\hrulefill[/tex]
Part (b)To find the ordered pair associated with x = 5, substitute x = 5 into the equation:
[tex]\begin{aligned}x=5\implies y &= 0.8(5) + 50\\&=4+54\\&=54\end{aligned}[/tex]
The ordered pair associated with the equation x = 5 is (5, 54) and it means that the charge for driving the car for 5 miles is $54.
[tex]\hrulefill[/tex]
Part (c)To find how many miles the car was driven if the renter paid $187.60, set y = 187.60 and solve for x:
[tex]\begin{aligned}\implies 0.8x + 50&=187.60\\0.8x + 50-50&=187.60-50\\0.8x&=137.60\\\dfrac{0.8x}{0.8}&=\dfrac{137.60}{0.8}\\x &= 172\end{aligned}[/tex]
Therefore, if the renter paid $187.60, the car must have been driven for 172 miles.
A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 0.5 inches.
If one item is chosen at random, what is the probability that it is less than 4.6 inches long?
Answer:
Step-by-step explanation:
To solve this problem, we will use the properties of the normal distribution and standardize the given value using the formula:
z = (x - μ) / σ
where:
x = 4.6 inches (the given value)
μ = 5 inches (the mean)
σ = 0.5 inches (the standard deviation)
So we have:
z = (4.6 - 5) / 0.5
z = -0.8
Now we need to find the probability that the standardized value is less than -0.8. We can use a standard normal distribution table or a calculator to find this probability.
Using a standard normal distribution table, we can look up the probability for z = -0.8, which is 0.2119.
Therefore, the probability that a randomly chosen item is less than 4.6 inches long is 0.2119 or approximately 21.19%.
who is the first 6 millionth person to die
Answer: Beth Blauer
Step-by-step explanation:
The pulse rate of the male population is known to be normal, with a mean of 73 BPM and a standard deviation of 11.3. Find the sample size necessary to be within 2 BPM of the population mean with 95% confidence.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P67, the 67-percentile. This is the temperature reading separating the bottom 67% from the top 33%.
P67 =
°C
Answer:
Step-by-step explanation:
To find the temperature corresponding to the 67th percentile, we need to find the z-score that has an area of 0.67 to the left of it in the standard normal distribution. We can use a table or a calculator to find this z-score.
Using a standard normal distribution table, we can look up the value that corresponds to an area of 0.67 to the left of the mean, which is 0.44. This means that P(Z ≤ 0.44) = 0.67, where Z is the standard normal random variable.
Next, we can use the formula for standardizing a normal random variable to convert this z-score to the corresponding temperature on the thermometer scale:
z = (x - μ) / σ
where μ is the mean, σ is the standard deviation, and x is the temperature we want to find.
Rearranging this formula, we get:
x = μ + z * σ
Plugging in the values, we get:
x = 0 + 0.44 * 1.00
x = 0.44
Therefore, the temperature corresponding to the 67th percentile is 0.44°C.
4 x 1 1/5= multiply. Write the product as a mixed number.
Need help answering all 3 of these please anyone
a. The slope of AB is [tex]m = 1[/tex] and slope of BC is [tex]m = -4/7.[/tex]
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. The mid-point of Diagonal AC is [tex](0, -1/2)[/tex]
What are the Quadrilaterals?A clοsed shape nοted fοr having sides with variοus widths and lengths is a quadrilateral. It is a clοsed, two-dimensional pοlygοn with fοur sides, fοur angles, and fοur vertices. Quadrilaterals include the trapezium, parallelοgram, rectangle, square, rhοmbus, and kite, amοng οthers.
a.
Slope is given by
[tex]A = (-2, 3) and B = (-5, 0)[/tex]
[tex]m = 1[/tex]
[tex]B = (-5, 0) and C = (2, -4)[/tex]
[tex]m = -4/7[/tex]
Thus, The slope of AB is m = 1 and slope of BC is [tex]m = -4/7[/tex] .
b. The best name for this quadrilateral would be a rectangle ABCD, as opposite sides and all angles are equal.
c. Midpoint of a segment is given by the 2 divided by of sum x and and sum of y
Thus, Diagonal [tex]A = (-2, 3)[/tex] and [tex]C = (2, -4)[/tex]
Midpoint [tex]= ((-2 + 2), (3 + -4))[/tex]
[tex]= ((0), (-1))[/tex]
Now divide them by 2
[tex]= ((0/2), (-1/2))[/tex]
[tex]= (0, -1/2)[/tex]
Therefore, the mid-point of Diagonal [tex]AC is (0, -1/2)[/tex]
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What is the slope of the line passing through the points (-1, -7) and (-9, -2)?
Answer:
m = -5/8
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-1, -7) (-9, -2)
We see the y increase by 5 and the x decrease by 8, so the slope is
m = -5/8
Write the equation of the circle centered at (4,-1) that passes through (13,8).
Answer:
[tex](x-4)^2+(y+1)^2=162[/tex]
Step-by-step explanation:
Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):
[tex](x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\[/tex]
Hence, the equation of the circle that meets these criteria is[tex](x-4)^2+(y+1)^2=162[/tex]
can you help me to solve this question?
By finding the derivative and evaluating it in x = -2, we will see that the slope is 12.
How to find the slope of the function at the given point?To find the slope of the tangent line at a given point, we need to take the derivative and evaluate it in the x-value of the given point.
Here we have the function:
f(x) = 3x² + 7
If we differentiate it with respect to x, we will get:
f'(x) = 2·3x
f'(x) = 6x
That is the derivative, now we want to find the slope at (-2, 19), to find the slope at that point we need to get:
f'(-2) = 6·-2
f'(-2) = -12
That is the slope of the graph.
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If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2
In response to the stated question, we may state that According to the inequality facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is: B. g > 1.5
What is inequality?In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.
We know that h > 3 and h - 2g = 0.
When we plug h = 2g into the first inequality, we get:
2g > 3
g > 1.5
As a result, we know that g must be bigger than 1.5, ruling out alternatives C and D.
Option A is not certainly true since we don't know if the value of g is bigger than 2.5.
Option E is also not certainly true, because we only know that g is more than 1.5, but not if it is bigger than 2.
According to the facts provided, the only choice that must be true is B, because g must be bigger than 1.5. As a result, the solution is:
B. g > 1.5
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If F1 = 4y - 6, F2 = 9y + 3 and F3 = -y - 8, simplify F1 × F2 - F3 in terms of y.
Answer:
To simplify F1 × F2 - F3 in terms of y, we need to first find the product of F1 and F2, and then subtract F3.
F1 × F2 can be expanded using the distributive property:
F1 × F2 = (4y - 6) × (9y + 3) = 4y × 9y + 4y × 3 - 6 × 9y - 6 × 3
= 36y^2 + 12y - 54y - 18
= 36y^2 - 42y - 18
Now we can subtract F3 from the result:
F1 × F2 - F3 = (36y^2 - 42y - 18) - (-y - 8)
= 36y^2 - 42y - 18 + y + 8
= 36y^2 - 41y - 10
Therefore, F1 × F2 - F3 in terms of y is 36y^2 - 41y - 10.
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