if 5x² +5x+xy=4 then the value of y'(4) is -21/4
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given expression is 5x² +5x+xy=4
Five times of x square plus five times of x plus x times of y equal to four.
Differentiate with respect to x.
10x+5+y(x)+xy'(x)
if x=4
10(4)+5+y(4)+4y'(4)=0
40+5-24+4y'(4)=0
21+4y'(4)=0
4y'(4)=-21
Divide both sides by 4
y'(4)=-21/4
Hence, if 5x² +5x+xy=4 then the value of y'(4) is -21/4
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For what value of n is the polynomial x^3 - 9x^2 + nx - 12 divisible by x - 3? Show work.
Answer:
B
Step-by-step explanation:
if a polynomial f(x) is divisible by (x - a) , then f(a) = 0
for the polynomial to be divisible by (x - 3) then the polynomial will equal zero when x = 3 , that is
3³ - 9(3)² + 3n - 12 = 0
27 - 9(9) + 3n - 12 = 0
27 - 81 + 3n - 12 = 0
3n - 66 = 0 ( add 66 to both sides )
3n = 66 ( divide both sides by 3 )
n = 22
what is (-5,-3) reflected over the Y axis
The point (-5,-3) reflected over the y-axis is (5, -3).
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
(-5, -3)
Along y-axis:
(x, y) → (-x, y)
So,
(-5, -3) → (-(-5), -3) = (5, -3)
Thus,
(5, -3) is the reflected point.
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9.03 divided by 0.15
9.03 divided by 0.15 is equal to 60.2.
What do you know about division?The opposite of multiplication in arithmetic is called division. It's used to determine how many times one quantity is contained inside another. Division is done by dividing the dividend by the divisor, which can be done visually by using the division sign () or a fraction bar (/). The quotient, which shows how many times the dividend can be divided by the divisor, is the operation's output. For instance, if you split up eight apples into four equally sized pieces, each piece would contain two apples. This division is denoted by the equation 8/4 = 2, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.
The division of 9.03 by 0.15 can be calculated as follows:
9.03 ÷ 0.15 = 9.03 / 0.15
= 60.2
So, 9.03 divided by 0.15 is equal to 60.2.
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according to the histogram, which range of length (in inches) contains the longest sampled eastern diamondback rattlesnake?
According to the histogram 87.5 - 90.5 range of length (in inches) contains the longest sampled eastern diamondback rattlesnake.
In statistics, a histogram is a graphic representation of data distribution. Each bar in the histogram represents a different type of data, and the histogram is displayed as a group of adjacent rectangles. Statistics is a discipline of mathematics that is used in many different fields.
Frequency, which may be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data. One type of graph that can be used to illustrate a frequency distribution visually is a histogram.
The range of a histogram is the x-axis breadth that the bars cover. Since histograms show bin values rather than actual data values, these numbers are approximations.
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Complete question:
Question According to the histogram, which range of length (in inches) contains the longest sampled Eastern diamondback rattlesnake? Provide your answer below: greater than but less than
HEEELP MEE!!
The population of a colony started with 1,120 grows at an annual rate of 4.98%. How much more would you have, at the same time if you used continuous growth, compared to a growth rate when the continuous reaches 3,480?
The time that is taken by the colony is 23 years.
What is the time taken for the growth?The exponential growth function can be used to account for the exponential increase in the number of the organisms that are to be found in the colony.
Given that we have that;
P=Poe^rt
P = Number at time t
Po = Number initially present
r = rate of growth
t = time taken
Thus;
3480 = 1120e^0.0498t
3480/1120 = e^0.0498t
3.1 = e^0.0498t
ln(3.1) = 0.0498t
t = ln3.1/0.0498
t = 23 years
There are 23 years
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Ernie scores 50 points in Level 1 of a video game.
In each subsequent level, he scores twice as many
points as he did in the previous level.
The Formula is [tex]a_n[/tex]= 50 ([tex]2^{n-1[/tex] ).
What is Sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite).
Given:
Ernie scores 50 points in Level 1 of a video game.
After II level the points would be
50 x 2 = 100
Then, after III level the points would be
100 x 2 = 200
So, the Recursive formula for the situation is
[tex]a_n[/tex]= a [tex]r^{n-1[/tex] where r is common ratio = 100/50 = 2
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The women’s basketball team played 30 home games and won 1/2 of them. They also won 2/3 of their 42 away games. How many games did they win?
Answer:
43 games
Step-by-step explanation:
The number of home games won by the women’s basketball team is 30 * 1/2 = 15.
The number of away games won by the women's basketball team is 42 * 2/3 = 28.
Therefore, the total number of games won by the team is 15 + 28 = 43.
On the last three physics exams a student scored 84, 87, and 92. What score must the student earn on the next exam to have an average of at least 90?
The student must score at least %.
(Simplify your answer. Type an integer or a decimal.)
The student must score the marks which should be ≥ 97
What is average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
Let x be the marks need to be scored in the next exam
Average = sum of marks/ number of exams
Given: score must the student earn on the next exam to have an average of at least 90
This means,
Average ≥ 90
sum of marks/ number of exams ≥ 90
( 84+ 87 +92+x)/4 ≥ 90
(263+x)/4 ≥ 90
=> 263+x ≥ (90 * 4)
=> 263+x ≥ 360
=> x ≥ 360 - 263
=> x ≥ 97
The student must score the marks which should be ≥ 97
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What is the surface area of a sphere with radius 8? Use 3.14 for pi and round your answer to the nearest hundredth if necessary.
Answer:
The formula for the surface area of a sphere with radius r is 4πr^2. Plugging in the given radius of 8, we get:
Surface area = 4π * 8^2 = 4π * 64 = 256π
Using an approximate value of π = 3.14, the surface area of the sphere is approximately:
256 * 3.14 = 803.84
Rounding to the nearest hundredth, the surface area of the sphere is approximately 803.84 square units.
Answer:
803.84cm²
SolutionArea of a sphere = 4πr²
When we put the given values we get
Area of a sphere = 4x3.14x8²
Area of a sphere = 4x3.14X16
= 804.25cm²
Rounding to the nearest hundredth we get,
803.84cm²
Please help me. A cone has a volume of 350 cubic meters. The area base is 70 square meters. What is the height of the cone?
On solving the provided question we can say that Area of the base = [tex]pi*r^2 = 70[/tex] => 350 (3/70) = h = 15 m
What is area?The size of an area on a surface can be expressed as an area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a planar region or planar region refers to the area of a form or planar layer. The total amount of space filled by a planar (2-D) surface or shape of an object is known as its area. Draw a square on a piece of paper using a pencil. a character with two dimensions. The area of a shape on paper is the space it takes up. Imagine that the square is composed of more compact unit squares.
[tex]pi * r^2 * h / 3[/tex]
Area of the base = [tex]pi*r^2 = 70[/tex]
350 = 70 * h / 3
350 = (70/3) * h
350 (3/70) = h = 15 m
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HELP PLEASE.
Write the following sentence as an equation. Use x to represent "a number."
A number subtracted from 18 amounts to 107.
The equation is
-
*** HELP
Answer:
-18 - x = 107
Step-by-step explanation:
Find f(x) if f is a linear function such that f(6)=4 and f(−5)=−6 .
Answer:
f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]
Step-by-step explanation:
The format of the linear function f(x) is ax + b. Thus, we can list the following equations:
4 = 6a + b .... (1)
-6 = -5a + b .... (2)
We can use the first equation to subtract the second equation getting: 10 = 11a. This means a = [tex]\frac{10}{11}[/tex]. From that, if we plug in the value of a into the first equation, we get 4 = [tex]\frac{60}{11}[/tex] + b, so b = [tex]-\frac{16}{11}[/tex]. Thus, f(x) =[tex]\frac{10}{11}[/tex]x [tex]-\frac{16}{11}[/tex]
CAN SOMEONE HELP WITH THESE QUESTIONS?
Answer:
Graphed line is shown below
Step-by-step explanation:
m = 1/3, (-3, 3)
y - y1 = m (x - x1)
y - 3 = 1/3 (x + 3)
y - 3 = (1/3)x + 1
y = (1/3)x + 4
Step by step please, need help. Good luck and thank you for your help
Angle of triangle AFC is 37°
What is an angle?An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.
From the given figure consider ABCF as trapezium,
Given that angle of triangle BCF is 37°
Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°
Therefore, ∠BCF + ∠CBF = 180°
⇒∠B = 180° - 37°⇒143°
Similarly ∠A = ∠B = 143°
⇒∠A+∠F=180°
⇒∠F=180°-143° ⇒ 37°
Hence, m∠AFC = 37°.
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You are given a coin. You do not know if it is a fair coin or not.
You want to figure out a way so that you can make a sound statement about the fairness of the coin.
One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails.
Describe probability in coin sample?Probability is a measure of the likelihood of an event occurring. In the context of a coin flip, the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes.
For a fair coin, the two possible outcomes are heads (H) and tails (T). The probability of getting heads or tails in a single coin flip is equal to 1/2, or 50%. This means that if you flip a fair coin 100 times, you would expect to get approximately 50 heads and 50 tails.
It's important to note that probability is a theoretical concept, and the actual outcome of a coin flip can never be predicted with 100% certainty. However, the law of large numbers states that as the number of coin flips increases, the ratio of heads to tails will approach the theoretical probability.
The concept of probability can also be applied to more complex events involving multiple coin flips. For example, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4, or 25%. The probability of any specific sequence of heads and tails can be calculated using the same method.
One way to figure out the fairness of the coin is to conduct a large number of coin flips and record the number of heads and tails. Then, calculate the proportion of heads and compare it to 0.5, which is the expected proportion for a fair coin. The larger the sample size, the more confident you can be in your conclusion about the fairness of the coin. If the proportion of heads is close to 0.5, it is likely that the coin is fair. If the proportion deviates significantly from 0.5, it is likely that the coin is not fair. It's also important to use a rigorous statistical method to test the hypothesis of fairness, such as a one-sample proportion test, to account for random fluctuations in the results.
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2. The mean incubation time of fertilized chicken eggs kept in an incubator is 21.3 days. Suppose that the incubation times are normally distributed and the standard deviation is 1.1 days. (4 pts)
Mean = 21.3
Sd= 1.1
a. What is the 22nd percentile for incubation times of chicken eggs? (2 pts)
b. Determine the two incubation times that mark off the middle (center) 95% of fertilized chicken eggs. (2 pts)
a) The 22nd percentile for incubation times of chicken eggs is of: 20.5 days.
b) The middle 95% of incubation times is in this following interval: (19.1, 23.5) days.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for this problem are given as follows:
[tex]\mu = 21.3, \sigma = 1.1[/tex]
The 22nd percentile is the value of X when Z has a p-value of 0.22, hence X when Z = -0.77, thus:
-0.77 = (X - 21.3)/1.1
X - 21.3 = -0.77 x 1.1
X = 20.5 days.
The middle 95% of incubation times is obtained from X when Z = -1.96(2.5th percentile) to X when Z = 1.96(97.5th percentile), hence:
-1.96 = (X - 21.3)/1.1
X - 21.3 = -1.96 x 1.1
X = 19.1 days.
1.96 = (X - 21.3)/1.1
X - 21.3 = 1.96 x 1.1
X = 23.5 days.
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=
Use the Percentiles flow chart interactive to answer the following question.
When finding the 35th percentile from a sample of 200 IQ scores, the locator L is found to be 80. What is the value of the 35th percentile?
Choose the correct answer below.
OA. The 80th IQ score in the sorted list
OB. The IQ score that is midway between the 35th and 36th scores in the sorted list.
OC. The IQ score that is midway between the 80th and 81st scores in the sorted list.
OD. The 35th IQ score in the sorted list
Next
C. An IQ score of 80 is more unusual than an IQ score of 120
is the false answer
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).
For P<90
Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.
For 90<P<110
then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.
therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.
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Find the degree of this polynomial.
K4
The degree of this polynomial is 4.
What is the polynomial?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using only addition, subtraction, and multiplication. Polynomials can have constants (numbers), variables (letters), and exponents (powers). A polynomial is named after the degree of its highest-degree term, with the degree being the exponent of the variable.
The degree of a polynomial is the highest exponent in the polynomial. In this case, the polynomial is "K4," which has only one term.
The degree of this polynomial is 4.
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4r^2+3s^2-rs r=-1 S=3
Need help with steps because everyone keeps saying it’s 26 but I get 28
Answer:
34
Step-by-step explanation:
4r² + 3s² - rs ← substitute r = - 1, s = 3 into the expression
= 4(- 1)² + 3(3)² - (- 1)(3)
= 4(1) + 3(9) - (- 3)
= 4 + 27 + 3
= 34
Tony, Hans, and Dante made flyers last Wednesday. The table below shows the number of flyers each person made and how much time each person spent.
Write the time spent per flyer for each person. Then determine who worked the fastest.
Among Tony, Hans and Dante, Dante made flyers the fastest and he took least time to do the work of making flyers.
What do we mean by time and work?Time and work deals with the time it takes an individual or group to complete a task and the efficiency of the work they do.
According to the information given in the question:
Tony made 8 flyers in 64 minutes
Hans made 3 flyers in 21 minutes
Dante made 6 flyers in 30 minutes
By observing, it says
Tony took 8 minutes to make 1 flyer
Hans took 7 minutes to make 1 flyer
Dante took 5 minutes to make 1 flyer
Hence, it can be concluded by time and work relationship that Dante was the fastest among the three competitors.
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The bag contains 20 red marbles, 30 white marbles, and 40 blue
marbles.
a. What is the ratio of red to blue marbles?
b. What is the ratio of white to red marbles?
c. If one marble is drawn from the bag, what is the probability that
marble will not be white?
When the product of 1 and 1 in subtroter fire no
of 1 and 1
a) The ratio of red to blue marbles is 1:2.
b) The ratio of white to red marbles is 3:2.
c) The probability of drawing a white marble from the bag is 33%.
What is the ratio?The ratio is the relative size of a value compared to another.
Ratios show the quantity of one variable contained in a larger variable.
On the other hand, the probability is the odds or likelihood that an expected outcome occurs given many possible outcomes.
Both ratios and probabilities can be expressed in fractions, decimals, and percentages because they are fractional values.
The number of red marbles in the bag = 20
The number of white marbles in the bag = 30
The number of blue marbles in the bag = 40
The total number of marbles in the bag = 90
a) The ratio of red to blue marbles = 20:40 = 1:2
b) The ratio of white to red marbles = 30:20 = 3:2
The sum of ratios of all marbles = 9 (2:3:4)
c) The probability of drawing a white marble from the bag = 3/9 = 0.33 or 33%
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substitute 4 for x and evaluate the expression below. (x-3)+4
Answer:
5
Step-by-step explanation:
First we do the equation in parathesis
4 - 3 = 1
Now we add 4.
1 + 4 = 5
Answer:
5
Step-by-step explanation:
(x - 3) + 4
(4 - 3) + 4
1 + 4
5
Two trains, Train A and Train B, weigh a total of 147 tons. Train A is heavier than Train B. The difference of their weights is 65 tons. What is the weight of each train?
Answer:
A: 106 tonsB: 41 tonsStep-by-step explanation:
Given trains A and B have weights that total 147 tons, with train A being heavier by 65 tons, you want the weight of each.
Sum and DifferenceThe relations given in the problem can be expressed as ...
A + B = 147 . . . . . . the total weight
A - B = 65 . . . . . . . the difference of weights (A is heavier)
SolutionThe equations can be added to eliminate the B variable:
(A +B) +(A -B) = (147) +(65)
2A = 212 . . . . simplify
A = 106 . . . . . divide by 2
The other weight can be found any number of ways. One way is to subtract the difference here:
B = A -65 = 106 -65 = 41
Train A weighs 106 tons; train B weighs 41 tons.
__
Additional comment
You will see "sum and difference" problems in many forms. The solution is always the same: the greater value is half the sum of the given numbers; the lesser value is half their difference.
A = (147 +65)/2 = 212/2 = 106
B = (147 -65)/2 = 82/2 = 41
Evaluate −2x+17 when x=−8.
. The x-intercepts of y = f(x) are -1, 3, and 6. Find the x-intercepts of
(a)y = f(2x)
(b) y = 2f(x)
(c) y = f(x + 2)
Compare the appearance of each graph to the appearance of the graph y = f(x).
(d)y = f(mx)
(A) the x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.
(B) the x-intercepts of y = 2f(x) are 1, 3, and 6.
(C) the x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.
How did we get the values?(a) To find the x-intercepts of y = f(2x), we need to find the values of x for which f(2x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(2x) are (-1)/2, 3/2, and 6/2.
(b) To find the x-intercepts of y = 2f(x), we need to find the values of x for which 2f(x) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the x-intercepts of y = 2f(x) are the same: -1, 3, and 6.
(c) To find the x-intercepts of y = f(x + 2), we need to find the values of x for which f(x + 2) = 0. Since x-intercepts of y = f(x) are -1, 3, and 6, the corresponding x-intercepts of y = f(x + 2) are (-1 - 2), (3 - 2), and (6 - 2), which are -3, 1, and 4.
(d) The appearance of y = f(mx) will be a compression or expansion of the graph of y = f(x), depending on the value of m. If m < 1, the graph of y = f(mx) will be a compression of the graph of y = f(x) along the x-axis. If m > 1, the graph of y = f(mx) will be an expansion of the graph of y = f(x) along the x-axis. The x-intercepts of y = f(mx) can be found by finding the values of x for which f(mx) = 0.
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uppose the number of goals scored per game in an under 14 boys indoor soccer league follows a Poisson distribution with 3.3 goals per game. Define x as the number of goals scored in a game. You will answer questions concerning the probabilities of different values of x in this sample Excel spreadsheet: A B 1 P(x = 2) =POISSON.DIST(2,3.3, FALSE) 2 P(x = 5) 3 P(x > 3)
A excel spreadsheet computes likelihood of various upsides of objectives scored in a game utilizing the POISSON.DIST capability. The equation for x=2, 5 and x>3 objectives is given.
In the Succeed calculation sheet, Segment A rundowns the various upsides of x that we need to track down the probabilities for.
Segment B contains the relating equation to ascertain the likelihood utilizing the POISSON.DIST capability.
The recipe in cell B1 works out the likelihood of scoring 2 objectives in a game, P(x = 2), utilizing the POISSON.DIST capability with the contentions 2, 3.3, and Misleading.
The equation in cell B2 computes the likelihood of scoring 5 objectives in a game, P(x = 5), utilizing the POISSON.DIST capability with the contentions 5, 3.3, and Misleading.
The recipe in cell B3 works out the likelihood of scoring multiple objectives in a game, P(x > 3), utilizing the POISSON.DIST capability with the contentions 3, 3.3, and Valid. The Genuine contention works out the combined conveyance capability, which gives the likelihood of getting a worth not exactly or equivalent to the contention. To track down the likelihood of getting a worth more prominent than the contention, deduct the combined dissemination capability from 1.
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find the area of the region bounded by the three lines below. [hint: you will have to split up the integral into two parts.] y
The area of the region bounded by the three lines is 4.
The region bounded by the three lines y = 0, y = x and y = 2x is a triangle. To find the area of this region, we need to split the integral into two parts. The first part is the area of the triangle formed by y = 0, y = x and y = 2x. This can be found by integrating y from 0 to x, and x from 0 to 2x. The second part is the area of the triangle formed by y = 0, y = x and y = 0. This can be found by integrating y from 0 to x, and x from 0 to 0.
Therefore, the area of the region bounded by the three lines is given by:
[tex]A = 1/2 ∫x=0 to 2x ∫y=0 to x dy dx + 1/2 ∫x=0 to 0 ∫y=0 to x dy dxA = 1/2[x^2/2]_0^2x + 1/2[x^2/2]_0^0\\A = x^2 \\A = 4[/tex]
The area of the region bounded by the three lines is 4.
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The fraction 9/21 is in lowest terms? A. True B. False
Answer:
B) False
Step-by-step explanation:
It can be simplified to 3/7 as they both have the common factor 3.
claire has a points card for a movie theater. she receives 75 rewards points just for signing up. she earns 13.5 points for each visit to the movie theater. she needs at least 210 points for a free movie ticket. use the drop-down menu below to write an inequality representing vv, the number of visits she needs to make in order to get a free movie ticket.
Using the drop-down menu below to write an inequality is V ≥ 10. The number of visits she needs to make in order to get a free movie ticket is 10.
We have,
75 rewards points just for signing up.
earns 13.5 points for each visit to the movie theater
she needs at least 210 points for a free movie ticket
To write the inequality representing v is,
75 + 13.5v ≥ 210
13.5v ≥ 210 - 75
13.5 v ≥ 135
v ≥ 10
Therefore, by solving inequality the number of visits she needs to make in order to get a free movie ticket is 10.
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if PX equals to x cube + 3 x square - 2 X + 4 then find value of P2 P - 2 and p0if PX = x³ + 3 x square - 2 X + 4 find the value of p2p minus 2 and p0
Answer: The polynomial P(x) = x³ + 3x² - 2x + 4 is a cubic polynomial with the following properties:
p2 = 2: the coefficient of the x² term in P(x)
p - 2 = -2: the constant term in P(x)
p0 = 4: the coefficient of the x³ term in P(x)
So, p2 = 2, p - 2 = -2, and p0 = 4.
Step-by-step explanation: