In the next 20 students surveyed, you would expect 5 to own a dog and a cat
How many of the next 20 students surveyed would you expect to own a dog and a cat?From the question, we have the following parameters that can be used in our computation:
Dog = 42
Cat = 34
Dog and cat = 15
Neither = 9
This means that
P(Dog and cat) = 15/100
When evaluated, we have
P(Dog and cat) = 5/20
So, when the next 20 students surveyed, we have
Dog and cat = 5/20 * 20
Evaluate
Dog and cat = 5
Hence, the number of dogs and cats is 5
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Suppose that you measure the flow rate of blood in an artery. You find that your measurements are well-fit be the equation dᏙ /dt =10 - 2 cos(120t)
in units of milliliters per second.
a) What volume of blood flows through the artery in 10 seconds? (include units)
b) What volume of blood flows through the artery in one minute? (include units)
The volume of blood flow through the artery in one minute is 600 milliliters.
We can integrate the given equation to get the volume of blood flow.
a) Integrating both sides of the equation with respect to time from 0 to 10 seconds, we get:
∫dᏙ = ∫(10 - 2cos(120t)) dt
ΔᏙ = [10t - (1/60)sin(120t)] from 0 to 10
ΔᏙ = [(10 x 10) - (1/60)sin(1200)] - [(10 x 0) - (1/60)sin(0)]
ΔᏙ ≈ 100 - 0
So, the volume of blood flow through the artery in 10 seconds is 100 milliliters.
b) To find the volume of blood flow through the artery in one minute, we need to integrate the given equation from 0 to 60 seconds:
∫dᏙ = ∫(10 - 2cos(120t)) dt
ΔᏙ = [10t - (1/60)sin(120t)] from 0 to 60
ΔᏙ = [(10 x 60) - (1/60)sin(7200)] - [(10 x 0) - (1/60)sin(0)]
ΔᏙ ≈ 600 - 0
So, the volume of blood flow through the artery in one minute is 600 milliliters.
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SOMEONE HELP PLS, giving brainlist to anyone who answers
Answer:
[tex]s = \frac{3(1 - {6}^{9}) }{1 - 6} = 6046617[/tex]
The sum of this finite geometric series is 6,046,617.
A company had a profit of $4,758 in January and a profit of -$3,642 in February. The company's profits for the months of March through May
were the same in each of these months. By the end of May, the company's total profits for the year were -$1,275.
What were the company's profits each month from March through May? Enter the answer in the box.
The company's profits for March through May were each -$797.
What was the company's profits for March through May?Let's start by adding the profits for January and February:
Profit for January + Profit for February = $4,758 + (-$3,642) = $1,116
We know that the company's profits for March through May were the same in each of these months, so let's call this common profit "X". Therefore, the total profit for these three months would be:
3 * X = 3X
Adding up the profits for all five months gives us the total profit for the year:
$1,116 + 3X = -$1,275
Subtracting $1,116 from both sides gives us:
3X = -$2,391
Dividing both sides by 3 gives us:
X = -$797
Therefore, the company's profits for March through May were each -$797.
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Which expressions are equivalent to 6\cdot6\cdot6\cdot6\cdot66⋅6⋅6⋅6⋅66, dot, 6, dot, 6, dot, 6, dot, 6 ?
The expressions equivalent to 6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 are 1296\cdot396\cdot2376 and 839808\cdot36.
Find out which expression is equivalent to the given expressions?We can use the associative property of multiplication to group the factors in different ways while preserving their product. For example, we can group the first four 6's together and then multiply by the remaining 6 and 66:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 = (6\cdot6\cdot6\cdot6)\cdot(6\cdot66)\cdot(6\cdot6\cdot66)
= 1296\cdot396\cdot2376
Alternatively, we can group the last two 6's together and then multiply by the remaining factors:
6\cdot6\cdot6\cdot6\cdot66\cdot6\cdot6\cdot6\cdot66 = (6\cdot6\cdot6\cdot6\cdot66)\cdot(6\cdot6)
= 839808\cdot36 is the equivalent expression.
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Find the probability that a randomly
selected point within the circle falls
in the red shaded area (square).
r = 4 cm
4 √2 cm
[? ]%
round to the nearest tenth of a percent.
The probability that a randomly selected point within the circle falls in the red shaded area is approximately 49.3%.
To find the probability that a randomly selected point within the circle falls in the red shaded area, we need to find the ratio of the area of the red shaded region to the total area of the circle.
The area of the circle is π[tex]r^{2}[/tex] = π[tex](4cm)^{2}[/tex] = 16π [tex]cm^{2}[/tex].
The diagonal of the square is equal to the diameter of the circle, which is 8cm. Therefore, the length of each side of the square is 4√2 cm.
The area of the square is (4√2 [tex]cm)^{2}[/tex] = 32 [tex]cm^{2}[/tex].
The area of the red shaded region is the difference between the area of the circle and the area of the square, which is 16π - 32 [tex]cm^{2}[/tex].
So, the probability that a randomly selected point falls in the red shaded area is:
[(16π - 32)/16π] × 100% ≈ 49.3%
Therefore, the probability that a randomly selected point within the circle falls in the red shaded area is approximately 49.3%.
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the graph of a sinosudial function has a maximum point at (0,5) and then has a minimum point at (2pi, -5)
The equation of the sinusoidal function is y = 5sin(x).
How to graph sinusoidal function?
To solve this, we need to find the equation of the sinusoidal function that has a maximum point at (0,5) and a minimum point at (2π,-5).
First, we know that the function is a sine function because it has a maximum at (0,5) and a minimum at (2π,-5).
Second, we can find the amplitude of the function by taking half the difference between the maximum and minimum values. In this case, the amplitude is (5-(-5))/2 = 5.
Third, we can find the vertical shift of the function by taking the average of the maximum and minimum values. In this case, the vertical shift is (5+(-5))/2 = 0.
Finally, we can find the period of the function by using the formula T=2π/b, where b is the coefficient of x in the equation of the function. In this case, we know that the function completes one cycle from x=0 to x=2π, so the period is 2π.
Putting it all together, the equation of the function is y = 5sin(x)
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The double dot plot shows the values in two data sets. express the difference in the measures of center as a multiple of the measure of variation.
no troll comments or i will hack ur device and find out where u live ! okay :)
The difference in measures of center as a multiple of the measure of variation can be expressed using the coefficient of variation.
How to express difference in data?To express the difference in measures of center as a multiple of the measure of variation, you can use the coefficient of variation (CV).
The CV is calculated by dividing the standard deviation (measure of variation) by the mean (measure of center), and then multiplying by 100 to express the result as a percentage.
For example, if the standard deviation of one dataset is 5 and the mean is 10, the CV would be 50%. If the standard deviation of another dataset is 2 and the mean is 8, the CV would be 25%.
To express the difference in measures of center as a multiple of the measure of variation between these two datasets, you would calculate the difference in their means (10-8=2) and divide it by the CV of the combined dataset ((5/10 + 2/8)/2 = 47.5%).
Therefore, the difference in measures of center is approximately 0.042 times the measure of variation (2/47.5%).
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QUICK!!
A group of students were surveyed about what they want to be when they grow up. The table provided shows the choices that the students made. Use the information in the table to answer the following questions. Round all answers to the nearest whole number.
Teacher Doctor Athlete
Boys 24 28 56
Girls 45 31 26
The marginal relative frequency of boys and girls who want to be a teacher is
%.
The joint relative frequency of girls who want to be an athlete is
%.
The conditional relative frequency of students that selected doctor, given that those students are boys is
%
The marginal relative frequency of boys and girls who want to be a teacher is 32.86%.
The joint relative frequency of girls who want to be an athlete is 12.38%.
The conditional relative frequency of students that selected doctor, given that those students are boys is 25.93%.
We'll use the terms marginal relative frequency, joint relative frequency, and conditional relative frequency to analyze the data in the table.
1. The marginal relative frequency of boys and girls who want to be a teacher is:
First, find the total number of students who want to be a teacher (boys + girls):
24 (boys) + 45 (girls) = 69 (total students)
Next, find the total number of students surveyed (sum of all entries in the table):
24 + 28 + 56 + 45 + 31 + 26 = 210
Now, calculate the marginal relative frequency of boys and girls who want to be a teacher (total students who want to be a teacher / total students surveyed):
69 / 210 ≈ 0.3286
Multiply by 100 to get the percentage:
0.3286 * 100 ≈ 32.86%
2. The joint relative frequency of girls who want to be an athlete is:
Find the number of girls who want to be an athlete: 26
Calculate the joint relative frequency (number of girls who want to be an athlete / total students surveyed):
26 / 210 ≈ 0.1238
Multiply by 100 to get the percentage:
0.1238 * 100 ≈ 12.38%
3. The conditional relative frequency of students that selected doctor, given that those students are boys:
Find the total number of boys surveyed (sum of boys row):
24 + 28 + 56 = 108
Calculate the conditional relative frequency (number of boys who want to be a doctor / total boys surveyed):
28 / 108 ≈ 0.2593
Multiply by 100 to get the percentage:
0.2593 * 100 ≈ 25.93%
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Pythagorean Theorem help quickly please
Using the Pythagorean theorem, the height of the ramp in the given diagram is 8.9 ft
Pythagorean theorem: Calculating the height of the ramp
From the question, we are to determine how high the ramp is
From the Pythagorean theorem which states that "in a right triangle, the square of the longest side, that is hypotenuse, equals sum of squares of the two other sides".
In the given diagram,
We have a right triangle
The measure of the hypotenuse is 21 ft
One of of the side measures 19 ft
Now, we will calculate x
By the Pythagorean theorem, we can write that
h² + 19² = 21²
h² = 21² - 19²
h² = 441 - 361
h² = 80
h = √80
h = 8.94427 ft
h ≈ 8.9 ft
Hence, the ramp is 8.9 ft high
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Find the area of the region bounded by the
curves:
y = 10 - x^2
y = x^2 + 8
The area of the region bounded by the curves is 4/3 square units.
To find the area of the region bounded by the curves y = 10 - [tex]x^2[/tex] and y = [tex]x^2[/tex] + 8, we need to find the points of intersection between the two curves.
Setting the two equations equal to each other, we have:
10 - [tex]x^2[/tex] = [tex]x^2[/tex] + 8
Simplifying, we get:
[tex]2x^2[/tex] = 2
[tex]x^2[/tex] = 1
x = ±1
Substituting x = 1 into either equation gives us:
y = 10 - [tex]1^2[/tex] = 9
And substituting x = -1 gives us:
y = 10 - [tex](-1)^2[/tex] = 10
So the two curves intersect at the points (1, 9) and (-1, 10).
To find the area of the region bounded by the curves, we need to integrate the difference between the two equations with respect to x, from x = -1 to x = 1:
∫[10 - [tex]x^2[/tex]] - [[tex]x^2[/tex] + 8] dx, from x = -1 to x = 1
= ∫(2 - 2[tex]x^2[/tex]) dx, from x = -1 to x = 1
= [2x - (2/3)[tex]x^3[/tex]] from x = -1 to x = 1
= 4/3
So
The area of the region bounded by the curves y = 10 - [tex]x^2[/tex] and y = [tex]x^2[/tex] + 8 is 4/3 square units.
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Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4). Determine whether or not triangle PQR is a right triangle. Show all calculations for full credit.
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Triangle PQR is not a right triangle.
To determine whether triangle PQR is a right triangle, we need to check if any of its angles is a right angle (90 degrees). We can use the slope formula to find the slopes of the sides of the triangle and check if any of the slopes are negative reciprocals (perpendicular) to each other.
Let's calculate the slopes of the sides PQ, QR, and RP:
Slope of PQ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 1) / (3 - 0)
= 1 / 3
Slope of QR = (y₂ - y₁) / (x₂ - x₁)
= (-4 - 2) / (5 - 3)
= -6 / 2
= -3
Slope of RP = (y₂ - y₁) / (x₂ - x₁)
= (1 - (-4)) / (0 - 5)
= 5 / (-5)
= -1
Now, let's check if any of the slopes are negative reciprocals of each other. We can compare the products of the slopes:
Product of PQ slope and QR slope = (1/3) * (-3) = -1
Product of QR slope and RP slope = (-3) * (-1) = 3
Product of RP slope and PQ slope = (-1) * (1/3) = -1/3
Since the product of the slopes of QR and RP is not equal to -1, triangle PQR is not a right triangle.
Therefore, triangle PQR is not a right triangle.
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The height of the storage space is 6 feet. The length is 2 times the width. The volume of the storage is 48 cubic feet. What is the width and length of the storage space
Step-by-step explanation:
Let's use the formula for the volume of a rectangular prism, which is:
V = lwh
where V is the volume, l is the length, w is the width, and h is the height.
We are given that the height is 6 feet, and the volume is 48 cubic feet. Therefore, we can solve for the product of the length and width:
lw = V / h = 48 / 6 = 8
We are also given that the length is twice the width, so we can substitute 2w for l:
(2w)w = 8
Simplifying this equation, we get:
2w^2 = 8
Dividing both sides by 2, we get:
w^2 = 4
Taking the square root of both sides, we get:
w = 2
Therefore, the width of the storage space is 2 feet. Since the length is twice the width, the length is:
l = 2w = 2(2) = 4
So the length of the storage space is 4 feet.
The solution of a quadratic equation are x=-7 and 5. Which could represent the quadratic equation, and why?
An answer option that could represent the quadratic equation, and why is: B. x² + 2x - 35 = 0, the factors are (x + 7) and (x - 5) and (x + 7)(x - 5) = x² + 2x - 35.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;
y = (x + 7)(x - 5)
y = x² + 2x - 35
x² + 2x - 35 = 0
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The snow globe below is formed by a hemisphere and a cylinder on a cylindrical
base. The dimensions are shown below. The base is slightly wider than the globe
with a diameter of 10cm and height of 1cm.
10 cm
4cm
3cm
Part C: If each globe is individually packaged into a box, what are the minimum
dimensions of the box?
The minimum dimensions of the box will be 7 cm × 6 cm × 6 cm
What do we by dimension?A dimension is described as the measurement of something in physical space such as length, width, or height.
We know that the there will be maximum dimension when the height of the cylinder and the radius of the hemisphere are aligned together.
Maximum height = 4 cm + 3 cm = 7 cm
Maximum diameter = 2 × 3 cm = 6 cm
Therefore, we can see that the minimum dimensions of the box are :
7 cm × 6 cm × 6 cm.
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What is the difference in minutes between the shortest collection.
The difference in the shortest collection times before and after the well installation is 20 minutes, calculated by subtracting the shortest time after installation (25 minutes) from before (45 minutes), as shown in the box and whiskers plot.
This is calculated by subtracting the shortest collection time after well installation (25 minutes) from the shortest collection time before well installation (45 minutes):
45 - 25 = 20 minutes.
This can be seen in the box and whiskers plot provided, where the lowest value for each distribution is denoted by the beginning of the whiskers.
So, the difference is before and after the well installation is 20 minutes.
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--The given question is incomplete, the complete question is given
" What is the difference in minutes between the shortest collection times before and after the well was installed"--
Mrs Gibson is sending a package to her son through the mail the package is a rectangular prism is 12 inches long,12 inches wide and 48 inches high what is the volume in cubic feet
The volume of the package which is 12 inches long, 12 inches wide, and 48 inches high is 6912 inches³ or 4 cubic feet.
Given length of the package which is in rectangular prism shape (L) = 12 inches
similarly, width of the package (W) = 12 inches
height of the package (H) = 48 inches
To know the volume of the package which is in the rectangular prism shape the formula is V= L x W x H
The substituting the given values in the above equation, we can obtain the volume of the package.
So,
L x W x H = 12 x 12 x 48 = 6912 inches³
To convert the cubic inches into the cubic feet we have to divide the obtained value by 1728.
So, [tex]\frac{6912}{1728}[/tex] = 4 feet³
From the above explanation, we can conclude that the volume of the given package of rectangular prism shape is 4 feet³.
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How do you solve for average daily balance?
Therefore , the solution of the given problem of unitary method comes out to be (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period).
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
You must be aware of an account's daily balance over a specific time period in order to determine the average daily amount. how to get an average daily balance:
The time frame for which you wish to compute the average daily balance should be chosen. This could, for instance, be a month, a quarter, or a year.
Find the account balance at the end of each day during the specified period.
Sum up each day's balance for the duration.
By the number of days in the time frame, divide the sum. You are then given the daily average balance.
The formula for determining the typical daily balance is as follows:
=> (Sum of Daily Balances) / Average Daily Balance (Number of Days in Period)
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Pls help, answer both of the questions with explanation.
The Phillips family bought 8 bags of cookies. Each bag had 17 cookies. They have since eaten 29 of the cookies. How many cookies do they have left?
Answer:107
Step-by-step explanation:8*17-29=107 so our answer is 107
PLEASE HELP!! How can you find the annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100? What does knowing the APR allow you to do?
APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100
What is the annual percentage rate?The formula for APR (annual percentage rate) is given as;
APR = ((F / P) x 12) x 100
Where;
F is the finance charge for the loanP is the total amount borrowed12 represents the number of months in a yearThe annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;
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Find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1]
Answer:
The maximum is when both X and y = 1.The maximum value of the function is 3.When both X and YY are equal to 0, the minimum value is 0
The absolute maximum value is 3 and the absolute minimum value is 0.
To find the absolute maximum and minimum values of f(x,y) = x^2 + 2y^2 on the square [0,1] x [0,1], we need to consider both the interior and the boundary of the square.
First, check for critical points in the interior by finding the partial derivatives and setting them equal to zero:
fx = 2x and fy = 4y
Setting them equal to zero, we have:
2x = 0 => x = 0
4y = 0 => y = 0
The only critical point in the interior is (0,0).
Next, evaluate f(x,y) on the boundary of the square [0,1] x [0,1]. The boundary consists of four segments: x=0, x=1, y=0, and y=1.
1. x=0: f(0,y) = 2y^2 (for y in [0,1])
2. x=1: f(1,y) = 1 + 2y^2 (for y in [0,1])
3. y=0: f(x,0) = x^2 (for x in [0,1])
4. y=1: f(x,1) = x^2 + 2 (for x in [0,1])
Now, compare the values of f at the critical point and boundary points to find the absolute maximum and minimum:
Absolute minimum: f(0,0) = 0
Absolute maximum: f(1,1) = 3
So the absolute maximum value is 3 and the absolute minimum value is 0.
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(1) Begin with a 1-by-1 square, J. Attach squares which are half as wide (and half as tall) to the middle of each side of Jį to form J2. Attach squares half as wide as those squares to every . outer edge of J2 in order to make J3. Repeat. F F2 F3 (a) Find the area of Jg. (b) If we continue in this way forever, does the area of Joo converge? If so, what does it converge to?
Previous question
Starting with a 1-by-1 square, a sequence of squares J1, J2, J3, ... is created by attaching squares half as wide as the previous squares to the outer edges of each successive square. The area of J∞, the limit of this sequence, is 4/3.
To find the area of J1, we simply calculate the area of the original 1-by-1 square, which is 1.
To find the area of J2, we need to attach squares half as wide (and half as tall) to the middle of each side of J1. The area of each attached square is (1/2)² = 1/4, so the total area added to J1 is 4(1/4) = 1. Thus, the area of J2 is 1 + 4(1/4) = 2.
To find the area of J3, we need to attach squares half as wide as the squares added in the previous step to every outer edge of J2. The area of each attached square is (1/4)² = 1/16, so the total area added to J2 is 4(1/16) = 1/4. Thus, the area of J3 is 2 + 4(1/4) = 3.
We can continue this process to find the areas of J4, J5, and so on. In general, the area of Jn is equal to the area of the previous square plus the area added by the attached squares, which is 4(1/2^(n-1))^2 = 1/2^(2n-2). Therefore, the area of Jn is 1 + 1/4 + 1/16 + ... + 1/4^(n-1) = (4/3)(1 - 1/4^n).
As n approaches infinity, the area of Jn approaches the limit of (4/3)(1 - 0) = 4/3. Therefore, the area of J∞, the limit of the sequence, is 4/3.
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PLS HLEP AND SHOW WORK I WILL MATK BRAINLYEST
Answer:
38. (A) True
39. (B) False
Step-by-step explanation:
The set of people working in the summer consists of both female an male since there is no determiner to show that the 80% of students are a specific gender. Therefore, the answer to the first question is True (A).
My expression for finding the probability of being female and working part time in summer only is:
[tex]\frac{84}{100} \\\\ \\ \\ \\[/tex][tex](\frac{1}{2} *\frac{80}{100})\\[/tex][tex]=\frac{42}{125}[/tex] which is also equal to 0.336. Therefore the second question is false.
Please forgive me if I'm wrong but I'm open to any correction or criticisms.
PLEASE HURRY DUE IN 2 HOURS
Explain how the shapes shown have been sorted.
Two groups of shapes. In group A, one shape has four equal side lengths of three, and no right angles. The opposite sides are parallel. Two shapes have two pairs of opposite equal side lengths. One shape has side lengths of four and eight. The other side lengths are three and two. Opposite sides are parallel, and there are no right angles. In group B there are three four sided shapes. One has opposite equal side lengths of seven and four and four right angles. One shape has four equal side lengths of three and four right angles. One shape has one set of opposite parallel sides and one right angle. None of the side lengths in the last shape are equal.
The image is below if you don't want to read all that, And PLEASE actually answer the question.
The figure with opposite sides are parallel and equal is parallelogram.
From the group A:
In first image opposite sides are parallel and equal.
One pair of parallel sides = 4 units and the another pair of parallel sides = 8 units
So, it is parallelogram.
In second image opposite sides are parallel and all the sides are equal.
So, it is rhombus.
In third image opposite sides are parallel and equal.
One pair of parallel sides = 3 units and the another pair of parallel sides = 2 units
So, it is parallelogram.
From the group B:
In first image opposite sides are parallel and equal.
One pair of parallel sides = 4 units and the another pair of parallel sides = 7 units and all angles measures equal to 90°.
So, it is rectangle.
In second image one pair of opposite sides are parallel.
So it is trapezium.
In third image opposite sides are parallel and all sides equal.
All angles measures equal to 90°.
So it is square.
Therefore, the figure with opposite sides are parallel and equal is parallelogram.
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solve this and I will give u brainlist.
Aria ate the pictured slice of pizza. If the original
pizza was 8 inches in diameter, what is the area
of the slice she ate?
Answer:
Step-by-step explanation:
50.24n2
True or false: the lateral surface of cone a is exactly 1/2 the lateral surface area of cylinder b
The lateral surface area of a cone can be less than or greater than half the lateral surface area of a cylinder, depending on the specific dimensions of each shape. The given statement is true.
It depends on the specific dimensions and measurements of cone A and cylinder B. In general, however, it is not true that the lateral surface area of a cone is exactly half the lateral surface area of a cylinder with the same base and height.
The lateral surface area of a cone is given by πrl, where r is the radius of the base and l is the slant height of the cone. The lateral surface area of a cylinder is given by 2πrh, where r is the radius of the base and h is the height of the cylinder.
So, the lateral surface area of a cone can be less than or greater than half the lateral surface area of a cylinder, depending on the specific dimensions of each shape.
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-8
Find the distance, d, of AB.
A = (-7, -7) B = (-3,-1)
-6 -4
A
-2
B -2
-4
-6
-8
d = √x2-x1² + y2 - Y₁|²
d = [?]
Round to the nearest tenth.
Distance
Step-by-step explanation:
Using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
where A = (x1, y1) and B = (x2, y2), we can find the distance between points A and B as follows:
d = √[(-3 - (-7))² + (-1 - (-7))²]
d = √[4² + 6²]
d = √52
d ≈ 7.2
Therefore, the distance between points A and B is approximately 7.2 units, rounded to the nearest tenth.
Find f'(-2) for f(x) = ln(5x² + 20x + 1). Round to 3 decimal places, if necessary.
To find f'(-2), we need to first find the derivative of f(x) using the chain rule.
f'(x) = (1/(5x² + 20x + 1)) * (10x + 20)
Then, we can plug in x = -2 to get f'(-2):
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = 0
Therefore, f'(-2) is equal to 0.
To find f'(-2) for f(x) = ln(5x² + 20x + 1), we first need to find the derivative of f(x) using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
1. Let u = 5x² + 20x + 1. Then, f(x) = ln(u).
2. Find the derivative of f(x) with respect to u: f'(x) = d[ln(u)]/du = 1/u.
3. Find the derivative of u with respect to x: du/dx = d(5x² + 20x + 1)/dx = 10x + 20.
4. Apply the chain rule: f'(x) = (1/u) * (du/dx) = (1/(5x² + 20x + 1)) * (10x + 20).
Now, to find f'(-2), simply substitute -2 for x in the derivative:
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = (1/(-19)) * 0
Since any number multiplied by 0 is 0, we have:
f'(-2) = 0.000
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solve for the value of x .
80(x+15)
=60
Answer:
x = [tex]\frac{-57}{4}[/tex]
Step-by-step explanation:
solve for the value of x .
80(x+15)=60
80(x + 15) = 60
80x + 1200 - 60 = 0
80x + 1140 = 0
80x = -1140
x = -1140/80
x = [tex]\frac{-57}{4}[/tex]
Answer:
-14.25
Step-by-step explanation:
Given: 80 (x+15) = 60
Solution: On opening the brackets, we get
> 80x + 80 * 15 = 60
> 80x + 1200 = 60
Then, taking 1200 to the other side of the equation,
80x = 60 - 1200
Therefore, 80x = -1140
Now, dividing both sides by 80, we get:
80x/80 = -1140/80
So, x= -14.25
Hope this helps!
