Answer: B
Step-by-step explanation: because
Please help me this is due after class (20 mins) (I-Ready Math)
YOU GET 20 POINTS!!!!
Here's the picture
The value of h in the given parallelogram is 6 units, which can be found by using the formula for the area of a parallelogram.
In the given parallelogram, we can see that the base is 12 units long and the distance between the base and the opposite side is 6 units.
To find the value of h (the height or distance between the base and the opposite side), we can use the formula for the area of a parallelogram which is:
Area = base x height
Since we know the area of the parallelogram is 72 square units (given in the diagram), we can plug in the values we know and solve for h:
72 = 12 x h
h = 72/12
h = 6
Therefore, the value of h in the parallelogram is 6 units.
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Given the right triangle in the diagram below, what is the value of x, to the nearest foot
Therefore, the value of x, to the nearest foot, is A. 11 in the right triangle in the diagram below.
What is triangle?A triangle is a two-dimensional geometrical shape with three sides and three angles. It is a polygon with the least number of sides. Triangles are classified based on the length of their sides and the measure of their angles. The three sides of a triangle can be classified as equal, two equal sides, or three unequal sides. Triangles can also be classified based on their angles as acute (all angles less than 90 degrees), right (one angle is equal to 90 degrees), obtuse (one angle greater than 90 degrees), or equiangular (all angles are equal). The interior angles of a triangle always add up to 180 degrees. The longest side of a right triangle is called the hypotenuse, and it is opposite to the right angle. The Pythagorean theorem is used to find the missing side of a right triangle. Triangles are widely used in mathematics, physics, engineering, and other fields. They form the basic building block of more complex geometrical shapes and structures.
Here,
Using trigonometry, we can find that:
tan(40°) = x/14
Multiplying both sides by 14, we get:
x = 14 * tan(40°)
Using a calculator, we get:
x ≈ 11.0
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Complete question:
Given the right triangle in the diagram below. what is the value of x, to the nearest foot?
A. 11
B. 17
c. 18
D. 22
suppose the mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars. if incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 73 million dollars? round your answer to four decimal places.
The probability that a randomly selected firm will earn less than 73 million dollars is 0.9842.
The mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars, we need to find the probability that a randomly selected firm will earn less than 73 million dollars.
We can assume that the income distribution of firms is normal. Therefore, we can use the z-score formula to find the required probability.
We have, z = (X - μ) / σ, where X is the income of the firm, μ is the mean income, and σ is the standard deviation.
z = (73 - 45) / 13
z = 2.15
Using the z-table, we can find the area under the standard normal curve to the left of z = 2.15.
The area to the left of Z-score of 2.15 is 0.984, the probability that a randomly selected firm will earn less than 73 million dollars is 0.9842
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suppose there is a bag with 50 balls. 20 red, 15 blue, 5 pink, 10 green. you choose 2 balls at random without replacement. what is the chance you picked 1 red and 1 blue?
The chance that we picked 1 red and 1 blue is 0.2448 or 24.48%.
When we choose two balls at random without replacement, there are 50C2 = (50*49)/(2*1) = 1225 ways to choose two balls from 50 balls. Using the conditional probability formula, P(A and B) = P(A) * P(B|A), where A is the event of choosing a red ball and B is the event of choosing a blue ball.
P(A) = (20/50) = 0.4 (Probability of choosing a red ball at random from the bag)
P(B|A) = (15/49) = 0.306 (Probability of choosing a blue ball at random from the bag after choosing a red ball in the first trial)
Similarly, P(B) = (15/50) = 0.3 (Probability of choosing a blue ball at random from the bag)
P(A|B) = (20/49) = 0.408 (Probability of choosing a red ball at random from the bag after choosing a blue ball in the first trial)
Therefore, P(choosing one red and one blue) = P(A and B) + P(B and A) = P(A) * P(B|A) + P(B) * P(A|B)
= 0.4 * 0.306 + 0.3 * 0.408
= 0.1224 + 0.1224
= 0.2448 or 24.48%
Therefore, the chance that we picked 1 red and 1 blue is 0.2448 or 24.48%.
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a study was conducted to evaluate the stress level of senior business students at a particular college. forty students were selected at random from the senior business class, and their stress level was monitored by attaching an electrode to the frontalis muscle (forehead). for the forty students, the mean emg (electromyogram) activity was found to be 35.8 microvolts. in addition, the standard deviation of the emg readings was found to be 2.5 microvolts. what would be the 99% confidence interval on the true mean emg activity for all seniors in the class? (you should be using statistical software such as statcrunch.) group of answer choices [34.7296, 36.8704] [34.7296, 36.7804] [34.7456, 36.0566] [34.9672, 36.7840]
The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]
To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula
CI = X ± Zα/2 (σ/√n)
where
X = sample mean = 35.8
Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.
σ = sample standard deviation = 2.5
n = sample size = 40
Substituting these values into the formula, we get
CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].
Therefore, the correct option is (a) [34.7296, 36.8704]
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Elyse has a gift card to a local movie theater. the graph shows the amount of money remaining on her gift card based on the number of movies she has seen.
a. write an equation to represent the situation.
b. interpret the slope and y-intercept in the context of the situation.
a. The equation to represent the situation is y = -12x + 120, where x is the number of movies and y is the amount of money remaining on the gift card.
What is money?Money is a medium of exchange that is widely accepted as a way to pay for goods and services or to settle debts. Money also serves as a store of value, providing a way for people to save for the future. Money is generally created through government-backed fiat currencies, such as the U.S. dollar, which are issued and regulated by central banks. Money can also be created in the form of crypto-currencies, such as Bitcoin, which are not issued by any single government or central bank. Money is essential for economic growth and stability, as it allows for efficient exchanges of goods and services. Money can also be a source of financial security, providing people with a way to manage their finances and plan for the future.
b. The slope of -12 indicates that for every movie that Elyse sees, she will spend $12 from her gift card. The y-intercept of 120 indicates that if Elyse has not seen any movies, she will have $120 remaining on her gift card.
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The situation is,
a) The line equation is [tex]y = -3x - 6[/tex]
b) The line's y-intercept is -6, which indicates that when the amount of movies x = 0 , the amount on gift y = -6
c) The slope of the line is -3, indicating that as the number of movies x increases, the rate of change of the amount on the gift is declining.
What is an Equation of a line?a). The equation provides the line's slope.
Slope,
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Changing the numbers indicated in the slope equation,
Slope,
[tex]m=\frac{(6-12)}{(4-2)}[/tex]
Slope m = -6/2
Slope m = -3
The slope is -3
The equation of the line is,
[tex]y - y_1 = m ( x - x_1 )[/tex]
Substitute the given values in the equation,
[tex]y - 12 = -3 ( x - 2 )[/tex]
Simplify the equation,
[tex]y - 12 = -3x + 6[/tex]
Adding 12 on both sides
[tex]y = -3x - 6[/tex]
The equation of line is [tex]y = -3x - 6[/tex]
b). The y-intercept of the equation of line [tex]y = -3x - 6[/tex] is [tex]-6[/tex], when [tex]x=0[/tex]
c). The slope of the line [tex]y = -3x - 6[/tex] is [tex]m = -3[/tex] and the value is decreasing
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The completr question and graph attached below,
c. What is the slope, and what does it mean in the context of the situation?
list the horizontal, vertical, and diagonal cross-sections for the rectangular prism, triangle prism, cylinder, cone, and square pyramid.
De acuerdo con la información, podemos inferir que el volumen total de la figura sería 1,476.58 cm³
How to find the volume of the figure?To find the volume of the figure we must divide it into different sections because it has cones, pyramids, hemispheres, cylinders, and rectangular cubes. Below is the procedure:
Volume of rectangular segments:
4*4*11 = 176176 * 2 = 35215*8*4=480480 + 352 = 832Volume of the pyramids:
First we must calculate the height of the pyramids.
a² + b² = c²2² + b² = 13²b² = 13² - 2²b² = 165b = 12.84V = 1/3 *bhV = 1/3 * 16 * 12.84V = 68.4868.48 * 2 = 136.96Cone volume:
First we need to calculate the height of the cone.
a² + b² = c²5² + b² = 10²b² = 10² -5²b² = 75b = 8.66V=1/3hπr²V = 1/3 * 8.66 * 3.14 * 5²v = 226.60226.60 * 2 = 453.2Cylinder volume:
V = πr²hV = π 5² 18V=3.14*25*18V = 1,4131,413 * 2 = 2,826V = πr²hV = 3.14 * 1² * 16V = 50.24Volume of the hemisphere:
V = 4/3 πr³V = 4/3 3.14 * 1³V = 4.18Finally we just have to add all the values and we will obtain the total volume of the figure:
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A pavement 4m wide is constructed along the outer side of the boundary of a square shaped ground having it's side of 13m length. Find the cost of levelling the pavement at the rate of RS 1. 25 per square meter
A pavement 4m wide is constructed along the outer side of the boundary of a square shaped ground having it's side of 13m length. The cost of levelling the pavement at the rate of Rs 1.25 per square meter is Rs 340.
As per given information,
Side of a square shaped ground = 13 m
Width of pavement constructed = 4 m
We need to find the cost of levelling the pavement at the rate of Rs 1.25 per square meter.
Area of the square shaped ground = Side × Side= 13 × 13= 169 sq.m
Area of the square shaped ground along with pavement constructed
= (13 + 8) × (13 + 8)
= 21 × 21
= 441 sq.m
Area of the pavement constructed
= Area of the square-shaped ground along with pavement constructed - Area of the square shaped ground
= 441 - 169
= 272 sq.m
Cost of levelling 1 sq.m of pavement = Rs 1.25
Cost of levelling 272 sq.m of pavement = 272 × Rs 1.25 = Rs 340
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Help please, it’s simple I’m just slow
10 v^5 w^10
CHEESEburgeCheeseburger
HELPPPPPP! WILL GIVE THE BRAINLIEST ANSWER
Factorise these expressions as far as possible.
5a² + 4ab =
6p - pq - 5pr =
8st +9su + 7sv =
8pq² +9qr+ 7pqr =
2a²b + ab² - 6ab =
6t2u² +8tu²y + 5tuw =
18abc²-42a²bc + 18ab²c =
24pqrs +56q²rs - 40qrs =
Answer:
5a² + 4ab = a(5a+4b)
6p - pq - 5pr = p(6-q-5r)
8st +9su + 7sv = s(8t+9u+7v)
8pq² +9qr+ 7pqr = q(8p²+7pr+9r)
2a²b + ab² - 6ab = ab(2a+b-6)
6t²u +8tu²y + 5tuw = tu(6t+8uy+5w)
18abc²-42a²bc + 18ab²c = 6abc(3c-7a+3b)
24pqrs +56q²rs - 40qrs = 8qrs(3p+7q-5)
for a normal distribution, with a mean of 37 and a standard deviation of 3.7, what is the probability of randomly drawing a participant with a score of 34 or less?
The probability of randomly drawing a participant with a score of 34 or less is 0.2088 or approximately 20.88%.
The probability of randomly drawing a participant with a score of 34 or less from a normal distribution with a mean of 37 and a standard deviation of 3.7 can be calculated as follows:
First, we must convert the score of 34 or less to a z-score:z = (X - μ) / σ = (34 - 37) / 3.7 = -0.81. The probability of obtaining a score of 34 or less can be determined using the standard normal distribution table or a calculator that has the capability to compute probabilities of the standard normal distribution.Using the standard normal distribution table, the area to the left of -0.81 is 0.2088. Therefore, the probability of randomly drawing a participant with a score of 34 or less is 0.2088 or approximately 20.88%.
The standard deviation (SD) is a measure of the degree of variability or deviation of a distribution's scores from the mean or average value of the distribution. The standard deviation is expressed in the same units as the original distribution's scores, whether they are income, test scores, or some other measure of performance. It can be considered a statistic that quantifies the variability of data values, and the deviation is the amount by which a value differs from the mean or average value.
The probability of obtaining a specific score or range of scores from a distribution can be computed using the mean and standard deviation of that distribution by converting the score(s) to a z-score(s) and looking up the appropriate area on a standard normal distribution table or using a calculator that has the capability to compute probabilities of the standard normal distribution.
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9. A helicopter spots two landing pads below. The straight-line distance
from the helicopter to the pads is 14 miles to Landing Pad A and 8 miles
to Landing Pad B. If the landing pads are 20 miles apart, find the angle
of depression from the helicopter to Landing Pad B.
In response to the stated question, we may state that As a result, the Pythagorean theorem angle of depression from the helicopter to Landing Pad B is around 16.7 degrees.
what is Pythagorean theorem?The Pythagorean theorem is a fundamental mathematical principle that describes the connection between the sides of a right triangle. It asserts that the sum of the squares of the other two sides' lengths equals the square of the hypotenuse's length (the side opposite the right angle). The mathematical theorem is as follows: c2 = a2 + b2 Where "c" denotes the hypotenuse length and "a" and "b" indicate the lengths of the other two sides, known as the legs.
We can calculate the angle of depression from the helicopter to Landing Pad B using trigonometry.
Let we make a diagram:
B
/|
/ |
/ | 8 miles
14 / |
/θ |
/ |
/ |
/______|______ A
20 miles
Using trigonometry, we can deduce:
tan(θ) = opposite / adjacent
The opposing side in this example is 14 - 8 = 6 miles (since the helicopter is 14 miles from Landing Pad A and 8 miles from Landing Pad B, and the pads are 20 miles apart). The distance between the two sides is 20 miles (the distance between the landing pads).
tan(θ) = 6 / 20
tan(θ) = 0.3
θ = arctan(0.3)
θ ≈ 16.7 degrees
As a result, the angle of depression from the helicopter to Landing Pad B is around 16.7 degrees.
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A big cube has 10 small cubes on each side.
a. How many small cubes does the big cube have in total?
b. If three times as many cubes are placed per side.
Will three times as many small cubes be needed to
build the big cube?
a) There are 1,000 small cubes in the large one.
b) if each side has 3 times more cubes, then the total number of cubes will be 27 times larger.
How many small cubes does the big cube have in total?So we know that the large cube has 10 small cubes in each side.
Then each one of the faces of the cube will have:
10*10 = 100 small cubes on it.
Now, if we look at one of the faces, you can see 10 of these 100 square arrays on it, then the total number of small cubes is:
10*100 = 1000 small cubes.
b) If there are 3 times as many cubes per side, then each side has 30 cubes now, and the total number of cubes needed will be:
30*30*30 = 27,000
This is 27 times the amount of small cubes that we had before, then here the answer is no.
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A student is building a squirrel feeder for a family member. The figure is a model of the feeder.
A rectangular prism with dimensions 2 and three fourths inches by 16 and one half inches by 4 inches.
How much feed can the container hold?
twenty-seven and one-half in3
sixty-eight and three-fourths in3
ninety and three-fourths in3
one hundred eighty-one and one-half in3
The container can hold the feed equal to volume = 181.5 cube
A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism. It is referred to as a prism because of the length of its cross-section. The study of shapes and the arrangement of objects is known as Geometry. The surface area and volume of a rectangular prism are similar to those of other three-dimensional forms. The prism's net area is equal to its surface area.
To find how much feed the rectangular prism can hold you have to find its volume.
The formula to find the volume form a rectangular prism is:
Volume= Length x Width x Height
Now we must insert the values you have given:
Volume= 2.75 x 16.50 x 4
When you multiply that out it comes to:
Volume= 181.5
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Mariah has an after school babysitting job, This is a record of the number of hours she worked last week on Monday 2 1//2 on Tuesday it was 3 1/2 Wednesday 2 1/4 and Thursday 3 2/3 and she gets paid 6$ per hour how much money would she make? And also this is improper fractions as well
Answer: 71 1/2$
Step-by-step explanation:
Here is a list of numbers: 8.5, 1.2, 7.6, 3.8, 8.1, 9.4, 8.9, 0.7, 2.7 State the median. Give your answer as a decimal.
The median of the numbers 8.5, 1.2, 7.6, 3.8, 8.1, 9.4, 8.9, 0.7, 2.7 is 7.6.
How to find the median of numbers?The median of numbers is the value that's exactly in the middle of a dataset when it is ordered.
Therefore, before we find the middle value of the dataset, we have to arrange the numbers in ascending or descending order.
Hence, let's find the median of 8.5, 1.2, 7.6, 3.8, 8.1, 9.4, 8.9, 0.7, 2.7
Firstly, let arrange the numbers in ascending order.
Hence,
0.7, 1.2, 2.7, 3.8, 7.6, 8.1, 8.5, 8.9, 9.4
Therefore,
median = 7.6
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Ella is using paint to make a blackboard on her wall. The blackboard will cover a rectangular area of 44 square feet. The equation below can be used to determine w, the width of the blackboard. (w -2 ) ( w + 2 ) = 12 Create a diagram and determine the width and the length of the blackboard.
The width of the blackboard is 4 feet and the length is 11 feet.
How to find the width of the blackboard?To solve the equation[tex](w - 2) (w + 2) = 12[/tex]for the width of the blackboard, we can use the distributive property to simplify the left-hand side:
[tex]w^2 - 4 = 12[/tex]
Then we can add four to both sides:
[tex]w^2 = 16[/tex]
When we take the square root of both sides, we get:
w = ±4
We choose the positive solution because the width of the blackboard cannot be negative:
w = 4
We can calculate the length of the blackboard by dividing the area by the width:
l = 44 square feet / 4 feet = 11 feet
As a result, the blackboard's width is 4 feet and its length is 11 feet.
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PLEASE HELP ME & FAST !!!
The percentage of 65 out of 140 will be 46.428%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
[tex]\text{Percentage (P) = [Final value - Initial value] / Initial value x 100}[/tex]
The whole numbers are 65 and 140.
Then the percentage is written as,
[tex]P = (65 \div 140) \times 100[/tex]
[tex]P=0.46428 \times 100[/tex]
[tex]P=46.428\%[/tex]
The percentage of 65 out of 140 will be 46.428%.
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Find x
Find y
Need explanation
Step-by-step explanation:
Well, since this is a 45, 45, 90 triangle, it means that the given side and y have the same length.
Y = 1.5sqrt(2)
this means that X, the hypotenuse is equal to 1.5sqrt(2)^2 + 1.5sqrt(2)^2 = X^2
X is equal to 2.44948974278
If $4,323 was withheld during the year and taxes owed were $4,576:
a. Would the person owe an additional amount or receive a refund?
b. What is the amount? [Make sure to show your work]
Answer:
a. Since taxes owed ($4,576) are greater than the amount withheld ($4,323), the person would owe an additional amount.
b. The additional amount owed can be calculated by subtracting the amount withheld from the taxes owed:
Additional amount owed = Taxes owed - Amount withheld
= $4,576 - $4,323
= $253
Therefore, the person would owe an additional $253.
Please mark my answer as brainliest!
7. The expression below is evaluated as shown. In which step does the first
mistake appear?
The mistake in the solution of the expression is in step 3, where the product should be solved first.
In which step is the first mistake?Here we have the expression:
0.5*(3*5 + 1) - 2
And we also have the solution in steps, and we want to find in which step we have a mistake.
The first step gives:
0.5*(15 + 1) - 2
Where the first product is solved.
The second step is
0.5*16 - 2
Where we solved the parentheses.
The third step gives:
0.5*14
Here they subtracted the 2 from the 16, but this is incorrect, the first thing that needs to be solved here is the product between 0.5 and 16, we should get:
0.5*16 - 2
8 - 2
6
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Which expression represents the distance between point J and point K? J=6, -2 K= 6, -9
Using the distance formula of coordinate geometry the expression represents the distance between point J and point K where J= (6, -2) and K= (6, -9) is 7 units.
To find the distance between point J and point K, we use the distance formula, which involves the coordinates of the two points in a coordinate plane.
Identify the coordinates of point J and point K. In this case, we are given that J has coordinates (6, -2) and K has coordinates (6, -9).
Substitute the values of the coordinates into the distance formula, which is d = √[(x2 - x1)² + (y2 - y1)²].
For x1 and y1, use the coordinates of point J, which are x1 = 6 and y1 = -2.
For x2 and y2, use the coordinates of point K, which are x2 = 6 and y2 = -9.
Simplify the formula by substituting the values and solving:
d = √[(6 - 6)² + (-9 - (-2))²]
d = √[0² + (-7)²]
d = √[49]
d = 7
Therefore, the distance between point J and point K is 7 units.
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in how many ways can first, second, and third prizes be awarded in a contest with 170 contestants? your answer is
There are 4,826,640 possible ways to award first, second, and third prizes in a contest with 170 contestants.
To calculate this, use the formula nP3, where n is the number of contestants (170) and P3 represents the permutation of 3 elements. This can be simplified to P(170, 3) = 170! / (170 - 3)! = 170 x 169 x 168 = 4,826,640.
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Find an angle � θ coterminal to − 90 6 ∘ −906 ∘ , where 0 ∘ ≤ � < 36 0 ∘ 0 ∘ ≤θ<360 ∘
The angle that satisfies the necessary requirements is 1041° - 2(360°) = 321°. Coterminal angles are those with the same terminal point in the standard position.
To understand, follow the 2 basic steps:
Step 1: Find the specified angle.
Step 2: Finding a coterminal angle.
Tally up or tally down a multiple of 360.
θ = 1041°
Every multiple of 360 degrees added or subtracted results in an angle that is coterminal with the provided angle.
Hence, 1041° - 2(360°) = 321° is an angle that satisfies the necessary requirements.
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(x-4)(3x+4)=0 the solution is x=
Answer:
x=4, -4/3
Step-by-step explanation:
(x-4)(3x+4)=0
Using the zero product property, we can set each factor to zero and solve.
x-4 =0 3x+4 =0
x=4 3x =-4
x=4 x = -4/3
The solutions for x are:
x=4, -4/3
Answer:
4, -4/3
Step-by-step explanation:
Find and explain the error in the student’s work below.
Solve 2x² - 5x -12 = 0 using the Quadratic Formula.
The error made by the student is in simplifying the expression inside the square root.
What is the quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The student made an error in simplifying the expression inside the square root.
The expression should be simplified as follows:
25 + 4(2)(-12) = 25 - 96 = -71
So the correct expression inside the square root is -71, not 121.
Therefore, the correct solution using the Quadratic Formula is:
x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))
x = (5 ± √(25 + 96))/4
x = (5 ± √121)/4
x = (5 ± 11)/4
Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.
Therefore, the error made by the student is in simplifying the expression inside the square root.
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when conducting a logistic regression analysis, what is the problem of class imbalance in a dataset?
Class imbalance is a common problem in logistic regression analysis, where one class of data significantly outnumbers the other.
Class imbalance can be problematic because it leads to an over-representation of one class and an under-representation of the other, which can bias the model’s prediction towards the more frequently occurring class.
Class imbalance can cause the model to focus on optimizing accuracy by predicting the majority class more often than the minority class, leading to an underestimation of the minority class. It can also reduce the model’s ability to capture the nuances of the data that can be associated with the minority class. To address this, techniques such as oversampling, undersampling, and cost-sensitive learning can be employed to balance the data and improve model performance.
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Answer:
Choice B: distance from home to library is length of HL
HL = 75 see calculations below
Step-by-step explanation:
use points (0,0) and (2.1, 7.2) to find HL:
HL = √(2.1 - 0)² + (7.2 - 0)² = √4.4 + 51.8 = √56.25 = 7.5
Using the substitution u = 4x - 3, the integral of x ( 4x - 3 ) ^ 10 dx is equivalent to which of the following?
Answer:
Step-by-step explanation:
If we use the substitution u = 4x - 3, then du = 4 dx. Solving for dx, we get dx = du/4. Also, we can solve for x in terms of u: x = (u + 3)/4.
Substituting these values into the integral, we get:
∫ x (4x - 3)^10 dx = ∫ [(u + 3)/4] * u^10 * (du/4) = (1/16) ∫ (u + 3) * u^10 du = (1/16) ∫ (u^11 + 3u^10) du = (1/16) [(u^12)/12 + (3u^11)/11] + C = (1/192) * u^12 + (3/176) * u^11 + C
Substituting back for u = 4x - 3, we get:
(1/192) * (4x - 3)^12 + (3/176) * (4x - 3)^11 + C
So the integral of x(4x - 3)^10 dx is equivalent to (1/192) * (4x - 3)^12 + (3/176) * (4x - 3)^11 + C.
The integral of the function ∫x ( 4x - 3 )¹⁰ is given by A=( 1/16 ) ∫(u¹¹ + 3u¹⁰ )du
What is the integral of a function?The mathematical procedure known as the integral of a function depicts the accumulation of a quantity over a period of time or the region beneath a curve. It is used in calculus and is represented by the symbol ∫
In math, the integral of a function f(x) with respect to x is written as f(x) dx, where f(x) is the function being integrated and dx is the change in the variable x that is infinitesimally small. The antiderivative or integral of the function is the outcome of the integration.
Given data ,
Let the value of the function be f ( x ) = ∫x ( 4x - 3 )¹⁰
On substituting the value of u = 4x - 3 , we get
du/dx = 4
So , On replacing x with (u + 3)/4, and dx with du/4 in the integral:
∫x(4x - 3)¹⁰ dx = ∫((u + 3)/4)(4(u - 3))¹⁰ du
On further simplifying , we get
∫((u + 3)/4)(4(u - 3))¹⁰ du = ∫(1/4)(4(u + 3))(u - 3)¹⁰ du
Hence , the integral is A = ( 1/16 ) ∫(u¹¹ + 3u¹⁰ )du
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The complete question is attached below :
Using the substitution u = 4x - 3, the integral of x ( 4x - 3 ) ^ 10 dx is equivalent to which of the following?
1 1/3 + 2 1/4. 8 5/8-7 1/2 =
Answer:
9/8
Step-by-step explanation:
1 1/3 + 2 1/4 = (4/3 + 9/4) = (16/12 + 27/12) = 43/12
8 5/8 - 7 1/2 = (69/8 - 15/2) = (69/8 - 60/8) = 9/8
Therefore, 1 1/3 + 2 1/4 = 43/12 and 8 5/8 - 7 1/2 = 9/8.