A classmate claims that ( f ⋅ g)' = f ' ⋅ g' for any functions f and g. Show an example that proves your classmate wrong.
This is not true for all functions. To prove this, an example is given below. Let f(x) = x and g(x) = x².
What is function?A function is a relation that associates each element of a set, called the domain, to exactly one element of another set, called the range. It is a type of correspondence between two sets, where each element of one set is associated with exactly one element of another set.
The first derivative of f(x) is f ' (x) = 1 and the first derivative of g(x) is g ' (x) = 2x.
Therefore, ( f ⋅ g )' = ( x ⋅ x2 )'
= 1 ⋅ 2x + x ⋅ 2
= 2x + 2 ≠ 1 ⋅ 2x + 2x
= 4x
= f ' ⋅ g '
This example proves that the statement (f⋅g)' = f'⋅g' is incorrect. It is important to note that this does not mean that the statement is not true for all functions. It simply means that for the particular example given, the statement is not correct.
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What is the length of GH?
Answer: 52-9 = 43 units
Step-by-step explanation:
What two numbers multiply to -35 and add to get -18
he two numbers that multiply to -35 and add to get -18 are -5 and 3.
To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.
Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:
-5 + 3 = -2
So, -5 and 3 are the two numbers that multiply to -35 and add to -18.
look at the picture.
Answer:
Using order of operations:
[tex] \frac{12a}{2} - 3a \times 5[/tex]
[tex]6a - 3a(5)[/tex]
[tex]6a - 15a = - 9a[/tex]
[tex] - 9 \times 4 = - 36[/tex]
can anyone help please either one
The function N for d days of both rumors are N(d) = 2 + 5d and N(d) = 2(3)^d
How many students know the rumor on day 0Here, the number of students are the students that start the rumor i.e. Susanna and Liz
So, we have
JB = 2 studentsRihanna = 2 studentsHow many students know the rumor on day 2For the Justin Beiber rumor, the rumor spreads at a linear rate of 5 per day
So, we have
JB day 2 = 2 + 5(2) = 7
For the Rihanna rumor, the rumor spreads at an exponential rate of 3
So, we have
Rihanna day 2 = 2 * (3)^2 = 18
Days for students to knowUsing the functions, we have
JB
2 + 5x = 32 students
5x = 30
x = 6 days
Rihanna
2(3)^x = 162 students
3^x = 81
x = ln(81)/ln(3)
x = 4 days
The function N for d daysJB
N(d) = 2 + 5d
Rihanna
N(d) = 2(3)^d
So, we have
d JB Rihanna
0 2 2
1 7 6
2 12 18
3 17 54
4 22 162
5 27 486
6 32 1458
7 37 4374
8 42 13122
9 47 39366
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The decimal grid shown below is shaded and marked with Xs to model an expression
(Picture shown below)
Which expression could be modeled by this decimal grid?
A. 0.20 x 0.30
B. 0.020 x0.030
C. 0.020 x 0.30
D. 0.20 x 0.030
The expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression: (Math Operator, Number/Variable, Math Operator).
We have a total of 10 columns and 10 rows.
Total boxes = 10×10 ⇒ 100
Number of shaded boxes = 3×10 ⇒ 30
Each box contains X's out of 100 that is:
= 30/100
= 0.30
We can represent a number of columns in decimal such that:
= 20/100 = 0.20
The expression becomes 0.20×0.30.
Thus, the expression 0.20×0.30 could be modeled by the given decimal grid option (A) is correct.
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Please I want answer!
The subtraction expression for each length is given as follows:
OB = 3 - (-3).AB = 4 - (-2).How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence the distance OB is given as follows:
OB = sqrt((3 - (-3))² + (4 - 4)²)
OB = 3 - (-3).
The distance AB is given as follows:
AB = sqrt((-2 - (-2))² + (4 - (-2))²)
AB = 4 - (-2)
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5. The class finishes seeing the Small
Animals at 1:30. They will get back at
school in 30 minutes.
What time will it be then? Choose a
way to show the time.
4. A rectangular prism has height of 2¾ cm, the length is 1¼ cm and the height 4 cm, what is the volume?
Answer:
13.75 cm³
Step-by-step explanation:
In order to find the area of a rectangular prism you only need to multiply the width height and length together:
2.75 * 1.25 = 3.4375
3.4375 * 4 = 13.75
Hope this helps!
write a quadratic function in standard form that passes through (-4,0) , (5,0) , and (3,14) .
Given the circle below with secants JKL and NML, find the length of JK. Round to the nearest tenth if necessary.
Using the Intersecting secants theorem, the length of JK in the given diagram is 17
Intersecting secants theorem: Calculating the length of of JKFrom the question, we are to determine the length of JK in the given diagram.
The diagram shows a circle with intersecting secants.
From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".
Then,
We can write that
JK × KL = NM × ML
From the given diagram,
KL = 14
NM = 14
ML = 17
Substituting the values
JK × 14 = 14 × 17
JK = (14 × 17) / 14
JK = 17
Hence, the length of JK is 17
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please help with this question
The probability of the sample mean being less than 25.3 is given as follows:
0.9713 = 97.13%.
The sample mean would not be considered unusual, as it has a probability that is greater than 5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation 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 of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576[/tex]
The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:
Z = (25.3 - 25)/0.1576
Z = 1.9
Z = 1.9 has a p-value of 0.9713.
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A company uses six filling machines of the same make and model to place detergent into cartons that show a label of 32 ounces. The production manager has complained that the six machines do not place the same amount of fill into the cartons. A consultant requested that 20 filled cartons be selected randomly from each of the six machines and the content of each carton carefully weighed. The response is the deviation from 32 ounces.
(a) Is this study experimental, observations, or mixed?
(b) Identify all factors, factor levels, and factor-level combinations. For each factor indicate if it is experi- mental or observational.
(c) What type of design is being implemented here?
(d) We import the data and display the structure of the dataframe. We also coerse the variable Machine to a factor, and display the factor levels.
(a) This study is observational because the consultant is not manipulating any variables or imposing treatments on the machines.
(b) The factors are:
Machine (experimental factor): There are six machines, labeled A through F.
Carton (observational factor): There are 20 cartons selected randomly from each machine.
Deviation from 32 ounces (response variable): This is the weight difference between the actual fill amount and the target fill amount of 32 ounces.
The factor levels are:
Machine: A, B, C, D, E, F
Carton: 1, 2, 3, ..., 20
The factor-level combinations are all possible pairs of machine and carton, such as A-1, A-2, ..., F-20.
(c) This is a nested design because the 20 cartons selected from each machine are not interchangeable between machines.
(d) Here's an example code snippet in R to import the data and display the structure of the dataframe:
data <- read.csv("filling_machine_data.csv")
data$Machine <- factor(data$Machine)
levels(data$Machine)
Assuming the data is stored in a CSV file called "filling_machine_data.csv", the code reads in the data, coerces the Machine variable to a factor, and displays the factor levels of Machine
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Graph the line with slope 3 passing through the point (5, 3)
A graph of the line with slope 3 passing through the point (5, 3) is shown in the image attached below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (5, 3) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 3 = 3(x - 5)
y = 3x - 15 + 3
y = 3x - 12
In conclusion, we would use an online graphing calculator to plot the equation y = 3x - 12 as shown in the graph attached below.
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Lily has 4 cups of apples, 5-½ cups of watermelon, and cups of
grapes. She needs 2½ times of each fruit to make her fruit bowl. How
much of each fruit does she need? Do not round. Write your answer as
a whole number or as a mixed number. Use "/" as a fraction bar. Do
not label your answers.
a. Apples
b. Watermelons
c. Grapes
a. Apples: Lily needs 10 cups of apples for her fruit bowl.
b. Watermelons: Lily needs 13-3/4 cups of watermelons for her fruit bowl.
c. Grapes: The amount of grapes that Lily has is not given
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
To make her fruit bowl, Lily needs 2½ times the amount of each fruit she currently has.
a. Apples:
2½ × 4 cups = 10 cups
Therefore, Lily needs 10 cups of apples for her fruit bowl.
b. Watermelons:
2½ × 5-½ cups = (2 × 5 + 1/2) × 5/2 cups = 13-3/4 cups
Therefore, Lily needs 13-3/4 cups of watermelons for her fruit bowl.
c. Grapes:
The amount of grapes that Lily has is not given, so we cannot calculate how much she needs for her fruit bowl.
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-10-9-8
Which inequality is graphed on the number line?
OA) x>-7
OB) x < -7
C) x ≤ -7
D) xz -7
Answer:
a) x > -7
Step-by-step explanation:
an open circle (blank) means the greater than or less than symbols (< or >) and a close circle (filled in) means ≤ or ≥. the lining to your right looks more bold than the lining to your left so it's an; open circle, on -7, with the lining bold to your left.
in conclusion, x (the open circle) > -7
HELPPPP PLEASEEEEEEEEE
So, the length of WZ is 24 in kite WXYZ with diagonals WY and XZ.
What is triangle?A triangle is a closed, two-dimensional geometric shape that is formed by three line segments, called sides, that intersect at three points, called vertices. Triangles are one of the most basic shapes in geometry and are studied extensively in mathematics. The properties of triangles depend on the length of their sides and the size of their angles. Triangles can be classified based on the length of their sides as equilateral, isosceles, or scalene, and based on the size of their angles as acute, right, or obtuse. In an equilateral triangle, all three sides are of equal length. In an isosceles triangle, two sides are of equal length, while the third side is of a different length. In a scalene triangle, all three sides are of different lengths.
Here,
Since WXYZ is a kite, we know that its diagonals, WY and XZ, intersect at a right angle and bisect each other. Let M be the point of intersection of the diagonals, so that MW = MY and MX = MZ.
We can use the Pythagorean theorem to find MW and MX, and then use the fact that they are equal to find WZ.
Using the Pythagorean theorem in right triangles WMX and WMY, we have:
MW² = WX² - MX²
= 17² - 5²
= 264
MY² = WY² - MW²
= 13² - 264
= 25
MX² = XZ² - MZ²
= 17² - 13²
= 144
Since MW = MY, we have MW = √(25)
= 5
Therefore, WZ = 2MX
= 2√(144)
= 2*12
= 24
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1. Harold and his pet chicken, Simone, leave their home traveling by bicycle at a constant-
speed that allows them to cover 500 feet in 2 minutes.
a) Express the rate of speed of Harold and Simone traveling on their bicycle in feet per
minute.
In miles per hour.
Answer:
Step-by-step explanation:
minute= 250 per minute
mph = 1500/5280
A chess board is made using the ratio of square length to king's height, 3.5 inches to 4.5 inches. If a chess board is made with a king's height of 2.25 inches, what is the length of the square?
The length of the square is 1.75 inches, while the king's height is 2.25 inches.
Define length.
The length of an object or the extent of a one-dimensional object along its longest dimension is measured physically. It is a basic idea in physics and geometry and is frequently expressed in terms of meters (m), centimetres (cm), feet (ft), or inches (in).
According to the information provided, the square length to king's height ratio is 3.5 to 4.5 inches. Let's use this ratio to determine the square's length when the king is 2.25 inches tall.
We may make a proportion to get the square's length:
(square length) / (king's height) = 3.5/4.5
king's height = 2.25
Let's substitute the given values:
(square length) / 2.25 = 3.5/4.5
To solve for the length of the square, we can cross-multiply:
(square length) = (2.25) x (3.5/4.5)
(square length) = 1.75
Therefore, the length of the square is 1.75 inches, while the king's height is 2.25 inches.
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the dahlia is the national of Mexico. a florist sold bouquets of dahlias to 15 of the first 20 customers who came into his shop. Based on the experimental probability, how many bouquets of dahlias should the florist expect to sell on a day with 120 customers?
120 × 5 ÷ 20
= 120 × 5/20
= 6 × 15
= 90 Answer.
The number of dahlias should the florist expect to sell on a day with 120 customers is 90 bouquets.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Sold bouquets=15
Total customers=120
Now,
In this case, the number of successful outcomes is 15, and the number of total outcomes is 20.
So the experimental probability is:
2015=43
To find the expected number of bouquets of dahlias to sell on a day with 120 customers, you need to multiply the experimental probability by the number of customers.
In this case, you need to multiply 3/4 by 120:
3/4×120=3×120/4
=360/4
=90
Therefore, by the unitary method the answer will be 90 bouquets
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Let the Universal set be the letters a through j: U = {a, b, ..., i, j}.
The elements of the sets A ∩ (B ∪ C) is {b, c, i}.
How to find the element of a set?A universal set (U) is a set which has elements of all the related sets, without any repetition of elements.
Therefore,
U = {a, b, ….. i, j}
A = {b, c, i, j}
B = {a, c, g, i}
C = {a, b, d, i}
Therefore, let's find the elements A ∩ (B ∪ C).
Hence,
(B ∪ C) = {a, b, c, d, i, g}
A = {b, c, i, j}
Finally,
A ∩ (B ∪ C). = {b, c, i}
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What are the solution(s) of -1/2x + 4 = x+1
Answer:
2
Step-by-step explanation:
just did it on end 2022 test quiz
32 to the power of negative 4 fifths
Answer:
0.0625
Step-by-step explanation:
hope this helps :)
A trapezoid is 64 m2. The height is 12 cm and one base is 4 cm. What is the length of the missing base?
The length of the missing base is approximately 6.67 cm.
How to calculate the length of trapezoidBy applying the formula for the area of a trapezoid, we will be able to solve for the missing base.
Recall that the formula for the area of a trapezoid is:
A = [tex]\frac{1}{2} * h * (b_{1} + b_{2})[/tex]
where
A = area
h = height
b₁ and b₂ are the lengths of the parallel bases.
From the question, we are given:
A = 64 m²
h = 12 cm
b₁ = 4 cm.
Plug these values into the formula above to solve the missing base
64 = [tex]\frac{1}{2} * 12 * (4+ b_{2})[/tex]
Multiplying both sides by 2:
128 = 12(4 + b₂)
Simplifying:
128 = 48 + 12b₂
80 = 12b₂
b₂ = 80/12 = 20/3
b₂ = 6.67
Therefore, the length of the missing base is approximately 6.67 cm.
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Let c stand for the number of cousins sawyer has. Which bar model represents the problem?
The bar model that represents the number of cousins that Sawyer has, given the cousins Hazel has is the fourth bar model.
How to find the bar model ?The letter " c " is meant to represent the number of cousins that Sawyer has, in relation to those that Hazel has. This means that bar models A and C are out because they represent the cousins as B.
The question shows that Hazel has twice the number of cousins that Sawyer has. This means that if Sawyer's cousins are represented as " c " then Hazel would be 2 c. This is shown in the last bar model so this is the correct bar model.
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First part is:
Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?
Need help will give brainliest and 5 stars! :)
Answer:
2.362
Step-by-step explanation:
Use calculator: 2.361727836
Round: 2.362
Suppose the probability that an adult watches the news at least once per week is 0.60. We randomly survey 8 people. Let X = the number that watch the news at least once per week. Find the probability that at least 6 adults watch the news.
The answer of the given question based on the probability is , the probability that at least 6 adults watch the news is approximately 0.755.
What is Probability?Probability is measure of likelihood or chance of event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. Probability is used to analyze random experiments and events, and it is an essential concept in statistics, mathematics, and many other fields.
This is a binomial probability problem, where X follows a binomial distribution with n = 8 and p = 0.60. We want to find the probability that at least 6 adults watch the news, which can be written as:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ...
To solve , we use binomial probability formula:
P(X = k) =(n choose k) *p^k *(1 - p)^(n - k)
where "n choose k" is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.
Using this formula, we can find the probabilities for each value of k:
P(X = 6) = (8 choose 6) * 0.60⁶ * 0.40² = 0.311
P(X = 7) = (8 choose 7) * 0.60⁷ * 0.40¹ = 0.276
P(X = 8) = (8 choose 8) * 0.60⁸ * 0.40⁰ = 0.168
Note that we can also use binomial probability table or calculator with binomial probability function to find the probabilities.
Then, we can add these probabilities to get the probability that at least 6 adults watch the news:
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + ... = 0.311 + 0.276 + 0.168 + ...
This is a infinite series, but we can stop at P(X = 8) since the probabilities become very small after that.
P(X ≥ 6) = 0.755
Therefore, the probability that at least 6 adults watch the news is approximately 0.755.
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A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During
one particular week, the two cars went a combined total of 1725 miles, for a total gas consumption of 45 gallons. How many gallons were consumed by each of
the two cars that week?
First car: gallons
Second car: gallons
The first car consumed 15 gallons of gas
The second car consumed 30 gallons of gas during the week
To solve this problemLet's denote the number of gallons consumed by the first car as x, and the number of gallons consumed by the second car as y.
We know that the total gas consumption is 45 gallons, so:
x + y = 45
We also know that the total distance traveled is 1725 miles, and that the fuel efficiency (miles per gallon) of the first car is 35, and of the second car is 40. Using this information, we can write another equation:
35x + 40y = 1725
We now have two equations with two unknowns, which we can solve simultaneously to find x and y.
Multiplying the first equation by 35, we get:
35x + 35y = 1575
Subtracting this equation from the second equation, we get:
5y = 150
y = 30
Substituting y = 30 into the first equation, we get:
x + 30 = 45
x = 15
Therefore, the first car consumed 15 gallons of gas, and the second car consumed 30 gallons of gas during the week.
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1. What is 2x + 4 = 10?
A. x = 3
B. x = 4
C. x = 5
D. x = 6
2. 25 / 5 x 7 = ?
A. 175
B. 185
C. 195
D. 205
3. 100 - 50 + 10 - 5 = ?
A. 55
B. 60
C. 65
D. 70
4. 24 / 6 = ?
A. 4
B. 5
C. 6
D. 7
5. A triangle has base 6 inches and height 8 inches. What is the area?
A. 24 sq in
B. 32 sq in
C. 40 sq in
D. 48 sq in
6. What is the greatest common factor of 36 and 56?
A. 4
B. 8
C. 12
D. 16
7. What is the square root of 121?
A. 11
B. 12
C. 13
D. 14
8. If 2x + 4 = 14, what is x?
A. 5
B. 6
C. 7
D. 8
9. (3x - 5) + (7x + 1) = ?
A. 10x - 4
B. 11x - 4
C. 12x - 4
D. 13x - 4
10. What fraction is 5/12?
A. 1/2
B. 1/3
C. 1/4
D. 1/5
Required Answers :
1. 2x + 4 = 10
[tex]\: :\implies [/tex] 2x = 10 - 4
[tex]\: :\implies [/tex] 2x = 6
[tex]\: :\implies [/tex] x = 6/2
[tex]\: :\implies [/tex] x = 3.
Hence, Option (A) x = 3 is the answer.
2. 25/5 × 7 = ?
[tex]\: :\implies [/tex] 5 × 7
[tex]\: :\implies [/tex] 175/5
[tex]\: :\implies [/tex] 35
Hence, The required answer is 35.
3. 100 - 50 + 10 - 5 = ?
[tex]\: :\implies [/tex] 50 + 5
[tex]\: :\implies [/tex] 55
Hence, Option (A) 55 is the answer.
4. 24 / 6 = ?
[tex]\: :\implies [/tex] 24 ÷ 6
[tex]\: :\implies [/tex] 4
Hence, Option (A) 4 is the answer.
5. A triangle has base 6 inches and height 8 inches. What is the area?
Area of triangle = ½ × Base × Height
[tex]\: :\implies [/tex] 1/2 × 6 × 8
[tex]\: :\implies [/tex] 1/2 × 48
[tex]\: :\implies [/tex] 48/2
[tex]\: :\implies [/tex] 24 sq. in
Hence, Option (A) 24 sq in is the answer.
6. What is the greatest common factor of 36 and 56?
36 = 1,2,3,4,6,9,12, 18 and 36.
56 = 1,2,4,7,8,14,28 and 56.
Hence, Option (A) 4 is the answer.
7. What is the square root of 121?
[tex]\: :\implies [/tex] 11 × 11
[tex]\: :\implies [/tex] 121
Hence, (A) 11 is the answer
8. If 2x + 4 = 14, what is x?
[tex]\: :\implies [/tex] 2x + 4 = 14
[tex]\: :\implies [/tex] 2x = 14 - 4
[tex]\: :\implies [/tex] 2x = 10
[tex]\: :\implies [/tex] x = 10/2
[tex]\: :\implies [/tex] x = 5
Hence, Option (A) 5 is the answer
9. (3x - 5) + (7x + 1) = ?
[tex]\: :\implies [/tex] 3x - 5 + 7x + 1
[tex]\: :\implies [/tex] 10x - 5 + 1
[tex]\: :\implies [/tex] 10x - 4
Hence, Option (A) 10x - 4 is the answer.
10. What fraction is 5/12?
[tex]\: :\implies [/tex] 1/2 (approximately)
Hence, Option (A) 1/2 is the answer.
6) Given the points A(-4, 5) and B(6, 0), find
bolthe coordinates of the point P on the line
segment AB that partitions AB into the
ratio 2:3. Plot P along with segment AB.
Answer: (0, 3)
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