The linear approximation of f(1.07) using the tangent line is T(1.07) is 10.77, which is slightly lower than the actual value f(1.07) = 11.77.
First, we need to find the derivative of the function f(x) = x + 10x.
The derivative is given by:
f'(x) = 1 + 10
Next, we need to find the tangent line at the point (a, 6), which means we need to find the value of "a" that makes the tangent line pass through (a, 6). To do this, we use the equation of the tangent line:
y - 6 = (1 + 10)(x - a)
y = (1 + 10)(x - a) + 6
Now we need to use the value of "a" to find the value of f(a) and then use this to find the value of the linear approximation of f(1.07).
Let's assume that the value of "a" is 1.
So, f(a) = f(1) = 1 + 10(1) = 11
And the equation of the tangent line is:
y = (1 + 10)(x - 1) + 6 = 11x - 4
Now, to find the value of the linear approximation of f(1.07), we use the equation of the tangent line:
T(1.07) = 11 * 1.07 - 4 = 10.77
Finally, we compare this value with the actual value of f(1.07), which is:
f(1.07) = 1.07 + 10 * 1.07 = 11.77
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10.
Which graph shows the following system of equations and its solution?
ows the following system of equations and its solution?
The graph that shows the following system of equations and its solution is graph number C
How to determine the graph?A graph is the graphical representation of equations on a graph sheet
The given equations are
-4x-3y=4
4x-y=-4 Solving the equations
In equation 1
When x = 0
-3y = 4
y=-4/3 (0, -4/3)
When y = 0
-4x = 4
x= -1 (-1, 0)
In equation 2 when x = 0
-y = -y = 4 (0, 4)
When y = 0
4x=-4 x=-1 (-1, 0)
When these coordinates are used to plot the graph, graph number is is obtained.
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If the two legs of an isosceles right triangle measure 7 inches which of the following represents the length of its hypotenuse
the length of its hypotenuse will be 7√2 inches.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given, the two legs of an isosceles right triangle measure 7 inches
Since,
From the Pythagorean theorem:
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
So,
Hypotaneuse² = base² + height²
in our case,
Base = height = 7 inches
Thus,
Hypotaneuse = √(7² + 7²)
Hypotaneuse = 7√2 inches
Therefore, the length of its hypotenuse will be 7√2 inches.
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–1/2 (12x – 2) = –6x – 1
The given function has no solution it will be false for all real values of x.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given a function –1/2 (12x – 2) = –6x – 1
Simplifying the given function using the rule of PEMDAS
=> –1/2 (12x – 2) = –6x – 1
multiply by -2 on both sides
=> 12x - 2 = 12x +2
==> 4 = 0
Therefore, the given function has no solution it will be false for all real values of x.
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The figure below was made with a scale of 1 unit =6cm.
Draw the figure with a new scale of 1 unit =2cm.
You can place your figure anywhere on the grid on the right.
The new diagram with a scale factor of 1 unit = 2cm will look the same
as each new grid now represents 2 cm.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, A drawing represented by a scale factor of 1 unit = 6cm,
Where every grid unit represents 6 cm.
The new drawing model will look exactly the same as now each grid unit represents 2cm feet.
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A survey was conducted among 200 students of age groups 7–12 years and 13–18 years to find their favorite movie genre. The students had to select any one genre from comedy, action, or adventure. Out of the 100 students in the age group 7–12 years who participated in the survey, 55 liked action or adventure movies. The total number of students of both age groups who liked comedy was 98. Using a two-way table, compute the total number of students in the age group 13–18 years who liked action or adventure movies.
Answer:the answer is 47
Step-by-step explanation:
100 - 55 = 45, which represents the 7-12 year olds who chose comedy
98 - 45 = 53, people in 13-18 who chose comedy
100 - 53 = 47 which represents the people of 13-18 who chose action and adventure
HOPE THIS HELPS!!!!
Given P(x)= x^3 + 3x^2 + x + 3. Write P in factored form (as a product of linear factors). Be sure to write the full equation, including P(x)=.
The factored form of the equation P(x) = x³ + 3x² + x + 3 is P(x) = (x+1)(x² + 2x + 3).
An equation is a mathematical expression that shows that two things are equal.
One common method for finding the factored form of a polynomial equation is to use the Rational Root Theorem, which states that if a rational number a/b is a root of the polynomial equation, then (x-a/b) is a factor of the polynomial equation.
We can then use long division to divide the polynomial by the linear factor, repeat the process with the remaining polynomial, and continue this process until the polynomial is fully factored.
The polynomial equation
=> P(x) = x³ + 3x² + x + 3
can be factored as
=> (x+1)(x² + 2x + 3).
The equation P(x) = (x+1)(x² + 2x + 3) is now written as a product of two linear factors, (x + 1) and (x² + 2x + 3).
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Carpet City charges $5 per square foot for a type of carpet. They charge an additional $95 for installation. Westside Carpet also charges an installation fee and a constant rate for the same carpet. The table shows the cost including installation for various amounts of the carpet at Westside Carpet. Which store charges more per square foot for the carpet?
Answer:
Step-by-step explanation:
Answer is A
3250 is the total cost
$95 is the cost of installation
Cost for 642 square feet
=3250 - 95=3155
Cost of installation per square feet = 3155/642=4.91
Cost of Carpet City per square feet = $5
Cost of Westside carpet per square feet = $4.91
So Carpet City charges more
find x please will give brainliest!
The value of the angle x is 120 degrees
How to determine the value of the variableIt is important to note the following;
The sum of angles in a triangle is 180 degreesAngles on a straight line is 180 degreesAlternate angles are said to be equal or congruentFrom the information given in the diagram, we have that;
The variable x is laying on a straight line with one end of the triangle.
Also, angle 60 is alternate to the same angle on a straight line with x
So, we have that;
60 degrees + x degrees = 180 degrees
Solve mathematically as;
60 + x = 180
collect like terms
x = 180 - 60
Subtract the values
x = 120 degrees
Hence, the value is 120 degrees
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Tessa did 3/5 of her homework problems on Saturday. On Sunday, she did 1/3 of what was left plus the last 4 problems. How many problems did Tessa do over the weekend?
The total problems assigned over the weekend are 15.
Let's assume the total number of problems assigned = x.
Given that problems solved on Saturday is 3/5 of her total questions. This is represented as:
(3/5)x
The remaining problems are:
1 - (3/5)x = (2/5)x
On, Sunday the problems solved are 1/3 of the remaining. This is represented as:
(1/3)*(2/5)x = (2/15)x
The remaining problems are:
(1 - 1/3)(2/5 x) = (2/3) * (2/5)x = 4/15x
Given that the final number of problems remaining are 4, that is:
(4/15)x = 4
x = 4 (15/4)
x = 15
Hence, the total problems assigned over the weekend are 15.
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given target's financial statements, calculate the common size value for licensed content. (enter percentages as decimals and round to 4 decimals)
The common size value for licensed content is 0.0848.
To calculate the common size value for licensed content, first, we need to find the total revenue of the company. We can get this information from the company's financial statements.
Let's assume the total revenue of the company is $100,000.
Next, we need to find the amount of money spent on licensed content. Let's assume that the amount spent on licensed content is $8,500.
Now, to calculate the common size value for licensed content, we need to divide the amount spent on licensed content by the total revenue, and multiply the result by 100.
So, the common size value for licensed content is:
Common size value = (8,500/100,000) x 100 = 0.0848
Therefore, the common size value for licensed content is 0.0848 (rounded to 4 decimals).
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On the number line below, p represents a number. what is the value of the opposite of that number
Answer:
I believe D.
Step-by-step explanation:
Since the number on the number line is 1 and 2/4, the opposite would be the negative version, -1 and 2/4. Hope this helped!
what is 5 divided by 1/6
Answer:
30
Step-by-step explanation:
to divide by a fraction, multiply by the reciprocal of it
the reciprocal of 1/6 is 6
5*6=30
The number of chirps that crickets make is closely related to the temperature in after environment. When the temperatures between 12 and 38°C ,we can tell the temperature by counting the number of chirps.
Answer:
65
Step-by-step explanation:
cuz I said so
Bobby purchased land for $6500 in 1989. The value of the land depreciated by 1.6% per year, use an exponential function to find the approximate value of the land in 1999.
Answer: The exponential function to model the value of the land over time t (in years) is given by:
V(t) = 6500 * e^(-0.016t)
So, to find the value of the land in 1999 (10 years after 1989), we can plug in t = 10 into the equation:
V(10) = 6500 * e^(-0.016 * 10) = 6500 * e^(-0.16) = 6500 * 0.8499 = 5524.935
Therefore, the approximate value of the land in 1999 was approximately $5524.935.
Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and
thumb drive. Troy bought 5 notebooks and 15 thumb drives for $395. Lisa bought 12 notebooks and 8 thumb
drives for $248. Find the cost of each notebook and each thumb drive.
The cost of each notebook =
The cost of each thumb drive =
Answer:
notebook: $4thumb drive: $25Step-by-step explanation:
You want the cost of a notebook and a thumb drive when 5 notebooks and 15 thumb drives costs $395, while 12 notebooks and 8 thumb drives cost $248.
EquationsThe two purchases can be described by the equations ...
5n +15d = 395 ⇒ n +3d = 7912n +8d = 248 ⇒ 3n +2d = 62SolutionSubtracting the second equation from 3 times the first, we have ...
3(n +3d) -(3n +2d) = 3(79) -(62)
7d = 175
d = 25 . . . . . . . divide by 7
Substituting into the first equation gives ...
n +3(25) =79
n = 4 . . . . . . . subtract 75
The cost of each notebook is $4; the cost of each thumb drive is $25.
__
Additional comment
It is often easier to solve a system of equations when they are written in standard form. Here, we made the coefficients mutually prime by dividing each equation by the greatest common factor. For the first equation, we divided by 5; for the second equation, we divided by 4. This is especially useful if one of the coefficients ends up being 1.
How could you count on by 5s or 10s to add 20+6 on a number line?
To add 20 and 6 using a number line, you would start at 20 and count on by 5 once (for 25) and then by 1 once (for 26). Counting on by 10s isn't feasible as 6 isn't a multiple of 10.
Explanation:To add 20 and 6 using counting on by 5s or 10s with a number line, you would start at number 20, then you would progress along the line in increments of 5 until you've added 6. However, since 6 is not a multiple of 5, you would need to count on by 5 once (to get to 25) and then count on by one, one more time (to get to 26). If you were counting on by 10s, you wouldn't be able to, as 6 isn't a multiple of 10.
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TIME REMAINING
53:26
To be able to go on the band trip, four band members each get a part-time job. Each person has 5 weeks in which to save his or her money. Analyze the four individual plans below and decide which of the four people will reach his or her goal of saving $285?
Member A: Works 8 hours per week at $6.15 per hour
Member B: Works 10 hours per week at $5.85 per hour
Member C: Works 7 hours per week at $7.25 per hour
Member D: Works 9 hours per week at $6.35 per hour
The solution is, Only member B and D will reach their goal.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Given;
Amount to be saved = $285
Total time to save money = 5 weeks
Now,
For member A:
Working hours = 8 per week
per hour earnings = $6.15
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 8 × 5 × 6.15
= $246
For member B:
Working hours = 10 per week
per hour earnings = $5.85
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 10 × 5 × 5.85
= $292.5
For member C:
Working hours = 7 per week
per hour earnings = $7.25
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 7 × 5 × $7.25
= $253.75
For member D:
Working hours = 9 per week
per hour earnings = $6.35
Therefore,
The total amount collected
= working hours per week × Total weeks × Earning per hours
= 9 × 5 × $6.35
= $285.75
Since, the amount earned by member B and D is greater than the goal amount and the amount earned by member A and C is less than the goal amount
therefore,
Only member B and D will reach their goal.
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Car A travels at 55 miles per hour and Car B travels at a greater speed of x miles per hour. Choose the expression that represents how many miles farther Car B travels in two hours.
Answer: Let's assume that Car B travels at a speed of x miles per hour. The expression that represents how many miles farther Car B travels in two hours compared to Car A is:
(x - 55) * 2
This expression calculates the difference in speed between Car B and Car A (x - 55) and then multiplies it by the number of hours (2) to get the total distance Car B travels farther than Car A in two hours.
Step-by-step explanation:
A rectangular vegetable garden will have a width that is 2 feet less than the length area of 48 square feet. If represents the length, then the length can be found by s equation:
x(x - 2) = 48
What is the length, x, of the garden?
The length is
feet.
Answer:
8ft
Step-by-step explanation:
solve equation of x²-2x-48=0
(x-8)(x+6)=0
so x=8 or -6
only 8 is correct
Write an equation to represent each function. Input (x) Output (y) 1 2 6 12 3 18 24 5 30
One possible equation that represents the function is:
y = 2x, which can also be written as y = 2 * x.
Here's how the function values correspond to the equation:
When x = 1, y = 2 * 1 = 2
When x = 2, y = 2 * 2 = 4
When x = 3, y = 2 * 3 = 6
When x = 5, y = 2 * 5 = 10
And so on.
Note that there are other equations that could also represent the same function, but y = 2x is one possible option.
Answer:
is there a picture I can see
PLEASE HELP LIMITED TIME! VERY URGENT.
Look at the added image.
Assign the following correlation coefficients, r-values, to the appropriate graph:
-0.1,
-0.75,
0.88,
0.43
The correlation coefficient, r, for each of the graph is:
Graph 1: 0.88.
Graph 2: 0.43
Graph 3: -0.75
Graph 4: -0.1.
How to Estimate the Correlation Coefficient, R-value, from a Scatter Plot?You can visually examine the graph to determine the direction and strength of the relationship between the two variables.
If the points tend to form a straight line sloping upwards to the right, the correlation is positive, indicating that the two variables are positively related (as one variable increases, so does the other). If the points tend to form a straight line sloping downwards to the right, the correlation is negative, indicating that the two variables are negatively related (as one variable increases, the other decreases).
The strength of the correlation is determined by how tightly the points are clustered around the line. If the points are tightly clustered around the line, the correlation is strong. If the points are scattered more widely, the correlation is weak.
Once you have determined the direction and strength of the relationship, you can estimate the correlation coefficient using a rough approximation. For example, if the correlation is positive and the points are tightly clustered around the line, the correlation coefficient is likely to be close to +1. If the correlation is negative and the points are widely scattered, the correlation coefficient is likely to be close to -1. If there is no clear relationship, the correlation coefficient is likely to be close to 0.
Therefore:
Graph 1 has an r-value of 0.88.
Graph 2 has an r-value of 0.43 because the points are moderately farther apart from each other and slopes upwards.
Graph 3's r-value would be -0.75 because the points are closer to each other and slopes downwards to the left.
Graph 4's r-value would be -0.1.
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Use the remainder theorem to quickly check if (x-3) is a factor of f(x)=2x^3-4x^2-8
Answer:
2x^2 + 4x +2 is questiont and 28 is remainder ok
Darvin Furniture marks up the price of a dining room set 60%. What will be the selling price of a dinning room set that Darvin buys for $1400?
Answer: $2240
Step-by-step explanation:
$1400 x 1.60 = $2240
The members of a cooking club are making cakes, which they will sell at a street fair for $8 apiece. It cost $36 for a booth at the fair, and the ingredients for each cake cost $6. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How much will the sales and expenditures be? How many cakes will they have sold? PLEASE ANSWER AS QUICK AS POSSIBLE!!
They need to sell 18 pieces to cover their expenditures (have a profit of zero).
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
How many cakes will they have sold?
We know that the costs are:
$36 for the booth at the fair.
$6 for each piece of cake they sell.
And the revenue is:
$8 for each piece of cake.
So, the profit (the difference between the revenue and the cost) for selling x pieces is:
p(x) = $8*x - $6*x - $36
p(x) = $2*x - $36
We want to find the value of x such that p(x) = 0, then:
0 = $2*x - $36
x = $36/$2
= 18
They need to sell 18 pieces to cover their expenditures (have a profit of zero).
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25% of 48 is what value? 12 23 30 42
Answer:
12 is the correct answer
Step-by-step explanation:
12 is correct ans
The 2000 CDC growth charts were developed using a reference population of infants. A pediatrician looks up one of the charts and finds that the 5th percentile for weights of baby boys at 10-1/2 months is 16.7 pounds. This means that ______of the 10-1/2-month-old baby boys in the reference population weigh 16.7 pounds or less, and ______of these baby boys weigh 16.7 pounds or more.
This means that 5% of the 10-1/2-month-old baby boys in the reference population weigh 16.7 pounds or less, and 95% of these baby boys weigh 16.7 pounds or more.
Percentile WeightThe determination is based on the definition of a percentile. A percentile is a value below which a certain percentage of the data falls. So, in this case, if a weight of 16.7 pounds is at the 5th percentile for 10-1/2-month-old baby boys, then 5% of the baby boys in the reference population have a weight of 16.7 pounds or less. This also means that the remaining 95% of the baby boys in the reference population have a weight of more than 16.7 pounds.
The calculation of percentiles is based on the ranking of the data set. The data is first sorted in ascending order and then divided into 100 equal parts, with each part representing a percentile. The value at each percentile is the value below which a certain percentage of the data falls.
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whats this i need help
The minimum number of bins that she will need to safely stock the extra clothing will be 24
How to calculate the word problemA word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
The minimum number of bins that she will need to safely stock the extra clothing will be:
= 350 / 15
= 24 rounded up.
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What is the difference of 85.23 and 2.676
Answer:
82.554
Step-by-step explanation:
take 85.23 subtract from 2.676;
= 85.23-2.676
=82.554
A line passes through the point (5,-5) and has a slope of -2
Find the Pearson coeffiecent of skewness formula and use the SKEW function in Excel to measure the skewness of the following data set: 418, 184, 264, 347, 485, 382
Round all calcuated values to the hundreths.
The value that tells us the skewness of the data that we have here is -0.4273
How to solve for the skewnessThe skewness of the data distribution is the statistic that is used to tell us of the level of asymmetry that is in the data set.
In order to solve for the skewness, we would have to use Microsoft excel
All of values would be entered into the formula
SKEW (418, 184, 264, 347, 485, 382)
The output that it would display can be rounded to -0.427
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