Answer:
$26
Step-by-step explanation:
40% of 65 = 0.4 × 65 = 26
if function is differentiable at a, where a>0 is an element of real numbers, evaluate the following limit
limit f(x)-f(a)/√x-√a as x approaches a
Answer: We can use algebraic manipulation to simplify the expression:
(f(x) - f(a)) / (sqrt(x) - sqrt(a))
Multiplying the numerator and denominator by the conjugate of the denominator, we get:
[(f(x) - f(a)) / (sqrt(x) - sqrt(a))] * [(sqrt(x) + sqrt(a)) / (sqrt(x) + sqrt(a))]
Simplifying the numerator, we get:
[f(x) - f(a)] * [sqrt(x) + sqrt(a)]
Expanding the numerator, we get:
f(x) * sqrt(x) + f(x) * sqrt(a) - f(a) * sqrt(x) - f(a) * sqrt(a)
We can simplify this expression by subtracting and adding f(a) * sqrt(x) to get:
f(x) * sqrt(x) - f(a) * sqrt(x) + f(a) * sqrt(x) + f(x) * sqrt(a) - f(a) * sqrt(a)
Factoring out common terms in the first two and last two terms, we get:
sqrt(x) * [f(x) - f(a)] + sqrt(a) * [f(x) - f(a)]
Now we can simplify further by factoring out the common factor of [f(x) - f(a)]:
[f(x) - f(a)] * [sqrt(x) + sqrt(a)] / [sqrt(x) - sqrt(a)]
At this point, we can take the limit as x approaches a. Note that this expression is in the indeterminate form 0/0. We can use L'Hopital's rule to evaluate the limit. Differentiating the numerator and denominator with respect to x, we get:
[f'(x) * (sqrt(x) + sqrt(a)) + (f(x) - f(a)) / (2 * sqrt(x))] / [1 / (2 * sqrt(x))]
Taking the limit as x approaches a, we get:
[f'(a) * (sqrt(a) + sqrt(a)) + (f(a) - f(a)) / (2 * sqrt(a))] / [1 / (2 * sqrt(a))]
Simplifying, we get:
2 * f'(a) * sqrt(a)
Therefore, the limit of (f(x) - f(a)) / (sqrt(x) - sqrt(a)) as x approaches a is equal to 2 * f'(a) * sqrt(a).
Step-by-step explanation:
Please help me to do this i really need it.
First correct Answer gets Brainliest.
Answer:
Step-by-step explanation:
-3≤ x = graph 6
-3 > x = graph 3
x≥ 3 = graph 2
x ≤ 3 = graph 4
3 > x = graph 1
x > 3 = graph 5
the closed circles means greater/less than or equal to
the open circle means greater/less than
the direction of the arrow tells you if the number is greater than x or less than x
Read the situations in the table below. Then drag a graph and equation to represent
each situation indicate whether each of the relationships is proportional or non-
proportional
Answer:
Step-by-step explanation:
"Tamara runs 5 miles each week"
Let Tamara runs 'x' weeks then equation that represents the total distance covered by Tamara will be,
1). y = 5x
2). Here 'y' is directly proportional to the number of weeks 'x'.
3). And the graph when plotted will start from 0. Therefore, graph (1) will be the graph for the given equation.
"Tamara runs 5 minutes more than she walks each day."
1). If Tamara walks 'x' minutes daily and she runs for y minutes then relation between x and y will be,
y = x + 5
2). y and x are non proportional.
3). Graph will have y-intercept = 5
Answer:
ik somebody answer already n stuff
Step-by-step explanation:
grace thought of a number, added 7, multiflied by 3, took away 5 and divided by 4 to give an answer of 7
Answer:
Step-by-step explanation:
To find the number that Grace thought:
We'll represent the unknown number as "x."
"Added 7": This can be represented as (x + 7).
"Multiplied by 3": This becomes 3 * (x + 7).
"Took away 5": This is represented as 3 * (x + 7) - 5.
"Divided by 4": This gives (3 * (x + 7) - 5) / 4.
"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.
Now we can solve for x:
(3 * (x + 7) - 5) / 4 = 7
Multiply both sides by 4 to eliminate the denominator:
3 * (x + 7) - 5 = 28
Simplify the left side:
3x + 21 - 5 = 28
Combine like terms:
3x + 16 = 28
Subtract 16 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the number that Grace thought of is 4.
20 points
Use Pythagoras' theorem to work out the
height of the equilateral triangle below.
Give your answer in centimetres
(cm)
Answer:
9 × √3 cm or approximately 15.59 cm
Step-by-step explanation:
(look at the picture)
what is slope 1 and 2?
Answer:
Lets calculate the slope of the line 'l'
Slope is rise over run of a line, so we will see how much the y of the line changes by changing x by 1
So, basically we will select a point on the line and see how much the y-value increases for the point rightward to our point
we see that the y increased by 1 and hence, its slope is 1
Now, the slope of line 'k'
again, we will select a point and go one point to the right
here, we see that the y increases by 2
therefore the slope of line 'k' is 2
For f(x)= 1/x^2-3 substitute 3 for x in the function to solve for f(3)
Answer:
f(3) = 1/(3)^2-3
Step-by-step explanation:
To solve for when x=3, we simple replace x with 3
f(3) = 1/(3)^2-3
Theo solved n + 5 = 11 for the unknown. The steps he took are shown.
He started with 5 tiles.
5 tiles.
Then he added tiles as he counted up to 11.
6 tiles.
He realized he added 6 more tiles to his original 5 to make 11. So he found the unknown to be 6.
How could Theo check his work? Check all that apply.
He could substitute 5 for n in the original equation and add.
He could substitute 6 for n in the original equation and add.
He could subtract 5 from 11 and check that the answer is 6.
He could subtract 11 from 5 and check that the answer is 6.
He could put all the tiles in 1 pile to count them to see if there are 11 in all.
Answer:
the second one, the fourth one, and the fifth one
Step-by-step explanation:
the probability that a student selected in our class will pass mathematics test is 2/3 how many students are likely to feel mathematics in the art class with 69 students
Out of 69 students in the art class, around 23 are expected to fail the mathematics test, assuming the probability of passing given is 2/3.
To determine how many students are likely to fail mathematics in the art class, we need to use the given probability of passing the mathematics test, which is 2/3.
First, let's find the probability of failing the mathematics test. Since passing and failing are complementary events (i.e., if the probability of passing is p, then the probability of failing is 1 - p), we can calculate the probability of failing as 1 - 2/3, which simplifies to 1/3.
Now, let's consider the art class, which has a total of 69 students. If the probability of failing mathematics is 1/3, then approximately 1/3 of the students in the art class are likely to fail the mathematics test.
To find the number of students likely to fail, we multiply the probability of failing (1/3) by the total number of students in the art class (69).
(1/3) * 69 ≈ 23
Therefore, approximately 23 students are likely to fail mathematics in the art class of 69 students based on the given probability of passing the mathematics test.
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An open box is to be made by cutting a square from each corner of a -foot-by- -foot piece $ ) of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume? ( foot in)
Answer:
x = L/6 is the side of the square at the corner
Step-by-step explanation:
Let´s call "x" the side of the square at the edge, then if the cardboard is L*L the volume of the open box is:
V = ( L - 2*x ) * ( L - 2*x) * x
V(x) = [L² - 2*L*x - 2*L*x +4*x²]*x
V(x) = L²*x - 4*L*x² + 4*x³
Taking derivatives on both sides of the equation we get:
V´(x) = L² - 8*L*x + 12* x²
V´(x) = 0 L² - 8*L*x + 12* x² = 0
Solving for x
12*x² - 8*L*x + L² = 0
x₁,₂ = 8*L ±√ 64*L² - 48*L² / 24
x₁,₂ = 8*L ±√16*L² / 24
x₁,₂ = 8*L ± 4*L / 24
x₁ = 12*L /24 then e dismiss x₁ is not a feasible solution
x₂ = 4*L/24
x₂ = L/ 6 = x
24 = 3y Solve for y and show work
Answer:
y=8
Step-by-step explanation:
because 3×8 is 24
and 8 would be the missing number
20, 18, 21, 18, 22, 24, 18, 23, 23, 24 Explain the meeting of the interquartile range as it relates to the number of students in the kindergarten classes
The interquartile range of the data-set is of 5.5, which means that the middle 50% kindergarten classes has a number of students that differ by at most 5.5.
What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile(Q1) is the median of the first half of the data-set, and is also the 25th percentile.The third quartile(Q3) is the median of the second half of the data-set, and is also the 75th percentile.The interquartile range(IQR) represents the middle 50% of the distribution, and is given by Q3 - Q1.For this problem, the ordered data-set is given by:
18, 18, 18, 20, 21, 22, 23, 23, 24, 24.
There are 10 elements, hence:
The first half is 18, 18, 18, 20, which has median (18 + 18)/2, hence Q1 = 18.The second half is 23, 23, 24, 24, which has median (23 + 24)/2, hence Q3 = 23.5.Then the IQR is:
Q3 - Q1 = 23.5 - 18 = 5.5.
The IQR is of 5.5, which means that the middle 50% kindergarten classes has a number of students that differ by at most 5.5.
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To the nearest degree, what is the measure of the central angle for bathing?
The central angle of Bathing = 108 degrees.
In the given pie chart,
Since we know,
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.
The whole circle is 360 degrees
which represents 100%.
It is given that,
Bathing = 30%
So have need to find 30% of 360 degrees.
Therefore,
Bathing = (30/100)x360
= (30/10) x 36
= 3x36
= 108
Hence,
The central angle = 108 degrees.
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The complete question is:
To the nearest degree, what is the measure of the central angle for bathing?
Can a trapezoid that is not isosceles be drawn on a square lattice.
Answer:
yes it can my dear yesss trapezoids it can
Answer:
I am not sure about this one
Use the Compound interest formula to compute the total amount accumulated and the interest earned.
$3000 for 5 years at 5% compound quarterly.
The total amount accumulated after 5 years is $____
(Round to the nearest cent as needed)
The total amount accumulated after 5 years is $3,846.11
The interest earned after 5 years is $846.11
What is the total amount accumulated and the interest earned?When an amount earns a compound interest, it means that the amount grows at an exponential rate. This means that both the amount invested and the interest that has already being earned increases in value at each compounding time.
The formula for calculating future value when there is quarterly compounding:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = quarterly interest rate = annual interest rate / number of compounding = 5% / 4 = 1.25%m = number of compoundingN = number of yearsFV = 3000 x (1 + 0.0125)^(4 x5)
FV = 3000 x (1.0125)^20 = $3,846.11
Interest is the difference between the future value of the amount invested and the amount invested.
Interest = future value - amount invested
$3,846.11 - $3000 = $846.11
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206) A recipe for cupcakes calls for 3-
3
10
200
7
sugar. Julio accidentally put in 4-
10
How many extra cups did he put in?
cups of
cups.
Julio accidentally put in an extra 1/10 cup of sugar.
To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).
The difference can be calculated as follows:
Actual amount - Required amount = Extra amount
= 4/10 - 3/10
= 1/10
Therefore, Julio accidentally put in an extra 1/10 cup of sugar.
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Please help urgent thank you
If he wants an average of 84, he needs to get at least 93 points.
What score does he need to get in the next test?Remember that the average value between 3 values A, B, and C is:
(A + B + C)/3
Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:
(76 + 83 + x)/3 = 84
159 + x = 252
x = 252 - 159
x = 93
So he needs to get at least 93 points in the next exam.
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Instructions: Identify the key features of the following graph. If the Domain is all real numbers, type in 'All Real" into the Domain box
Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)
How to determine the key features?Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:
Vertex: The graph's vertex is at (-1, -5), which indicates that the graph extends upwards (because y = -5 is the minimal value).A vertical line at x = -1 serves as the graph's axis of symmetry. The graph is split into two symmetrical sections by this line.Y-intercept: The graph's y-intercept is at (0, -3), which indicates that here is where the graph and y-axis connect.The graph has a minimum point at y = -5, which is also the vertex of the graph and the lowest point on it.The graph's domain is set as "All Real" or "(-, )", which signifies that it spans all real values on the x-axis horizontally.Range: The graph's range is defined as y -5, which indicates that it climbs vertically from -5 and above on the y-axis.The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).
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- b/0.1 +2.9= -35.1 no links or anything just the answer
Answer:
b = 3.8
Step-by-step explanation:
- b/0.1 +2.9= -35.1
Subtract 2.9 from each side
- b/0.1 +2.9-2.9= -35.1-2.9
-b/.1 = -38
Multiply each side by -.1
-b/.1 * (-.1) = -38 *(-.1)
b = 3.8
What is the distance between the two points at(-3,8) and(-3,-7)
Answer:
\(\boxed {\boxed {\sf 15}}\)
Step-by-step explanation:
Distance is calculated using this formula:
\(d=\sqrt {(x_2-x_2)^2+(y_2-y_1)^2\)
where (x₁, y₁) and (x₂, y₂) are the points. We are given (-3,8) and (-3,7). Therefore;
\(x_1= -3 \\y_1= 8 \\x_2= -3 \\y_2= -7\)
Substitute the values into the formula.
\(d= \sqrt {(-3--3)^2+(-7-8)^2\)
Solve inside the parentheses.
-3 - - 3= -3+3= 0 -7 - 8 = -15\(d= \sqrt {(0)^2+(-15)^2\)
Solve the exponents.
0²=0*0= 0 -15²= -15*-15=225\(d=\sqrt {0+225\)
\(d=\sqrt {225\)\(d= \pm 15\)
A negative number for distance doesn't make sense, so the distance must be 15.
Nina worked 12 hours on Monday, 7 hours on Wednesday, and 7 hours on Friday.Here gross pay for all 3 days was $236.21. What was her hourly rate?Round answer to a hundredths place. If answer does not have a hundredths placethen include zeros so that it does have a hundredths place
First, find the total amount of time that Nina worked. Then, divide the gross pay over the total amount of time (measured in hours) that Nina worked to find the hourly pay rate.
Since Nina worked 12 hours on Monday, 7 hours on Wednesday and 7 hours on Friday, the total amount of time that Nina worked was:
\(12+7+7=26\)Since her gross pay was $236.21, divide 236.21 over 26 to find the hourly rate:
\(\frac{236.21}{26}=9.085\)Since the last nonzero digit of the number 9.085 is a 5, round it up to the hundredths place.
Therefore, the hourly rate is equal to 9.09 dollars per hour.
The measure of one small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
Answer:
x + x - 45 = 90
2x - 45 = 90
2x = 135
x = 67.5, so x - 45 = 22.5
The other two angles measure 22.5° and 67.5°.
Combine like terms to simplify the expression:
12x-3(3x-5)+24
Answer:
3(x+13)
Step-by-step explanation:
use the distributive property to multiply -3 by
3x -5
12x -9x + 15 + 24
then
combine 12x and -9x to get 3
add 15 + 24 to get 39
In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
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Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
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Solve the system of equations :-)
Thank you
A news agent conducted a survey of business magazine subscribers in a town and found that there was
circulation of only three business magazines. He made the Venn diagram below to show the number of
subscribers to each of the three magazines: Board Review, Strategy and Finance, and Investor Journal
394 subscribers are represented in the venn diagram.
What is venn diagram?Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.
Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.
according to the venn diagram
196+41+21+52+84 = 394
There are 394 subscribers
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72. Evaluate 5a + 3a2 when a = - 3
\(5a + 3 {a}^{2} \\ = 5( - 3) + 3( { - 3}^{2} ) \\ = - 15 + 3(9) \\ = - 15 + 27 \\ = 12\)
I hope I helped you^_^
Answer:
12
Step-by-step explanation:
5a + 3a^2 when a = -3
~Substitute
5(-3) + 3(-3)^2
~Simplify
-15 + 3(9)
-15 + 27
12
Best of Luck!
X-4=12 what does x equal
Answer:
x = 16
Step-by-step explanation:
So we do the fancy inverse thing:
x - 4 + 4 = 12 + 4
x = 16
A non-inverting amplifier with gain 10 is ealized using an operational amplifier having open-loop gain 10^5. What is the feedback factor β
a. 99.99x10^-3
b. 9.99x10^-3 c. 10
d. 90.9x10^-3
The feedback factor β is 90.9x10^-3 option d is correct.
A non-inverting amplifier with a gain of 10 is realized using an operational amplifier with an open-loop gain of 105.
The non-inverting amplifier circuit is shown below:
Non-inverting amplifier circuit In the circuit above, the gain of the amplifier is given by:
$$\begin{aligned}A_v &= \frac{v_o}{v_i}\\&
= 1 + \frac{R_f}{R_1}\\\
therefore \frac{R_f}{R_1} &= A_v - 1\\&
= 10 - 1\\
&= 9\end{aligned}$$
The feedback factor βb is given by:
$$\begin{aligned}\beta_b &= \frac{R_f}{R_f + R_1}\\\
therefore R_1 &
= \frac{R_f}{\beta_b} - R_f\\
&= R_f \left(\frac{1}{\beta_b} - 1\right)\\&
= R_f \left(\frac{1 - \beta_b}{\beta_b}\right)\end{aligned}$$
Substituting the value of Rf/R1 from above:
$$\begin{aligned}\frac{R_f}{R_1} &= 9\\\frac{R_f}{R_f \left(\frac{1 - \beta_b}{\beta_b}\right)} &= 9\\\frac{1}{\left(\frac{1 - \beta_b}{\beta_b}\right)} &
= 9\\\frac{\beta_b}{1 - \beta_b} &
= \frac{1}{9}\\\beta_b &= \frac{1}{10.99}\\&
= 0.0909\end{aligned}$$
Therefore, the feedback factor βb is 0.0909 or 90.9 x 10-3. The answer is option d.
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Gabriel made 6 small meatloaves. He cut each meatloaf into fourths.
How many
1
4
-size pieces of meatloaf does Gabriel have? please respond this message will be due till sunday
Answer:
24 1/4 sized pieces
Step-by-step explanation:
If there are 4 pieces in each loaf just multiply by 6 and you got your answer.