C+78=47 what is The answer for C
Using L’Hôpital’s Rule, evaluate
heeeeeelp
The value of the given limit expression is 1.
Given is limit expression [tex]\lim _{x\to \infty }\left(x^{\frac{1}{3x}}\right)[/tex], we need to use L’Hôpital’s Rule to solve it,
So,
[tex]\lim _{x\to \infty \:}\left(x^{\frac{1}{3x}}\right)[/tex]
Using the exponent rule,
[tex]=\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right)[/tex]
Applying the chain rule,
[tex]\lim _{x\to \infty \:}\left(e^{\frac{1}{3x}\ln \left(x\right)}\right) = 1[/tex]
Hence the value of the given limit expression is 1.
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Lingenburger Cheese Corporation has 6.4 million shares of common stock outstanding, 200,000 shares of 3.8 percent preferred stock outstanding, par value of $100, and 120,000 bonds with a semiannual coupon of 4.8 percent outstanding, par value $1,000 each. The common stock currently sells for $54 per share and has a beta of 1.08, the preferred stock currently sells for $103 per share, and the bonds have 15 years to maturity and sell for 107 percent of par. The market risk premium is 7.5 percent, T-bills are yielding 2.4 percent, and the company's tax rate is 22 percent. eBook Hint Print a. What is the firm's weight of equity, debt, and preferred stock.
The weights of equity, debt, and preferred stock, based on the market value of each component, of Linge burger Cheese Corporation, are as follows:
Weight of equity = 69.87%Weight of preferred stock = 4.17%Weight of debt = 25.96%.What is the firm’s weight of equity, debt, and preferred stock?Firstly, we calculate the market value of each capital component and divide the result by the total market value of the firm. This process determines the weights of equity, debt, and preferred stock.
The market value of equity is the number of shares outstanding multiplied by the current share price.
Common stock:Number of shares outstanding = 6.4 million
Market value per share = $54
Common stock beta = 1.08
Market value = $345.6 million (6.4 million × $54)
3.8% preferred stock:Number of shares outstanding at $100 par value = 200,000
Market value per share = $103
Market value = $20.6 million (200,000 × $103)
4.8% Bonds:Number of bonds outstanding, par value $1,000 each = 120,000
Maturity period of bonds = 15 years
Market value per bond = 107 percent of par
Market value of debt = $128.4 million (120,000 × 1.07 × $1,000)
T-bill yields = 2.4%
Corporate tax rate = 22%
Total market value = $494.6 million ($345.6 million + $20.6 million + $128.4 million)
Weight of equity = 0.6987 or 69.87% ($345.6 million ÷ $494.6 million)
Weight of preferred stock = 0.0417 or 4.17% ($20.6 million ÷ $494.6 million)
Weight of debt = 0.2596 or 25.96% ($128.4 million ÷ $494.6 million)
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A normal distribution has a mean of 146 and a standard deviation of 4. Find the z-score of the data value of 153
Answer:
To find the z-score of a data value, we use the following formula:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean of the distribution, and σ is the standard deviation.
Given a normal distribution with a mean (μ) of 146 and a standard deviation (σ) of 4, and a data value (x) of 153, we can plug these values into the formula:
z = (153 - 146) / 4
z = 7 / 4
z = 1.75
Thus, the z-score of the data value 153 is 1.75.
I don’t understand this one here I need help
Assuming [tex]f(x)=x^2[/tex].
[tex]y=x^2\\x=-\sqrt y \vee x=\sqrt y[/tex]
Since [tex]x\geq0[/tex] only [tex]x=\sqrt y[/tex] is valid.
Therefore
[tex]f^{-1}(x)=\sqrt{x}[/tex]
For the linear equation 5x+4y=16, express y in terms of x
please help!!!
Answer:
y = 4 - 1.25x
Step-by-step explanation:
5x + 4y = 16
subtract 5x from both sides
4y = 16 - 5x
divide all by 4
y = 4 - 1.25x
The following is a list of weights, in pounds, of dogs at a bark park. Is the mean, median, or mode likely to be the best
measure of the center for the data set?
35, 39, 37, 37, 38, 34, 35, 37,65
answer :
median or 37
explanation :
median is not influenced by an outlier like 65 in the dataset
steps :
to get the median
arrange the weights in order from smallest to largest:
34, 35, 35, 37, 37, 37, 38, 39, 65
median = middle value = 37
37 has :
four weights before it &
four weights after it
so the median weight is 37 pounds.
Based on the graphs of f (x) and g(x), what is (f ⋅ g)(1)?
The value of the composite function (f . g)(1) when evaluated is 6
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
The graph of the function f(x)
Also, we have
The graph of the function g(x)
The composite function (f . g)(1) is calculated as
(f . g)(1) = f(1) * g(1)
From the graph, we have the following values
f(1) = -2
Also, we have
g(1) = 3
So, we have
(f . g)(1) = 2 * 3
Evaluate
(f . g)(1) = 6
Hence, the composite function (f . g)(1) when evaluated is 6
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Helena lost her marbles but then she found them and put them in 4 bags with m marbles in each bag she had 3 marbles left over that didn’t fit in the bags how many marbles did Helena have in all I need help
Use the table that shows the recent population, in millions, of the ten largest U.S. cities.
Find the mean absolute deviation. Round to the nearest hundredth.
The mean absolute deviation =________million.
The mean absolute deviation of the population is:
1.50 million
How to calculate the mean absolute deviation of a data set?Mean absolute deviation (MAD) is a measure of the average absolute distance between each data value and the mean of a data set. The formula for MAD is:
MAD =∑|x-m|/n
∑ is known as Sigma and means to sum up
| | are vertical bars that mean absolute value
x is each value
m is the mean
n is the total number of data points in your data set
n = 10
m = (1.5 + 3.8 + 1.3 + 1.6 + 2.9 + 1.4 + 0.9 + 2.3 + 8.4 + 1.3)/10
= 25.4/10
= 2.54
∑|x-m| = |1.5-2.54| + |3.8-2.54| + |1.3-2.54| + |1.6-2.54| + |2.9-2.54| + |1.4-2.54| +|0.9-2.54| + |2.3-2.54| + |8.4-2.54| + |1.3-2.54|
= 1.04 + 1.26 + 1.24 + 0.94 + 0.36 + 1.14 + 1.64 + 0.24 + 5.86 + 1.24
= 14.96
MAD =∑|x-m|/n = 14.96/10 = 1.496
Rounding to the nearest hundredth:
MAD = 1.50
Therefore, the mean absolute deviation of the population is 1.50 million
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A lorry tank was 4/5 full of petrol. when the Guage indicate 72litres. what is the full capacity of the tank?
The calculated full capacity of the tank is 90 liters
From the question, we have the following parameters that can be used in our computation:
Proportion = 4/5
This is represented as
Size = 72 liters
Using the above as a guide, we have the following:
4/5 * x = 72 liters
Where
x = the full capacity of the tank
So, we have
x = 72 * 5/4
Evaluate
x = 90
Hence, the full capacity of the tank is 90 liters
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Based on proportions, if a lorry tank was ⁴/₅ full of petrol when the gauge indicates 72 liters, the full capacity of the tank is 90 liters.
What is proportion?Proportion refers to the fraction or portion of a whole value, quantity, or number.
Proportions are ratios equated to each other.
We can depict proportions using fractions, decimals, or percentages.
The fraction of the lorry tank of petrol = ⁴/₅ (0.80)
If ⁴/₅ = 72 liters, proportionately, the full tank = 90 liters (72 ÷ 0.80)
Thus, we can conclude that when the lorry tank is full the quantity of petrol in it is 90 liters.
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In the circle below, IK is a diameter. Suppose mIJ=78 and mILJ=69 . Find the following.
m
m
Applying the inscribed angle theorem, the indicated measures in the circle are: a) m<JIK = 51°; b) m<KJL = 51°.
How to Find the Measures in the Circle Using the Inscribed Angle Theorem?Recall that the measure of an intercepted arc is equal to twice the measure of an inscribed angle, based on the inscribed angle theorem.
We are given the following:
m(IJ) = 78°
m<IJL = 39°
Therefore, we have:
a. m<JIK = 1/2(m(JK)) [based on the inscribed angle theorem]
m(JK) = 180 - m(IJ)
m(JK) = 180 - 78 = 102°
Thus:
m<JIK = 1/2(102)
m<JIK = 51°
b. m<KJL = 1/2(m(KL) [based on the inscribed angle theorem]
m(IL) = 2(IJL)
m(IL) = 2(39) = 78°
m(KL) = 180 - m(IL) = 180 - 78
m(KL) = 102°
m<KJL = 1/2(m(KL) = 1/2(102)
m<KJL = 51°
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Complete Question:
In the circle below, IK is a diameter. Suppose m(IJ) = 78° and m(IJL) = 39°. Find the following.
a. m<JIK
b. m<KJL
Missing image is attached below.
Could someone help I’m having a hard time with this question
The cost of covering 1 unit² should be $2.477 to be in the budget and the total area to be covered is 3027.22 ft².
Given is a blueprint we need to find area that be covered and then the cost of covering the area,
So, we will find the area by splitting the figure into different shapes,
So the area =
Ar(rectangle) + Ar(semicircle) + Ar(triangle) + Ar(square)
= 9×3 + 3.14×2²/2 + 1/2×3×1 + 3³
= 27 + 6.28 + 1.5 + 27
= 61.78 units²
Since 1 unit = 7 ft
So, 1 unit² = 49 ft²
therefore, 61.78 units² = 61.78 × 49 = 3027.22 ft²
Since our budget is $7500
Costing of covering the area = 3027.22 × x = 7500
x = $2.477
Hence the cost of covering 1 unit² should be $2.477 to be in the budget.
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Question 1, 11.2.41
ways
A club with sixteen members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no perso
more than one office, in how many ways can those offices be filled?
Answer:
16 x 15 x 14 = 3,360
Explain why the probability of rolling a sum from 2 to 12 is 100%. [C:2]
The probability of rolling a sum from 2 to 12 on 2 dices is 100%
Given the data,
The two dice should be rolled.
Now, there are 36 possibilities that might occur while rolling two normal six-sided dice. The reason for this is that when rolling two dice, the total number of outcomes is the product of the numbers of outcomes for each die, and each die has six potential outcomes (numbers 1 through 6).
The resultant 36 results are as follows:
1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 4-3, 4-4, 4-5, 4-6
5-1, 5-2, 5-3, 5-4, 5-5, 5-6
6-1, 6-2, 6-3, 6-4, 6-5, 6-6
When using two dice, there are a total of 36 possibilities that might occur.
As a result, the results' total ranges from 2 to 12.
Hence , the probability is 100 %
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On a number line, point L is located at -2.5, and point M is at 6.5. If the ratio LK to KM is 6:3, where is point K on the number line?
Point K is located at 3.5 on the number line.
To find point K on the number line, we need to apply the ratio LK to KM, which is 6:3. First, we can simplify this ratio to 2:1.
Next, we will find the total distance between points L and M. The distance LM = 6.5 - (-2.5) = 9 units.
Now, we can divide this distance into 3 equal parts, as per the simplified ratio 2:1. Each part will be 9/3 = 3 units long.
Since LK is 2 parts of the ratio, we will multiply the length of one part (3 units) by 2. LK = 3 * 2 = 6 units.
Finally, we'll find the coordinates of point K by adding the length of LK to the coordinate of point L. So, K = -2.5 + 6 = 3.5.
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Answer:
Point K is at 3.5
Step-by-step explanation:
I just took the test
1-
Find the area of the shaded region.
f(x)=x4-12x³ +48x², g(x)=44x+105
--
***
--
The area is 389.0 (Type an integer or a simplified fraction.)
340
(-1,61)
L
-
(5,325)
Foo
8
1
The total area of the regions between the curves is 389.0 square units
Calculating the total area of the regions between the curvesFrom the question, we have the following parameters that can be used in our computation:
f(x) = x⁴ - 12x³ + 48x²
g(x) = 44x + 105
With the use of graphs, the curves intersect ar
x = -1 and x = 5
So, the area of the regions between the curves is
Area = ∫x⁴ - 12x³ + 48x² - 44x - 105
This gives
Area = ∫x⁴ - 12x³ + 48x² - 44x - 105
Integrate the expression
Area = x * (x⁴ - 15x³ + 80x² - 110x - 525)/5
Recall that x = -1 and x = 5
So, we have
Area = (-1) * ((-1)⁴ - 15(-1)³ + 80(-1)² - 110(-1) - 525)/5 - (5) * ((5)⁴ - 15(5)³ + 80(5)² - 110(5) - 525)/5
Evaluate
Area = 388.8
Approximate
Area = 389.0
Hence, the total area of the regions between the curves is 389.0 square units
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A bag contains 20 pieces of candy. There are 8 grape pieces, 7 cherry pieces, and 5 lemon pieces. One piece is drawn from the bag. Suppose 2 grape pieces, 1 cherry piece, and 1 lemon piece are removed from the bag.
What is the theoretical probability of drawing each flavor now? Enter answer as a decimal number with a leading zero. Example: 0.5
Step-by-step explanation:
20+8+7+2=37
Question 4
The table below shows the scores of a group of students on a 10-point quiz.
Frequency
Test Score
3
4
5
6
7
8
9
10
4
1
0
3
3
5
1
6
The mean score on this test is:
1 pt194 Details
Enter an integer or decimal number [more..)
The median score on this test is:
Question Help: Video 1 Video 2
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The mean score of the test is 7.13.
The median score of the test is 7.
What is the mean and median score on the test?To get mean score, we have to multiply each test score by its corresponding frequency, sum up products and then divide by the total frequency.
Mean score = EF/ n
Mean score = (34 + 41 + 50 + 63 + 73 + 85 + 91 + 106) / (4 + 1 + 0 + 3 + 3 + 5 + 1 + 6)
= (12 + 4 + 0 + 18 + 21 + 40 + 9 + 60) / 23
= 164 / 23
= 7.13
To find the median score, we will arrange the scores in ascending order: [tex]3, 4, 4, 4, 4, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10.[/tex]
Since there are 23 scores, the median will be the 12th score (in the middle). So, the median score = 7.
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What is the area of the object above?
14 cm²
62 cm²
24 cm²
84 cm²
The area of the object in the image shown in the attachment below is calculated as: 62 cm².
How to Find the Area of the Object?The area of the object can be found by decomposing the figure into two rectangles - larger rectangle and smaller rectangle.
Area of the larger rectangle = length * width
Length of the larger rectangle = 5 cm
Width of the larger rectangle = 4 cm
Area of the larger rectangle = 5 * 4 = 20 cm²
Area of the smaller rectangle = length * width
Length of the larger rectangle = 7 cm
Width of the larger rectangle = 6 cm
Area of the larger rectangle = 7 * 6 = 42 cm²
Area of the object = 20 + 42 = 62 cm².
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A pet store has 10 puppies, including 3 poodles, 4 terriers, and 3 retrievers. If Rebecka selects one puppy at random, the pet store replaces the puppy with
a puppy of the same breed, then Aaron chooses a puppy at random. Find the probability that they both select a poodle.
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
The probability that Rebecka and Aaron both select a poodle is 0.09 or 9/100.
We have,
There are 3 poodles out of 10 puppies, so the probability that Rebecka selects a poodle is 3/10.
After Rebecka selects a poodle and it is replaced with another poodle, there are still 3 poodles out of 10 puppies.
This means,
The probability that Aaron selects a poodle, given that Rebecka selected a poodle, is also 3/10.
Now,
P(both select a poodle) = P(Rebecka selects a poodle) × P(Aaron selects a poodle | Rebecka selected a poodle)
= (3/10) × (3/10)
= 9/100
= 0.09
Therefore,
The probability that Rebecka and Aaron both select a poodle is 0.09 or 9/100.
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After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
1: The required table is described below.
2: The range is (0,36)
3: X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)
What is line?A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.
We are given that,
y = -x² + 36
The equation of the rainbow is represented by the parabola,
Now, we are required to find a linear equation which cuts the graph of the parabola at two points.
Let us consider the equation joining the points (-6,0) and (0,36), given by .
y = 6x + 36
So, the corresponding table for the linear equation is given by,
x y = 6x + 36
-6 0
0 36
1 42
6 72
Now, we will answer the questions corresponding the functions.
1. Domain and Range of the rainbow.
Since, the equation of the rainbow is
y = -x² + 36
So, from the figure, we get that,
Domain is the set of all real numbers.
Range is the set {y | y ≤ 36}
Here, domain represents the points which are used to plot the path of the rainbow and range represents the points which are form the rainbow.
Not all points make sense in the range as the parabola is opening downwards having maximum point as (0,36).
2. X and Y-intercepts of the rainbow.
As, the 'x and y-intercepts are the points where the graph of the function cuts x-axis and y-axis respectively i.e. where y=0 and x=0 receptively'.
We see that from the figure below,
X-intercepts are (-6,0) and (6,0) and the Y-intercept is (0,36)
Here, these intercepts represents the point where the parabola intersects the individual axis.
3. Is the linear function positive or negative.
As the linear function is represented by the upward flight of the drone.
So, the linear function is a positive function.
y = 6x + 36
4. The solution of the system of equations is the intersection points of their graphs.
So, from the figure, we see that the equations intersect at the points (-6,0) and (0,36).
Thus, the solution represents the position when both the drone and rainbow intersect each other.
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Triangles A and B are similar. Triangle A is shown below.
The shortest side of triangle B is 6cm. What is the length of the other two sides?
The length of the other two sides of triangle B are determined as:
9 cm and 12 cm.
How to Find the Length of the Sides of Similar Triangles?When solving for the length of the side of triangles that are are similar, note that their sides have lengths that are proportional to each other.
Thus, since triangles A and B are similar, it means they will have side corresponding side lengths that are proportional, therefore:
Let x represent the length of the longest side of triangle B and y represent the medium side.
Therefore, we have:
4/6 = 6/y
4y = 36
4y/4 = 36/4
y = 9 cm
4/6 = 8/x
4x = 48
x = 12 cm
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IXL S.10…Geometry…Explain Down Below Please
The area of the shaded region, to the nearest hundredth can be calculated as approximately: 1,195.71 mm².
What is the Area of the Shaded Region?The area of the shaded region can be found using the area of circle, which is: Area = πr²
Therefore, area of the shaded region = area of larger circle - area of smaller circle.
Area of larger circle:
radius (r) = 14 + 6.6 = 20.6 mm
Area of larger circle = 3.14 * 20.6² = 1,332.4904 mm²
Area of smaller circle:
radius (r) = 6.6 mm
Area of larger circle = 3.14 * 6.6² = 136.7784 mm²
Area of the shaded region = 1,332.4904 - 136.7784 = 1,195.71 mm².
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Find the range and the interquartile range of the data. Determine if there are outliers. 8, 9, 1, 5, 5, 7, 9, 12, 15
Answer:
The range is the difference between the highest and lowest values in a set of data. In this case, the range is 15 - 1 = 14.
The interquartile range (IQR) is the difference between the third and first quartiles of a set of data. The first quartile (Q1) is the middle value of the lower half of the data, and the third quartile (Q3) is the middle value of the upper half of the data. In this case, the IQR is Q3 - Q1 = 12 - 5 = 7.
There are no outliers in this data set. An outlier is a data point that is significantly different from the rest of the data points. In this case, all of the data points are within 14 of the mean, which is 8.5. Therefore, there are no outliers.
Here is a summary of the range and IQR of the data set:
Range: 14
IQR: 7
Step-by-step explanation:
Answer: Range: 14 IQR: 7
Step-by-step explanation:
What is the solution to this system of linear equations?x − 3y = −2x 3y = 16(7, 3)(3, 7)(−2, −3)(−3, −2)
The solution to the system of linear equations is (14, 16/3).
To find the solution to the given system of linear equations, we can use the method of substitution. First, we can solve the second equation for y by dividing both sides by 3, which gives us y = 16/3. .
We can then substitute this value of y into the first equation and solve for x. This gives us x - 3(16/3) = -2, which simplifies to x = 14. This point represents the intersection of the two lines, where they cross over each other on the coordinate plane.
The other answer choices given in the question are not valid solutions to the system of equations.
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Answer:
C
Step-by-step explanation:
Learn with an example
Factor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
6c³-9c
The greatest common factor is 3C and GCF form of polynomial is 3c(c² - 3).
The given polynomial is
6c³-9c
We can write it as;
3c(c² - 3)
We know that
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor (HCF) is another name for it.
Therefore 3c is its GCD.
Divide each term of polynomial 3c,
6c³ ÷ 3c = 2c² and -9c ÷ 3c = -3
Thus,
3c(c² - 3) is the factored version of the polynomial with the highest common factor.
Also if GCD is 1 then after dividing each term by 1 we get same result
thus the polynomial be 3c(c² - 3).
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Find the numerical value of the log expression.
log a = -1
log b = -6
log
a²
64c4
log c = 3
The numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] is 10 when log a = -1, log b = -6 and log c = 3.
Given that,
We have to find the numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] when log a = -1, log b = -6 and log c = 3.
We know that,
The use of a logarithm can be applied to solve issues that cannot be resolved using the concept of exponents simply. A logarithm is simply a different way to define exponents.
So,
Take the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex]
= [tex]log\frac{a^2}{b^4c^4}[/tex]
= log a² - log(b⁴c⁴) [ from [tex]log\frac{x}{y}[/tex] = log x-log y ]
= log a² - (log b⁴ + log c⁴) [ from log (xy) = log x + log y ]
= 2log a - 4log b - 4log c [ from log xⁿ = nlog x ]
= 2( -1) - 4(-6) - 4(3)
= -2 + 24 - 12
= 24 - 14
= 10
Therefore, The numerical value of the logarithm expression that is [tex]log\frac{a^2}{b^4c^4}[/tex] is 10.
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PLEASE ANSWER URGENTLY
What is the domain of y = cot x?
A. (0,pi)
B. all x ≠ kpi/2, where k is an integer
C. all x ≠ pi/2 + kpi, where k is an integer
D. all x ≠ kpi, where k is an integer
E. (-00,00)
The domain of y = cot x is (d) all x ≠ kπ, where k is an integer
Calculating the domain of y = cot x?From the question, we have the following parameters that can be used in our computation:
y = cot x
The domain of the function y = cot x is the set of input values the function can take
As a general rule
The function y = cot x is undefined at the points x = πk where x is an integer
This means that the domain of the function is the set of all real numbers except x = πk
Hence, the domain of y = cot x is (d)
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Write an expression without using the absolute value symbols
The absolute value function can be written as:
if x > 5, then |7 - (12 - x)| = x - 5if x = 0, then |7 - (12 - x)| = 0if x < 5, then |7 - (12 - x)| = 5 - xHow to write the absolute value function?Here we have the function:
|7 - (12 - x)|
We can simplify this to get.
|7 - 12 + x| = |x - 5|
Now, if the argument is positive, then the function is equal to the argument.
If the argument is negative, the function is equal to minus the argument.
Then we can write:
if x > 5, then |7 - (12 - x)| = x - 5
if x = 0, then |7 - (12 - x)| = 0
if x < 5, then |7 - (12 - x)| = 5 - x
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