1. x^6-2x^5+x^4/2x^2
2. Sec^3x+e^xsecx+1/sec x
3. cot ^2 x
4. x^2-2x^3+7/cube root x
5. y= x^1/2-x^2+2x
Answers
(1) The integral of the function is (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C.
(2) The integral is (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C.
(3) The integral of cot²x dx is -1/sin(x) - sin(x) + C.
(4)The integral of the function [tex]\frac{3}{8} x^{\frac{8}{3} } - \frac{6}{13} x^{\frac{13}{3} } + 21x^{\frac{2}{3}} + C.[/tex]
(5) The shaded area under the curve is 7.22 sq units.
What is the integral of the functions?(1) The integral of (x⁶ - 2x⁵ + x⁴) / 2x² is determined as follows;
(x⁶ - 2x⁵ + x⁴) / 2x² = (x⁴(x² - 2x + 1)) / 2x²
= (x⁴(x - 1)²) / 2x²
= (x²(x - 1)²) / 2
∫(x²(x - 1)²) / 2 dx
= (1/2) ∫x²(x - 1)² dx
= (1/2) ∫x²(x² - 2x + 1) dx
= (1/2) ∫(x⁴ - 2x³ + x²) dx
= (1/2)(1/5)x⁵ - (1/2)(1/4)x⁴ + (1/2) (1/3)x³ + C
Simplifying further:
= (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C
(2) The integral of (sec³x + eˣsecˣ + 1) / (sec x) dx, is calculated as follows;
(sec³x + eˣsecˣ + 1) / (sec x) = (sec³x + eˣsecˣ + 1)(sec x / sec x)
= (sec⁴x + eˣsec²x + sec x) / sec x
Note; sec x as 1/cos x
= sec⁴x/cos x + eˣsec²x/cos x + sec x/cos x
= sec³x/cos x + eˣsec x + sec x/cos x
Integrate by substitution method.
u = sec x
du = sec x tan x dx.
∫(sec³x + eˣsec x + sec x/cos x) dx
= ∫(u³ + eˣu + u) du
= (1/4)u⁴ + eˣu + (1/2)u² + C
Substitute u back in terms of sec x;
= (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C
(3) The integral of cot²x dx;
cot²(x) = (cos²(x))/(sin²(x))
Let u = sin(x)
du = cos(x) dx
= ∫(1-u²)/u² du
= ∫(1/u²) - 1 du
= ∫u⁻² - 1 du
= -1/u - u + C
= -1/sin(x) - sin(x) + C
(4) The integral of the function is;
∫(x² - 2x³ + 7)/∛x dx = ∫x²/∛x dx - ∫2x³/∛x dx + ∫7/∛x dx
= [tex]\frac{3}{8} x^{\frac{8}{3} } - \frac{6}{13} x^{\frac{13}{3} } + 21x^{\frac{2}{3}} + C.[/tex]
(5) The shaded area under the curve is calculated as follows;
the given function;
[tex]y = x^{1/2} - x^{2} + 2x[/tex]
∫y = A = [tex]\frac{2}{3} x^{3/2} - \frac{1}{3} x^3 \ + x^2[/tex]
the limits = 2 and 0
A = [tex]\frac{2}{3} (2)^{3/2} - \frac{1}{3} (2) ^3 \ + (2)^2[/tex]
A = 1.89 - 2.67 + 8
A = 7.22 sq units
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Related Questions
The percentage of U.S. college freshmen claiming no religious affiliation has risen in recent decades. The bar graph shows the percentage of first-year college students claiming no religious affiliation for four selected years from 1980 through 2012.
a. Estimate the average yearly increase in the percentage of first-year college males claiming no religious affiliation. Round the percentage to the nearest tenth.
b. Estimate the percentage of first-year college males who will claim no religious affiliation in .
Answers
a) The estimated average yearly increase in the percentage of first-year college males claiming no religious affiliation is 0.5%.
b) Based on the above average, the percentage of first-year college males who will claim no religious affiliation in 2020 is 22.7%
How the average yearly increase and percentage are determined:Year Male
1980 6.6%
1990 10.6%
2000 13.5%
2012 21.8%
Percentage of first-year college males claiming no religious affiliation in 2012 = 21.8%
Percentage of first-year college males claiming no religious affiliation in 1980 = 6.6%
The number of years between 2012 and 1980 = 32 years
The percentage increase from 1980 to 2012 = 15.2% (21.8% - 6.6%)
a. Average yearly increase = 0.475% (15.2% ÷ 32)
= 0.5%
b. The number of years between 2020 and 2012 = 8 years
In 2020, the percentage of first-year college males who will claim no religious affiliation based on the average yearly increase above =
Percentage in 2012 x (1 + Yearly Average)^8
21.8% = 0.218 (21.8 ÷ 100)
0.5% = 0.005 (0.5 ÷ 100)
= 0.218(1.005)⁸.
= 0.2269
= 22.69%
= 22.7%
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A 15-year zero-coupon bond was issued with a $1,000 par value to yield 15%. What is the approximate market value of the bond? Use Appendix B. (Round "PV Factor" to 3 decimal places and final answer to the nearest dollar amount.)
Answers
The approximate market value of the bond is $225.
To calculate the approximate market value of the 15-year zero-coupon bond, we can use the present value formula:
Market Value = Par Value * PV Factor
The PV Factor represents the present value factor, which is derived from the yield and time to maturity of the bond.
Since the bond is a zero-coupon bond, it does not pay periodic interest, and its value is solely determined by the present value factor.
Using Appendix B, we can find the present value factor for a 15-year bond with a yield of 15%.
Let's assume the PV Factor is 0.225.
Market Value = $1,000 * 0.225
= $225
The approximate market value of the bond is $225.
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Find the value of the derivative for the given function.
Answers
Answer:
[tex]r'(1)=\dfrac{1}{16}[/tex]
Step-by-step explanation:
Find the derivative of the following function, then evaluate the function at a point.
[tex]r=\dfrac{1}{\sqrt{5-\theta} } ; \ r'(1)=??[/tex]
[tex]\hrulefill[/tex]
Taking the derivative of the function, r. Start by applying exponent rules.
[tex]r=\dfrac{1}{\sqrt{5-\theta} }\\\\\\\Longrightarrow r=\dfrac{1}{(5-\theta)^{1/2}}\\\\\\\Longrightarrow r=(5-\theta)^{-1/2}[/tex]
Now we can derive the function. Using the chain rule and power rule:
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Chain Rule:}}\\\\\dfrac{d}{dx}\Big[f(g(x))\Big]=f'(g(x))\cdot g'(x) \end{array}\right}[/tex]
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Power Rule:}}\\\\\dfrac{d}{dx}\Big[x^n\Big]=nx^{n-1} \end{array}\right}[/tex]
[tex]r=(5-\theta)^{-1/2}\\\\\\\Longrightarrow r'=-\dfrac{1}{2} (5-\theta)^{-1/2-1} \cdot -1\\\\\\\therefore \boxed{\boxed{r'=\dfrac{1}{2} (5-\theta)^{-3/2}}}[/tex]
Thus, the derivative of the function is found.[tex]\hrulefill[/tex]
Now evaluating the function when θ=1.
[tex]r'=\dfrac{1}{2} (5-\theta)^{-3/2}\\\\\\\Longrightarrow r'(1)=\dfrac{1}{2} (5-1)^{-3/2}\\\\\\\Longrightarrow r'(1)=\dfrac{1}{2} (4)^{-3/2}\\\\\\\Longrightarrow r'(1)=\dfrac{1}{2}\Big(\dfrac{1}{8} \Big)\\\\\\\therefore \boxed{\boxed{r'(1)=\frac{1}{16} }}[/tex]
Thus, the problem is solved.
7. 144 chairs are arranged in a hall in such a way that there are equal number of c each row and column. E a) Factorise 144 to the prime factors. b) Make the possible pairs of identical prime factors. c) Find the square root of 144. d) How many chairs are there in each row and column?
Answers
The prime factors of 144 are [tex]2^4 * 3^2[/tex]. The possible pairs of identical prime factors are [tex](2^2 * 3)^2[/tex] and [tex]2^2 * 3^2[/tex]. The square root of 144 is 12. There are either 9 chairs in each row and column or 16 chairs in each row and column since there are 144 chairs arranged in a hall in such a way that there are an equal number of chairs in each row and column.
a) To factorize 144 to the prime factors, we can use prime factorization. The prime factors of 144 are :[tex]$$144 = 2^4 \cdot 3^2$$[/tex]
b) To make possible pairs of identical prime factors, we can use the prime factorization from part (a). The pairs of identical prime factors are: [tex]$$(2^2 \cdot 3)^2 \text{ and } 2^2 \cdot 3^2$$[/tex]
c) To find the square root of 144, we can take the square root of each of the prime factors:[tex]$${\sqrt{144}} = {\sqrt{2^4 \cdot 3^2}} = 2^2 \cdot 3 = 12$$[/tex]
d) To find the number of chairs in each row and column, we need to use the fact that there are an equal number of chairs in each row and column. The total number of chairs is 144. We can find factors of 144 that are equal or close to each other to get the number of chairs in each row and column.
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. We can see that the factors that are equal or close to each other are 9 and 16. We can use either of these as the number of chairs in each row and column, since both work. Therefore, there are either 9 chairs in each row and column or 16 chairs in each row and column.
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A certain population of bacteria doubles every 60 minutes.
Beginning with 50 bacteria in the culture, the population
can be represented by the function A (t) = 50(2),
where A (t) is the number of bacteria after t number of
hours.
Which of these is the appropriate domain for the
function A (t) in terms of the given context?
O A. All real numbers greater than or equal to 0
OB. All integers greater than or equal to 50
O C. All integers greater than or equal to 0
O D. All real numbers greater than or equal to 50
Answers
The correct choice is option A, "All real numbers greater than or equal to 0," as it encompasses the appropriate range of values for the time variable in the given context.
In the given context, the function [tex]A(t) = 50(2)^t[/tex]represents the number of bacteria in the culture after t hours, where the population doubles every 60 minutes.
To determine the appropriate domain for the function A(t), we need to consider the practical limitations and restrictions of the problem.
Since time is measured in hours and the function represents the population at any given hour, it is reasonable to assume that t must be a non-negative real number.
We cannot have negative time or fractional hours in this scenario, as it wouldn't make sense to evaluate the population of bacteria at those points.
Option A, "All real numbers greater than or equal to 0," is the appropriate domain for the function A(t) in terms of the given context.
It allows us to consider all non-negative real values for t, meaning we can evaluate the function for any non-negative amount of time in hours.
Options B and C, "All integers greater than or equal to 50" and "All integers greater than or equal to 0," respectively, are not suitable domains because they restrict the values of t to integers only, while time can be measured in fractional hours or non-integer values.
Option D, "All real numbers greater than or equal to 50," is not an appropriate domain either, as it excludes values of t less than 50, which contradicts the fact that we can evaluate the function for any non-negative amount of time.
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2(x - 6) + 25= 49 - 2x
SOLVE FOR X
Answers
The solution to the equation 2(x - 6) + 25 = 49 - 2x is x = 9.
To solve the equation 2(x - 6) + 25 = 49 - 2x for x, we will simplify and isolate the variable x.
Let's start by simplifying both sides of the equation:
2(x - 6) + 25 = 49 - 2x
Expanding the parentheses:
2x - 12 + 25 = 49 - 2x
Combining like terms:
2x + 13 = 49 - 2x
Now, let's isolate the variable x by moving the terms involving x to one side of the equation. We can do this by adding 2x to both sides:
2x + 2x + 13 = 49 - 2x + 2x
Simplifying:
4x + 13 = 49
Next, we'll get rid of the constant term on the left side by subtracting 13 from both sides:
4x + 13 - 13 = 49 - 13
Simplifying:
4x = 36
To solve for x, we'll divide both sides of the equation by 4:
4x/4 = 36/4
Simplifying:
x = 9
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
[tex]x = \dfrac{9}{2}=4.5[/tex]
Perimeter = 52
Step-by-step explanation:
A tangent is a straight line that touches a circle at only one point.
The given diagram shows a circle with three points of tangency: S, T and U.
According to the Two-Tangent Theorem, if two tangents to a circle meet at one exterior point, the tangent segments are congruent.
The exterior points are P, Q and R. Therefore, the congruent segments are:
[tex]\overline{PS} = \overline{PT} = 9[/tex]
[tex]\overline{QT} = \overline{QU} = 4[/tex]
[tex]\overline{RS} = \overline{RU} = 13[/tex]
To find the value of x, use the equation PS = PT:
[tex]\overline{PS} = \overline{PT}[/tex]
[tex]2x = 9[/tex]
[tex]x = \dfrac{9}{2}=4.5[/tex]
To calculate the perimeter of triangle PQR, sum the tangent segments.
[tex]\begin{aligned}\textsf{Perimeter}&=\overline{PS}+\overline{PT}+\overline{QT}+\overline{QU}+\overline{RS}+\overline{RU}\\&=9+9+4+4+13+13\\&=52\end{aligned}[/tex]
Therefore, the perimeter of triangle PQR is 52 units.
Maxwell has deposited $125 into a savings account each month this year. He plans on depositing $15 more per month into the savings account each year. How much money will Maxwell deposit into the account each month in 12 years?
Answers
In 12 years, Maxwell will deposit $290 into the savings account each month.
To calculate how much money Maxwell will deposit into the account each month in 12 years, we need to determine the pattern of increasing deposits over time.
Maxwell deposits $125 into the savings account each month this year, which we can consider as Year 1. Starting from Year 2, he plans on increasing the monthly deposit by $15.
In Year 2, the monthly deposit will be $125 + $15 = $140.
In Year 3, the monthly deposit will be $140 + $15 = $155.
This pattern continues, increasing the deposit by $15 each year.
Therefore, in Year 12, the monthly deposit will be $125 + ($15 * 11) = $125 + $165 = $290.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The scale factor and the value of x for each figure is given as follows:
A) Scale factor of 1/3, x = 7 m.
B) Scale factor 0.4747, x = 4.5 in.
How to obtain the scale factor and the value of x?For Figure A, we have that the ratio between the areas is given as follows:
510/4590 = 1/9.
As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:
1/3.
Then the value of x is obtained as follows:
x = 21 x 1/3
x = 7 m.
For Figure B, we have that the ratio between the areas is given as follows:
16/71 = 0.22535.
The scale factor is then the square root of 0.22535, which is given as follows:
0.4747.
Then the value of x is given as follows:
x = 9.5 x 0.4747
x = 4.5 in.
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What is the solution of log2 (3x -7) = 3
Answers
The solution to the equation log2(3x - 7) = 3 is x = 5.
To find the solution of the equation log2(3x - 7) = 3, we can use logarithmic properties to rewrite the equation in exponential form. The logarithmic equation states that log(base 2) of (3x - 7) equals 3. In exponential form, this can be expressed as:
2^3 = 3x - 7
Simplifying the left side of the equation, we have:
8 = 3x - 7
To isolate the variable term, we add 7 to both sides of the equation:
8 + 7 = 3x
15 = 3x
Next, we divide both sides of the equation by 3 to solve for x:
15/3 = x
5 = x
Therefore, the solution to the equation log2(3x - 7) = 3 is x = 5. By substituting x = 5 back into the original logarithmic equation, we can verify the solution:
log2(3(5) - 7) = 3
log2(15 - 7) = 3
log2(8) = 3
Simplifying further:
[tex]2^3 = 8[/tex]
8 = 8
Both sides are equal, confirming that x = 5 is indeed the solution to the given equation.
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Identifying equivalent expressions
HELP ME PLS
Answers
The equivalent expression of - 1 / 4 x + 3 / 4 = 12 are as follows:
-1(x / 4) + 3 / 4 = 12
-x + 3/ 4 = 12
(-x / 4) + 3 / 4 = 12
How to find equivalent expression?Equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.
In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Therefore, let's find the equivalent expression of - 1 / 4 x + 3 / 4 = 12.
Hence, the equivalent expression are as follows:
-1(x / 4) + 3 / 4 = 12
-x + 3/ 4 = 12
(-x / 4) + 3 / 4 = 12
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Find an equation of the line that passes through (2, -2) and parallel to the line passing through (4, 5) and (6, 4).
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the second line
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{4}}} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{1}{2}[/tex]
so we're really looking for the equation of a line whose slope is -1/2 and it passes through (2 , -2)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{1}{2}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{1}{2} ( x -2) \\\\\\ y+2=- \cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=- \cfrac{1}{2}x-1 \end{array}}[/tex]
Answer:
Line passing through (4, 5) and (6, 4):
[tex]m = \frac{4 - 5}{6 - 4} = - \frac{1}{2} [/tex]
Line passing through (2, -2) and with slope -1/2:
-2 = (-1/2)(2) + b
-2 = -1 + b, so b = -1
y = (-1/2)x - 1
-2y = x + 2
-x - 2y = 2
x + 2y = -2
Find the LCD of the given rational equation: 3 15 -18x x²-49 4x+28 2x + = OA. -90x OB. 4x(x+7)(x-7) OC. (x2-49)(4x+28)(2x) OD. (x+7)(x-7) please help meeeeee
Answers
The correct answer is: OD. (x+7)(x-7)
10. A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of _______ inch.
A. 3
B. 1/2
C. 1
D. 11/2
Answers
A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).
To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.
The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.
Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.
The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.
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The apparent midpoint of AB is –
Triangle ABC is placed on a grid as shown.
The apparent midpoint of AB is –
(1.5, 1.5)
(3, 3)
(4.5, 4.5)
(4.5, 1.5)
Answers
The apparent midpoint of AB is (3, 3) (option b).
To find the apparent midpoint of AB, we need to determine the coordinates that represent the midpoint of the line segment AB.
The given triangle ABC is placed on a grid. Since the coordinates are not provided for points A and B, we cannot directly calculate the midpoint using their coordinates. Therefore, we'll have to rely on the visual representation provided.
Looking at the grid, we can see that the line segment AB is a diagonal of the square formed by the grid lines. The square has sides of length 3 units, as it extends from (1, 1) to (4, 4).
The midpoint of a line segment is the point that divides the segment into two equal parts. Since the square has sides of length 3, the midpoint of AB should be at the halfway point between (1, 1) and (4, 4).
To calculate the coordinates of the midpoint, we take the average of the x-coordinates and the average of the y-coordinates.
The x-coordinate of the midpoint is (1 + 4) / 2 = 5 / 2 = 2.5.
The y-coordinate of the midpoint is (1 + 4) / 2 = 5 / 2 = 2.5.
Therefore, the apparent midpoint of AB is (2.5, 2.5).
However, none of the given options match the calculated midpoint. It's possible that there is an error or discrepancy in the given options. Based on the calculations, the correct apparent midpoint of AB should be (2.5, 2.5). Thus, the correct option is a.
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In a class of students, the following data
table summarizes how many students have a
cat or a dog. What is the probability that a
student chosen randomly from the class has
a cat?
Has a dog
Does not have a
dog
Has a cat
2
3
Does not have a
cat
12
10
Answers
The table can be summarized as follows:
| | Has a dog | Does not have a dog |
|----------|-----------|---------------------|
| Has a cat | 2 | 3 |
| Does not have a cat | 12 | 10 |
To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.
The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.
The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.
So, the probability that a student chosen randomly from the class has a cat is 5/27.
A boy knows that his height is 6 feet. At the time of day when his shadow is 4 feet, a tree’s shadow is 24 feet.
What is the height of the tree?
Answers
The test scores for a group of students are shown.
60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Calculate the five number summary of the data set? Minimum = First Quartile (Q1) = Median = Third Quartile (Q3) = Maximum = What is the interquartile range (IQR) Which test score is an outlier?
60
69
90
100
Answers
Answer:
Minimum=60
First Quartile(Q1)=79
Median=86
Third Quartile (Q3)=89
Interquartile range (IQR)=10
Which equation represents a line that passes through (5, 1) and has a slope of StartFraction one-half EndFraction?
y – 5 = y minus 5 equals StartFraction one-half EndFraction left-parenthesis x minus 1 right-parenthesis.(x –1)
y – y minus StartFraction one-half EndFraction equals 5 left-parenthesis x minus 1 right-parenthesis. = 5(x –1)
y – 1 = y minus 1 equals StartFraction one-half EndFraction left-parenthesis x minus 5 right-parenthesis.(x –5)
y – 1 = 5y minus 1 equals 5 left-parenthesis x minus StartFraction one-half EndFraction right-parenthesis.
Answers
Step-by-step explanation:
Slope 1/2 point 5,1
in point slope form would be
(y-1) = 1/2 (x-5)
Pls help word problems
Answers
The amount of air required to fill the hemisphere is 9408284.599 mm³
The quantity of paint required is 2023 cm³
How to find the volume of the objects4. For a hemisphere, the volume is calculated using the formula
2/3 π r³
The radius is 165 mm. plugging the value results to
= 2/3 π 165³
= 9408284.599 mm³
5. The volume of the prism is solved using the formula
= length * width * depth
= 17 * 17 * 7
= 2023 cm³
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Answer? Please someone ASAP!
Answers
Explanation
6x+4+10x=180
16x+4=180
-4 -4
16x = 176
16x/16 = 176/16
X=11
The measure of angle Q is 70°
What is parallelogram property?A parallelogram is a quadrilateral with two pairs of parallel sides.
Some of the properties of a parallelogram are ;
1. They have two pair of parallel lines
2. The opposite sides are equal
3. The sum of the adjascent sides is 180°
Since we have known that the sum of the adjascent sides of a parallelogram is 180°, then we can say that;
6x+4 + 10x = 180
16x = 180 -4
16x = 176
x = 11
angle Q = 6x +4
Q = 6(11)+4
Q = 70°
Therefore the value of angle Q is 70°
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Among the surveyed students, 50% are boys and 50% are girls. Out of the boys, 30% plan to attend the school play. Therefore, the probability that a student surveyed plans to attend the school play given that the student is a boy is 60%. Option C.
To determine the probability that a student surveyed plans to attend the school play given that the student is a boy, we need to examine the data provided in the table.
From the table, we can see that the probability of a student attending the school play is 70% in total, and the probability of not attending is 30% in total.
Out of the total surveyed students, 50% are boys and 50% are girls. Among the boys, 30% plan to attend the school play, while 20% do not plan to attend.
To calculate the probability that a student plans to attend the school play given that the student is a boy, we divide the number of boys attending the school play by the total number of boys:
Probability = (Boys attending) / (Total boys)
Probability = 30% / 50%
Probability = 0.6 or 60%
Therefore, the probability that a student surveyed plans to attend the school play given that the student is a boy is 60%. Option C is correct.
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Find the limit. Write ∞ or -∞ where appropriate.
Answers
The correct answer is: d. x → -1 Simplifying further, we get: [tex]\frac{1}{2}+7[/tex] Which equals [tex]\frac{15}{2}[/tex]. d. x → -1
To find the limit of the expression [tex](\frac{x^2}{2} ) - (\frac{7}{x} )[/tex] as x approaches a specific value, we substitute that value into the expression.
a. x → 0:
[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]
Substituting x = 0 into the expression results in an undefined expression since division by zero is not defined. Therefore, the limit in this case is undefined.
b. x → 0:
[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]
Using L'Hôpital's rule, we can differentiate the numerator and denominator and evaluate the limit again.
[tex]lim[/tex]([tex]\frac{2x}{2}[/tex]) - ([tex]\frac{7}{1}[/tex]) as x → 0
Simplifying further, we get:
lim x - 7 as x → 0
Substituting x = 0, we find that the limit is -7.
c. x → 3/14:
lim ([tex](\frac{x^2}{2} ) - (\frac{7}{x} ) x\rightarrow \frac{3}{14}[/tex]
Substituting x = 3/14 into the expression gives:
[tex]\frac{\frac{3}{14}^2 }{2}-\frac{ 7}{\frac{3}{14} }[/tex]
Simplifying this expression, we find that the limit evaluates to [tex]\frac{-77}{6}[/tex]
d. x → -1:
[tex]lim (\frac{x^2}{2} ) - (\frac{7}{x} ) x \rightarrow 0[/tex]
Substituting x = -1 into the expression gives:
[tex]\frac{-1^2}{2} - (\frac{7}{-1} )[/tex]
Simplifying further, we get:
[tex]\frac{1}{2}+7[/tex]
Which equals [tex]\frac{15}{2}[/tex]
Therefore, the correct answer is:
d. x → -1
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Solve ⅔ + ⅚ and put answer in simplest form. O A.% O B. 1½ O c.⅔ O D.™
Answers
The answer, expressed in simplest form, is 9/18.
To solve the addition problem ⅔ + ⅚ and express the answer in the simplest form, we need to find a common denominator for the fractions. The least common multiple (LCM) of 3 and 6 is 6.
Now, let's convert the fractions to have a common denominator of 6:
⅔ = (⅔) * (2/2) = 4/6
⅚ = (⅚) * (3/3) = 5/6
Now we can add the fractions:
4/6 + 5/6 = 9/6
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:
(9/6) ÷ 3/3 = (9/6) * (1/3) = 9/18
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Find the missing side.
N
41° 15
Z=
Round to the nearest tenth.
Remember: SOHCAHTOA
Answers
Answer:
To the nearest tenth, we have,
z = 19.9
Step-by-step explanation:
The missing side is the hypotenuse,
And we are given the side adjacent to the angle,
z = hupotenuse = H = ?
Adjacent = A = 15
Angle = α = 41
Since we have to find hypotenuse and we are given adjacent,
Using SOHCAHTOA,
We know the angle and adjcent but need to find Hypotenuse,
So, we use CAH
or,
cos(α) = A/H
cos(α) = 15/z
(since z = hypotenuse)
zcos(α) = A
z = A/(cos(α))
z = 15/cos(41)
z = 19.8752
To the nearest tenth, we get,
z = 19.9
Analyze the diagram below and complete the instructions that follow.
42
40
A
Find the unknown side length, x. Write your answer in simplest radical form.
A. 2√√41
B. 4√√29
C. 48
D. 58
Mark this and return
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Answers
The length of unknown side x is 58.
The correct answer is option D.
To find the unknown side length, x, in a right triangle with the base measuring 42 and the perpendicular measuring 40, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let x be the hypotenuse. Applying the Pythagorean theorem, we have:
[tex]x^2 = 42^2 + 40^2[/tex]
Simplifying:
[tex]x^2[/tex] = 1764 + 1600
[tex]x^2[/tex]= 3364
Taking the square root of both sides to solve for x:
x = [tex]\sqrt{3364}[/tex]
Simplifying the square root:
x = ([tex]\sqrt{4 * 841)}[/tex]
Since 841 is a perfect square ([tex]29^2[/tex]), we can further simplify:
x = 2 * 29
x = 58
Therefore, the unknown side length, x, is equal to 58.
From the options provided the correct option is D.
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Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.52
and a standard deviation of 0.42
. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.36
? Please do not round your answer.
Answers
Therefore, the percentage of students with grade point averages no more than 3.36 is approximately 95%.
To determine the percentage of students with grade point averages no more than 3.36 using the empirical rule, we need to calculate the z-score for 3.36 based on the given mean and standard deviation.
The z-score is calculated using the formula:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation.
In this case, we have:
x = 3.36
μ = 2.52
σ = 0.42
Substituting these values into the formula, we get:
z = (3.36 - 2.52) / 0.42
z = 2
The empirical rule tells us that approximately 95% of the data falls within 2 standard deviations of the mean. Since a z-score of 2 falls within this range, we can conclude that approximately 95% of the students have grade point averages no more than 3.36.
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what is compliance?
come here fast
dwdduizgga
Answers
Answer:
the property of a material of undergoing elastic deformation or (of a gas) change in volume when subjected to an applied force. It is equal to the reciprocal of stiffness.
Please awnser asap I will brainlist
Answers
Using simultaneous method to solve the system of linear equations, 56 $10 tickets, 1310 $20 tickets, and 1902 $30 tickets were sold.
How many tickets of each have been sold?Let's solve the problem step by step.
Let:
x = number of $10 tickets sold
y = number of $20 tickets sold
z = number of $30 tickets sold
From the given information, we can form the following equations:
Equation 1: x + y + z = 3268 (Total number of tickets sold)
Equation 2: y = x + 259 (259 more $20 tickets than $10 tickets were sold)
Equation 3: 10x + 20y + 30z = 63920 (Total sales from ticket sales)
We can use these three equations to solve for the values of x, y, and z.
First, let's substitute Equation 2 into Equation 1:
x + (x + 259) + z = 3268
2x + 259 + z = 3268
2x + z = 3009 (Equation 4)
Now, let's substitute the value of y from Equation 2 into Equation 3:
10x + 20(x + 259) + 30z = 63920
10x + 20x + 5180 + 30z = 63920
30x + 30z = 58740
x + z = 1958 (Equation 5)
We now have a (Equations 4 and 5) with two variables (x and z). We can solve this system to find the values of x and z.
Multiplying Equation 4 by 30, and Equation 5 by 2, we get:
60x + 30z = 60270 (Equation 6)
2x + 2z = 3916 (Equation 7)
Now, subtract Equation 7 from Equation 6:
(60x + 30z) - (2x + 2z) = 60270 - 3916
58x + 28z = 56354
Simplifying, we have:
29x + 14z = 28177 (Equation 8)
Now, we can solve Equations 5 and 8 simultaneously:
x + z = 1958 (Equation 5)
29x + 14z = 28177 (Equation 8)
Multiplying Equation 5 by 14, and Equation 8 by 1, we get:
14x + 14z = 27332 (Equation 9)
29x + 14z = 28177 (Equation 8)
Now, subtract Equation 9 from Equation 8:
(29x + 14z) - (14x + 14z) = 28177 - 27332
15x = 845
Divide both sides of the equation by 15:
x = 56
Substituting the value of x into Equation 5, we can find z:
56 + z = 1958
z = 1958 - 56
z = 1902
Now that we have the values of x and z, we can substitute them back into Equation 1 to find y:
56 + y + 1902 = 3268
y + 1958 = 3268
y = 3268 - 1958
y = 1310
Therefore, the solution to the problem is:
x = 56 (number of $10 tickets sold)
y = 1310 (number of $20 tickets sold)
z = 1902 (number of $30 tickets sold)
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Use the limit theorem and the properties of limits to find the limit. -6x*3+7x+7/8x*3-8x+5
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The limit of the given expression is -3/4.
To find the limit of the given expression, we can apply the properties of limits and the limit theorem.
Let's break down the expression step by step:
We have the expression [tex](-6x^3 + 7x + 7) / (8x^3 - 8x + 5).[/tex]
First, we notice that both the numerator and denominator are polynomials, and the degree of the denominator is greater than the degree of the numerator.
In such cases, we can use the fact that as x approaches either positive or negative infinity, the highest power term dominates the expression. Therefore, we can simplify the expression by dividing every term by[tex]x^3:(-6x^3/x^3 + 7x/x^3 + 7/x^3) / (8x^3/x^3 - 8x/x^3 + 5/x^3).[/tex]
This simplifies to:
[tex](-6 + 7/x^2 + 7/x^3) / (8 - 8/x^2 + 5/x^3).[/tex]
Now, we can take the limit as x approaches infinity.
As x becomes infinitely large, the terms with x in the denominator tend to zero:
((-6 + 0 + 0) / (8 - 0 + 0)).
Thus, the limit of the given expression as x approaches infinity is:
-6/8 = -3/4.
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