Find X and round to the nearest tenth.
The side length x of the triangle rounded to the nearest tenth is 31.3.
What is the numerical value of x?The figure in the image is a right triangle.
Angle θ = 38°Adjacent to angle θ = 40Opposite to angle θ = xTo determine the value of x, use trigonometric ratio.
Tangent = Opposite / Adjacent
tan( 38° ) = x / 40
Solve for x
x = tan( 38° ) × 40
x = 0.781285 × 40
x = 31.3
Therefore, the value of x is 31.3.
Learn more about trigonometric ratio here: brainly.com/question/28016662
#SPJ1
Find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
Answer:
5025π m³
Step-by-step explanation:
the figure consists of two figures;
a cone and phere
volume of a cone=1/3πr²h
volume of hemisphere=2/3πr³
1/3×π×15×15×37=2775π
2/3×π×15×15×15=2250π
sum up the volumes
2775π+2250π
=5025π m³
Question 1(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 12.
The IQR is the best measure of variability, and it equals 12.
The range is the best measure of variability, and it equals 3.
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Question 7(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 6.5.
The mean is the best measure of center, and it equals 7.
The median is the best measure of center, and it equals 7.
The mean is the best measure of center, and it equals 6.5.
The median of 20 is the most accurate to use since the data is skewed.
Option C is the correct answer.
What is a histogram?A histogram is a representation of the distribution of data with intervals.
We have,
The data given shows a histogram that is skewed to the right.
Now,
Since the data is skewed.
The median is a better measure of the center of data than the mean.
Now,
Arrange the data in order:
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
Median = middle value.
Median = 20
Thus,
The median of 20 is the most accurate to use since the data is skewed.
Learn more about histograms here:
https://brainly.com/question/16819077
#SPJ1
Answer:
your question is a bit confusing...
Step-by-step explanation:
Rehan proved by mathematical induction that for all the positive integers,
is divisible by 3. Can you find an integer counterexample to show that this statement is not true? Explain.
A counterexample that shows that all the integers are not divisible by 3 is given as follows:
2.
How to obtain the counterexample?The statement for this problem is given as follows:
"All the positive integers are divisible by 3".
The statement is false, as only numbers whose sum of the digits is a multiple of 3 are divisible by 3, hence for example, the number 2 is not divisible by 3.
The counterexample is the statement that proves that a conjecture(another statement) is false, hence the number 2 is the counterexample showing that not all positive statements are divisible by 3.
More can be learned about conterexamples at brainly.com/question/3637836
#SPJ1
Which two integers is /80
[tex] \sqrt{80} [/tex]
between? (A) 9 and 10 B) 7 and 8 8 and 9 D 11 and 12
A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (*)A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (*). Observe that, if n=0 or 1 , the Bernoulli equation is linear. For other values of n , the substitution u=y^(1-n) transforms the Bernoulli equation into the linear equation du/dx + (1-n)P(x)u=(1-n)Q(x).Consider the initial value problemxy'+y=3xy^2, y(1)=-3(a) This differential equation can be written in the form (*) withP(x)=?Q(x)=?n=?(b) The substitution u=BLANK will transform it into the linear equation du=dx+ BLANK u=BLANK(c)Using the substitution in part (b), we rewrite the initial condition in terms of x and uu(1)=?(d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).u(x)=?(e)(e) Finally, solve for yy(x0=?
The solution of the the linear equation is y = 3/(x - 9xlnx)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
xy' + y = 3xy², y(1) = -3
This is Bernoulli equation: y' + (1/x)y = 3y²;
Let u = y^(1 - 2) = 1/y is new function.
Then u' = - y'/y
or
y' = -u'/u²;
y = 1/u.
Substitute all this in our ODE: - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.
we get linear, 1st order not homogenies ODE:
integrated factor:
μ = e∫(-1/x)dx = e-lnx = 1/x²
u'·1/x - 1/x2 = -3/x;
(u/x)' = - 3/x; u/x
= ∫(-3/x)dx;
u/x = -3lnx + C;
u = - 3xlnx + Cx;
y =1/u = 1/(- 3xlnx + Cx)
To get C ,use initial conditions:
y(1) = 3;
3 = 1/(-3·1·ln1 + C);
C = 1/3;
y = 3/(x - 9xlnx)
The solution of the the linear equation is y = 3/(x - 9xlnx)
To learn more about the solution of an equation from the given link
https://brainly.com/question/22688504
#SPJ4
The solution of the the linear equation is y = 3/(x - 9xlnx)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
xy' + y = 3xy², y(1) = -3
This is Bernoulli equation: y' + (1/x)y = 3y²;
Let u = y¹⁻² = 1/y is new function.
Then u' = - y'/y
or
y' = -u'/u²;
y = 1/u.
Substitute all this in our ODE: - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.
we get linear, 1st order not homogenies ODE:
integrated factor:
μ = e∫(-1/x)dx = e-lnx = 1/x²
u'·1/x - 1/x2 = -3/x;
(u/x)' = - 3/x; u/x
= ∫(-3/x)dx;
u/x = -3lnx + C;
u = - 3xlnx + Cx;
y =1/u = 1/(- 3xlnx + Cx)
To get C ,use initial conditions:
y(1) = 3;
3 = 1/(-3·1·ln1 + C);
C = 1/3;
y = 3/(x - 9xlnx)
The solution of the the linear equation is y = 3/(x - 9xlnx)
To learn more about the solution of an equation from the given link
brainly.com/question/22688504
#SPJ4
Find the point slope form of a line with Slope: 6/7 that passes through (-5,4)
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 6/7. Then the equation is given as,
y = (6/7)x + c
The equation passes through (-5, 4). Then we have
4 = (6/7) (-5) + c
4 = -30/7 + c
c = 58 / 7
Then the equation is given as,
y = (6/7)x + 58/7
7y = 6x + 58
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
Select the correct answer. If f(x)=x^2/x+3, find f(x+h)
The function operation f( x + h ) in the function f(x) = x² / (x + 3 ) is ( x + h )² / (x + h + 3 ).
What is the function operation f(x + h ) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = x² / (x + 3 )f( x + h ) = ?To determine f( x + h ), replace all the occurrence of x with (x + h) in the function and simplify.
f(x) = x² / (x + 3 )
f(x + h) = ( x + h )² / (( x + h ) + 3 )
f(x + h) = ( x + h )² / (x + h + 3 )
Therefore, the operation f(x + h) equals ( x + h )² / (x + h + 3 ).
Learn more about functions here: brainly.com/question/2541698
#SPJ1
Simplify the following union and or intersection. [2,3] ∪ (3,∞)
The union of the set elements is [2, ∞)
How to determine the union or the intersectionFrom the question, we have the following parameters that can be used in our computation:
[2,3] ∪ (3,∞)
The above is a union set
The definition of the union set is that we write out all the elements in the set
Using the above as a guide, we have the following:
[2,3] ∪ (3,∞) = [2, ∞)
Read more about sets at
https://brainly.com/question/24713052
#SPJ1
A city planner designs a park that is a quadrilateral with vertices at J(−3, 1), K(3, 3), L(5, −1), and M(−1, −3). There is an entrance to the park at the midpoint of each side of the park. A straight path connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane represents 10 meters, what is the total length of the paths to the nearest meter? Round your answer to the nearest whole number.
Answer: To determine the length of the paths connecting the entrance to the opposite entrance, we first need to find the midpoint of each side of the park. Then, we will use the distance formula to calculate the distance between each pair of midpoints.
Let's begin by finding the midpoint of each side of the park.
JK: (-3 + 3, 1 + 3) / 2 = (0, 2)
KL: (3 + 5, 3 - 1) / 2 = (4, 2)
LM: (5 - 1, -1 - -3) / 2 = (2, -2)
MJ: (-1 + -3, -3 + 1) / 2 = (-2, -1)
Next, we'll use the distance formula to calculate the distance between each pair of midpoints.
JK: sqrt((4 - 0)^2 + (2 - 2)^2) = sqrt(16 + 0) = 4
KL: sqrt((2 - 4)^2 + (-2 - 2)^2) = sqrt(16 + 16) = 4 sqrt(2)
LM: sqrt((-2 - 2)^2 + (-1 + 2)^2) = sqrt(16 + 9) = sqrt(25) = 5
MJ: sqrt((-2 - 0)^2 + (-1 - 2)^2) = sqrt(4 + 9) = sqrt(13)
The total length of the paths is 4 + 4 sqrt(2) + 5 + sqrt(13), which when rounded to the nearest whole number is 14.
Step-by-step explanation:
A wildlife biologist captured and released 34 trouts from two different lakes and measured them to the nearest inch. She captured 17 of the fish from Fralest Lake and 17 of the fish from Lake Reverwalk. She then calculated the following statistical information.
Based on these samples, what generalization can be made?
A. At least half of the trout in Lake Reverwalk measure between 12 and 18 inches.
B. At least half of the trout in both lakes measure between 12 and 18 inches.
C. Not enough information is provided to draw any of these conclusions.
D. At least half of the trout in Fralest Lake measure between 12 and 18 inches.
The requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.
Thus, the requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ1
Find the shortest distance between the line L1 passing through the points A =
(3,2,1) and B = (2,1,0) and the line L2 passing through the points C = (2,4,−1) and
D = (3,0,−2)
The shortest distance between the two skew lines is equal to 11√38 / 38 units.
How to find the shortest distance between two skew lines in space
According to linear algebra, lines are defined by vectorial equations of the form:
(x, y, z) = P(x, y, z) + t · T(x, y, z)
Where:
P(x, y, z) - Point contained in the line.t - Parameter.T(x, y, z) - Vector slope.And the shortest distance between two skew lines is determined by the following expression:
[tex]d = \frac {|[P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)]|}{|T_{1} (x, y, z) \times T_{2} (x, y, z)|}[/tex]
First, determine the points contained in each line:
P₁(x, y, z) = (3, 2, 1)
P₂(x, y, z) = (2, 4, - 1)
Second, find each vector slope:
T₁(x, y, z) = (2, 1, 0) - (3, 2, 1)
T₁(x, y, z) = (- 1, - 1, - 1)
T₂(x, y, z) = (3, 0, - 2) - (2, 4, - 1)
T₂(x, y, z) = (1, - 4, - 1)
Third, determine the vector subtraction:
P₂(x, y, z) - P₁(x, y, z) = (2, 4, - 1) - (3, 2, 1)
P₂(x, y, z) - P₁(x, y, z) = (- 1, 2, - 2)
Fourth, determine the cross product:
T₁(x, y, z) × T₂(x, y, z) = (- 1, - 1, - 1) × (1, - 4, - 1)
T₁(x, y, z) × T₂(x, y, z) = (- 3, - 2, 5)
Fifth, use the dot product:
[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = (- 1, 2, - 2) \,\bullet\,(- 3, - 2, 5)[/tex]
[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = 3 - 4 - 10[/tex]
[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = - 11[/tex]
Sixth, calculate the norm of the cross product:
|T₁(x, y, z) × T₂(x, y, z)| = √[(- 3)² + (- 2)² + 5²]
|T₁(x, y, z) × T₂(x, y, z)| = √38
Finally, determine the shortest distance between the two skew lines:
d = |- 11| / √38
d = 11 / √38
d = 11√38 / 38
To learn more on shortest distances between two lines: https://brainly.com/question/30241855
#SPJ1
Which of the following would NOT be an example of a boogie-woogie bass line?
A. F-A-C-D-Eb-D-C-A
B. G-B-D-E-F-E-D-B
C. C-D-E-F-G-F-E-D
D. C-E-G-A-Bb-A-G-E
Answer: Option D, "C-E-G-A-Bb-A-G-E" is not an example of a boogie-woogie bass line. Boogie-woogie is a genre of blues music that is characterized by a repetitive bass pattern that usually consists of 8th notes. The bass line is usually made up of the root note, fifth note, and octave of a chord, and it is played in a swung or shuffle rhythm. The most common boogie-woogie bass line consists of the notes of a I-IV-V chord progression in a 12-bar blues structure. Option D deviates from this typical pattern and therefore would not be considered a boogie-woogie bass line.
Step-by-step explanation:
If you want to solve the equation by completing the square, then rearrange the equation as x2−6x=11 and add 9 to each side. If you want to solve the equation by using the quadratic formula, rearrange the equation as x2−6x−11=0 and substitute the values of 1, −6 , and −11 into the formula. Round to the nearest hundredth.
Solution of equation x² - 6x = 11 are, x = 7.47 and x = - 1.47
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The equation is,
⇒ x² - 6x = 11
Now, Solve the equation by completing the square as,
⇒ x² - 6x = 11
Add 9 both side, we get;
⇒ x² - 6x + 9 = 11 + 9
⇒ (x - 3)² = 20
⇒ x - 3 = √20
⇒ x - 3 = ± 4.47
This gives two solutions,
⇒ x - 3 = 4.47
⇒ x = 4.47 + 3
⇒ x = 7.47
⇒ x - 3 = - 4.47
⇒ x = - 4.47 + 3
⇒ x = - 1.47
Thus, Solution of equation x² - 6x = 11 are,
⇒ x = 7.47 and x = - 1.47
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ1
100 POINTS HELPWhich column on an accounting worksheet may not balance at the end of an accounting period?
A. The Adjusted Trial Balance
B. The Trial Balance
D. The Adjustments
C. The Income Statement
Answer: C
Step-by-step explanation:
The column on an accounting worksheet that may not balance at the end of an accounting period is the Adjustments column.
The Adjustments column on an accounting worksheet includes all the adjusting entries that are needed to update the accounts before the financial statements are prepared. These adjustments can include accruals, deferrals, depreciation, and other adjustments that need to be made to the accounts to accurately reflect the financial position of the company.
Since the Adjustments column is used to record these adjusting entries, it is possible that this column may not balance at the end of the accounting period, as the adjustments may not perfectly offset each other. However, this is not a problem, as the purpose of the worksheet is to help prepare the financial statements, not to balance each individual column.
Therefore, the correct answer is option D, the Adjustments column.
Answer:
C. The Income Statement
Step-by-step explanation:
The Income Statement column on an accounting worksheet may not balance at the end of an accounting period.
An accounting worksheet is a tool used by accountants to help organize and summarize financial information and to prepare financial statements. The worksheet is typically a multi-column form that includes columns for the unadjusted trial balance, adjustments, adjusted trial balance, income statement, and balance sheet.
The Adjustments column is used to record adjusting entries and to update the account balances to reflect accruals, deferrals, and other accounting adjustments. The Adjusted Trial Balance column is the result of the adjustments made in the Adjustments column and should include all the account balances that will be used to prepare the financial statements.
Pica is a disorder in which individuals eat substances
People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.
what is eating disorder ?Recurrent episodes of binge eating are the hallmark of a specific type of eating disorder called binge eating disorder. Food addiction and compulsive overeating are both symptoms of this eating disorder. Uncontrollable and quick eating without feeling hungry, as well as negative emotions, depressive symptoms, and guilt over the eating, are prominent symptoms of this illness.
given
People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.
Pica is a kind of pagophagia. It entails consuming ice, snow, or ice water excessively.
Individuals who have pica are not forced to consume ice due to a physical condition like anaemia.
To know more about eating disorder visit :-
https://brainly.com/question/13261012
#SPJ1
Express the given quantity as a single logarithm. (Enter your answer using function notation - use In(x) instead of In x.) In(a + b) + In(a - b) – 4 Inc Differentiate the function. (Enter your answer using function notation - use In(x) instead of In x.) f(x) = 5.2 In(4x) - 52 Differentiate the function. (Enter your answer using function notation - use In(x) f(t) = sin(3 In x) Differentiate the function. (Enter your answer using function notation - use In(x) f(x) = ln(4 sin’z)
The given quantity as a single logarithm are as follows:
1. 20.8In(4x)
2. 3cos(3Inx)Inx
3. 4cos'zln'z
What is function?Function ve process of state of instruction that text input papa mississippi start x and output function ladki company it's a programming language allow me the code to create the complex command with simple instruction for example function in the used to it to numbers together a generator and i'm number from san also be combined to create more public sequence are instruction.
Express the given quantity as a single logarithm: In(a + b) + In(a - b) - 4Inx = In[(a+b)(a-b)] - 4Inx
Differentiate the function f(x) = 5.2In(4x) - 52: f'(x) = 20.8In(4x)
Differentiate the function f(t) = sin(3Inx): f'(t) = 3cos(3Inx)Inx
Differentiate the function f(x) = ln(4sin'z): f'(x) = 4cos'zln'z
To know more about function click-
brainly.com/question/25638609
#SPJ4
You are examining the data with a stem-and-leaf plot. Here is the start of the plot. Finish the plot.
The stem-and-leaf plot is finished as follows:
4| 1 3 7.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
To complete the stem-and-leaf plot, we must obtain the measures above 40 from the table, which are given as follows:
41, 43 and 47.
Considering the format of the plot, the plot is completed as follows:
4| 1 3 7.
More can be learned about stem-and-leaf plots at https://brainly.com/question/8649311
#SPJ1
Translate triangle P by the vector 2
y
P
4
3
No W
2
1
-5 -4 -3 -2 -10
-1
2344
-2
-3
-4
2 3 4 5
Step-by-step explanation:
The translation of triangle P by the vector (2, 3) results in the triangle being moved 2 units to the right and 3 units up. The new coordinates of the triangle are (6, 7), (4, 6), and (3, 5).
Please help due tonight
Answer:
x = 24, y = 12
Step-by-step explanation:
We can use the law of sines to solve for x
The law of sines says the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides (and angles)
In this triangle
the side with length 12√3 is opposite 60°
the side with length x is opposite 90°
Using the law of sines,
[tex]\dfrac{12\sqrt{3}}{\sin60}=\dfrac{x}{\sin 90}\\[/tex]
sin 60 = [tex]\dfrac{\sqrt{3}}{2}[/tex]
sin 90 = 1
[tex]\rightarrow \dfrac{12\sqrt{3}}{\dfrac{\sqrt{3}}{2}}=\dfrac{x}{1}\\\\\\x = 12\sqrt{3} \div \dfrac{\sqrt{3}}{2}}\\\\\textrm{When dividing fractions, flip the divisor and multiply}\\\\\rightarrow 12\sqrt{3} \times \dfrac{2}{\sqrt{3}}\\\\\textrm{$\sqrt{3}$ cancels out from numerator and denominator}:\\\\\\\rightarrow x = 12 \times 2 = \boxed{24}\\\\\\[/tex]
To solve for y we can again use the law of sines
[tex]\dfrac{y}{\sin 30} = \dfrac{x}{\sin 90}\\\\\textrm{again, as before $\sin 90$ is 1}\\\\\rightarrow \dfrac{y}{\sin 30} = x\\\\\rightarrow x = \dfrac{y}{\sin 30}\\\\\rightarrow y = x \sin 30\\\\\sin30 = \dfrac{1}{2}[/tex]
So y = x/2 = 24/ 2 = 12
ans:
x = 24, y = 12
Note
Another way to solve this question is to first recognize the triangle as a 30-60-90 right triangle
In a triangle of this kind, if the longest side side is a, the shortest side is a/2, and the third side is √3/2a
We could have solved this in this manner also
Here longest side = x, shortest side is y
The other side is 12√3 = x √3/2
So x = 12√3 ÷ √3/2 = 24 (as in the first method)
y = x/2 = 12
This approach is ok too, I find it less intuitive and we have to remember the ratios
Missing value in frequency distribution table
Based on the data, the total number of people would be 350. So the missing value in the table would be 54.
How to find missing value from table?To find the missing value of people in the graph we must do the following procedure. We must add the number of people who are already registered in the graph in the frequency column.
Additionally, we must establish a total number of people, for example 350. In this case we must subtract the result of the people registered in the graph from the total number of people:
350 - 295 = 54.
Then we can establish that the remaining number of people (54) corresponds to the frequency table.
Note: This question is incomplete. The complete information is here:
Total number of people: 350
Learn more about frequency in: https://brainly.com/question/5102661
#SPJ1
about two Daily Food Drive by Mr. Garcia's Homeroom Mean number of canned goods collected: 18.75 Median number of canned goods collected: 18 Range of data: 11 IOR of data: 4.25 The range for Mr. Garcia's homeroom is less than the range for Ms. Vicario's homeroom. The IQR for Mr. Garcia's homeroom is less than the IQR for Ms. Vicario's homeroom. The number of canned goods collected by Ms. Vicario's homeroom was more variable than the number of canned goods collected by Mr. Garcia's homeroom.
Mr. Garcia's homeroom had a more consistent collection of canned goods.
Ms. Vicario's homeroom varied more widely with the collection of canned goods.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
The two daily food drives:
Mr. Garcia:
The mean number of canned goods collected = 18.75.
The median number of canned goods collected = 18.
The range of data for Mr. Garcia's homeroom = 11.
The IQR (interquartile range) of data = 4.25.
Ms. Vicario's homerooms:
The range of data = greater than 11.
The IQR of data = greater than 4.25.
The number of canned goods collected = more variable than the number of canned goods collected by Mr. Garcia's homeroom.
Based on these observations.
We can conclude that,
Mr. Garcia's homeroom had a more consistent collection of canned goods. i.e
Smaller range and IQR.
Ms. Vicario's homeroom varied more widely with the collection of canned goods.
i.e
Wider range and IQR
Thus,
Mr. Garcia's homeroom had a more consistent collection of canned goods.
Ms. Vicario's homeroom varied more widely with the collection of canned goods.
Learn more about the interquartile range here:
https://brainly.com/question/29204101
#SPJ9
Consider a market characterized by the following inverse demand and supply functions: PX = 50 − 4QX and PX = 10 + 2QX. Compute the surplus producers receive when a $30 per unit price floor is imposed on the market.
A $75
B $35
C $25
D $50
Computing the surplus producers receive when a $30 per unit price floor is imposed on the market is option C.$25.
How did we get the value?To calculate the surplus producers receive, we need to find the difference between the price they receive at a given quantity and the price they would have received in the absence of the price floor.
When a price floor of $30 per unit is imposed on the market, the quantity supplied and demanded at this price are:
QX = (50 - 30)/4 = 5 units (demand)
QX = (30 - 10)/2 = 10 units (supply)
So, the surplus received by the producers is the difference between the price floor and the price they would have received in the absence of the price floor:
Surplus = 30 - (10 + 2 * 10) = 30 - 30 = $0.
However, the surplus for consumers is the difference between the price they would have paid in the absence of the price floor and the price floor:
Surplus = (50 - 4 * 5) - 30 = 25 - 30 = -$5.
So, the total surplus received by producers and consumers combined is $0 + (-$5) = -$5, which means that the price floor imposes a dead weight loss on the market.
learn more about surplus producers: https://brainly.com/question/17267471
#SPJ1
Complete the sentence below.
The time shown is
15:40
past/to
in the morning/afternoon
Answer:
uajajjahajajaaajjsjaja
The time shown is 15:40, which indicates that it is 20 minutes to 4 o'clock in the afternoon.
How to complete the statementThe time displayed is 15:40, which is consistent with a 24-hour clock. It indicates that there are now 20 minutes left until 6:00.
The time 15:40 is in the afternoon because the afternoon begins at 12:00 and lasts until 18:00.
The 24-hour clock format avoids any doubt regarding AM (morning) or PM (afternoon/evening), it is vital to highlight.
As a result, 15:40 specifies that it is in the afternoon and that there are still 20 minutes until 4 o'clock.
Learn more about time at: https://brainly.com/question/479532
#SPJ2
A large bowl can hold 3.5 pints. A smaller bowl can hold less than 60% of the amount. Graph the possible amounts, in quarts, that can be held by the smaller bowl.
Answer: qt=0.6
Step-by-step explanation:
3.5=
60%=0.6
qt=0.6
A credit sale of $2700 is made on July 15, terms 2/10, n/30, on which a return of $300 is granted on July 18. What amount is received as payment in full on July 24?
Answer:
$2,450
Step-by-step explanation:
2/10, n/30 = discounts of 2%
Credit sale = $2,700
Sale return = $200
Net Receivable =$ 2,700 - $ 200 = $2,500
Discount = 2,500 x %2 = 50
Payment Receipt = $2,500 - $50 = $2,450
please give brainliest
What is the conjugate? x-\sqrt(2)
Answer:
[tex]x+\sqrt{2}[/tex]
Step-by-step explanation:
The conjugate of [tex]x-\sqrt{2}[/tex] would simply be [tex]x+\sqrt{2}[/tex]. All you have to do is simply change the sign to its opposite.
I already graphed it but I need yo figure out the solution. PLEASE HELP:)
I will give you brainlest!!!!
The solution of the system of equations is equal to (3, 4).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by ordered pair (3, 4).
Read more on a graph here: brainly.com/question/4546414
#SPJ1
a home with a swimming pool recently sold in the area for 250,000 another home in the same area that does not have a swimming pool but is similar in all other respects sold recently for 230,000 what can you assume from this information.a. All swimming pools cost $20.000b. The aproximate value of pool in that area is $20.000c. No home without a pool in that area will sell for more than $230.000d. Homes without a pool will sell faster in that area than homes with a pool
The correct answer is option b.The approximate value of pool in that area is $20.000c.
What is approximate value?A value that is similar to another value but not exactly equal to it is referred to as an approximation number. When the outcomes of the numerical calculations are unknown, the approximation is applied. They are typically used when greater place value decimal numbers emerge as a result.
Approximate value of a pool in the area = Value of home with a swimming pool in the area - Value of home without a swimming pool in the same area.
Value of home with a swimming pool in the area = $250,000
Value of home without a swimming pool in the same area = $230,000.
The approximate value of pool in the area = 250000 - 230000 = 20000.
Hence, the correct answer is option b. The approximate value of pool in that area is $20.000c.
Learn more about approximate value here:
https://brainly.com/question/2140926
#SPJ4
College level
Attached photo.
The value of b form the logarithmic equation [tex]log_b}3=0.7925[/tex] is 3.9998688.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given that, [tex]log_b}25=2.3219[/tex] and [tex]log_b}3=0.7925[/tex].
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
We know that, logₐN=x is written exponential form as aˣ=N
Here, [tex]b^{2.3219}=25[/tex]
b=4.00006709
[tex]b^{0.7925}=3[/tex]
b=3.9998688
Therefore, the value of b is 3.9998688.
To learn more about the logarithmic equation visit:
https://brainly.com/question/14406101.
#SPJ1