HELPPP!!!
Does your residual plot show that the linear model from the regression calculator is a good model? Explain your reasoning.
Answers
A careful examination of the residual plot is crucial in determining the goodness of fit for the linear model.To determine whether the linear model from the regression calculator is a good model, we need to analyze the residual plot.
A residual plot is a graphical representation of the differences between the observed values and the predicted values from the linear model.
If the residual plot exhibits random scatter around the horizontal line (y = 0) with no discernible pattern, it suggests that the linear model is a good fit for the data. This indicates that the model captures the underlying linear relationship between the variables adequately, and the residuals have no systematic bias or trend.
However, if the residual plot displays a distinct pattern, such as a curved shape, a funnel shape, or an increasing/decreasing trend, it indicates that the linear model may not be appropriate. In such cases, the model may not be capturing all the relevant information or may be missing higher-order relationships.
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Related Questions
PLEASE HELP TODAY I WILL GIVE BRAINLIST
Answers
Answer: Triangle C only
Step-by-step explanation: using the formula to find out if the triangle are right angle (a^2+b^2=c^2) the legs are supposed to equal to the hypotenuse. A and B arentaren't equal to the hypotenuse
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
19. A. 108 mm²
B. 404.5 in²
Step-by-step explanation:
19:
Area of Big triangle: ½*base*height
=½*(18mm+10mm)+12mm
=168mm²
Area of Small triangle=½*base*height
=½*10mm*12mm
=60mm²
Now
Area of shaded region=Area of Big triangle - Area of Small triangle
=168-60
=108 mm²
Therefore Area is 108mm².
20.
We know that:
Area of Parallelogram=Base*Height
here
Base=26 in
let's find height
Sin 45°=Opposite/Hypotenuse
Sin 45°=Height/22
Height=Sin 45°*22
Height=[tex]\frac{1}{\sqrt{2}}*22=11\sqrt{2}[/tex]=15.56
Now,
Area of parallelogram= base*height=26*15.56=404.5 in²
Therefore, Area of Parallelogram=404.5 in²
Consider the diagram.
Line l is a perpendicular bisector of line segment R Q. It intersects line segment R Q at point T. Line l also contains point S. Line segment R S is 3 x + 2. Line segment S Q is 5 x minus 8.
What is QS?
Answers
The length of line segment QS is 17.
To find the length of line segment QS, we need to determine the values of x and then substitute them into the given equations.
Given:
Line segment RS = [tex]3x + 2[/tex]
Line segment SQ = [tex]5x - 8[/tex]
Since line l is the perpendicular bisector of line segment RQ, it means that line segments RS and SQ are equal in length.
Therefore, we can set up an equation:
[tex]3x + 2 = 5x - 8[/tex]
To solve for x, we can start by isolating the variable terms on one side:
[tex]2 + 8 = 5x - 3x[/tex]
[tex]10 = 2x[/tex]
Dividing both sides by 2:
[tex]x = \frac{10}{2}[/tex]
[tex]x = 5[/tex]
Now that we have found the value of x, we can substitute it into the equation for line segment SQ:
[tex]SQ = 5x - 8[/tex]
[tex]SQ = 5(5) - 8[/tex]
[tex]SQ = 25 - 8[/tex]
[tex]SQ = 17[/tex]
Therefore, the length of line segment QS is 17.
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A round wading pool has a diameter of 115cm and is 25cm deep. A hose is filling the pool at a rate of 34,000cm^3 per minute.
Answers
Therefore, it will take approximately 7.67 minutes to fill the wading pool completely.
The round wading pool has a diameter of 115 cm and a depth of 25 cm. To find the volume of the pool, we can use the formula for the volume of a cylinder, which is
V = πr^2h.
Since the pool is round, the radius (r) is half the diameter, which is
115 cm / 2 = 57.5 cm.
Plugging in the values, we have
V = π(57.5 cm)^2 * 25 cm ≈ 260,979 cm^3.
The hose is filling the pool at a rate of 34,000 cm^3 per minute.
To determine how long it will take to fill the pool, we divide the volume of the pool by the rate of filling:
260,979 cm^3 / 34,000 cm^3/min ≈ 7.67 minutes.
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A data set consists of 3 numbers, a
, b
, and c
. Write an algebraic expression, in terms of a
, b
, and c
, to represent the mean of the new set of numbers obtained by
Answers
The universal set for sets A, B, and C is {0, 1, 2, 3, 4, 5, 6, 8}.
The universal set is the set that contains all the elements under consideration. In this case, we have three sets: A, B, and C. To determine the universal set for all three sets, we need to identify the set that includes all the unique elements from each of the individual sets.
Set A contains the elements {1, 3, 5}, Set B contains the elements {2, 4, 6}, and Set C contains the elements {0, 2, 4, 6, 8}. To form the universal set, we need to combine all these elements without any repetition.
By observing the elements in Sets A, B, and C, we can see that the universal set would be the set that includes all the unique elements from these sets. Therefore, the universal set for all three sets is the set that contains {0, 1, 2, 3, 4, 5, 6, 8}.
This means that any element that is present in at least one of the sets A, B, or C is included in the universal set. It covers all the possible elements that can be found in these sets.
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Question
If set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then write the universal set for all three sets.
Assume that you buy a 49,000 VNĐ milk tea cup everyday, 30 days per month. As 12 months interest rate - 6.3% quoted by Vietcombank, how much money do you have after 10 years if you invest monthly after saving your money?
Answers
Answer:
To calculate the future value of your monthly investments after saving your money, i can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Monthly investment amount
r = Monthly interest rate
n = Number of months
Given:
Monthly investment amount (P) = 49,000 VNĐ
Monthly interest rate (r) = 6.3% / 12 = 0.00525
Number of months (n) = 10 years * 12 months/year = 120 months
Plugging in these values, i can calculate the future value:
FV = 49,000 * ((1 + 0.00525)^120 - 1) / 0.00525
Calculating this expression, the future value is approximately 7,565,000 VNĐ.
Therefore, after 10 years of investing 49,000 VNĐ per month and earning an interest rate of 6.3% per year, you would have approximately 7,565,000 VNĐ.
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
PLEASE HELP URGANT I WILL GIVE BRAINLIST
Answers
Answer:74
Step-by-step explanation:
DCB arc's degree is equal to 2*<DAB so,
arc DCB=106*2=212 degrees
cicle is 360 degrees total, so,
360-212=148 degrees
and it is arc DAB which is arc for <DCB and same rule applies here:
arc DAB=2*<DCB
<DCB=DAB/2=148/2=74
Functions of Random Variables
Answers
The statement for the function of random variable "The density of Y can be found by differentiating the CDF of Y" is false.
Why is the statement on deafferenting random variable false?The density of a random variable can be found by differentiating its CDF, but only if the random variable is continuous. The random variable X in this case is discrete, so its density cannot be found by differentiating its CDF.
The CDF of a discrete random variable is a step function, which means that it has a jump discontinuity at each point where the value of the random variable changes.
The derivative of a step function is a Dirac delta function, which is a mathematical object that represents a point mass at a specific value. The density of a discrete random variable is the sum of the Dirac delta functions at each point where the value of the random variable changes.
In this case, the CDF of Y is a step function, so its derivative is a Dirac delta function. The density of Y is the sum of the Dirac delta functions at each point where the value of Y changes. However, the value of Y can only change at integer values, so the density of Y is a discrete function, not a continuous function.
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find the front and side elevation
Answers
The sketch of the front elevation and the side elevation of the prism are added as an attachment
How to draw the front elevation and the side elevation of the prismFrom the question, we have the following parameters that can be used in our computation:
The prism
Using the figure as a guide, we understand that:
The front elevation is a rectangle of 2m by 0.5m
While the side elevation is a rectangle merged with a trapezoid
Next, we draw the elevations (see attachment)
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Who is correct and why?
Selena is incorrect because she should have substituted the values for the variables first, and then simplifed.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Drake is incorrect because he should have simplified first, before substituting the values for the variables.
Drake is correct because he substituted the values for the variables first, and simplified correctly.
Answers
Selena and Drake both are correct.
Selena: According to the statement, Selena is said to have not substituted the values for the variables first and then simplified.If she did not follow the correct order of operations, it's possible that she made an error.Drake: According to the statement, Drake is said to have substituted the values for the variables first and then simplified. This order seems to align with the correct order of operations, but without further details, it is not possible to determine if he made any mistakes during the process.For such more questions on
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What is the value of y?
150%
O A. 85
O B. 65
O C. 75
OD. 55
95°
Answers
Hello!
angle1 = (360° - 2 * 150°)/2 = 30°
angle2 = (360° - 2 * 95°)/2 = 85°
y° = 180° - (30° + 85°) = 65°
The correct answer is 65°The foci of an ellipse are at $F_1 = (0,2)$ and $F_2 = (2,0).$ The ellipse passes through the origin, and intersects the $x$-axis at one other point. What is this point of intersection?
Answers
The point of intersection of the ellipse with the x-axis is $(\pm \sqrt{2}, 0)$.
To find the point of intersection of the ellipse with the x-axis, we can start by considering the distance between the foci $F_1$ and $F_2$. Using the distance formula, we find that the distance between $F_1$ and $F_2$ is $\sqrt{(2-0)^2 + (0-2)^2} = \sqrt{8} = 2\sqrt{2}$.
Since the ellipse passes through the origin, the sum of the distances from any point on the ellipse to the foci will be equal to the length of the major axis. In this case, the sum of the distances is $2a$, where $a$ represents the semi-major axis.
Since the foci are located at $(0,2)$ and $(2,0)$, we can see that $2a = 2\sqrt{2}$. Solving for $a$, we find $a = \sqrt{2}$.
Now, we can write the equation of the ellipse centered at the origin as $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Since the ellipse passes through the origin, we know that the y-coordinate of the point of intersection on the x-axis is 0.
Substituting $y = 0$ into the equation, we have $\frac{x^2}{(\sqrt{2})^2} + \frac{0^2}{b^2} = 1$, which simplifies to $\frac{x^2}{2} = 1$.
Solving for $x$, we find $x = \pm \sqrt{2}$.
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A number is thrice the other number and their sum is 80. (i) Express the above statements in the form of linear equations. (ii) Find the numbers.
Answers
Statement 1:
a is thrice to b or: a = 3*b
Statememt 2:
Their (a’s and b’s) sum is 80: a+b =80
Together we have the two linear equations:
a=3b
a+b=80
Solving them can be done by using the fact that a is equal to 3b and plugging this into the second equation:
3b + b = 80
Now 3 apples plus 1 apple is 4 apples, right? So 3b + b = 4b !
4b = 80
No we divide by 4 and get the result for b:
b = 20
Now how do we find a? Well we know that a = 3b. So we just plug the solution for b into this equation:
a = 3 * 20 = 60.
That means the two numbers were 20 and 60
The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average test score in your science class, where x is the number of the test taken.
x g(x)
1 81
2 83
3 85
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)
I really only need the math average (the first question) please thank you ill give brainliest + 100 points
Answers
Answer:
a) 81
b) 83
c) science
Step-by-step explanation:
a)
f(x) = 0.5x + 80
gn x = 2 tests
⇒ f(2) = 0.5(2) + 80
= 1 + 80
= 81
b)
gn x = 2
g(2) = 83
c)
we have g(x) = mx + b
m = (y₂-y₁)/(x₂-x₁)
= (83 - 81)/(2 - 1)
m = 2
for g(1),
g(1) = m(1) + b
81 = 2(1) + b
b = 81 -2
b = 79
⇒ g(x) = 2x + 79
and f(x) = 0.5x + 80
for 4 tests, we have x = 4
g(4) = 2(4) + 79
= 8 + 79
g(4) = 87
f(4) = 0.5(4) + 80
= 2 + 80
f(4) = 82
g(4) = 87 > f(4) = 82
∴Science class has a higher average
A photo has a side length 4 inches and 6 inches in length .After the enlargement the length becomes 5 more inches what is the length of the photo
Answers
Therefore, the length of the photo after the enlargement is 9 inches.
The initial length of the photo is given as 4 inches. After the enlargement, the length becomes 5 more inches. To find the final length, we can add 5 inches to the initial length.
Initial length of the photo: 4 inches
Additional length after enlargement: 5 inches
Final length = Initial length + Additional length
Final length = 4 inches + 5 inches
Final length = 9 inches
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sum of 2 number is 34,678 if one of the number is 30,020 what is the other number
Answers
The other number is 4, 658
How to determine the valueAlgebraic expressions are described as expressions that are made up of terms, variables, constants and factors.
These algebraic expressions are also made up of arithmetic operations such as;
AdditionMultiplicationDivisionBracketParenthesesSubtractionFrom the information given, we have that;
sum of 2 number is 34,678
If one of the number is x and the other is 30, 020
Then, we have that;
x + 30,020 =34, 678
collect the like terms, we have;
x = 34, 678 - 30, 020
x = 4, 658
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harm, Inc. is a pharmaceutical company with 100 million shares ag at $10/share and debt outstanding of $ 250 million. The firm has ered beta of 1.00 and a pre-tax cost of debt of 4.5%. The risk-free s 3.5%, the marginal tax rate is 40% and the equity risk premium o. A. What is the cost of equity capital? B. What is the after-tax cost of debt? C. What is the WACC? ow assume that the firm plans to borrow $ 500 million and buy back ock. If this will triple the default spread on the debt (both new and xisting), estimate the new cost of capital for the firm after the ecapitalization. D. What is the cost of equity after restructuring? E. What is after-tax cost of debt after restructuring? F. What is the WACC after restructuring? Now assume that the firm does buy back stock with the $ 500 million and pays$ 11/share. G. Estimate the value (price) per share for the remaining shareholders in the company. (You can assume no growth in perpetuity).
Answers
The following are the solutions to the given problem:A. Cost of Equity Capital:Given,Beta of the firm = 1.00Risk-Free Rate (Rf) = 3.5%Equity Risk Premium = 6%Cost of Equity (Re) = Rf + Beta*(Equity Risk Premium)Re = 3.5% + 1.00(6%)Re = 9.5%B. After-Tax Cost of Debt:Given,
Pre-tax cost of debt = 4.5%Tax rate = 40%
After-tax cost of debt (Rd) = Pre-tax cost of debt x (1 - Tax Rate)Rd = 4.5% x (1 - 0.40)Rd = 2.7%C. Weighted Average Cost of Capital (WACC):Given,
Weightage of Equity (We) = 100 million shares / 100 million shares + 250 million of debtWe = 28.57%Weightage of Debt (Wd) = 250 million of debt / 100 million shares + 250 million of debt
Wd = 71.43%WACC = (We x Re) + (Wd x Rd)WACC = (28.57% x 9.5%) + (71.43% x 2.7%)WACC = 3.91%D. Cost of Equity after Restructuring:Given,New Default Spread = 3 x Old Default SpreadOld Default Spread = 2.7% - 3.5%Old Default Spread = -0.8%New Default Spread = 3 x -0.8%
New Default Spread = -2.4%New After-tax Cost of Debt (Rd) = 2.7% + (-2.4%)Rd = 0.3%New Weightage of Debt (Wd) = 750 million of debt / 100 million shares + 750 million of debt
Wd = 88.24%New Weightage of Equity (We) = 100 million shares / 100 million shares + 750 million of debtWe = 11.76%New Cost of Equity (Re) = 9.5%Re = 9.5%New WACC
= (We x Re) + (Wd x Rd)New WACC = (11.76% x 9.5%) + (88.24% x 0.3%)New WACC = 0.53%E. After-tax Cost of Debt after Restructuring:Given,
New After-tax Cost of Debt (Rd) = 0.3%F. WACC after Restructuring:New WACC = 0.53%G. Value (Price) per Share for the Remaining Shareholders in the Company:Given,
New Shares = 500 million / $11 per share = 45,454,545 shares New Equity Shares = 100 million shares + 45,454,545 shares = 145,454,545 shares Value of Equity = 145,454,545
shares x $11 per shareValue of Equity = $1,600,000,000Value per Share for the Remaining Shareholders in the Company = $1,600,000,000 / 100 million sharesValue per Share for the Remaining Shareholders in the Company = $16.00 per share.
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The measure of one of the small angles of a right triangle is 45 more than 4 times the measure of the other small angle. Find the measure of both angles.
Answers
Answer:
Step-by-step explanation
You start by knowing that a triangle has 180 degrees in total and this is a right triangle so your total needs to add up to 90. Using the formula 90 subtract 45 then divided by 4+1 and there is your smaller angle.
Why are the lines y = 5x − 1 and 10x + 2y = 0 perpendicular
Answers
Answer:
The lines are not perpendicular because the product of their slopes is not -1.
Step-by-step explanation:
y = 5x - 1
slope = 5
10x + 2y = 0
2y = -10x
y = -5x
slope = -5
The slopes are 5 and -5.
5 × (-5) = -25
The product of the slopes is -25, not -1, so the lines are not peropendicular.
Answer:
The line are not perpendicular. Perpendicular lines after opposite reciprocals.
Step-by-step explanation:
Change 10x + 2y = 0 into the slope intercept form of a line.
Subtract 10x from both sides
10x - 10x + 2y = 0 - 10 x
2y = -10x Divide both sides by 2
y = -10x/2
y = -5x.
The slope of the first equation is 5 ( y = 5x -1 ).
The slope of the second equation is -5 ( y = -5x )
The opposite reciprocal of 5 would be -1/5 not -5.
So these lines are not perpendicular.
Helping in the name of Jesus.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
20. A. 357.8 in³
B. 1231.5 yd³
Step-by-step explanation:
20.
A.
Volume of Pyramid : ⅓*base area * height
here,
Base area = area of rectangle=length*breadth =10*8=80in²
Now
Height can be calculated by using Pythagorous theorem
height =[tex]\sqrt{(slant\: height)^2-(\frac{breadth}{2})^2}[/tex]
height =[tex]\sqrt{14^2-(\frac{8}{2})^2}=\sqrt{196-16}=\sqrt{180}=13.42 in[/tex]
height =13.4 in
Now
Volume of pyramid = ⅓*base area *height
Volume of Pyramid=⅓*80*13.42
Volume of Pyramid=357.8 in³
B.
Volume of cone = ⅓*area of base* height
Here
slant height=24 yd
height =?
diameter=14yd
radius =14/2=7 yd
Let's find the height:
By using the Pythagorous theorem,
slight height²=radius²+height²
substituting value
25²=7²+height²
height²=25²-7²
height =[tex]\sqrt{576}[/tex]=24 yd
Now
Area of Base= πr²=π*7²=153.94 yd²
Now
Volume = ⅓*area of base*height =⅓*153.94*24=1231.5 yd³
So,
Volume of cone is 1231.52 yd³.
Sketch an angle 0 in standard position such that 0 has the least possible positive measure, and the point (-2,√3) is
on the terminal side of 0. Then find the values of the six trigonometric functions for the angle. Rationalize denominators
if applicable.
Answers
The trigonometric functions for the angle with the least possible positive measure and the point (-2, √3) on the terminal side are:
sin(0) = √3/2
cos(0) = -1/2
tan(0) = -√3
csc(0) = 2/√3
sec(0) = -2
cot(0) = -1/√3
To sketch an angle in standard position, we start by placing the initial side along the positive x-axis. Since we want the angle with the least possible positive measure, we choose the smallest positive angle, which is 0 degrees or 0 radians.
Next, we plot the point (-2, √3) on the terminal side of the angle. This point lies in the third quadrant of the coordinate plane. We draw a line segment from the origin to this point, representing the terminal side of the angle.
To find the values of the trigonometric functions, we can use the coordinates of the point (-2, √3) to determine the side lengths of a right triangle. The x-coordinate (-2) represents the length of the adjacent side, and the y-coordinate (√3) represents the length of the opposite side. The hypotenuse can be found using the Pythagorean theorem.
Using the values of the sides, we can calculate the trigonometric functions:
sin(0) = opposite/hypotenuse = √3/2
cos(0) = adjacent/hypotenuse = -1/2
tan(0) = opposite/adjacent = -√3
csc(0) = 1/sin(0) = 2/√3
sec(0) = 1/cos(0) = -2
cot(0) = 1/tan(0) = -1/√3
The trigonometric functions for the angle with the least possible positive measure and the point (-2, √3) on the terminal side are:
sin(0) = √3/2
cos(0) = -1/2
tan(0) = -√3
csc(0) = 2/√3
sec(0) = -2
cot(0) = -1/√3
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Given that ABCD is a rhombus, what is the value of x?
B
(4x-25)
A
OA. 29
B. 23
C. 46
D. 38
OE. 45
O F. Cannot be determined
Answers
The value of x in the rhombus ABCD is determined as 23.
option B.
What is the value of x?The value of x is calculated by applying the following formula as shown below.
the diagonals of a rhombus intersects at 90 degrees;
the complementary angle of (4x - 25) = 90 - (4x - 25)
90 - (4x - 25) = x (alternate angles are equal)
90 - 4x + 25 = x
115 = 4x + x
115 = 5x
divide both sides of the equation by 5 to obtain the value of x;
5x = 115
x = 115 / 5
x = 23
Thus, the value of x in the rhombus ABCD is determined as 23.
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URGENT
in the first month that moiras marmalade stand was open, moira sold 145 jars of marmalade. In the second month, Moira sold 203 jars of marmalade. write the number she sold in the second month as a percentage of the number sold in the first month
Answers
Therefore, Moira sold approximately 140% as many jars in the second month compared to the first month. This means the number of jars sold in the second month was 140% of the number sold in the first month.
To find the second month's sales as a percentage of the first month's sales, we need to divide the number of jars sold in the second month by the number sold in the first month and then multiply by 100 to get the percentage.
Number of jars sold in the second month: 203
Number of jars sold in the first month: 145
Percentage of second month's sales = (203 / 145) * 100 ≈ 140%
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need help with this ASAP
Answers
Answer:
The answer is,
[tex]\sqrt{3}/2[/tex]
Step-by-step explanation:
Since we have cos10cos20 - sin10sin20,
We can use the formula,
cos(a+b) = (cosa)(cosb) - (sina)(sinb)
So, we have,
cos10cos20 - sin10sin20 = cos(10 + 20)
= cos(30)
cos(30) = sqrt(3)/2
[tex]cos(30) = \sqrt{3}/2[/tex]
Evaluate the following expression when x = -4 and y = 4.
x^6-x/4y
A. 1,023/4
B. 1,025/4
C. 16,385/4
D. -1,023/4
Answers
Answer: The correct answer is option C. 16,385/4.
Step-by-step explanation: First of all, we evaluate the expression x^6. Putting x= -4 gives (-4^6) which is equal to 4096. The next part (-x/4y) on substituting x = -4 and y =4 gives us the positive expression (1/4).
Adding both these parts, we get (4*4096+1)/4. This is finally evaluated as (16,384+1)/4, which is equal to the required answer of 16,385/4.
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answers
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = [tex]\frac{PQ}{AB +BQ}[/tex]
[tex]=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}[/tex]
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
[tex]PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}[/tex]
[tex]= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4[/tex]
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
Read the problem and decide whether it has too much or too little
information.
On Saturday at the Boxerville Carnival, 800 people attended. On Sunday, 650
people attended. On Monday, 250 people attended. On Tuesday, 350 people
attended. How many people attended the Boxerville Carnival on the
weekend?
Answers
The problem provides the attendance numbers for four specific days of the Boxerville Carnival: Saturday (800 people), Sunday (650 people), Monday (250 people), and Tuesday (350 people). The question asks for the total number of people who attended the carnival on the weekend.
Given that the information about Saturday and Sunday attendance is provided, we have enough information to determine the total number of people who attended the carnival on the weekend. We can simply add the attendance numbers for Saturday and Sunday:
800 + 650 = 1450 people.
Therefore, the problem has sufficient information to calculate the total attendance on the weekend. It is not excessive or lacking in detail, allowing us to accurately find the desired answer.
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What number must you add to complete the square x2+4x=15
Answers
Answer: 19
Step-by-step explanation:
x^2+4x-15=0. To complete the square, it needs to be (x+2)^2, which is x^2+4x+4. Thus, you need to add 19.
Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Which journey required more petrol?
Answers
Othniel used 2/5 of a full tank of petrol to travel to Kumasi and 2/6 of the full tank of petrol to travel to Accra. Therefore, the journey to Kumasi required more petrol by simplifying the fractions.
To compare the amount of petrol used for the journeys to Kumasi and Accra, we'll calculate the fractions of the full tank of petrol used for each journey.
Let's assume that the full tank of petrol has a capacity of 1 unit.
Othniel used 2/5 of the full tank of petrol to travel to Kumasi.
The fraction of the full tank of petrol used for the journey to Kumasi is 2/5, which is equivalent to 0.4.
Othniel used 2/6 of the full tank of petrol to travel to Accra.
To compare the fractions accurately, we need to make the denominators equal. Since the least common multiple (LCM) of 5 and 6 is 30, we'll convert the fractions to have a denominator of 30.
Converting the fraction 2/5 to have a denominator of 30:
(2/5) * (6/6) = 12/30
Converting the fraction 2/6 to have a denominator of 30:
(2/6) * (5/5) = 10/30.
Comparing the fractions, we find that Othniel used 12/30 of the full tank of petrol to travel to Kumasi and 10/30 of the full tank of petrol to travel to Accra.
Since 12/30 is greater than 10/30, the journey to Kumasi required more petrol.
Simplifying the fractions, we have:
Journey to Kumasi: 12/30 = 2/5.
Journey to Accra: 10/30 = 1/3.
Therefore, the journey to Kumasi required more petrol than the journey to Accra.
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