Final answer:
To determine the angular size of an object with a diameter of 3 inches from 4 yards away, one can use the formula θ = d / D to calculate θ in radians, which is then converted to degrees, resulting in an angular size of approximately 1.19°.
Explanation:
To find the angular size of a circular object with a 3-inch diameter viewed from a distance of 4 yards, one can use the following formula for angular size θ (in radians): θ = d / D, where d is the diameter of the object and D is the distance to the object.
First, we convert the diameter and the distance to the same units. There are 36 inches in a yard, so 4 yards is 144 inches:
Diameter (d): 3 inchesDistance (D): 4 yards = 144 inchesThen, we calculate the angular size in radians:
θ = d / D = 3 inches / 144 inches = 0.0208333...
This can be converted to degrees by multiplying with 180/π:
θ(in degrees) = 0.0208333... * (180/π) = 1.19° (approximately).
Thus, the angular size of the object is approximately 1.19° when viewed from a distance of 4 yards.
Suppose the line of best fit is being found for some data points that have an r-value of 0.657. If the standard deviation of the x-coordinates is 2.445, and the standard deviation of the y-coordinates is 9.902, what is the slope of the line to three decimal places?
Answer: 2.661
Step-by-step explanation:
A P E X
Which answer correctly describes the relationship between two of the lines in the figure?
Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450
What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\
Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Explanation:-
Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]
To simplify, rewrite the numbers inside the root in the product of primes, we get
[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]
Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
PLEASE HELP
Probability allows a person to effectively measure the risks in selecting one alternative over others.
True
False
House is 50.0 ft long and 26 ft wide and has 8.0-ft- m high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters?
Your Cell Phone plane cost 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan
Answer:
F( x) = 0.35 x + 55
-10-2v<6 and 6v+12<-6.
need some help with this problem i keep messing a step
A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?
15 * 4 2/3 please help
4 2/3 = 14/3
15 = 15/1
14/3 * 15/1 = 14*15=210, 3*1 = 3
210/3 = 70
answer is 70
What is 320 1/4 rounded to the nearest whole number?
PLEASE HELP!!!
The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 15) (–4, 36) (3, 15) and (4, 12) (–3, 33) and (–4, 36)
Answer:
C
Step-by-step explanation:
or (3, 15) and (4, 12)
Sam scored 43 48 and 42 points on 3 test how many points should he get on the fourth test to get in average score of 50
(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.
The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.
A catering service offers 12 appetizers, 6 main courses, and 7 desserts. A banquet chairperson is to select 6 appetizers, 2 main courses, and 5 desserts for a banquet. In how many ways can this be done?
C: -5/2 D: 5/2 help please
identify the graph of the equation. What is the angle of rotation for the equation? 13x^2+6sprt3xy+7y^2-16=0
Answer:
The answer is ellipse; 30° ⇒ answer (d)
What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?
The value of the cumulative standardized normal distribution at z is 0.8770. the value of z is
Final answer:
To find the z-score corresponding to a cumulative area of 0.8770 in a standard normal distribution, one can look up this area in a z-table or use statistical software, yielding a z-score of approximately 1.15.
Explanation:
The question involves finding the value of z in a standard normal distribution given that the cumulative area to the left of z is 0.8770.
The z-score is a measure that describes the position of a raw score in terms of its distance from the mean, measured in standard deviations.
To find the value of z corresponding to an area of 0.8770, one would typically use a z-table or statistical software. The z-table lists areas to the left (cumulative probabilities) for different z-values.
For an area of 0.8770, the z-score is approximately 1.15. This calculation is based on the standard normal distribution, where the mean is 0 and the standard deviation is 1.
3. what is the simplified form of x+4/7 - x+3/x+5
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
Simplify the expression, then we have
⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]
⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]
⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]
⇒ (x² + 2x - 1) / 7(x + 5)
The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.
More about the Algebra link is given below.
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A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?
A.75%
B.60
C.25%
D.40%
The solution would be like this for this specific problem:
Given:
{0, 1, 2, 3, 4}
Success = 2, 3, and 4
Solution:
Success = 3 numbers
Sample = 5
= 3 / 5
= .6
= .6 * 100%
= 60%
So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.
To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.
If x varies directly with y and x = 3.5 when y = 14, find x when y = 18.
Answer:
the value of x= 4.5
Step-by-step explanation:
If x varies directly with y and x = 3.5 when y = 14
x varies directly with y , so equation is x= ky
where k is the constant of proportionality
x = 3.5 when y = 14, use the given values and find out k
Plug in the given values in x=k y
3.5= k * 14
Divide by 14 on both sides
0.25= k
So the value of k = 0.25
Now find out x when y= 18
x= ky
x= 0.25 * 18= 4.5
Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.
Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.
Answer:
Number One / Letter A
Step-by-step explanation:
Add 2, subtract 2x, then divide by 2.
Hope This Helps!
Please help me ASAP.
David had a coupon for the grocery store. He graphed on the x-axis what his total bill would be if he didn’t use the coupon and graphed on the y-axis what his total bill would be if he used the coupon.
Based on the information in the graph, if David’s bill came to $66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?
a.$64
b. $65
c. $67
d. $68
Answer:
d. $68Step-by-step explanation:
First, let's find the equation of the line.
The slope is defined by
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Where we are gonna use points (2,0) and (9,7).
[tex]m=\frac{7-0}{9-2}=\frac{7}{7}=1[/tex]
Then, we use the point-slope formula to find the equation.
[tex]y-y_{1} =m(x-x_{1} )\\y-0=1(x-2)\\y=x-2[/tex]
So, if David's bill came to $66 after coupon, it means [tex]y=66[/tex].
Replacing this value in the equation, we have
[tex]y=x-2\\66=x-2\\x=66+2\\x=68[/tex]
Therefore, the price without coupon is $68.
Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong. (1 point)
Step 1: x equals negative 8 plus or minus the square root of the quantity eight squared minus four times one times seven, end quantity, all over two times one.
Step 2: x equals negative 8 plus or minus the square root of sixty-four minus twenty-eight all over two times one.
Step 3: x equals negative 8 plus or minus the square root of thirty-six all over two times one.
Step 4: x equals negative 8 plus or minus six all over two.
Step 1
Step 2
Step 3
Step 4
Her mistake is in the first step, she wrote the equation incorrectly.
Solving quadratic equations:
A general quadratic equation:
ax^2 + bx + c = 0
has the solutions:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, the equation is:
y = x^2 - 8x + 7
And what Joyce writes in each step is:
Step 1:
x = (-8 ± √(8^2 - 4*1*7))/(2*1)
Then we can already see the mistake.
Notice that in the given equation, we have:
b = -8
And the general solution has:
x = (-b ± √(b^2 - 4ac))/(2a)
-b would be equal to 8, then what Joyce must have written here is:
x = (8 ± √((-8)^2 - 4*1*7))/(2*1)
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If you start with a number divide it by 4 then multiply it by two you end up with 8 squared
8 squared = 64
so
(x/4)*2 = 64
divide x/4 by 2 to get x/2=64
now multiply both sides by 2 to get x=128
x = 128
I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?
Answer:
56
Step-by-step explanation:
(15 POINTS) Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0).
An equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
What is equation of ellipse?"The standard form of equation of ellipse with center (0, 0) is, [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
What are vertices of the standard ellipse?"The vertices of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm a,0)[/tex] "
What is focus of the standard ellipse?"The foci of the standard ellipse [tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex] are [tex](\pm c,0)[/tex], where [tex]c^{2} =a^{2}- b^{2}[/tex] "
For given question,
The center of the ellipse is at the origin.
Using the standard form of equation of the ellipse,
[tex]\frac{x^2}{a^2} +\frac{y^2}{b^2} =1[/tex]
A vertex at (13, 0)
⇒ (a, 0) = (13, 0)
⇒ a = 13
And a focus at (12, 0).
⇒ (c, 0) = (12, 0)
⇒ c = 12
We know, [tex]c^{2}= a^{2}- b^{2}[/tex]
Now, we find the value of b i.e., minor axis
[tex]\Rightarrow 12^{2} =13^{2}- b^{2}\\\\\Rightarrow b^2=169-144\\\\ \Rightarrow b^2=25\\\\\Rightarrow b=\pm 5[/tex]
Substituting these values in the standard form of equation of ellipse with center (0, 0),
[tex]\Rightarrow \frac{x^2}{a^2} +\frac{y^2}{b^2} =1\\\\\Rightarrow \bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
Therefore, an equation in standard form for an ellipse with its center at the origin, a vertex at (13, 0), and a focus at (12, 0) is [tex]\bold{\frac{x^2}{169} +\frac{y^2}{25} =1}[/tex]
The correct answer is option (A)
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A coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. What statistic should he study?
The statistic that the coach should study is mean or the average score of the two teams. If the coach wants to know if football players who warm up before a game will score more points than those who don't warm up. He will break the team up into two groups and make sure each player gets equal time on the field. He will then count how many points each player makes during the game. After counting them, add the scores of the group that he divided and then divided it by the number of player in that group to get an average score on teams that warm up or do not warm up before the game.