Answer: 60 inches
Step-by-step explanation:
Given: A frame in the shape of right triangle with the longest side = 87 inches
The height of the frame is labeled as 63 inches.
Let 'x' be the third side of the frame then by Pythagoras theorem of right triangle , we have
[tex]87^2=x^2+63^2\\\\\Righatrrow\ x^2=87^2-63^2\\\\\Rightarrow\ x^2=3600\\\\\Rightarrow\ x=\sqrt{3600}=60[/tex]
Hence, the length of the third side of the window frame = 60 inches.
Which of the following indicates that the roots of a quadratic are irrational
a) discriminant is zero
b) discriminant is negative
c) discriminant is rational
d) discriminant is prime
A plane left Atlanta at 11:30 a.m. and flew to an airport near Boston. The plane was due at Boston at 3:15 p.m. The plane arrived 25 minutes late. The time of the trip was?
Answer: 4 HOURS AND 10 MINUTES
Step-by-step explanation:
1 HOUR IS 60 MINUTES.
60X4=240 MINUTES
240 MINUTES+10 MINUTES=250 MINUTES
250 MINUTES=4 HOURS AND 10 MINUTES.
The time elapsed during the trip is 4 hours 10 minutes.
Given that,
The plane left Atlanta at 11:30 a.m. and flew to an airport near Boston.
The plane was due at Boston at 3:15 p.m.
In mathematics, it deals with numbers of operations according to the statements.
Since A plane takes off from Atlanta at 11:30 a.m. and landed at Boston airport at 25 minutes later than the actual time of arrival.
The time of arrival was 3:15 PM but because of the delay, at 3:40 the plane landed at Boston airport. For 3:40 pm we have 15:40 on a 24-hour clock. So,
The time elapsed = 15:40 - 11:30
= 4 : 10
Implies 4 hours 10 minutes
Thus, the time elapsed during the trip is 4 hours 10 minutes.
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Which of the following is not equivalent to the formula d = rt?
[tex] \frac{d}{r}= t[/tex]
r = dt
[tex] \frac{d}{t} = r[/tex]
[tex]\frac{d}{rt} = 1[/tex]
Answer:
Option B, r=dt is not equivalent
Step-by-step explanation:
We have given that : The formula d=rt
To find which is not equivalent in the following
so,
1) [tex]\frac{d}{r}=t[/tex] is equivalent
2) [tex]r=dt[/tex] is not equivalent because, [tex]r=\frac{d}{t}[/tex]
3) [tex]\frac{d}{t}=r[/tex] is equivalent
4) [tex]\frac{d}{rt}=1[/tex] is equivalent
therefore option B is not equivalent.
About 15% of the population of a large country is allergic to pollenallergic to pollen. if two people are randomly selected, what is the probability both are allergic to pollen? what is the probability at least one is allergic to pollenallergic to pollen?
Answer:
(a) 0.0225
(b) 0.225
Step-by-step explanation:
It is given that 15% of total population is allergic to pollenallergic to pollen.
Thus, Probability of an individual s/he has allergy is 0.15
Thus, The probability that two person is selected and both has allergy is 0.15 × 0.15 = 0.0225
And the Probability that at least one person is suffered from allergy from that two person = P(allergic and non-allergic) + P(non-allergic and allergic)
⇒ 0.15 × (1 - 0.15) + (1 - 0.15) × 0.15
⇒ 0.15 × 0.85 + 0.85 × 0.15 = 0.225
A number is no more than five. How would you graph this inequality?
A. Draw an open circle on 5 and shade to the left.
B. Draw a closed circle on 5 and shade to the left.
C. Draw an open circle on 5 and shade to the right.
D. Draw a closed circle on 5 and shade to the right.
Answer:
the answer is B
Step-by-step explanation:
My teacher said it was
A furniture factory makes 5 recliners for every 3 couches. If the factory makes a total of 56 recliners and couches in a day, how many recliners were made? Select the correct proportion to solve this problem.
The speed of light is about nine hundred eighty million feet per second. What is that speed in scientific notation?
Answer:
The answer is 9.8*10^8
i think
Step-by-step explanation:
the real number √13 belongs to which set of numbers
What type of triangle has side lengths 2, √11, and √15? please leave details as to how you got to your conclusion im confused
Answer:
right triangle.
Step-by-step explanation:
The given length of the three sides of the triangle are
[tex]2,\sqrt{11},\sqrt{15}[/tex]
We will now check whether these three numbers are Pythagorean triple or not. If it is a Pythagorean triple then the triangle will be a right triangle.
Pythagorean triple:- If the sum of square of any two sides is equal to the square of the third side then the lengths are Pythagorean triple and the triangle is a right triangle.
Now, we do the below operation:
[tex]2^2+(\sqrt{11})^2\\\\=4+11\\\\=15[/tex]
Now, let us square the third side
[tex](\sqrt{15})^2\\\\=15[/tex]
Since, we got both values equal. Hence, the length of sides are Pythagorean triple.
And therefore, the triangle is right triangle.
Factor the following.
A spinner and 4 cards are shown below: A spinner with 5 equal sectors is shown in the figure. The colors Green, Blue, Purple, Yellow, and Red are marked on it. The arrow points at the purple color. Four cards are shown on the right side. The colors Red, Yellow, Blue, and Pink are marked on them. Jane spins the spinner and selects a card without looking. What is the probability that the spinner stops at purple and a pink card is selected?
The probability of the spinner landing on purple and a pink card being selected is 1/20 or 5%.
Explanation:The subject of this question is probability, a branch of Mathematics. Let's determine the probability of the spinner landing on purple and choosing the pink card. There are 5 equal sectors in the spinner, which means every color has a 1/5 chance to be chosen on any spin. Therefore, the probability of it landing on purple is 1/5.
As for the cards, there are four of them, meaning each card also has a 1/4 chance of being selected. Therefore, the probability of selecting a pink card is 1/4.
Because these are independent events (one does not affect the outcome of the other) we can calculate the simultaneous probability by multiplying the individual probabilities. Thus, the total probability of the spinner landing on purple and a pink card being selected is (1/5) * (1/4), which equals 1/20 or 5%.
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in 2006, the population of a certain country per square mile of land was 81. In 2014, the persons per square mile was 85.24. assume the relationship between years, x, and persons per square mile,y, is a linear relationship
The population density in the country increased at a rate of about 0.53 persons per square mile each year between 2006 and 2014, demonstrating a linear relationship.
Explanation:You are looking at a linear relationship between years and population density in a particular country. Years are represented by 'x' and persons per square mile are represented by 'y'. To find the relationship, we need to identify the slope of the line, which represents the rate of change in population density per year.
To find the slope, we subtract the y-values and divide by the change in x-values: (85.24 - 81) / (2014 - 2006) = 0.53 persons per square mile per year.
This tells us that, on average, the population density in this country increased by about 0.53 persons per square mile each year between 2006 and 2014.
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The population density of the country increased at a linear rate of around 0.53 persons per square mile each year between 2006 and 2014.
Explanation:In this problem, we are dealing with a linear relationship between years(x) and persons per square mile(y). Here, we need to find the slope of the line to understand the rate at which the population density is increasing per year. The slope of a line in a linear relationship is given by the formula slope = (y2 - y1) / (x2 - x1). Here, (x1, y1) refers to the year and population density in 2006 which are (2006, 81) respectively, and (x2, y2) refer to the year and population density in 2014 which are (2014, 85.24) respectively.
Substitute these values into the formula:
Slope = (85.24 - 81) / (2014 - 2006)= 0.53 (approx).
So, the population density increase was about 0.53 persons per square mile per year between 2006 and 2014.
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How would you describe the difference between the graphs of f(x)=2/3 x^3 and g(x)=2/3(-x)^3
If 5 executives attend a meeting and all shake hands before and after the meeting, how many handshakes occur?
the raptors have lost 5 out of their last 11 games.They have not had any ties or forfeits. What is The ratio of wins to losses for the raptors?
Answer: 6:5
Step-by-step explanation:
Given: The total number of games played by raptors = 11
The number of games lost by them = 5
Then, the number of wins = 11-5=6
We know that the ratio of A to B is given by :-
[tex]A:B[/tex]
Similarly, the ratio of wins to losses for the raptors is given by :-
[tex]\text{Number of wins: Number of losses}\\\\=6:5[/tex]
Hence, the ratio of wins to losses for the raptors = 6:5
Answer:
B
Step-by-step explanation:
Aimee is flying a plane for the first time! The air traffic controller tells her to fly at 500 m above the ground or higher. Write an inequality that is true only for elevations (h) at which Aimee should fly.
To represent the elevations at which Aimee should fly her plane, the inequality h ≥ 500 is used, where h represents Aimee's elevation in meters. This indicates that Aimee must fly at an elevation of 500 meters or higher, as per the air traffic controller's instructions.
Explanation:The question asks for an inequality that represents elevations at which Aimee should fly her plane, according to the instructions given by the air traffic controller. Aimee is told to fly at 500 meters above the ground or higher. To write this inequality, we let h represent the elevation (in meters) at which Aimee should fly. Therefore, the inequality that only allows for elevations 500 meters or higher is: h ≥ 500.
This inequality means that Aimee's elevation, h, should be greater than or equal to 500 meters. This is a simple linear inequality in one variable, which is a fundamental concept in algebra. Understanding how to represent real-world scenarios with inequalities is crucial in solving problems related to constraints and conditions that have a range of possible values.
Which function below has the following domain and range?
Domain:
{−9,−5,2,6,10}
Range:
{−2,0,8}
Select one:
a.
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
b.
{(−9,10),(−2,8)}
{(−9,10),(−2,8)}
c.
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
d.
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
Answer:
The correct option is d.
Step-by-step explanation:
Domain is the set of all possible inputs or the values of x and the range is value of output or y.
In option a,
The given function is
{(−2,−5),(8,10),(0,6),(−2,−9),(0,2)}
Domain = {-2,0,8}
Range = {-9,-5,2,6,10}
Therefore option a is incorrect.
In option b,
The given function is
{(−9,10),(−2,8)}
Domain = {-9,-2}
Range = {8,10}
Therefore option b is incorrect.
In option c,
The given function is
{(−9,−2),(−5,0),(2,8),(6,5),(10,9)}
Domain = {-9,-5,2,6,10}
Range = {-2,0,5,8,9}
Therefore option c is incorrect.
In option d,
The given function is
{(2,0),(−5,−2),(10,8),(6,0),(−9,−2)}
Domain = {-9,-5,2,6,10}
Range = {-2,0,8}
Therefore option d is correct.
The perimeter of a rectangular field is 376 yards. if the width of the field is 89 yards, what is its length?
Answer:
Step-by-step explanation:
The length of the field will be calculated as:
P=2(L+W)
P=376
W=89
thus substituting the values in the equation we get;
376=2(L+89)
376/2=(L+89)
solving for L;
188=L+89
L=188-89
L=99 yards
therefore the length is 99 yards
How many different arrangements of the letters in the word SCHOOL are there?
A) 1440
B) 720
C) 360
D) 120
Evaluate the expression and enter your answer in the box below. 8 + |10|
Keiko is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Keiko has been adding money. Suppose that x and y are related by the equation =20x+550=y .
* Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What was the starting amount of money in the account?
What is the change per week in the amount of money in the account?
the starting amount would be the 550, because it doesn't have a variable assigned to it.
change per week is 20 since it is being multiplied by the number of weeks
The starting amount of money in the account was $550
The change per week in the amount of money in the account per week is by $20.
We have a equation - 20x+550=y
where -
x represent the number of weeks Keiko has been adding money and y represent the total amount of money in the account (in dollars).
We have to determine -
1). What was the starting amount of money in the account.
2). What is the change per week in the amount of money in the account.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to question, we have -
20x+550=y
Rearranging the equation, we get -
y = 20x + 550, which is a equation of straight line with slope = 20.
Now, in order to calculate the starting amount of money in the account, put x = 0 above, we get -
y = 20 x 0 + 550 = $550
Money in the account during week 1 = M(1) = 20 x 1 + 550 = $570
Money in the account during week 2 = M(2) = 20 x 2 + 550 = $590
Change per week in the amount of money in the account = M(2) - M(1) = $590 - $570 = $20
Hence,
The starting amount of money in the account was $550
The change per week in the amount of money in the account per week is by $20.
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y = 7x - 53 y = -4x + 35 a. ( -3, -8) c. ( -8, 3) b. ( 8, 3) d. No solution
How many times bigger is a metric ton than a kilogram?
Petrolyn motor oil is a combination of natural oil and synthetic oil. it contains 5 liters of natural oil for every 6 liters of synthetic oil. if 498 liters of synthetic oil are used, how many liters of petrol oil will be made
Select all that apply. Which of the following represent the same ratio?
A. 2 to 3
B. 2:5
C.3 to 2
D.2/3
A business is using two painters to paint 3 offices, each with 1,200 square feet of wall space. one painter can paint 190 square feet per hour. the other painter can paint 130 square feet per hour. how long will it take the two painters working together to paint the 3 offices?
In a computer game, when choosing a character there are 5 choices for hair style, 3 choices for eye color, and 7 choices for outfits. How many different characters are possible if you were to choose 1 hair style, 1 eye color, and 1 outfit?
105
140
22
15
Determine whether the formula describes y as a function of x. Explain your reasoning.
y = -x
Write the equation of the line with a slope of 4 that contains the point (5, 8).
Select one:
a. y=4x−27
b. y=4x−12
c. y=4x+28
d. y=4x+8
Mind helping a brother here! 20 points! Thanks!