Use the Law of Sines to find the missing angle in the triangle. Find m
Suppose the number of gallons of gasoline per day used by a car is normally distributed with a mean of 2.2 gallons and a standard deviation of 1.2 gallons.
What is the difference in gallons per day used by a car with a z-score of 3 and another car that has a z-score of 0?
A. 1.2
B. 2.6
C. 3.6
D. 4.6
The perimeter of square A is 28 feet less than the perimeter of square B. The area of square A is 161 square feet less than the area of square B. If x and y are the side lengths of square A and square B, respectively, what is the value of x + y?
A fire fighter has to get to a burning building as quickly as he can. there are three paths that he can take. he can take his fire engine over a large hill (5 miles) at 10 miles per hour. he can take his fire engine through a windy road (7 miles) at 9 miles per hour. or he can drive his fire engine along a dirt road which is 8 miles at 12 miles per hour.
Final answer:
The firefighter should take the path over the large hill as it will take the shortest amount of time to reach the burning building.
Explanation:
The firefighter has three paths to choose from in order to reach the burning building:
Path 1: The firefighter can take the fire engine over a large hill, which is 5 miles long, at a speed of 10 miles per hour.
Path 2: The firefighter can take the fire engine through a windy road, which is 7 miles long, at a speed of 9 miles per hour.
Path 3: The firefighter can drive the fire engine along a dirt road, which is 8 miles long, at a speed of 12 miles per hour.
The firefighter will need to calculate the time it takes to travel each path and choose the path that allows him to reach the burning building quickest.
Let's calculate the time for each path:
Path 1: Time = Distance / Speed = 5 miles / 10 miles per hour = 0.5 hours = 30 minutes
Path 2: Time = Distance / Speed = 7 miles / 9 miles per hour ≈ 0.78 hours ≈ 47 minutes
Path 3: Time = Distance / Speed = 8 miles / 12 miles per hour ≈ 0.67 hours ≈ 40 minutes
Based on the calculations, the firefighter should take Path 1 over the large hill, as it will take him the shortest amount of time to reach the burning building.
While Joey was standing outside on a sunny day, his shadow was 5 feet long. The shadow of a nearby Oak tree was 12 feet long. If Joey is 6 feet tall, how tall is the Oak tree?
A. 15.6 feet
B. 14.4 feet
C. 10 feet
D. 13.4 feet
1. Through music, literature, and painting, the romantic artists attempted to
(1 point)make people fall in love.
express their love for women.
stir the emotions.
get people to reject modern innovations.
2. What do the writers Walter Scott, Mary Shelley, Edgar Allen Poe, and William Wordsworth have in common?
(1 point)They were all men.
They were all French.
They were all English.
They were all romantic writers.
3. Romantic painters aimed to
(1 point)mirror the artist’s imagination.
re-create nature.
meet the highest standards of the École des Beaux-Arts.
f,
The value of the investment is expected to grow by 3% per year.
How long will it take to double?
A. About 4 years
B. About 6 years
C. About 12 years
D. About 24 years
Answer:
D. About 24 years
Step-by-step explanation:
Compounding is the means the future value of an amount saved today while discounting means the present value of a future amount.
In other words, we discount to know the present value of $1 in the future while we compound to know the future worth of $1 saved today.
Let the value of the investment be x. if it is expected to double in n years then using the compound interest formula
fv = pv(1 + r)^n
where fv and pv are the future and present values respectively and n is the time, r is the growth rate
2x = x(1 + 0.03)^n
2 = (1.03)^n
log 2 = log (1.03)^n
= n log 1.03
n = log 2/ log 1.03
n = 23.44
This is approximately 24 years hence option D is right
A delivery person is scheduled to pick up 9 crates of patio pavers. Each crate weighs 14 ton. How much weight will the delivery person need to plan for?
Explain how you can tell without calculating whether the sum of a positive number and a negative number will be positive, negative, or zero.
The Smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
Which of the following would be an appropriate scale to use on an 8 1/2 by 11 sheet of paper for a sketch of the room and carpet?
1 inch = 1 foot
1 inches = 1 foot
1/2 inch = 1 foot
2 inches = 1 foot,
The room scale will only fit on an 8 1/2" X 11" page if 1/2 iinch = 1 foot is used. If we take the largest measurement 15 X 20......the 15 would hang over the edge of the paper no matter which way we turn it. With the 1/2" we can get 17 feet on the 8 1/2 side and and 22 on the 11" side.
1/2 inch = 1 foot is the correct answer
Joe has some pocket money. He spends 90% of it. He has 50p left. How much pocket money did he have?
Plutonium -25 has a half live of 6 hours . George has 5000 grams of plutonium -25 . How much plutonium-25 will hearse have after 4 days
Side ab in triangle abd corresponds to which side of triangle abc? ab bc ac
Answer:
The correct answer to this question going by the reference photo is AC (answer) that corresponds to AB.
Step-by-step explanation:
Answer:
it is AC
Step-by-step explanation:
option c
Probabilities are between 0 and 1. A probability of 0 means that an event occur or that it is for the event to occur. If it is unlikely that the event will occur, then the probability of that event is . If it is equally likely that the event will occur or that the event will not occur, then the probability is . If it is very likely that the event will occur, then the probability of that event is . If the event will definitely occur, then the probability of that event is . A sample space has probability when all of the possible outcomes of the sample space have probabilities.
closer to zero equal to one impossible real numbers one-half will not closer to one uniform equal
Final answer:
Probability measures the likelihood of an event occurring, with values between 0 (impossible) to 1 (certain). A probability closer to 0 implies unlikeliness, one-half means equal likelihood, and closer to 1 suggests high likelihood. The probabilities in a uniform sample space are equal for all outcomes.
Explanation:
Probabilities are mathematical measures between 0 and 1. A probability of 0 means an event will not occur, or it is impossible for the event to happen. Conversely, if the probability is equal to one, it means the event will definitely happen. When it's unlikely that the event will occur, the probability is closer to zero. If there's an equal chance the event will occur or not, the probability is one-half (0.5). For events that are very likely to occur, the probability is closer to one. A sample space is considered uniform when all the possible outcomes have equal probabilities.
To calculate the probability of an event A in a uniform sample space, count the number of outcomes for event A and divide by the total number of outcomes in the sample space. This is the theoretical probability of A. For example, when tossing a fair coin, there is an equal likelihood of landing on heads or tails, which are mutually exclusive events, each with a probability of 0.5, and together they form the sample space with a total probability of 1.
The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any right triangle.
a 2 + b 2 = c 2
Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle.
Answer: a = square root of (c^2 - b^2)
Step-by-step explanation:
find the inverse of the following function:
[tex]f(x)=-2 \sqrt{3x-1} -5 [/tex]
if x \geq 1/3[/tex]
If 1 Chinese yuan equals 0.1558 U.S. dollars, then 1 U.S. dollar equals approximately how many Chinese yuan?
A. 0.4185
B. 0.1558
C. 6.1558
D. 6.4185
Answer:
1 U.S. dollar equals 6.4185 Chinese yuans. The correct answer is D.
Step-by-step explanation:
- The first step is to get a fraction between the currencies. The fraction is obtained by dividing the 1 yuan by 0.1558 U.S. dollars.
[tex]fraction=\frac{1\, \, yuan}{0.1558\, \, U.S.\, \, dollars.}[/tex]
- The second step is to multiply the previous fraction by 1 U.S. dollar.
[tex]\frac{1\, \, yuan}{0.1558\, \, U.S.\, \, dollars}\times 1\, \, U.S.\, \, dollars[/tex]
As you can see, the U.S. dollar units can be cancelled and yuan remains.
[tex]\frac{1\, \, yuan}{0.1558}\times 1[/tex]
- The last step is to perform the division.
[tex]1\, \, U.S.\, \, dollars=6.4185\, \, yuans[/tex]
Thus, 1 U.S. dollar equals 6.4185 Chinese yuans. The correct answer is D.
Does 6(x+2)>x-3 have a solution
In a statistics class there are 11 juniors and 6 seniors; 2 of the seniors are females; 6 of the juniors are males. if a student is selected at random, what is the probability that the student is either a junior or a female?
enter your answer as a fully reduced fraction.
Answer: [tex]\dfrac{13}{17}[/tex]
Step-by-step explanation:
Given: Number of juniors = n(J)= 11
Number of seniors = 6
Total students n(S)=[tex]11+6=17[/tex]
Number of seniors are which are females =2
Number of juniors are which are males =6
Then, number of juniors which are females = [tex]11-6=5[/tex]
Now, total females n(F)=[tex]2+5=7[/tex]
such that number of juniors which are females n(J∩F) = [tex]5[/tex]
Now, the number of students either a junior or a female is given by :_
[tex]n(J\cup F)=n(J)+n(F)-n(J\cap F)\\\\\Rightarrow n(J\cup F)=11+7-5=13[/tex]
Now, the probability that the student is either a junior or a female is given by :-
[tex]P(J\cup F)=\dfrac{n(J\cup F)}{n(S)}=\dfrac{13}{17}[/tex]
Anna and Bill share some money in the ratio 2:5
Anna gets £A
Bill gets £B
Carl and Donna share twice as much money as Anna and Bill share.
They share the money in the ratio 3:1
Carl gets £C
Donna gets £D
Find A:B:C:D in its simplest form
The ratio A:B: C:D in its simplest form is 4:10:15:5.
Let's denote the total amount of money shared by Anna and Bill as M. Since Anna and Bill share this money in the ratio of 2:5, Anna gets 2/7 of M and Bill gets 5/7 of M.
So, we have:
Anna's share (A) = (2/7)M
Bill's share (B) = (5/7)M
Carl and Donna share twice as much money as Anna and Bill, which means the total amount of money shared by Carl and Donna is 2M. They share this money in a ratio of 3:1.
Therefore:
Carl's share (C) = (3/4)(2M) = (3/2)M
Donna's share (D) = (1/4)(2M) = (1/2)M
Now, we want to find the ratio A:B:C: D. To do this, we need to express all shares in terms of the same unit. Since Anna and Bill's total money is M, we will express Carl and Donna's shares in terms of M as well.
We have:
A = (2/7)M
B = (5/7)M
C = (3/2)M
D = (1/2)M
To find the ratio A:B: C:D, we can compare the coefficients of M:
A:B:C:D = (2/7)M : (5/7)M : (3/2)M : (1/2)M
To simplify this, we can multiply each term by the least common multiple (LCM) of the denominators, which is 14. This will give us the ratio in whole numbers without changing the proportions.
Multiplying each term by 14, we get:
A:B:C:D = (2/7)*14 : (5/7)*14 : (3/2)*14 : (1/2)*14
A:B: C:D = 4:10:15:5
Therefore, the simplest form of the ratio A:B: C:D is 4:10:15:5.
factor each polynomial 9x-6 a.9(x-6) b.3(3x-2) c.6(3x-1) d.3x
The correct answer is b) 3(3x - 2)
In order to factor this, you have to find the greatest common factor of 9x and 6. Since 6 does not have an x in it, we cannot pull out an x. Instead we have to look for the biggest whole number that goes into 9 and 6, which is 3.
Next, to take the 3 out, we need to divide each term by 3.
9x/3 = 3x
-6/3 = -2
So the 3 comes out and the results above go together in the parenthesis.
3(3x - 2)
[tex] 9x-6=3(3x-2)\implies\text{B} [/tex]
Solve by factoring 4x^2+16x+12=0
How many different towers can you make using one red, one blue and one yellow block?
Final answer:
Using permutation principles, one can determine that six different towers can be made from one red, one blue, and one yellow block, by multiplying the number of choices for each position (3 x 2 x 1).
Explanation:
The question is about determining the number of different towers that can be made using one red, one blue, and one yellow block. This type of problem involves understanding permutations, as each block can be placed in any order.
To calculate the permutations of the three blocks, we consider how many choices we have for each position in our tower. For the top position, there are three choices (red, blue, yellow), for the second position, there are two remaining choices, and for the last position, there is only one choice left. This gives us a total of 3 x 2 x 1 = 6 different towers. Each tower is a unique combination of the colors in a specific order.
What is the area of the composite figure whose vertices have the following coordinates? (−2, −2) , (3, −2) , (5, −4) , (1, −8) , (−2, −4) Enter your answer in the box. units²
What is the length of bc?
Trayvon sells candy bars at a price of $3 each. He purchases every order of 200 candy bars for $350. If the cost of shipping is $0.15 per bar, what is Trayvon’s profit function?
Which equation could have been used to create this graph?
A.
y = 5x
B.
y = x + 0
C.
y = x + 1
D.
y = x + 5
Answer:
Its b :)
Step-by-step explanation:
−2x+5y=13
16x+3y=25
Name at least two pieces of information that might be found in stock listings.
Lexi bought 1 2/5 of green grapes and 2 3/10 of red grapes. Grapes are 2.99 a pound.Did lexi spend more or less then $12?