Twenty-one people in a room have an average height of 5 feet 6 inches. a 22nd person enters the room. how tall would he have to be to raise the average height by 1 inch?
To raise the average height by 1 inch, the 22nd person would have to be 88 inches tall.
Explanation:To find how tall the 22nd person would have to be in order to raise the average height by 1 inch, we can use the concept of average. Currently, there are 21 people with an average height of 5 feet 6 inches. This means that the total height of all 21 people combined is 5 feet 6 inches multiplied by 21.
If we want to raise the average height by 1 inch, we need to add a certain amount of height to the total height of all the people in the room. Let's call this additional height 'x'. So the new total height would be the previous total height plus 'x'.
Since the total number of people in the room will become 22, the new average height will be the new total height divided by 22. We can set up an equation to solve for 'x':
5 feet 6 inches multiplied by 21 plus 'x' divided by 22 equals 5 feet 6 inches plus 1 inch.
To solve this equation, we can first convert the heights to inches: 5 feet 6 inches is equivalent to 66 inches. Now we can solve the equation:
66 multiplied by 21 plus 'x' divided by 22 equals 67.
Now we can simplify and solve for 'x':
1386 plus 'x' divided by 22 equals 67.
1386 plus 'x' equals 67 multiplied by 22.
1386 plus 'x' equals 1474.
Subtracting 1386 from both sides, we get 'x' equals 1474 minus 1386, which is 88 inches. Therefore, the 22nd person would have to be 88 inches tall to raise the average height by 1 inch.
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How much fruit juice (100%) is equivalent to 1 cup of fresh fruit?
a. 1/4 cup
b. 1 cup
c. 1 1/2 cups
d. 2 cups
e. 1/2 cup?
1 cup of fruit juice is equivalent to 1 cup of fresh fruit.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 cup of fresh juice.
Fresh juice and 1 cup of fresh fruit are the same.
So,
Fresh juice = 1 cup
Thus,
1 cup of fruit juice is equivalent to 1 cup of fresh fruit.
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Convert the angle 0(theta) =133pi/72 radians to degrees. can someone explain this to me step by step please?
The angle θ = 133π/72 radians is equivalent to 332.5° degrees.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To convert radians to degrees, use the following formula:
Angle in degrees = angle in radians × 180°/π
Here's how to apply this formula to the given angle:
θ= 133π/72 radians
θ in degrees = (133π/72) × 180°/π
θ in degrees = (133/72) × 180
θ in degrees = 332.5°
Therefore, the angle θ = 133π/72 radians is equivalent to 332.5° degrees.
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Write three measurments using grams and three measurements using milligrams total 15.4 grams
Label the terms in the expression as constant, linear, and quadratic. 4x2 + 3x - 6
how many positive integers under 50 are multiples of neither 4 nor 6
According to an automobile association of america report, 9.6% of americans traveled by car over the 2011 memorial day weekend and 88.09% stayed home. what is the probability that a randomly selected american stayed home or traveled by car over the 2011 memorial day weekend? p(stayed home or travelled by car)=
Answer:
First Part: 0.9769
Second Part: Some Americans may have traveled by other means
Step-by-step explanation:
First Part: You add 9.6 to 88.09 and put it in decimal form.
Second Part: Some Americans may have traveled by other means.
A 25 ft ladder is placed 7 feet from the wall. How high up the wall will the ladder reach?
A.18ft
B.20ft
C.22ft
D.24ft
The 24 feet high up the ladder will reach to the wall if the ladder height is 25 feet and is placed 7 feet from the wall.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Length of the ladder = 7 feet
The distance between the wall bottom end to ladder bottom end = 7 feet
As we can see in the diagram the ladder and wall making a right angle triangle ABC in which
AC = 25 feet
BC = 7 feet
Let's suppose the length of the wall is h feet
AB = h feet
From the Pythagoras theorem:
AC² = AB² + BC²
Put the values of AC and BC, we get
25² = h² + 7²
625 = h² + 49
625 - 49 = h² (subtract by 49 on both sides)
576 = h²
h = 24 feet (taking square root on both sides)
Thus, the 24 feet high up the ladder will reach to the wall.
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I'm barely on question 13 out of 25, need to speed up can someone help out
42 customers increased by 50%. How do I find the new amount?
In international morse code, each letter in the alphabet is symbolized by a series of dots and dashes: the letter a, for example, is encoded as "· –". what is the min- imum number of dots and/or dashes needed to represent any letter in the english alphabet?
The minimum number of dots and/or dashes needed to represent any letter in the English alphabet in Morse code is one. The letters 'E' and 'T' each use one symbol, dot and dash respectively.
Explanation:In International Morse code, each letter in the English alphabet is represented by a unique combination of dots and dashes. In regards to your question - the minimum number of dots and/or dashes needed to represent any letter in the English alphabet is one. The English letters 'E' and 'T' are represented by the single symbols "." (dot for 'E') and "-" (dash for 'T') respectively. Hence, this is the minimum for symbolizing any letter.
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According to the Rational Root Theorem, the following are potential roots of f(x) = 60x2 – 57x – 18. Which is an actual root of f(x)? , 3 6, -1/4,-6/5
Answer:
the answer is -1/4
Step-by-step explanation:
Final answer:
The actual root of the polynomial f(x) = 60x²– 57x – 18 among the given options is -6/5.
Explanation:
According to the Rational Root Theorem, possible roots of the polynomial equation f(x) = 60x² − 57x − 18 are the factors of the constant term (−18) divided by the factors of the leading coefficient (60). The roots could be ±1/60, ±1/30, ±1/20, ±1/15, ±1/12, ±1/10, ±1/6, ±1/5, ±1/4, ±1/3, ±1/2, ±1, ±2/5, ±3/5, ±6/5, ±9/5, ±18/5, ±2, ±3, ±6, ±9, ±18.
To determine which of the given options are actual roots of the polynomial, we substitute each value into the polynomial and check if it returns a value of zero:
Substituting x = 3 into f(x) gives 60(3)² − 57(3) − 18 = 540 − 171 − 18 = 351, which is not zero.
Substituting x = 6 into f(x) gives 60(6)² − 57(6) − 18 = 2160 − 342 − 18 = 1800, which is not zero.
Substituting x = −1/4 into f(x) gives 60(−1/4)² − 57(−1/4) − 18 = 15 − −14.25 − 18 = 11.25, which is not zero.
Substituting x = −6/5 into f(x) gives 60(−6/5)² − 57(−6/5) − 18 = 86.4 − −68.4 − 18 = 0, which is zero. Therefore, −6/5 is an actual root of the equation.
Thus, the actual root among the given options is −6/5.
Four players scored all of the points for their team in a basketball game. Player A scored 3535 of the points, Player B scored 8%8%, Player C scored 0.150.15, and Player D scored 17/100
Which choice lists the players in order from least to greatest based on the number of points they scored?
Please help me figure this out !!?
If you earn 30K a year and are taxed 10% what's your gross income and net income
Natasha ran 3.1 kilometers. Tonya ran 4 meters more than half as far as Natasha. How many meters did Tonya run?
Answer: 1554
It is correct from the math answer keys
Tonya run 1,554 meters.
Define distance ?
"Distance is the total path travelled by an object without considering the direction. "
Value used
1kilometer = 1000meters
According to the question,
Let x represents distance run by Tonya
Natasha ran = 3.1 kilometers
= 3100 meters
Therefore,
x = (3100 / 2) + 4
⇒ x = 1554 meters
Hence, Tonya run 1,554 meters.
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Tamar is thinking of a number in the hundredths. Her number is greater than 0.8 and less than 0.9. The greatest digit in the number is in the hundredths place. What number is Tamar thinking of? Explain.
Answer:
Therefore, Tamar is thinking of the number 0.89.
Step-by-step explanation:
Let x be the number Tamar is thinking of.
0.8 < x < 0.9
Since the greatest digits in the hundreths is greater digit, and there's an "8" in the tenths, the number can described as:
0.88< x < 0.9
There is only a single number in the hundredths that would fit the expression above, and that is 0.89.
Therefore, Tamar is thinking of the number 0.89.
Answer:
Let the be the number Tamar is thinking of. So from the above question,
0.8 < t < 0.9
Note that the greatest digits in the hundreths is greater digit, and there's an "8" in the tenths, the number can described as:
0.88< x < 0.9
There is only a number in the hundredths that would fit and that is 0.89.
Therefore, t = 0.89.
Step-by-step explanation:
What symbol is used to identify the standard error of m??
Lucy rode her bike around the block 4 times for a total of 1 mile yesterday. Today she wants to ride her bike 3/4 of a mile. how many times will she need to ride her bike around the block
Final answer:
Lucy will need to ride around the block 3 times today to cover 3/4 of a mile, as each lap around the block is 0.25 miles long.
Explanation:
Lucy rode her bike around the block and covered a total distance of 1 mile by doing so 4 times. Each lap around the block is therefore 0.25 miles long (1 mile ÷ 4 laps = 0.25 miles per lap). To cover 3/4 of a mile, Lucy needs to complete three laps (3/4 of a mile ÷ 0.25 miles per lap = 3 laps). This is because 3/4 divided by 1/4 (which is the distance of one lap) equals 3. Hence, Lucy will need to ride around the block 3 times today to cover 3/4 of a mile.
The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence? 14/13 25/7 4
The common difference of the arithmetic sequence is:
4
Step-by-step explanation:We kn ow that if the first term of an arithmetic sequence is a and d is the common difference of the sequence then the nth term of the sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]
Here we are given:
[tex]a=-3[/tex]
and
[tex]a_15=53\\\\i.e.\\\\a+(15-1)d=53\\\\i.e.\\\\a+14d=53[/tex]
Now using the value of a we have:
[tex]-3+14d=53\\\\i.e.\\\\14d=56\\\\i.e.\\\\d=4[/tex]
Find the difference 51/4 - 2 3/4
how ling it will take for an investment of 1950to accumulate to 2129.55at 6.5%pa simple interest
QUICKK EXPERTS/ACE/GENIUSES
( question #2 )
180 - 90 -18 = 72
Answer is D 72 degrees
Estimate how many pennies would you have to stack to reach from the floor to an average 8-ft ceiling.
To reach an 8-foot ceiling, you would need to stack approximately 1600 pennies. This is calculated by dividing the ceiling height in inches (96 inches) by the thickness of a penny, which is around 0.06 inches, and rounding to the nearest whole number.
To solve this problem, we need to understand that a penny is approximately 0.0598 inches thick. Since there are 12 inches in a foot, an 8-foot ceiling would be 96 inches tall. Therefore, to stack pennies from the floor to an 8-foot ceiling, you would divide 96 (the total inches of the ceiling height) by 0.0598 (the thickness of one penny).
Let's round 0.0598 inches to 0.06 inches for ease of computation. When we divide 96 by 0.06, we get approximately 1600 pennies. So, it would take roughly 1600 pennies to stack from the floor to an 8-foot ceiling.
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Prove that the expression 2x(x–6)–3(x2–4x+1) is negative for all values of x.
[1] seven conference calls are scheduled this morning between 10 and 11
a.m. [2] as a general rule, the company limits the number of conference calls to three per hour. [3] in the future, we should be more careful about scheduling calls. which sentence contains a flabby expression
Final answer:
The flabby expression is found in the sentence 'In the future, we should be more careful about scheduling calls,' which can be more concisely stated as 'In the future, we should schedule calls more carefully.'
Explanation:
The sentence that contains a flabby expression is: "In the future, we should be more careful about scheduling calls."
Flabby expressions are phrases or sentences that are wordy and can be expressed more concisely without losing their meaning. The sentence could be more directly stated as "In the future, we should schedule calls more carefully." By removing unnecessary words, the sentence becomes clearer and more to the point. Flabby expressions are usually considered poor writing style because they can make sentences needlessly long and obscure the main point.
Amma hikes 2and3/4 miles of nature trail in 1 hour and 15 minutes. How many miles does Amman hike per hour?
A scientific journal recently reported that there are currently 2,400 black rhinos in the world. The population of black rhinos is declining at a rate of 10% each year. Which of the following graphs represents the population of black rhinos, y, after x years?
Answer: the answer is B
Step-by-step explanation:
Answer:
The answer would be B
Step-by-step explanation:
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Judah collects toy cars.He buys his cars in packs of 12,18 and 24.He wants to arrange them in rows but all the rows have to be an equal amount of cars.What is the total amount of cars in rows that he can arrange his cars in
[tex]3(6 - 4y) - 2y > 5y - 153[/tex]