In a school, there are 150 students. Out of these 80 students enrolled for mathematics class, 50
enrolled for English class, 60 enrolled for physics class. The student enrolled for English cannot
attend any other class , but student of mathematics and physics can take two courses at a
time. Find the number of students who have taken both physics and mathematics.
a. 40
b. 30
c. 50
d. 20
By applying set theory, we calculate that 40 students are enrolled in both mathematics and physics classes after excluding the 50 English students who cannot attend any other classes.
Explanation:To find the number of students who have taken both physics and mathematics, we can subtract the number of English class students from the total because they cannot be in the group that takes both of the other two classes.
So, we have a total number of students who can take math or physics, which is 150 - 50 = 100 students.
Since there are 80 students in mathematics and 60 in physics, the maximum number could be 80 if every physics student also took mathematics.
But because we only have 100 students to distribute between the two subjects (excluding the English students).
The actual number of students who took both courses will be the total number for math and physics classes (80 + 60) minus the number of students who can take these classes, which gives us ;
140 - 100 = 40 students.
Therefore, the answer is 40 students have taken both physics and mathematics classes. This corresponds to choice a.
Which expression correctly represents "eight times the difference of four and a number"
which behavior is important for keeping your skeletal system healthy ?
A. Avoiding medical checkups
B. Eating Well
C. Playing with an injury
D. Playing the same sport all year long
Gerry spends $1.25 each day on lunch at school. On Friday's, she buys an extra snack for $0.55. How much money will she spend in two weeks
Gerry will spend $13.6 in two weeks
Further ExplanationFrom the problem given:
Gerry spend $1.25/day on lunch
Fridays spend extra $0.55
How much Gerry will spend in two weeks?
In one week, there are 5 school days
4 days (Monday to Thursday) Gerry spend $1.25/day
1 day, Fridays, Gerry spends $1.25+$0.55 = $1.80
So, in one week Gerry will spend :
= [tex]\boxed {(1.25 \times4) + 1.80\ }\\ =\boxed {5+1.80\ }\\ =\boxed {6.8\ }[/tex]
In two weeks, Gerry will spend :
[tex]=\boxed {2 \times 6.8\ }\\ =\boxed {13.6\ }[/tex]
When we are multiplying decimal numbers, the process the same as multiplying whole numbers except for the placement of the decimal point in the answer. In multiplying we don't need to line up the decimal point.
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Keywords: multiplication, decimal number multiplication, additional, decimal number additional, standard algorithm
A patrol unit has 13-gallon fuel tank and averages 15 miles per gallon of fuel used. If the officer assigned to the unit works four 10-hour shifts per week and typically drives 100 miles per shift. How much fuel will the officer's unit use in one week?
The officer's unit will use approximately 26.67 gallons of fuel in one week.
Explanation:To calculate the amount of fuel the officer's unit will use in one week, we need to determine the total distance driven in a week and then calculate the amount of fuel needed for that distance.
Since the officer works four 10-hour shifts per week, the total driving time in a week is 40 hours (4 shifts x 10 hours per shift). If the officer typically drives 100 miles per shift, then the total distance driven in a week is 400 miles (100 miles per shift x 4 shifts).
Now, let's calculate the amount of fuel needed for 400 miles at an average fuel economy of 15 miles per gallon.
Fuel used = Total distance driven / Fuel economy = 400 miles / 15 miles per gallon
Fuel used = 26.67 gallons
Therefore, the officer's unit will use approximately 26.67 gallons of fuel in one week.
find the value of X. (x + 90) 4x°
Jerry has 2 1\2 pounds of peanuts to share equally. He plans to share the peanuts amoung 5 people. How many pounds of peanuts will each person get? Express your answer in simplest form.
4.5w=5.1w-30, how do I solve it
which of these skills do you need more help with select all that apply
A. finding the square and square roots of numbers
B. idrntifying rational and irrational numbers
C. comparing values of rational and irrational numbers
D. evaluating perfect squares and cubes
E. using roots to represent solutions to equations
36 divided by 21312 awnser
Ernesto's bus arrived 51 minutes after he got to the bus stop. Determine what fraction of an hour Ernesto spent waiting for the bus. Write the fraction in the simplest form.
17/20 is the fraction of an hour Ernesto spent waiting for the bus
What is Fraction?A fraction represents a part of a whole.
Given that Ernesto's bus arrived 51 minutes after he got to the bus stop
We need to find the fraction of an hour Ernesto spent waiting for the bus
We know that 1 hour has 60 minutes.
Ernesto's waited 51 minutes out of 60 minutes or an hour.
So 51 minutes is the part and 60 minutes is the whole part
Then the fraction will be 51/60
51 and 60 are the multiples of 3.
Let us divide numerator and denominator by 3
17/20
Hence, 17/20 is the fraction of an hour Ernesto spent waiting for the bus
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write the product of 7×7×7×7 in exponential form
Product of 7×7×7×7 is 7⁴ in exponential form.
What is exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴
Given expression,
7×7×7×7
7 is multiplied to itself 4 times
= 7⁴
Hence, 7⁴ is the product of 7×7×7×7 in exponential form
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Can someone please help me :)
if (93 x p) + 84 = 85 then please equals:
0
1/93
1/85
1/84
1
Using the principle of solving algebraic expressions, the value of p in the equation is 1/93
Given the expression :
(93 × p) + 84 = 85Solving the expression in bracket :
93p + 84 = 85
Subtract 84 from both sides to isolate 93p
93p + 84 - 84 = 85 - 84
93p = 1
Divide both sides by 93 to isolate p
93p/93 = 1/93
p = 1/93
Therefore, the value of p in the expression is 1/93.
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Find a report in a newspaper magazine or on the Internet that uses results from a servery. Evaluate how the survey uses ratios to reach
conclusion
what is the smallest number
2.31
2.3
2.33
2.301
An investment is currently worth 1.035×108 dollars . Thirty years ago, the investment was worth 2.3×105 dollars. How many times greater is the value of the investment today than the value of the investment thirty years ago? A. 0.45 B.450 C.4500 D. 45,000
The correct option is: B. 450
Explanation
Current value of the investment is [tex]1.035\times 10^8[/tex] dollars and 30 years ago, the value of the investment was [tex]2.3\times 10^5[/tex] dollars.
Suppose, the value of investment today is [tex]n[/tex] times greater than the value of the investment thirty years ago.
So, the equation will be........
[tex]n(2.3\times 10^5)=1.035\times 10^8\\ \\ n= \frac{1.035\times 10^8}{2.3\times 10^5}=0.45\times 10^3 = 450[/tex]
Thus, the value of the investment today is 450 times greater than the value of the investment thirty years ago.
Answer: B. 450
Step-by-step explanation:
Given: An investment is currently worth =[tex]1.035\times10^8[/tex] dollars .
Thirty years ago, the investment was worth =[tex] 2.3\times10^5[/tex] dollars.
Now, the number of times the value of the investment today than the value of the investment thirty years ago is given by :-
[tex]n=\frac{1.035\times10^8}{2.3\times10^5}\\\\=0.45\times10^{8-5}........\text{Since }a^na^m=a^{m+n}\\\\=0.45\times10^3\\\\=0.45\times1000=450[/tex]
Hence, the value of the investment today is 450 times greater than the value of the investment thirty years ago.
Joanna joins a CD club. She pays $7 per month plus $10 for each CD that she orders. Write an inequality to find how many CDs she can purchase in a month if she spends no more than $100. Identify what your variable represents.
Jeremiah is saving money from a tutoring job.After the first three weeks,he saved $135.Assume the situation is proportional.Use the unit rate to write an equation relating the amount saved s to the number of weeks w worked.At this rate,how much will Jeremiah save after eight weeks?
What is the value of the expression? Drag and drop the answer into the box to match the expression. 0.9(1/2−2)+0.6
Solve for x. y=7x−7z−9
Answer:
The value of x is [tex]x=\frac{y+7z+9}{7}[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]y=7x-7z-9[/tex]
We need to solve the equation for x.
Add 7z to both the sides.
[tex]y+7z=7x-7z+7z-9[/tex]
[tex]y+7z=7x-9[/tex]
Add 9 to both the sides.
[tex]y+7z+9=7x-9+9[/tex]
[tex]y+7z+9=7x[/tex]
Divide both sides by 7.
[tex]x=\frac{y+7z+9}{7}[/tex]
Hence the value of x is [tex]x=\frac{y+7z+9}{7}[/tex].
This grid shows the location of four animals.
Where is Chewy located?
A:(3, 6)
B:(5, 1)
C:(6, 3)
D:(1, 5)
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, 9/20 cups from the third orange, 3/11 cups from the fourth orange, and 7/15 cups from the fifth orange. Patel estimates that he needs 2 cups of orange juice for his family. About how much more orange juice does he need?
The amount of juice needed is about 0.487 cups
Amount of oranges squeezed :
First orange = 4/17 cups
Second orange = 3/10 cups
Third orange = 9/20 cups
Fourth orange = 3/11 cups
Fifth orange = 7/15 cups
Total amount of oranges needed = 2 cups
The amount of extra orange needed = x
Adding :
(4/17 + 3/10 + 9/20 + 3/11 + 7/15) + x = 2
(13200 + 168300 + 252450 + 153000 + 261800) / 561000
(848750 / 561000) + x = 2
1.5129 + x = 2
x = 2 - 1.5129
x = 0.4871 cups
The amount of juice needed is about 0.487 cups
What are the opposites of the whole numbers from 35 to 45
The opposites of the whole numbers from 35 to 45 are; -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45.
How to label number opposites?
The opposite of a number is the opposite sign of that same number. Thus;
Opposite of a is -a.
Opposite of -b is b.
Now; Numbers from 35 to 45 are; 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45.
Thus, their opposites are; -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45.
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It was estimated that a giraffe would be 15.5 feet tall when fully grown. its actual height was 16.25 feet. what was the percent error between the actual and estimated values of height
The price changes from $450 to $396 what is the percent change?
A. 13.6% increase
B. 13.6% decrease
C. 12% increase
D. 12% decrease
PLEASE HELP ME ASAP! I HAVE A UNIT TEST! Jessica is filling glasses with water. Each glass holds 3/5 cup of water. She pours 4 1/5 cups of water into the glasses. How many glasses does she fill with water?
Helpppp meeeeeee eeeeeee
Answer:
no
Step-by-step explanation:
What is the product in simplest form? −5/12 ⋅ 8/13 Please answer
Doug is twice Anne's age. Doug is 34 years old. How old is Anne
([20-2+(46-15)+2]-(9+4)