Answer:
6.60
Step-by-step explanation:
Last weekend Jane studied 4 2 3 hours for her history final and 4 1 4 hours for her math exam. How many hours in all did Jane study for the two tests?
Jane studied a total of 5 11/12 hours for her history final and math exam.
Explanation:To find the total number of hours Jane studied for the two tests, we add together the number of hours she studied for each test. Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.
To add these fractions, we need to have a common denominator. The least common multiple of 3 and 4 is 12. We can convert 2/3 to 8/12 and 1/4 to 3/12.
Now we can add the fractions: 4 8/12 + 4 3/12 = 5 11/12.
Therefore, Jane studied a total of 5 11/12 hours for the two tests.
Final answer:
Jane studied a total of 7 3/4 hours for her history and math exams.
Explanation:
To find out how many hours Jane studied for the two tests, we simply need to add the hours she studied for each test together.
Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.
We can add these two fractions by finding a common denominator and then adding the numerators.
In this case, the common denominator is 12. So, we have (4 * 4 + 2) / 3 = 18/3 and (4 * 3 + 1) / 4 = 13/4.
Adding these fractions together, we get (18/3) + (13/4) = 54/12 + 39/12 = 93/12. Simplifying this fraction, we get 7 3/4 hours.
Therefore, Jane studied a total of 7 3/4 hours for the two tests.
Evaluate. 3−1⋅(4⋅6)⋅2−3 Enter your answer in the box.
The answer to this question is 1
Use synthetic division and the Remainder Theorem to find P(a).
P(x) = x3 + 4x2 − 8x − 6; a = −2
−2
0
18
20
Answer:
c: 18
Step-by-step explanation:
harold serves himself 1 1/2 ounces serving of cereal each morning. How many servings does he get from a box of his favorite cereal?
A teacher has 100 pencils in a cup. 16 are more sharp than dull. How many are dull and how many are sharp?
The measure of an angle is 8 greater than 3 times its supplement. Find he measurement of the angle.
Prove that there exists a unique real number solution to the equation x3 + x2 − 1 = 0 between x = 2/3 and x=1
To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem and the property of the derivative.
Explanation:To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem.
First, we substitute x = 2/3 into the equation and get a negative value (-1/27). Then, we substitute x = 1 into the equation and get a positive value (1).
Since the function is continuous between x = 2/3 and x = 1, and it changes sign, there must exist a solution somewhere between them.
To show that the solution is unique, we can use the fact that the derivative of the function, 3x² + 2x, is always positive for all real numbers.
This implies that the function is strictly increasing, so it can only intersect the x-axis at one point.
The length of a rectangle is twice its width. if the area of the rectangle is 200 yd2 , find its perimeter.
The perimeter of the rectangle is 60 yards
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the length of the rectangle be = a
Let the width of the rectangle be = b
The length of the rectangle is twice the width
So ,
a = 2b
The area of the rectangle is A = 200 yards²
The area of the rectangle is given by
Area of Rectangle = Length x Width
And , substituting the values for length and width , we get
Area of Rectangle = 2b x b
2b² = 200
Divide by 2 on both sides , we get
b² = 100
Taking square root on both sides , we get
b = 10
a = 2b
a = 20
Therefore , the length of the rectangle is 20 yards and width of the rectangle is 10 yards
Now , the perimeter of the rectangle is P = 2 ( length + width )
Perimeter of the rectangle P = 2 ( 10 + 20 )
= 2 x 30
= 60 yards
Hence , the perimeter of the rectangle is 60 yards
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John wants to buy a watermelon that weighs 5.7 pounds.The watermelon is priced at $1.58 per pound.How much is the total cost of the watermelon
Branliest offered
A. What is the circumference of the colony?
B. What is the radius of the colony?
Bacteria lives in groups called colonies colonies are usually circular the diameter of a particular bacterial colony is 12 mm their circumference of a circle is equal to Pi 3.14 times its diameter c= πd
One of the largest pumpkins ever grown weighed about 3/4 ton how many lb did the pumpkin weigh
I got it wrong !!! Please help and explain
25 * 2.5 = 62.5 *2 = 125
8x5 = 40
125 +40 = 165 square feet
Helppp 3 out of the 5 im gunna post!
look where the line is on the y axis at x =2
answer is y=-3
value is -3
In 1997, there were 43.2 million people who used free weights. Assuming the use of free weights increases 6% annually, which equation can be used to predict the number of people using free weights t years from 1997?
p = 43.2(0.06)t
p = 43.2(1.06)t
p = 43.2(0.94)t
p = 43.2(1.005)t
The correct equation to predict the number of free weight users is option B) p = 43.2(1.06)t. This equation accounts for a 6% annual increase in users.
Predicting the Number of Free Weight Users
In 1997, there were 43.2 million people using free weights. Given that the annual increase rate is 6%, we use the exponential growth formula to predict the number of people in future years. The correct equation to use is:
p = 43.2(1.06)t
This equation represents an exponential increase, where 'p' is the number of people using free weights and 't' is the number of years since 1997. This can be explained by the fact that a 6% annual increase multiplies the original number of users by 1.06 each year.
What metamorphic rock has nonfoliated texture?
Answer:
Marble, quartzite, and soapstone.Step-by-step explanation:
Non-foliated metamorphic rocks are those which don't have a rough texture, like foliated ones, their composition gives them this characteristics: not having layers or banded appearance.
Which expression is equivalent to sin^2 x-sin x - 2/sin x -2
A. sin x + 1
B. sin x − 1
C. sin2x
D. -sin2x
This figure shows the procedure for constructing a
A. Pair of parallel lines
B. Bisector of an angle
C. Perpendicular from a point on a line
D. Perpendicular bisector
Answer:
B
Step-by-step explanation:
Which characteristic is used to group artworks into periods or styles?
A: Abstract
B: Similar
Kate has 21 coins (nickels and dimes) in her purse. How many nickels and dimes does she have if she has $1.50? 3 nickels and 18 dimes 5 nickels and 16 dimes 12 nickels and 9 dimes 15 nickels and 6 dimes
Perform the indicated computation. write the answer in scientific notation. 12x10^4
A charity organization had a fundraiser where each ticket was sold for a fixed price. They had to sell a few tickets just to cover necessary production costs of $1200\$1200 $1200 dollar sign, 1200 . After selling 200200 200 200 tickets, they had a net profit of $12,000\$12{,}000 $12,000 dollar sign, 12, comma, 000 . Let P(n)P(n) P(n) P, left parenthesis, n, right parenthesis denote the net profit from the fundraiser PP P P (measured in dollars) as a function of the number of tickets sold nn n n . Write the function's formula
Answer:
[tex]P(n)=66n-1200[/tex]
Step-by-step explanation:
Let x be the revenue collected from selling each ticket.
We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.
Since we know that net profit is the difference between total revenue and total cost.
[tex]\text{Net profit}=\text{Total revenue- Cost}[/tex]
We can represent our given information in an equation to find the revenue collected from each ticket:
[tex]12000=200x-1200[/tex]
Let us solve for x by adding 1200 to both sides of equation.
[tex]12000+1200=200x[/tex]
[tex]13200=200x[/tex]
[tex]x=\frac{13200}{200}[/tex]
[tex]x=66[/tex]
Therefore, the revenue collected from selling each ticket is $66.
Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.
The revenue from selling n tickets will be 66n.
Production costs = 1200
[tex]P(n)=66n-1200[/tex]
Therefore, our desired function will be: [tex]P(n)=66n-1200[/tex].
Which statement is true?
A tortoise is walking in the desert. It walks for 3 minutes at a speed of 7.5 meters per minute. For how many meters does it walk?
When two angles are complementary what is the sum of their measures is 90 degrees. two complementary angles have the measure of 2x-10 degrees and 3x-10 degrees?
What is the measurements of ENV
Find the indefinite integral of [tex] \int\limits {\frac{5}{x^\frac{1}{2}+x^\frac{3}{2}} \, dx [/tex]
I have been able to simplify it to [tex] \int\limits {\frac{5\sqrt{x}}{x^3+x}} \, dx [/tex] but that is confusing,
I then did u-subsitution where [tex]u=\sqrt{x}[/tex] to obtain [tex] \int\limits {\frac{5u}{u^6+u^2}} \, dx [/tex] which simplified to [tex] \int\limits {\frac{5}{u^5+u}} \, dx [/tex], a much nicer looking integrand
however, I am still stuck
ples help
show all work or be reported
Answer:
[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]
in order to do so we can consider using u-substitution
let our
[tex] \displaystyle u = {x}^{ \frac{1}{2} } \quad \text{and} \quad du = \frac{ {x}^{ - \frac{1}{2} } }{2} [/tex]
to apply substitution we need a little bit arrangement
multiply both Integral and integrand by 2 and ½
[tex]\displaystyle 2\int \frac{1}{2} \cdot\frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]
factor out [tex]x^{\frac{1}{2}}[/tex]:
[tex]\displaystyle 2\int \frac{1}{2 {x}^{ \frac{1}{2} } } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]
recall law of exponent:
[tex]\displaystyle 2\int \frac{ {x}^{ - \frac{1}{2} } }{2 } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]
apply substitution:
[tex]\displaystyle 2\int \frac{5}{ 1+ {x}^{ } } du[/tex]
rewrite x as [tex]\big(x^{\frac{1}{2}}\big)^{2}[/tex]:
[tex]\displaystyle 2\int \frac{5}{ 1+ ( {x ^{ \frac{1}{2} } })^{ 2 } } du[/tex]
substitute:
[tex]\displaystyle 2\int \frac{5}{ 1+ ( u)^{ 2 } } du[/tex]
recall integration rule of inverse trig:
[tex] \displaystyle 2 \times 5 \tan^{-1}(u)[/tex]
simplify multiplication:
[tex] \displaystyle10 \tan^{-1}(u)[/tex]
substitute back:
[tex] \displaystyle10 \tan^{-1}( {x}^{ \frac{1}{2} } )[/tex]
simplify if needed:
[tex] \displaystyle10 \tan^{-1}( \sqrt{x} )[/tex]
finally we of course have to add constant of integration:
[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]
and we are done!
what is the value of x in the equation 6= x/4 - 4
Answer:
c
Step-by-step explanation:
Carlos's gas tank is 19 full. after he buys 6 gallons of gas, it is 13 full. how many gallons can carlos's tank hold
Answer:
25
Step-by-step explanation:
Color in equations what to color in 1+2+3+4=10 What cubes to color in?
Triangle abc has been translated to create triangle a'b'c'. angles c and c' are both 32 degrees, angles b and b' are both 72 degrees, and sides bc and b'c' are both 5 units long. which postulate below would prove the two triangles are congruent? sss sas asa hl
ASA
Is the answer i got on my work