Answer:
10 kg water, 2 kg of sugar.....total of 12 kg of syrup
percentage of sugar is : 2/12 = 0.166 rounds to 0.17 = 17%
Step-by-step explanation:
Integrating sums of functions
Answer:
(a) -12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Swapping Limits]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^6_4 {f(x)} \, dx = 5[/tex]
[tex]\displaystyle \int\limits^4_{10} {f(x)} \, dx = 8[/tex]
[tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx[/tex]
Step 2: Solve Pt. 1
[Integral] Rewrite [Integration Property - Addition]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx[/tex]Step 3: Redefine
Manipulate the given integral values.
[Integrals] Combine [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx = \int\limits^6_{10} {f(x)} \, dx[/tex][Integral] Rewrite: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx[/tex][Integral] Substitute in integrals: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = 5 + 8[/tex][Integral] Add: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = 13[/tex][Integral] Rewrite [Integration Property - Swapping Limits]: [tex]\displaystyle -\int\limits^{10}_6 {f(x)} \, dx = 13[/tex][Integral] [Division Property of Equality] Isolate integral: [tex]\displaystyle \int\limits^{10}_6 {f(x)} \, dx = -13[/tex]Step 4: Solve Pt. 2
[Integral] Substitute in integral: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6[/tex][Integral] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)[/tex][Integral] (Parenthesis) Subtract: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)[/tex][Integral] Multiply: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40[/tex][Integral] Add: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12[/tex]Topic: AP Calculus AB/BC
Unit: Integration
Book: College Calculus 10e
Anna just accepted a job at a new company where she will make an annual salary of $66000. Anna was told that for each year she stays with the company, she will be given a salary raise of $4000. How much would Anna make as a salary after 6years working for the company? What would be her salary after t years?
Answer:
90000
Step-by-step explanation:
I put 4000 times 6 years then added that to 66000 then got 90000.
rotate 270° counterclockwise
Answer:
When rotating a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, we switch x and y and make x negative.
Step-by-step explanation:
Which equation represents this situation? y = 1.25x ) Which graph represents the situation?
The second graph represents the situation y=1.25x which has slope 1.25.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given equation is y= 1.25x
Slope is 1.25
Now let us plug in (1, 1.25) in the equation
1.25=1.25(1)
Hence, the second graph represents the situation y=1.25x which has slope 1.25.
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what is the slope help pls?
Answer:
y=7x-6
Step-by-step explanation:
You would first pick two coordinates in this case would be ( 0, -6), (1,1). You would find your slope by using the formula y2-y1/x2-x1. Which would give you a slope of 7/1 which is equal to 7. Then you would use point slope formula which is y-y1=m(x-x1). would would plug in the numbers and it would say
y-(-6)=7(x-0). Then you would simplify the y-(-6) which would be y+6 then you would distribute the 7. Your whole equation would look like y+6=7x+0. Then you would use inverse operations and subtract -6 from the left side of the equals and subtract it from 0 giving you -6. Therefore your whole equation would be y=7x-6. Hoped this helped.
How do the villagers investigate the hole?
Answer:
they get in a hole and they grab the dirt and examine it
Step-by-step explanation:
Answer:the shout and throw a pebble into the hole
Step-by-step explanation:
Can someone please help me with this?
Thank you! :)
Answer:
Nah that sounds like a you problem
Step-by-step explanation:
Answer:
my guess is 3/2x+65/3 or 2/3c
Elsa sells knitted hats for $5 each. Her goal is to make $300 in sales, so she wants to calculate how many hats she needs to knit (x). choose ALL equations in which x correctly represents the number of hats she needs to sell to meet her goal.
A) x/5 = $300
B) 5x = $300
C) $300x = 5
D) 300/5 = x
E) 5/300 = x
Answer:
B
Step-by-step explanation:
Answer:d and e
Step-by-step explanation:
YESIRRRRRRRRRRRRRRRRRRRRRRRRRRRR
Need help on this.. The first one that answer it first correctly gets a BRANLIST
Answer: The answer is C) J' (3,-1), K' (1,-4)
Step-by-step explanation: First, you need to find the location of J, which is located in Quadrant III. You go left 3, and go down 1, making the coordinates of J (-3,-1). Next, you need to find the location of K, which is also located in (-1, -4).
So, the question asks, "What are the coordinates of J' and K' after JK is reflected across the y-axis?"-- Well, first, which line is the x-axis, and which line is the y-axis?
The x-axis is the line that is horizontal(Across) while the y-axis is the line that is vertical( Up and Down).
So you bring J and Ks coordinated over the y-axis to Quadrant IV(4). You already know their original coordinates, so you place the as you would in the picture above, except that the line would be reflected.
the distance from the base of a flagpole to a point on the ground is 24 feet. the flagpole has a height of 18. what is x the distance from the top of the flagpole to the ground.
You can solve this by doing Pythagorean theorem. I think thats what its called... a^2+b^2=c^2. So 24 squared plus 18 squared is 900. The square root of 900 is 30. The legnth of the third side is 30.
The distance from the top of the flagpole to the ground is 30 feet.
What is Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
Given the distance from the base of a flagpole to a point on the ground = 24 feet
height of flagpole = 18 feet
the distance from the top of the flagpole to the ground is x
by Pythagorean theorem, we can find the distance
h² = b² + p²
h = hypotenuse = x
b = base = 24 feet
h = height = 18 feet
x² = 24² + 18²
x² = 576 + 324
x = √900
x = 30 feet
Hence the value of x is 30 feet.
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Which words have vertical symmetry for all of the letters in the word? Check all that apply. MOM DIZZY HIT SEAT WAXY
Answer: 1, 3, 5
1.) MOM 3.) HIT 5.) WAXY
Step-by-step explanation: i hope this helps :)
The words in which all letters have vertical symmetry are MOM, HIT, and WAXY so options (A),(C), and (E) are correct.
What is symmetry?If two figures look an exact shape but their size could be small or big then both figures are called similar figures.
When anything has identical pieces facing one another or revolving around an axis, it is said to be symmetrical.
Vertical symmetry is the way by which a latter will completely coincide about a vertical axis.
For example word "A".
If we take a vertical axis in the mid of the word "A" then about this axis the whole word will coincide by left and right.
Thus, another words are M, O, T, Y, H, X.
The words containing the above letters are MOM, HIT, and WAXY.
Hence "The words in which all letters have vertical symmetry are MOM, HIT, and WAXY".
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What is the value of x?
PLZ HELP ME< DON'T UNDERSTAND!!!!!!!!!!
Enter your answer in the box.
x = ?
A right triangle with vertices labeled as A, B, and C. Side C B is the base, and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 3. Base C B is labeled as 4. Segment A D is labeled as 2.25. Segment B D is labeled x.
Use triangle bisect or theorem.
Set up proportion:
X/ 2.25 = 4/3
Cross multiply:
3x = (4 x 2.25)
3x = 9
Divide both sides by 3:
X = 3
Complete the mapping of the vertices of ΔDEF.
D(2, –4) → D'
E(1, –1) → E'
F(5, 1) → F'
What is the rule that describes a reflection across the line y = x?
rx = y(x, y) →
Answer:
D I think
Step-by-step explanation:
GH=5 5; <H = 90
1. The mapping of the vertices of ΔDEF will be;
D(2, –4) → D' (-4, 2)
E(1, –1) → E' (-1 , 1)
F(5, 1) → F' (1, 5)
2. The rule of the reflection across the line y = x is;
[tex]r_{x} = _{y} (x , y)[/tex] → [tex]r_{y} = _{x} (y , x)[/tex]
What is Refection?
Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.
Given that;
The coordinates are,
D = (2, –4)
E = (1, –1)
F = (5, 1)
Now,
By the given image,
The mapping of the vertices of ΔDEF is;
D(2, –4) → D' (-4, 2)
E(1, –1) → E' (-1 , 1)
F(5, 1) → F' (1, 5)
And, The rule of the reflection across the line y = x is;
[tex]r_{x} = _{y} (x , y)[/tex] → [tex]r_{y} = _{x} (y , x)[/tex]
Because in the image its shows the line of reflection.
Therefore,
1. The mapping of the vertices of ΔDEF will be;
D(2, –4) → D' (-4, 2)
E(1, –1) → E' (-1 , 1)
F(5, 1) → F' (1, 5)
2. The rule of the reflection across the line y = x is;
[tex]r_{x} = _{y} (x , y)[/tex] → [tex]r_{y} = _{x} (y , x)[/tex]
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A godown measures 40 m * 25 m* 10 m. Find the maximum number of wooden crates
each measuring 1.5 m* 1.25 * 0.5
that can be stored in the godown.
Answer:
n = 10667
Step-by-step explanation:
The measure of a godown = 40 m × 25 m × 10 m
The measure of wooden crate = 1.5 m × 1.25 m × 0.5 m
We need to find the maximum number of wooden crates that can be stored in the godown. Let there are n wooden crates. So,
[tex]n=\dfrac{40\times 25\times 10}{1.5\times 1.25\times 0.5}\\\\n=10666.67[/tex]
or
n = 10667
Hence, there are approx 10667 wooden crates can be stored.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Answer:
480y
Step-by-step explanation:
multiply 6 x 8 x 60= 480
‼️‼️‼️‼️Please Help I really need to submit this by the end of the day and will automatically give branch to first answer‼️‼️‼️‼️‼️
Answer:
1. 9 = x
2. y = 2
Just copy these steps on paper, then submit.
Writing it yourself will help you, trust me :)
1. 2(x + 5) = 3x + 1
2(x + 5) = 3x + 1
Distribute the 2
2x + 10 = 3x + 1
-1 -1
2x + 9 = 3x
-2x -2x
9 = x
2. 3y - 4 = 6 - 2y
3y - 4 = 6 - 2y
+4 +4
3y = 10 - 2y
+2y +2y
5y = 10
Divide both sides by 5
y = 10/5
y = 2
At a baseball game, a vender sold a combined total of 172 sodas and hot dogs. The number of sodas sold was 58 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Calculate the slope of the points (3, 1) and (2, 4).
Answer:
m=-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
Use the formula y2-y1/x2-x1
4-1/2-3
3/-1
Therefore, the slope is -3
Write the 24 hour clock time which is 17min later than 13:55
Answer:
14:12
Step-by-step explanation:
Answer:
After entering a time in 24-hour format, this calculator lets you add and subtract a period to give a new time, also in 24 hour format. The 24 hour time format is also known as "military time".
For example, you could enter the time 15:00:00 (3 pm), then add 70 seconds to it which would give 15:01:10 ( 3:01 and 10 seconds pm).
A car salesperson makes 25% commission on each car sold. If the salesperson just sold a vehicle for $42,000, how much in commission was made?
Answer:
$10500
How I Found This Answer:
$42000 ÷ 4 = $10500
Hope This Helps.
The pyramid pictured below has a total surface area of 156 feet squared find the missing measurement
10 points is all i have
Answer:
maybe 36
Step-by-step explanation:
but can u help me What is the surface area of a square-based pyramid with a base length of 5 m and a slant height of 3 m?
Enter your answer in the box.
The missing measurement is 10 feet.
What is pyramid?A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.
To find the surface area of the pyramid, we can use the following formula,
A = (½)Pl + B.
Where P is the base perimeter, l is the slant height and B is the base area.
Here, the base is square-shaped.
Now, let the slant height be x.
A = (1/2)(4 × 6) (x) + (6)²
156 = 12x + 36
12x = 156 - 36
12x = 120
x = 10 feet.
Therefore, the required height is 10 feet.
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PPLLLLZZZZZ HHHEEELLLLPPPP
Answer:
11 1/3 sq yards
Step-by-step explanation:
4 1/4 x 2 2/3
change into improper fractions: 17/4 x 8/3 = 136/12 = 11 1/4
PLSS HELP ASAP!! I WILL GIVE YOU BRAINLYEST!!ONLY ANSWER IF U KNOW HOW TO!!
What is the difference between how you find the surface area of rectangular
prisms and how you find the surface area of triangular prisms? (write in complete sentences)
how can you get 2 1/2÷5/8
Answer: 4
Step-by-step explanation:
Change the 2.5 to an improper fraction, then multiply by the reciprocal of 5/8.
[tex]2\frac{1}{2} /\frac{5}{8} =\frac{5}{2}*\frac{8}{5}=\frac{40}{10} =4[/tex]
Conversion a mixed number 2 1/
2
to a improper fraction: 2 1/2 = 2 1/
2
= 2 · 2 + 1/
2
= 4 + 1/
2
= 5/
2
To find new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/
2
= 4/
2
b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs
Divide: 5/
2
: 5/
8
= 5/
2
· 8/
5
= 5 · 8/
2 · 5
= 40/
10
= 10 · 4/
10 · 1
= 4
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/
8
is 8/
5
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step , cancel by a common factor of 10 gives 4/
1
.
In words - five halfs divided by five eighths = four.
Use the FOIL method to check your answer from part A.
Answer: (3x=2) (x+2)
Step-by-step explanation:
Factor by grouping
Find the area of the shaded part (π=22/7)
Answer:
42cm square
Step-by-step explanation:
Frist find the area of the square. 14*14
Then find the Area of the circle.- (radius) one side of the square is the diameter so, diameter divided by 2 - 14/2=7
After that subtract the area of circle from the area of the square.
Answer:
first we find the area of the square.
area of square=side²
area of square =14²
area of square=196cm²
area of circle=pi×radius²
radius=14/2=7
area of circle=22/7×(7)²
area of circle =22/7×49
area of circle =154cm²
area of shaded region=area of square - area of circle
area of shaded= 196cm²-154cm²
area of shaded=42cm²
Bill bought a table on sale for $630. This price was 72% of the original price.
What was the original price?
Answer:
The original price was $875.
Step-by-step explanation:
a = p * w
630 = 72% * w
630 / 0.72 = $875
$875 should be the original price, I hope this helps!
PLZ HELP i jus want answer
Answer:
B. midpoint
Step-by-step explanation:
UT is located in the middle of UT as the lengths of ST and US are equal
A set of counters is numbered 1 through 12. Suppose you draw one counter without looking. What is the probability of choosing a number greater than 4?
Question 5 options:
2/3
1/12
1/3
1/6
Please answer this fast thank uuu :)
Answer:
x + 37 = 90
Step-by-step explanation:
Since complementary angles add up to 90 degrees, we would need to add 37 and x to equal 90 degrees. Therefore, x + 37 equals 90 degrees. As for solving, subtract 37 from both sides and you are left with x = 53.