12oz of the drink contains 159oz of calories.
To Calculate How many calories are in 12oz of the drinkA new energy drink advertises 106 calories for 8oz.
Based on the given conditions, formulate: 12*(106/8)
=12*(13.25)=159
Calories are in 12oz of the drink is 159oz
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a juice company produced 8064 cartons of juice in 21 days each day they produced the same the same number of carton and delivered those carton 216 area of coffee shops the cart the cartons were delivered in cases of six cartons per case and each coffee shop received an equal number of cases in each delivery. how many cases were delivered to each coffee shop each day
Answer:
The each coffee shops receives 4 cases of juice everyday.
Step-by-step explanation:
The juice company produced 8064 cartons of juice in 21 days each day they produced the same number of cartons.
Therefore, each day the company produces [tex]\frac{8064}{21} = 384[/tex] cartons.
The juice company delivers those cartons in 16 areas of coffee shops.
So, each coffee shop receives [tex]\frac{384}{16} = 24[/tex] cartons of juice.
Now, the cartons were delivered in cases of six cartons per case and each coffee shop received an equal number of cases in each delivery.
Hence, each coffee shops receives [tex]\frac{24}{6} = 4[/tex] cases of juice everyday. (Answer)
Which is equivalent to sin 51°?
A) cos 51°
B) cos 39°
C) tan 39°
D) tan 51°
The value which is equivalent to sin 51° is cos 39°. The correct option is B) cos 39°
Complementary angle theoremFrom the complementary angle theorem, we have that
The sine of an angle is equal to the cosine of its complementary angle
That is,
sin θ = cos (90° - θ)
Recall: Complementary angles sum up to 90°
Then, we can write that
sin 51° = cos (90° - 51°)
sin 51° = cos 39°
Hence, the value which is equivalent to sin 51° is cos 39°. The correct option is B) cos 39°
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helpppppp pleasee.Use the regression for Clothes-4-You coat sales to
make predictions.
How many coats should Clothes-4-You expect to sell
when the average temperature is 80°F?
What is the predicted temperature when 125 coats are
sold?
Answer:
1.) 26.2
2.) -22.9
Step-by-step explanation:
i took the test
25. Algebraically determine whether the function k(x) = x6 - x2 + 7 is odd, even, or neither. Explain your
reasoning
Answer: The function is EVEN.
Step-by-step explanation:
For this exercise it is important to remember that:
1. A function f(x) is even if and only if:
[tex]f(-x) = f(x)[/tex] for all "x"
2. A function f(x) is odd if and only if:
[tex]f(-x) = -f(x)[/tex] for all "x"
So knowing that, and given the following function k(x):
[tex]k(x)=x^6 - x^2 + 7[/tex]
You can plug [tex]-x[/tex] in for "x", order to know if this is even. Then, you get:
[tex]k(-x)=(-x)^6 - (-x)^2 + 7\\\\k(-x)=x^6-x^2+7[/tex]
Therefore, since:
[tex]f(-x) = f(x)[/tex]
You can determine that that the given function [tex]k(x)=x^6 - x^2 + 7[/tex] is Even.
Round 22,451 with 10
Answer:
22,450
Step-by-step explanation:
the ones place is below 5 so you keep the number
Answer:
22,450
Step-by-step explanation:
22,451 rounded to the nearest 10 is 22,450, as 1 rounds down to 0.
:)
8x= 4x - 32 solve for x
Solve for x.
8x=4x-32
Subtract 4x from both sides.
4x=-32
Divide by 4 on both sides.
x=-8
answer: x=-8
Answer:
x=-8
Step-by-step explanation:
8x=4x-32
4x-8x=32
-4x=32
x=32/-4
x=-8
On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot.
A. What percent of the total number of cars were in the parking lot on Friday?
Show your work.
B. What percent of the total number of cars were in the parking lot on Saturday?
Show your work.
Answer:
(A) 40%
(B) 60%
Step-by-step explanation:
Given:
Total number of cars = 200
Cars in parking lot on Friday = 120
Total number of cars = Total cars on Friday + Total cars on Saturday.
⇒ 200 = 120 + Total cars on Saturday.
⇒ Total cars on Saturday = 200 - 120 = 80
So, 80 cars were in parking lot on Saturday.
(A)
Percentage of cars in parking lot on Friday is given as:
[tex]=\frac{\textrm{Cars in parking lot on Friday}}{\textrm{Total cars parked}}\times 100\\\\=\frac{120}{200}\times 100\\\\=\frac{120}{2}=60\%[/tex]
Therefore, 60% of the cars were in the parking lot on Friday.
(B)
Now, since 60% of the cars were parked on Friday, the remaining percent will be on Saturday.
Therefore, percentage of cars in parking lot on Saturday = 100% - 60% = 40%. This can be verified with the same formula used in part (A).
[tex]=\frac{\textrm{Cars in parking lot on Saturday}}{\textrm{Total cars parked}}\times 100\\\\=\frac{80}{200}\times 100\\\\=\frac{80}{2}=40\%[/tex]
A rectangular lawn has a diagonal path
The lawn is 10 m wide and 15 m long,
Work out the length of the path.
Give your answer in surd form
To find the length of the diagonal path on a rectangular lawn, calculate the square root of the sum of the squares of its width and length.
Explanation:The length of the diagonal path can be found using the Pythagorean theorem.
Given the dimensions of the rectangular lawn (10 m wide and 15 m long),
the length of the diagonal path (d) is calculated as:
d = √(10^2 + 15^2) = √(100 + 225) = √325 = 5√13 m.
The sum of two numbers is 33.the larger number is 3 more than two times the smaller number.what are the numbers?
Answer: 10 and 23
Step-by-step explanation:
Let the first number be x and the second number be y.
Also , let x be the bigger number and y the smaller number.
From the first statement;
x + y = 33 ............................. equation 1
From the second statement
twice the smaller number = 2y
so, if the bigger number is 3 more than two times the smaller number, this means that
x = 2y + 3 .................................... equation 2
Solving the resulting linear equations by substitution method .
substitute x = 2y + 3 into equation 1 , that is
x + y = 33 becomes :
2y + 3 + y = 33
3y + 3 = 33
3y = 30
y = 10
Substitute y = 10 into equation 2 , that is
x = 2y + 3 becomes
x = 2(10) + 3
x = 20 + 3
x = 23
simplify the following expression -12[ 3y - 4x] - 10y
Answer:
-46y+48x
Step-by-step explanation:
Answer:
-46y + 48x
Step-by-step explanation:
-12(3y - 4x) -10y
-36y + 48x - 10y
-36y - 10y + 48x
-46y +48x
which expression is equal to (x+5)(-3x^2+15x-1)?
a. -3x^3+74x-5
b. -3x^3+30x^2-76x-5
c. -3x^3-76x-5
d. -3x^3+30x^2+74x-5
Answer:
-3x^3+74x-5
Step-by-step explanation:
(x+5)(-3x^2+15x-1)
-3x^3+15x^2-x-15x^2+75x-5
-3x^3+15x^2-15x^2+75x-x-5
-3x^3+74x-5
The given expression can be simplified to obtain -3x³ + 74x - 5. The correct option is (a).
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The given algebraic expression is (x + 5)(-3x² + 15x - 1).
It can be evaluated as follows,
(x + 5)(-3x² + 15x - 1)
⇒ x(-3x² + 15x - 1) + 5(-3x² + 15x - 1)
⇒ -3x³ + 15x² - x - 15x² + 75x - 5
⇒ -3x³ + 74x - 5
Hence, the product of the given expression is -3x³ + 74x - 5.
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Suppose an iphone loses 63% of its value each year. Write a function that represents the value of the phone after x years.
Answer:
The function which represent the phone value after x years f = i [tex](0.37)^{x}[/tex]
Step-by-step explanation:
Given as :
The rate of depreciation of i-phone value each year = r = 63%
The initial value of i-phone = $ i
The final value of i-phone = $ f
The time period for depreciation = x year
Now, According to question
The final value of i-phone = The initial value of i-phone × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, $ f = $ i × [tex](1-\dfrac{\textrm r}{100})^{\textrm time}[/tex]
Or, $ f = $ i × [tex](1-\dfrac{\textrm 63}{100})^{\textrm x}[/tex]
Or, $ f = $ i × [tex](0.37)^{x}[/tex]
So, The function which represent the phone value after x years = f = i [tex](0.37)^{x}[/tex]
Hence, The function which represent the phone value after x years f = i [tex](0.37)^{x}[/tex] Answer
Every student in the senior class is taking history or science and 85 of them are taking both. If there are 106 seniors taking history and 109 seniors taking science, how many students are in the senior class?
Number of students in senior class is 130
Solution:
Given that Every student in the senior class is taking history or science
85 of them taking both history and science
106 seniors takes history
109 seniors takes science
To find: number of students in senior class
Let A be the set of the students of the senior class that take history
Let B be the set of students of senior class that they science
The number of students in senior class is given by:
[tex]|A \cup B|=|A|+|B|-|A \cap B|[/tex]
Where,
A = 106 and B = 109 and |A n B| = 85
[tex]|A \cup B|=106+109-85=130[/tex]
Thus number of students in senior class is 130
Answer:
130
Step-by-step explanation:
Since 106 seniors are taking history and 109 seniors are taking science. If we add those numbers of seniors up we get 215, then we subtract the number of seniors that are taking both history and science because we counted them twice. So the total is 215 - 85 = 130. Therefore there are 130 students in the senior class.
find <ABC + <ADC
help... ASAP! :)
Answer:
Option D. 124°
Step-by-step explanation:
step 1
Find the measure of angle AOC
The triangle AOC is an isosceles triangle, because OA=OC=radius
so
[tex]m\angle OAC=m\angle OCA=28^o[/tex]
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
[tex]m\angle OAC+m\angle OCA+m\angle AOC=180^o[/tex]
substitute the given values
[tex]28^o+28^o+m\angle AOC=180^o[/tex]
[tex]56^o+m\angle AOC=180^o[/tex]
[tex]m\angle AOC=180^o-56^o[/tex]
[tex]m\angle AOC=124^o[/tex]
step 2
Find the measure of arc AC
we know that
[tex]arc\ AC=m\angle AOC[/tex] ----> by central angle
we have
[tex]m\angle AOC=124^o[/tex]
therefore
[tex]arc\ AC=124^o[/tex]
step 3
we know that
The inscribed angle is half that of the arc comprising
[tex]m\angle ABC=\frac{1}{2}[arc\ AC][/tex]
[tex]m\angle ADC=\frac{1}{2}[arc\ AC][/tex]
so
[tex]m\angle ABC=m\angle ADC[/tex]
therefore
[tex]m\angle ABC+m\angle ADC=2m\angle ABC=arc\ AC[/tex]
substitute the value of the arc AC
[tex]m\angle ABC+m\angle ADC=124^o[/tex]
What is Blaine's driving rate in miles per hour
Sorry, but I don't see any information for me to use to answer that question.
-6+3(2-4(-3)+6)+(-5)
Answer:
43
Step-by-step explanation:
Remove parenthesis.
−6+3(2−4⋅−3+6)−5
Multiply −4 by−3.
−6+3(2+12+6)−5
Add 2 and 12.
−6+3(14+6)−5
Add 14 and 6.
-6+3(20)-5
Multiply 3 by 20.
-6+60-5
Add -6+60.
54-5
Subtract 54 and 5.
43
Use the diagram to complete the table by matching the Theorem with the angle relationship.
Answer:
The Table with Correct reasons are as follows.
Step-by-step explanation:
The Table with Correct reasons are as follows
Answer Angle Relationship
c. Corresponding Angles ∠ 1 ≅ ∠ 5
d. Same Side Interior ∠ 4 + ∠ 5 = 180
a. Alternate Exterior Angles ∠ 3 ≅ ∠ 6
b. Alternate Interior Angles ∠ 4 ≅ ∠ 5
c. Corresponding Angles ∠ 2 ≅ ∠ 6
Write a line that passes through each pair of point (0,5)(-3,5)
Answer:
(5-5)/(-3-0)= 0/-3= 0
y - 5 = 0(x - 0)
y - 5 = 0
y = 5
How do I simplify -3(x-4)
Write the expression: the sum of the quantity h and 3 divided by 6.
A) h/6 + 3
B) h/3 + 6
C) h+3/6
D) 6/h+3
The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6 so option (C) is correct.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given,
The sum of the quantity h and 3 = h + 3
It is divided by 6 so, (h + 3)/6
Hence "The expression which represents the sum of the quantity h and 3 divided by 6 is (h+3)/6".
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round 98 inches to the nearest foot
Answer 8.17
Step-by-step explanation:
1.divide 98 by twelve, since there are 12 inches in a foot
98 \ 12
2.then round to the nearest tenth. 8.16 is rounded to 8.17
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 10 cubic feet and the volume of each large box is 24 cubic feet. A total of 23 boxes of paper were shipped with a combined volume of 426 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
x+y=23 and 10x+24y=426 can be used to determine the number of small and large boxes shipped where x represents the number of small boxes and y represent the number of large boxes.
Step-by-step explanation:
Given,
Volume of small box = 10 cubic feet
Volume of large box = 24 cubic feet
Total boxes shipped = 23
Combined volume = 426 cubic feet
Let,
x represent the number of small boxes.
y represent the number of large boxes.
x+y=23
10x+24y=426
x+y=23 and 10x+24y=426 can be used to determine the number of small and large boxes shipped where x represents the number of small boxes and y represent the number of large boxes.
Keywords: linear equation, addition
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12. The equation for line G is given by
5y = -2x - 20. Suppose line G is parallel to line R, and line E is perpendicular to line G. Point (-10,8) lies on both line R and line E.
Part A: Write an equation in slope-
intercept form for line R.
Part B: Write an equation in slope-
intercept form for line E.
Answer:
Step-by-step explanation:
line G :
5y = -2x - 20...put in slope intercept form (y = mx + b)
y = -2/5x - 4....the slope(m) = -2/5
Part A.) slope intercept form for line R...since R is parallel to G, it will have the same slope....so slope(m) = -2/5
(-10,8)...x = -10 and y = 8
slope(m) = -2/5
y = mx + b
8 = -2/5(-10) + b
8 = 4 + b
8 - 4 = b
4 = b
so ur equation is : y = -2/5x + 4 <=== part A answer
since line E is perpendicular to line G, it will have a negative reciprocal slope...all that means is flip the slope and change the sign....so the slope of line E is : (flip -2/5.....-5/2.....change the sign......5/2)
(-10,8)...x = -10 and y = 8
slope(m) = 5/2
y = mx + b
8 = 5/2(-10) + b
8 = -25 + b
8 + 25 = b
33 = b
so ur equation is : y = 5/2x + 33 <== part B answer
The equation for line R is y = -2/5x + 12. The equation for line E is y = 5/2x + 33.
Explanation:Part A: To write the equation for line R in slope-intercept form, we need to find the slope and the y-intercept. Since line R is parallel to line G, it will have the same slope. The slope of line G can be determined by dividing the coefficient of x by the coefficient of y: -2/5. We can use the point-slope form, y - y1 = m(x - x1), to find the equation. Substituting the coordinates of the point (-10,8), the equation for line R is y - 8 = (-2/5)(x + 10). Simplifying, we get the equation for line R: y = -2/5x + 12.
Part B: To write the equation for line E in slope-intercept form, we need to find the slope and the y-intercept. Since line E is perpendicular to line G, its slope will be the negative reciprocal of the slope of line G. The slope of line G is -2/5, so the slope of line E will be 5/2. Using the point-slope form and substituting the coordinates of the point (-10,8), the equation for line E is y - 8 = (5/2)(x + 10). Simplifying, we get the equation for line E: y = 5/2x + 33.
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Jake owns twice as many DVDs as Louis.Bo has sixty fewer DVDs than five times Louis’s collection. If Jake and Bo have the same amount of DVDs how DVDs are in Louis’s collection?
There are 20 number of DVD's in Louis collection
Solution:
Let "J" be the number of DVD's with Jake
Let "B" be the number of DVD's with Bo
Let "L" be the number of DVD's with Louis
Given that Jake owns twice as many DVDs as Louis
So we can say,
number of DVD's with Jake = 2(number of DVD's with Loius)
J = 2L ------ eqn 1
Given that Bo has sixty fewer DVDs than five times Louis’s collection
So we can say,
number of DVD's with Bo = 5 times number of DVD's with Louis - 60
B = 5L - 60 ---- eqn 2
Given that Jake and Bo have the same amount of DVDs
number of DVD's with Jake = number of DVD's with Bo
J = B ---- eqn 3
Let us solve eqn 1, 2, 3 to find value of "L"
From eqn 1 and eqn 3,
2L = B ----- eqn 4
Substitute eqn 4 in eqn 2
2L = 5L - 60
2L - 5L = -60
-3L = -60
L = 20Thus there are 20 number of DVD's in Louis collection
Louis has 30 DVDs in his collection.
Let's denote the number of DVDs Louis has as L. According to the problem, Jake owns twice as many DVDs as Louis, so Jake has 2L DVDs. Bo has sixty fewer DVDs than five times Louis's collection, which means Bo has 5L - 60 DVDs.
Since Jake and Bo have the same amount of DVDs, we can set their quantities equal to each other:
2L = 5L - 60
Now, let's solve for L:
5L - 2L = 60
3L = 60
L = 60 / 3
L = 20
Louis has 20 DVDs in his collection.
How do i find out what is 5% of 30
Answer: 1.5
Step-by-step explanation: To find 5% of 30, first write 5% as a decimal by moving the decimal point 2 places to the right to get .05.
Next, the word "of" means multiply, so we have (.05)(30) which is 1.5.
So 5% of 30 is 1.5.
Answer:
1.5
Step-by-step explanation:
To solve, you put (5%) in the calculator, then (30) next to it, and the calculator gives you your answer. I think that's the easiest way to do it.
The perimeter of a rectangle is 53 inches. The length of the rectangle is 5 less than twice it’s width. Solve the system using 2 equations.
Answer:
length of rectangle=16 inches
width of rectangle=10.5 inches
Step-by-step explanation:
given ,perimeter of rectangle=53 inches
let ,length of rectangle= l=2b-5
width of rectangle=b
p=2(l+b)
53=2(2b-5+b)
26.5=3b-5
31.5=3b
b=[tex]\frac{31.5}{3}[/tex]
b=10.5 inches
l=21-5=16 inches
Can somebody please help me with this problem??? I can't figure it out...
We can use the Pythagorean theorem to solve. (a² + b² = c²)
Fill in with what we know → 6² + b² = 11²
Simplify → 36 + b² = 121
Subtract 36 to both sides → 36 - 36 + b² = 121 - 36
Simplify → b² = 85
Take the root of both sides → √b² = √85
Simplify → b = 9.2195...
Round if necessary → 9.2195 = 9.22
Hence, b equals 9.2195.. (unrounded) or 9.22 (rounded).
Best of Luck!
PLEASE HELP ASAP
△DEF is similar to △RST .
Drag the answer into the box to match each part of △DEF with the corresponding part of △RST.
Answer:
see the attached figure
Step-by-step explanation:
we know that
If two triangles are similar, then its corresponding sides are proportional and its corresponding angles are congruent
Corresponding sides are named using pairs of letters in the same position on either side of the similarity statement
Corresponding angles are named using a letter in the same position on either side of the similarity statement.
therefore
Corresponding angles
∠D and ∠R
∠E and ∠S
∠F and ∠T
Corresponding sides
DE and RS
EF and ST
DF and RT
4cos+4sin^2=5 find cos
Answer:
cos θ = 1/2
Step-by-step explanation:
4 cos θ + 4 sin² θ = 5
Use Pythagorean identity.
4 cos θ + 4 (1 − cos² θ) = 5
4 cos θ + 4 − 4 cos² θ = 5
0 = 4 cos² θ − 4 cos θ + 1
0 = (2 cos θ − 1)²
0 = 2 cos θ − 1
cos θ = 1/2
Answer:
60° and 300°
Step-by-step explanation:
Before beginning to answer this question, you'll need a quick formula that will be very helpful trying to answer questions like this one:
[tex]sinx^2 + cosx^2 = 1[/tex]You'll see why this formula is useful soon.
Work:
[tex]4cosx+4sinx^2=5[/tex]
The way we want to go about answering this question is very similar to what we've learned in the past: factoring. In order to be able to factor though, we need to have only [tex]cosx[/tex] in our equation instead of both [tex]sinx[/tex] and [tex]cosx[/tex] like the above equation has. this is where the formula I showed earlier comes into play.Using the equation I showed earlier, we are going to get rid of the [tex]sinx[/tex].[tex]sinx^2+cosx^2=1[/tex]
We are going to isolate [tex]sinx^2[/tex] and then substitute what its equal to into the equation.[tex]sinx^2=-cosx^2+1[/tex]
Now Substitute this back into the original equation.[tex]4cosx+4(-cosx^2+1)=5[/tex]
Put this into standard form. Then we can factor.[tex]4cosx-4cosx^2+4=5[/tex]
[tex]-4cosx^2+4cosx+4=5[/tex]
[tex]4cosx^2-4cosx-4=-5[/tex]
[tex]4cosx^2-4cosx+1=0[/tex]
Let [tex]cosx[/tex] be [tex]u[/tex].[tex]4u^2-4u+1=0[/tex]
Look familiar? We could have factored before just the same, but this ensures there will be fewer mistakes while factoring.[tex](2u-1)^2=0[/tex]
Now let's change [tex]u[/tex] back to [tex]cosx[/tex][tex](2cosx-1)^2=0[/tex]
Set [tex]2cosx-1[/tex] equal to 0.[tex]2cosx-1=0[/tex]
[tex]2cosx=1[/tex]
[tex]cosx=1/2[/tex]
Hopefully if your teacher taught you unit circle properly, you will know that [tex]cosx=1/2[/tex] is asking for an angle. In this case, I know the angle because of memorization, but sadly the only way to learn this stuff is memorization, so I wont be able to show work for how I got my final answer. I'll have to just show calculator-wise how its done.[tex](cos^-^1)cosx=1/2(cos^-^1)[/tex]
[tex]x=60[/tex] [tex]x=300[/tex]
What is the most efficient way to solve the equation?
5j = 40
Answer: j = 8
Step-by-step explanation: To solve for j in this equation, we want to get j by itself on the left side of the equation. Since j is being multiplied by 5, to get j by itself, we need to divide by 5 on the left side of the equation. Since we divided by 5 on the left side, we must also divide by 5 on the right side.
On the left side, notice that the 5's cancel out so we are simply left with j. On the right side, we have 40 divided by 5 which gives us 8 so we have j = 8.
Finally, remember to check your answer by substituting an 8 back into the original equation. So we have 5 (8) = 40 which is a true statement so our answer checks. Remember to show all your work when solving equations.
The Answer is :J=8 =)