Answer:
4, 16 and 10
Step-by-step explanation:
Here we would like to work with a system of 3 equations, we need ti find them. Lets call s the 10oz coffees, m the 14oz and l the 20oz.
As Kyle sold $37.2 selling 3 different types of coffee at their respective prices we can say:
revenue = s*0.95 + m*1.15 + l*1.5 = 37.2 [equation 1]
And as he sold 30 cups:
s + m + l = 30 [equation 2]
And as the total volume of coffee is 464 oz:
s*10 + m*14 + l*20 = 464 [equation 3]
So, we have a system of 3 equations with three unknowns s, m and l.
Take the eq 2 and subtract m and l in both sides:
s = 30 - m - l
Now, take it and replace in the other 2:
(30 - m - l)*10 + 14m + 20l = 464 [eq 3]
0.95(30 - m - l) + 1.15m + 1.5l = 37.2 [eq 1]
Working with equation 3:
300 -10m -10l + 14m + 20l = 464
300 + 4m + 10l = 464
4m + 10l = 164 [equation 3']
Now with eq 1:
0.95(30 - m - l) + 1.15m + 1.5l = 37.2
28.5 - 0.95m - 0.95l + 1.15m + 1.5 l = 37.2
28.5 + 0.2m + 0.55l = 37.2
0.2m + 0.55l = 8.7 [equaiton 1']
Now we passed to a 2-equation system with eq 1' and eq 3'.
Take eq 3' and subtract 4m in both sides:
10l = 164 - 4m
Now divide by 10 in both sides
l = [164 - 4m]/10
Now, with this value for l replace in eq 1':
0.2m + 0.55 ( [164 - 4m]/10) = 8.7
0.2m + 0.055 (164 - 4m) = 8.7
0.2m + 9.02 - 0.22m = 8.7
- 0.02m = -0.32
m = -0.32/-0.02
m = 16 ----> 16 14oz coffees
Now replace m=16 in eq 1' or 3' to find l:
4m +10l = 164
64 + 10l = 164
10l = 100
l = 10 ----> 10 20oz coffees
So, finally we replace l=10 and m=16 in equaiton 2:
s + m + l = 30
s + 16 +10 = 30
s = 30 - 26
s = 4
So, Kyle filled 4 10oz coffes, 16 14oz coffees and 10 20oz coffees.
5 different mathematics books, 4 different French books and 2 different biology books are to be arrange on a shelf. How many different arrangements are possible, if
1. The books in each particular subject must all stand together?
2. Only the mathematics books must stand together.
Problem 1
A = 5! = 5*4*3*2*1 = 120 ways to arrange the math books
B = 4! = 4*3*2*1 = 24 ways to arrange the French books
C = 2! = 2*1 = 2 ways to arrange the biology books
D = 3! = 3*2*1 = 6 ways to arrange the three blocks of books, each block a different subject
E = A*B*C*D = 120*24*2*6 = 34560 different ways to arrange the books such that the subjects stick together
-------------
Answer: 34560========================================
Problem 2
Group all the math books to form one "book". This is the same as taking out the 5 math books and replacing it with one single math book. This single math book acts as a placeholder for all of the five books together as one block.
We have
1 math "book"
4 French books
2 biology books
So there are 1+4+2 = 7 "books" total and
7! = 7*6*5*4*3*2*1 = 5040 different ways to arrange those "books"
Within the math block of books, there are 5! = 120 ways to arrange things.
So overall we have 120*5040 = 604800
-------------
Answer: 604800Evelyn is using her grandmother's pancake recipe, but she wants to make 40% more pancakes than the recipe usually prepares. If her grandmother's recipe calls for 1/2 cup of flour, how much flour will Evelyn need to use? Show Work!
(A) 3/10 cup
(B) 1/2 cup
(C) 7/10 cup
(D) 1 3/10 cup
(C) 7/10 cup is the correct answer
Step-by-step explanation:
First of all we will calculate the 40% of grandmother's recipe then add it to the given flour in grandma's recipe
So,
The amount of flour in grandma's recipe = F_g = 1/2 cups
Calculating percentage
[tex]=40\%\ of\ \frac{1}{2}\\=\frac{40}{100}*\frac{1}{2}\\=\frac{2}{10}[/tex]
So Evelyn needs to add 2/10 cups more to the original quantity.
So,
Flour used by Evelyn:
[tex]=\frac{1}{2}+\frac{2}{10}\\\\=\frac{5+2}{10}\\\\=\frac{7}{10}\ cups[/tex]
Hence,
(C) 7/10 cup is the correct answer
Keywords: Percentage, Quantity
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Question 11 of 15 (1 point)
4.4 Section Exercise 18
Use the problem-solving flowchart.
Twice the sum of a number and two is seventeen less than five times the number. Find the
number. Round your answer to the nearest integer, if necessary.
The number is
The number is 7
Step-by-step explanation:
Let x be the number
then according to given statement
[tex]2(x+2) = 5x-17[/tex]
Simplifying
[tex]2x+4 = 5x-17[/tex]
Adding 17 on both sides
[tex]2x+4+17 = 5x-17+17\\2x+21 = 5x[/tex]
Subtracting 2x from both sides
[tex]2x+21-2x = 5x - 2x\\21 = 3x\\3x = 21[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} = \frac{21}{3}\\x = 7[/tex]
Hence,
The number is 7
Keywords: Linear equation, variables
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Your get a haircut that cost $23.if you tip the barber 10%,what is the final bill?
Answer:
$25.30
Step-by-step explanation:
The final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
You get a haircut that cost $23.if you tip the barber 10% of the total hair cut cost.
Let x be the final bill amount.
The value of x can be found as follows:
x = $23 + 10% of $23
x = 23 + (10/100)23
x = 23 + 0.1(23)
x = 23 + 2.30
x = $25.30
Thus, the final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.
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it took jack 360 seconds to walk home from school how many min did it take him
1 minute has 60 seconds. So dividing the number of seconds jack has to walk from school to home by 60 will give us minutes.
[tex]t=\dfrac{360\mathrm{s}}{60}=\boxed{6\mathrm{min}}[/tex]
Hope this helps.
Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.
An exponential function titled Bacteria Decay with x axis labeled Time, in Minutes, and y axis labeled Amount of Bacteria, in Thousands, decreasing to the right with a y intercept of 0 comma 60 and an x intercept of 18 comma 0.
0 ≤ x ≤ 18, −3.33
0 ≤ x ≤ 18, −0.3
0 ≤ y ≤ 60, −3.33
0 ≤ y ≤ 60, −0.3
In a recipe for double chocolate every 1/2 cup of milk calls for 2 cups of chocolate. if the recipe were increased to include 4 cups of chocolate, how much milk would be needed?
Answer:1 C milk
Step-by-step explanation:
1/2 C milk = 2 C chocolate
1 C milk = 4 C chocolate
Answer:
1 cup of milk
Step-by-step explanation:
If 1/2 cup of milk is needed for 2 cups of chocolate, and you need to find how much milk is needed for 4 cups, then you'd follow the same steps as going from 2 cups to 4, multiplying by 2.
2 cups chocolate x 2 = 4 cups chocolate
1/2 cup milk x 2 = 1 cup
5x - 9y=1
-7x + 2y = -5
9514 1404 393
Answer:
(x, y) = (43/53, 18/53)
Step-by-step explanation:
If we want to eliminate the x-terms, we multiply the first equation by 7 (opposite of the x-coefficient in the second equation), and we multiply the second equation by 5 (x-coefficient in the first equation). Then we add the result.
7(5x -9y) +5(-7x +2y) = 7(1) +5(-5)
35x -63y -35x +10y = 7 -25
-53y = -18 . . . . simplify. Note the x-terms are gone.
y = 18/53 . . . . . divide by -53
__
Putting this value of y in the first equation, we get ...
5x -9(18/53) = 1
5x = 1 + 162/53 = 215/53 . . . . . add 9y to both sides, simplify
x = 43/53 . . . . . . . . . . divide by 5
The solution is (x, y) = (43/53, 18/53).
what is the sign of 3/5 + 3/5
Final answer:
The sum of two positive numbers always has a positive sign, so the sum of 3/5 + 3/5 is positive.
Explanation:
The question what is the sign of 3/5 + 3/5 involves understanding the rules of addition for numbers with the same sign. According to the rules of addition:
When two positive numbers add, the answer has a +ve sign.
Since both fractions 3/5 and 3/5 are positive, their sum will also have a positive sign. Therefore, the sign of the sum 3/5 + 3/5 is +ve, which means the answer is also positive.
Which comparison is true?
O A. 0.3 > 0.09
B. 0.04 > 0.2
OC. 0.29 > 0.38
OD. 0.24 > 0.67
O E. 0.55 > 0.600
Answer:
0.3 > 0.09
Step-by-step explanation:
The comparison 0.3 > 0.09 is true.
0.3 = 0.300
0.300 > 0.009
All other options are false. They should have a less than sign instead of a greater than sign.
Final answer:
Upon comparison of decimal values in the given options, Option A (0.3 > 0.09) is the true comparison as 0.3 is greater than 0.09 when comparing the tenths place.
Explanation:
When comparing decimal numbers, you should look at the largest place value first and work your way to smaller place values to determine which number is larger. Let's evaluate each option:
A. 0.3 > 0.09: Comparing the tenths place, 3 is greater than 0. Therefore, this statement is true.
B. 0.04 > 0.2: Comparing the tenths place, 0 is less than 2. Therefore, this statement is false.
C. 0.29 > 0.38: Comparing the tenths place, both numbers are equal, but in the hundredths place, 9 is less than 8. Therefore, this statement is false.
D. 0.24 > 0.67: Comparing the tenths place, 2 is less than 6. Therefore, this statement is false.
E. 0.55 > 0.600: Comparing the tenths place, both numbers are equal, and in the hundredths place, 5 is equal to 0 followed by an additional 0, thus both numbers are equal and this statement is false.
Based on the above analysis, the correct answer is Option A. 0.3 > 0.09.
A farm is rectangular with an area of 1/2 square
miles. If the length of the farm is 1/3 miles, what
is its width? Input your answer as a fraction.
The width of a rectangular farm with area of 1/2 square mile and length of 1/3 mile is 1 1/2 miles.
Explanation:The area of a rectangle is found by multiplying length times width. In this case, we know that the area is 1/2 square mile and the length is 1/3 mile.
So we have the equation (Length) * (Width)= Area; so 1/3 * W = 1/2. To solve for W (width), you need to divide both sides of the equation by 1/3.You might remember that dividing by a fraction is the same as multiplying by its reciprocal. So, we divide 1/2 by 1/3, which is the same thing as 1/2 * 3/1. Doing this, we end up with the fraction 3/2, or 1 1/2.
So the width of the farm is 1 1/2 miles.
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Solve for x. 10 = − 2/3 x A) −6 B) −9 C) −15 D) −18
Answer:
x=-10/23
Step-by-step explanation:
-23x=10
x=10/-23
x=-10/23
Answer:
x = -15 thus c: is your answer
Step-by-step explanation:
Solve for x:
10 = (-2 x)/3
10 = (-2 x)/3 is equivalent to (-2 x)/3 = 10:
(-2 x)/3 = 10
Multiply both sides of (-2 x)/3 = 10 by -3/2:
(-3 (-2) x)/(2×3) = (-3)/2×10
(-3)/2×(-2)/3 = (-3 (-2))/(2×3):
(-3 (-2))/(2×3) x = (-3)/2×10
(-3)/2×10 = (-3×10)/2:
(-3 (-2) x)/(2×3) = (-3×10)/2
(-3)/3 = (3 (-1))/3 = -1:
(-2-1 x)/2 = (-3×10)/2
(-2)/2 = (2 (-1))/2 = -1:
--1 x = (-3×10)/2
(-1)^2 = 1:
x = (-3×10)/2
10/2 = (2×5)/2 = 5:
x = -35
-3×5 = -15:
Answer: x = -15
A satellite travels 29 1/2 miles every 4 1/3
seconds. What is its unit rate of speed?
Answer:
The speed at which the satellite travel is 6.80 miles per second
Step-by-step explanation:
Given as :
The distance cover by satellites = 29 [tex]\frac{1}{2}[/tex] miles
Or, The distance cover by satellites = [tex]\frac{59}{2}[/tex] miles
The Time taken by satellite to travel with this speed = 4[tex]\frac{1}{3}[/tex] sec
Or, The Time taken by satellite to travel with this speed = [tex]\frac{13}{3}[/tex] seconds
Let the Speed with which the satellite travel = s miles per second
Now, As we know
Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]
Or, s = [tex]\frac{\frac{52}{2}}{\frac{13}{3}}[/tex]
or, s = [tex]\frac{59\times 3}{2\times 13}[/tex]
∴ s = 6.80 mps
So, speed = s = 6.80 miles per second
Hence The speed at which the satellite travel is 6.80 miles per second Anwser
Write an inequality for the graph.
Answer:
x ≤ 3
This is because it is a closed circle.
Triangle ABC is an isosceles triangle. The length of the base is 20 meters and the corresponding height is 24 meters. Find the perimeter of ABC. (round your answer to the nearest tenth of a meter).
Final answer:
The perimeter of the isosceles triangle with a base of 20 meters and height of 24 meters is 60 meters.
Explanation:
The formula for the area of a triangle is 1/2 × base × height.
In this case, the base of the isosceles triangle is given as 20 meters and the corresponding height is given as 24 meters.
Using the formula, we can calculate the area: Area = 1/2 × 20 × 24 = 240 square meters.Next, we need to calculate the length of the two equal sides of the triangle.Since the triangle is isosceles, the length of the base is equal to the length of the two equal sides.So, each equal side of the triangle is equal to 20 meters.Finally, to find the perimeter of the triangle, we add up the lengths of all three sides.Perimeter = 20 + 20 + 20 = 60 meters.The width of a rectangle is 3/8 the length x of the rectangle. What is the perimeter of the rectangle?
Answer:
(11/4)x units
Step-by-step explanation:
for a rectangle,
perimeter = 2(length) + 2(width)
given:
length = x
width = (3/8)x
hence,
perimeter = 2(length) + 2(width)
perimeter = 2x + 2(3/8)x
perimeter = 2x + (3/4)x
perimeter = [2 + (3/4)]x
perimeter = (11/4)x
Jasmine has 3/4 cup of flour in a mixing bowl. After adding more flour to the mixing bowl, Jasmine says that she now has 5/8 cup of flour.
Why is her statement incorrect?
Answer:
6/8
Step-by-step explanation:
3/4 into eighths would be 6/8. She said she had 5/8 cups of flour.
HELP An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the investor's total profit was $104, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 5% was $(blank). The amount invested in the mutual fund that earned 3% was $(blank). (show your work)
Answer:
The amount invested in the mutual fund that earned 5% was $1,000
The amount invested in the mutual fund that earned 3% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested in the mutual fund that earned 5%
y ----> the amount invested in the mutual fund that earned 3%
we know that
[tex]x+y=2,800[/tex] ----> [tex]y=2,800-x[/tex] ----> equation A
[tex]5\%=5/100=0.05[/tex]
[tex]3\%=3/100=0.03[/tex]
[tex]0.05x+0.03y=104[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]0.05x+0.03(2,800-x)=104[/tex]
Solve for x
[tex]0.05x+84-0.03x=104[/tex]
[tex]0.05x-0.03x=104-84[/tex]
[tex]0.02x=20[/tex]
[tex]x=\$1,000[/tex]
Find the value of y
[tex]y=2,800-x[/tex]
[tex]y=2,800-1,000=\$1,800[/tex]
therefore
The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800
someone please help with 17!! leave work below
Answer:
The amount charged is proportional to the ears of corn
Step-by-step explanation:
Now I'm going to explain, but write it in your own words. It's proportional because the amount charged is completely reliant on how many ears of corn you are buying.
So for every 1 ear of corn, you pay about 33 cents
or
For every 2 ears of corn, you pay about 67 cents
The amount you pay completely relies on how many you're buyingadd 9 and 3, then add 6 to the result
Answer:
Step-by-step explanation:
18
9+3=12+6=18
Answer:
18
Step-by-step explanation:
Add 9 and 3;
9 + 3 = 12
Then add 6 to the result
12 + 6 = 18
Determine the intercepts of the line.
y=-3x+12y=−3x+12
Answer:
x-intercept=4 and y-intercept = 12
Step-by-step explanation:
To find the x-intercept, make the y=0:
0 = -3x+12
3x = 12
x=12/3
x=4
To find the y-intercept, make the x=0:
y = -3(0) +12
y = 0 +12
y = 12
Hope this helps!
Please mark brainliest if you think I helped! Would really appreciate!
Answer:
y=12,0
x=4,0
Step-by-step explanation:
for those who were just as confused as i was <3
pls use the diagram to answer the question thanks
Answer:
A) The smaller angle between 12 and 3 is 90° and that is [tex]\frac{1}{4}[/tex]th coordinate
B) The smaller angle between 2 and 3 is 30°
C) The angle between 4 and 6 is 60°
D) the angle between 6 and 9 is 90°
D) The angle between 6 and 12 is 180°
E) The angle between 7 and 8 is 30°
Step-by-step explanation:
Given as :
It is shown in diagram as ;
The circle with different angles from angle 1 to angle 12
Now, The figure is the complete circle, and the measure of all angles in a circle = 360°
The measure of semicircle = 180°
and each quadrant is divided in to 3 angles
Each right angle is further divided into three 30° angles
Again ,
A) The smaller angle between 12 and 3 is 90° and that is [tex]\frac{1}{4}[/tex]th coordinate
B) The smaller angle between 2 and 3 is 30°
C) The angle between 4 and 6 is 60°
D) the angle between 6 and 9 is 90°
D) The angle between 6 and 12 is 180°
E) The angle between 7 and 8 is 30° Answer
To divide a number by 100, move the decimal point _____.
two places to the right
three places to the left
two places to the left
three places to the right
Answer:
c. two places to the left
Step-by-step explanation:
Answer:
two places to the left
Step-by-step explanation:
-3 2/7 times .14 as a decimal and a fraction
Answer:
-0.46 or -23/50
Step-by-step explanation:
We note that 0.14 is easily divisible by 7, so we can do this using the distributive property:
(-3 2/7)(0.14) = (-1)(3 + 2/7)(0.14)
= (-1)(3×0.14 +2/7×0.14)
= (-1)(0.42 +0.04)
= -0.46 . . . . . decimal form
= -46/100 . . . . place value
= -23/50 . . . . remove common factor of 2; fraction form
The product is -0.46 or -23/50.
cos(t)=24/25, what does sin(t)=?
Answer:
The value of sin t is [tex]\frac{7}{25}[/tex]
Step-by-step explanation:
Given as :
cos (t) = [tex]\frac{24}{25}[/tex]
Since sin² t + cos² t = 1
So, sin² t = 1 - cos² t
or, sin² t = 1 - ([tex]\frac{24}{25}[/tex])²
or, sin² t = [tex]\frac{25^{2} - 24^{2} }{25^{2} }[/tex]
Or, sin² t = [tex]\frac{625 - 576}{625}[/tex]
Or , sin² t = [tex]\frac{49}{625}[/tex]
Or, sin t = [tex]\sqrt{\frac{49}{625} }[/tex]
So, sin t = [tex]\frac{7}{25}[/tex]
Hence The value of sin t is [tex]\frac{7}{25}[/tex] Answer
(-4,6); slope = -3/4
Answer:
y-6=-3/4(x+4)
Step-by-step explanation:
y-y1=m(x-x1)
m=-3/4
y-6=-3/4(x-(-4))
y-6=-3/4(x+4)
A loan of $46,000 is made at 7% interest, compounded annually. After how many years will the amount due reach $65,000 or more?
After 5.11 years, amount due reach $65,000 or more
Solution:
Given that a loan of $46,000 is made.
Rate of interest charged is 7% compounded annually
Need to determine number of years in which the amount due reach $65,000 or more.
In our case
Amount due A = $65000
Loan Amount that is principal P = $46000
Rate of interest r = 7%
Formula for Amount compounded anually is as follows:
[tex]\mathrm{A}=P\left(1+\frac{r}{100}\right)^{n}[/tex]
Substituting the values in above formula we get
[tex]\begin{array}{l}{65000=46000\left(1+\frac{7}{100}\right)^{n}} \\\\ {\frac{65000}{46000}=\left(\frac{107}{100}\right)^{n}} \\\\ {\Rightarrow 1.4130=(1.07)^{n}}\end{array}[/tex]
Applying log on both sides, we
[tex]\begin{array}{l}{\ln 1.4130=n \ln 1.07} \\\\ {=>\frac{\ln 1.4130}{\ln 1.07}=\mathrm{n}} \\\\ {=>\mathrm{n}=\frac{0.34571}{0.067658}=5.1096=5.11}\end{array}[/tex]
Hence after 5.11 years , amount due reach $65,000 or more
Can someone please explain to me HOW to transform this equation to determine if its an identity (8x+12y)^2+(6x+9y)=(10x+15y)^2
Answer:
See explanation
Step-by-step explanation:
Given
[tex](8x+12y)^2+(6x+9y)^2=(10x+15y)^2[/tex]
Note
[tex](8x+12y)^2=(4(2x+3y))^2=16(2x+3y)^2\\ \\(6x+9y)^2=(3(2x+3y))^2=9(2x+3y)^2\\ \\(10x+15y)^2=(5(2x+3y))^2=25(2x+3y)^2[/tex]
Since
[tex]16(2x+3y)^2+9(2x+3y)^2=(2x+3y)^2(16+9)=25(2x+3y)^2,[/tex]
this is an identity
determina la medida de cada uno de los angulos del triángulo ABC si se conoce que (3x+1)° (3x+4)° y (2x-1)°
Answer:
∠A=67°
∠B=70°
∠C=43°
Step-by-step explanation:
The correct question in English is
Determines the measurement of each of the angles of the triangle ABC if it is known that A=(3x+1)°,B=(3x+4)° and C=(2x-1)°.
we know that
The measure of the interior angles in a triangle must be equal to 180 degrees
so
∠A+∠B+∠C=180°
substitute the given values
[tex](3x+1)\°+(3x+4)\°+(2x-1)\°=180\°[/tex]
solve for x
[tex](8x+4)\°=180\°[/tex]
[tex]8x=180-4[/tex]
[tex]x=22[/tex]
Find the measure of each angle
∠A=(3(22)+1)=67°
∠B=(3(22)+4)=70°
∠C=(2(22)-1)=43°
Deja has two baskets of berries. One of the baskets has 3 3/8 pounds of berries and the other basket has 2 7/8 pounds of berries. She is going to split the berries evenly among 4 people. Witch measure is the best estimate for the number of pounds of berries each person would receive.
A) 1 1/4 pounds
B) 1 5/8 pounds
C) 2 7/8 pounds
D) 3 3/16 pounds
Answer:
(b) The number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.
Step-by-step explanation:
The amount of berries in first basket = 3 3/8 pounds
Now, [tex]3\frac{3}{8} = 3+\frac{3}{8} = 3 + 0.375 = 3.375[/tex]
So, the amount of berries in first basket = 3.375 pounds
The amount of berries in second basket = 2 7/8 pounds
Now, [tex]2\frac{7}{8} = 2+\frac{7}{8} = 2 + 0.875 = 2.875[/tex]
So, the amount of berries in second basket = 2.875 pounds
Now, the total berries = Berries in ( First + Second) basket
= 3.375 pounds + 2.875 pounds
= 6.25 pounds
So, the number of pounds each person would have = [tex]\frac{\textrm{Total weight of viable berries}}{\textrm{4}} = \frac{6.25}{4} = 1.5625[/tex]
Now, [tex]1.5625 = 1 + 0.5625 = 1 + \frac{5625}{10000} = 1 + \frac{5}{8} = 1\frac{5}{8}[/tex]
So, the number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.