Answer:
The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.
Step-by-step explanation:
The percentage concentration ([tex]r[/tex]), dimensionless, is determined by the following expression:
[tex]r = \frac{V_{sugar}}{V_{sugar}+V_{water}}[/tex] (1)
Where:
[tex]V_{sugar}[/tex] - Volume of sugar, measured in gallons.
[tex]V_{water}[/tex] - Volume of water, measured in gallons.
A 70 % sugar syrup means that there are 7 parts of sugar for each 10 parts of solution, that is, 7 parts of sugar and 3 parts of water. We need to add more water to dilute the solution to 40 %. Then, the new concentration must be equal to:
[tex]r' = \frac{V_{sugar}}{V_{sugar}+V_{water}+V'}[/tex] (2)
Where [tex]V'[/tex] is the addition of water needed to dilute the solution, measured in gallons.
If we now that [tex]V_{sugar} = 3.5\,gal[/tex], [tex]V_{water} = 1.5\,gal[/tex] and [tex]r' = 0.4[/tex], then the quantity of additional water is:
[tex]\frac{3.5\,gal}{5\,gal+V'} = 0.4[/tex]
[tex]3.5 = 0.4\cdot (5+V')[/tex]
[tex]3.5 = 2+0.4\cdot V'[/tex]
[tex]0.4\cdot V' = 1.5[/tex]
[tex]V' = 3.75\,gal[/tex]
The baker should add 3.75 gallon of water to 5 gallons of 70 % sugar syrup to make the 40 % syrup.
Answer:
3.75 gallons of water should be added
Step-by-step explanation:
Steven charges the following for repairing washing machines:
£24 call-out charge + £14 for each half-hour he spends on the repair
if a repair costs a customer £66, how long did it take?
What is the rate of change of y with respect to x for 25x-4y=50
Answer:
The rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Given
[tex]25x - 4y = 50[/tex]
Required
Determine the rate of change of y w.r.t x
[tex]25x - 4y = 50[/tex]
First, make y subject of formula
[tex]4y = 25x- 50[/tex]
Divide through by 4
[tex]y = \frac{25x}{4} - \frac{50}{4}[/tex]
[tex]y = \frac{25x}{4} - 12.5[/tex]
Next, we differentiate the above w.r.t to x
The result of the differentiation is the solution to the question
[tex]y' = 1 * \frac{25x^{1-1}}{4} -0[/tex]
[tex]y' = 1 * \frac{25x^0}{4}[/tex]
[tex]y' = 1 * \frac{25*1}{4}[/tex]
[tex]y' = \frac{25}{4}[/tex]
Hence, the rate of change is y with respect to x is [tex]\frac{25}{4}[/tex]
By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4
What is derivative?Rate of change of a function with respect to a variable is called derivative of that function with respect to that variable .
Here given relation is 25x-4y=0
[tex]\Rightarrow 4y=25x\\\\\Rightarrow y=\frac{25x}{4}[/tex]
We have to calculate rate of change of y with respect to x so we will calculate derivative of y with respect to x.
we can calculate derivative of y with respect to x as
[tex]\frac{dy}{dx}= \frac{d}{dx} (\frac{25x}{4})\\\\[/tex]
As 25/4 is constant we can take it out from derivative function as it is
[tex]\frac{dy}{dx}= (\frac{25}{4})\frac{dx}{dx}\\\\[/tex]
And we know derivative of a variable with respect to itself is 1
so
[tex]\frac{dy}{dx}= (\frac{25}{4})\times 1\\\\ \frac{dy}{dx}= \frac{25}{4}[/tex]
By calculating derivative of y with respect to x we got rate of change of y with respect to x for 25x-4y=0 is 25/4
To learn more about derivative visit: https://brainly.com/question/25081524
someone please help !!!
Factor completely:
4a^2+8a-140
Answer:
24a-140 is the correct answer
Step-by-step explanation:
4a²+8a-140
4a×4a=16a+8a-140
24a-140
make a the subject of this formula:
p=n^2+a/n+a
Step-by-step explanation:
we multiply both sides by the denominator on the right to eliminate fraction, so we have..
p*(n+a)= (n²+a/n+a)*n+a
so we have
p(n+a)= n²+a
so opening the bracket on the left hand side we have,
p*n+p*a
pn+pa
so,
pn+pa= n²+a
so collecting like terms we have,
pn-n²= a-pa
so removing a from the equation on the right hand side we have,
pn-n²=a(1-p)
dividing both sides by the equation in the bracket on the right hand side, we have..
pn-n²/(1-p)= a
a = pn-n²/1-p
or
a = n(p-n)/1-p
whats the answer im stuck ( -___-)
Answer:
(6r+7)+(13+7r)=13r+20
(13-1/2r)-(1-r)=12-1/2r
(-8-r)+(2r-4)=-12+r
Last one is r-13/6
Step-by-step explanation:
Which piecewise function is shown in the graph?
Answer:
The piecewise function is shown in the graph is
f(x) = -0.5x + 1, x < 0 2x - 2, x ≥ 0 ⇒ AStep-by-step explanation:
At first, you must find the equation of each line
The form of the equation of the line is f(x) = m x + b, where
m is the slope of the line which = Δy/Δxb is the y-intercept which is the y-coordinate of the point of intersection between the line and the y-axisFrom the graph
∵ The line to the left intersects the y-axis at point (0, 1)
∴ b = 1
∵ The line passes through points (0, 1) and (-2, 2)
∴ Δx = -2 - 0 = -2
∴ Δy = 2 - 1 = 1
→ Use them to find the value of m
∵ m = Δy/Δx
∴ m = [tex]\frac{1}{-2}[/tex]
∴ m = -0.5
→ Substitute the values of m and b in the form of the equation above
∴ f(x) = -0.5x + 1
∵ The domain of the function is the values of x
∵ The line starts with an empty circle
→ That means x = 0 does not belong to the domain
∴ The sign of inequality is < without equal
∴ The domain of f(x) is x < 0 ⇒ all values less than 0
∵ We have only one answer has f(x) = -0.5x + 1, x < 0
∴ The graph represents the first answer A
∴ The piecewise function is shown in the graph is
f(x) = -0.5x + 1, x < 0 2x - 2, x ≥ 0Answer:
a
Step-by-step explanation:
Write a slope-intercept form equation for a line that
passes through (0,4) and (2,-2).
Show the step by step process please.
Factor as the product of two binomials
(x^2 - 10x + 21)
Answer:
Step-by-step explanation:
x^2-10x+21
(x-7)(x-3)
find the 2 numbers that when multiplied make the last number or +21 and when combined make the middle number of -10. -7*-3 = 21 and -7+-3=10
Answer:
(x - 7)(x - 3)
Step-by-step explanation:
Given
x² - 10x + 21
Consider the factors of the constant term (+ 21) which sum to give the coefficient of the x- term (- 10)
The factors are - 7 and - 3 , since
- 7 × - 3 = + 21 and - 7 - 3 = - 10, thus
x² - 10x + 21 = (x - 7)(x - 3) ← in factored form
The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is
Y+ 7 = -
-- (x-10). What
is the standard form of the equation for this line?
O 2x - 5y = -15
2x - 5y = -17
2x + 5y = -15
2x + 5y = -17
Save and Exit
Answer:2x-5y=-15
Step-by-step explanation:
The mass of the copper cube is 90 grams, the mass of the gold cube is 193 grams, and the mass of the silver cube is 105 grams. Which shows the metals in order from the lowest density to the greatest density?
Answer: copper, silver, gold
Step-by-step explanation:
Answer:
copper siver gold
Step-by-step explanation:
i had this question too
Human cells come in a wide variety of shapes and sizes. The
mass of an average human cell is 2 x 10-11. Write this number in
standard form.
Answer:
2
Step-by-step explanation:
An adult ticket to a school play cost $5 and a student ticket cost $3. $460 dollars was collected and 120 tickets were sold. How many student tickets were sold?
If 500g of a material goes through four half-lives, how much material will be left? Round to two decimal places.
A. 125g
B. 62.5g
C. 250g
D. 31.25g
Jada earns twice as much money per hour as Diego. Diego earns twice as much money per hour as lin. Select all the graphs that could represent how much Jada, diego, and lin earn for different amounts of time worked.
Answer:
1 and 3Step-by-step explanation:
Let functions be
Jada = f(j)Diego = f(d)Lin = f(l)As per given ratios:
f(d) = 2f(l)f(j) = 2f(d) ⇒ f(j) = 4f(l)The smallest slope belongs to f(l), greater - f(d), the greatest - f(j)
Possible graphs reflecting the functions are graph 1 and graph 3
Matilda is selling hand-painted vases at a craft fair. She will
have to pay $200 to rent a booth at the fair. The cost of the
paint and other materials to create each vase is $5.50. She is
going to sell each vase for $14.00.
Part 1. Write an inequality to represent the situation in which
Matilda makes a profit. You must define any variable(s) you
use.
Part 2. How many vases must Matilda sell to make a profit?
Explain your reasoning.
Answer:
14x>200+5.5, She must sell 15 or more vases
Step-by-step explanation:
14x>200+5.5
14x>200+5.5
14x>205.5
x>14.68*
She must sell 15 or more vases
*You round up because you cannot sell a partial vase
Answer:
14v > 200 + 5.50v, she will have to sell 24 vases to make a profit
Step-by-step explanation:
It costs $5.50 PER VASE for materials, so you would subtract this from what she sells each vase for. 14 - 5.50 = 8.50. She makes an $8.50 profit per vase sold. We can write 8.50n > 200 to show her profit margin minus the booth fee. If she sold 24 vases, she would be making a profit and this would represent the lowest amount of vases she can sell to make a profit. We can write the inequality 24 ≤ n to show that she can sell 24 vases or more to make a profit.
14n > 200 + 5.50n
336 > 332, true
n > 23
Hope This Helps!
If -3d + 5 = -3 , then 3d - 9 =
Answer:
-3d+5=-3 is d=8/3
3d-9 is (d-3)
Step-by-step explanation:
What is 1.19047619048 as a fraction
Answer: 1.19047619048 as a fraction equals 119047619048/100000000000
Step-by-step explanation: To write 1.19047619048 as a fraction you have to write 1.19047619048 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
1.19047619048 = 1.19047619048/1 = 11.9047619048/10 = 119.047619048/100 = 1190.47619048/1000 = 11904.7619048/10000 = 119047.619048/100000 = 1190476.19048/1000000 = 11904761.9048/10000000 = 119047619.048/100000000 = 1190476190.48/1000000000 = 11904761904.8/10000000000 = 119047619048/100000000000
Answer:
119047619048/100000000000
Step-by-step explanation:
To write 1.19047619048 as a fraction you have to write 1.19047619048 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. And finally, we have: 1.19047619048 as a fraction equals 119047619048/100000000000
Which number is equivalent to 46/3?
Answer: 15.3 (with a repeating bar over the 3)
Answer:
15.3333
Step-by-step explanation:
i think it is that because its reocurring
Tina rode her bike a distance of 40 kilometers. How many miles did Tina ride? (1 mile ≈ 1.6 kilometers)
Answer:
64
Step-by-step explanation:
1.6 x 40 it's math
An advertisement reads “All Books 28 Percent Off.” A best-selling novel is originally priced at $18.99. About how much money will Gio save if he buys the novel on sale?
$2
$6
$10
$14
Answer:
6 dollars i think
Step-by-step explanation:
Answer:
Gio will save about $6.
Step-by-step explanation:
You would convert 28% to a decimal which is 0.28 and then multiply 0.28 by $18.99 and you would get $5.3172 which is closest to $6 so it would be B. about $6
A rancher raises five as many cows as horses. If he has 168 cows and horses, how many cows does he have? Complete the equations below, and then use substitution to solve. Let c represent the number of cows and h represent the number of horses Equation 1: c=_h Equation 2: c+h=_
Answer:
There are 28 horses and 140 cows
Step-by-step explanation:
Given
Animals: Cows and Horses
Represent Cows with c and Horses with h
For the first equation, we complete it as thus:
[tex]c = 5h[/tex]
This is so because there are 5 times as many c as h
The second equation will be completed as:
[tex]c + h = 168[/tex]
This is so because the total animals are 168
So, we have:
[tex]c = 5h[/tex]
[tex]c + h = 168[/tex]
Substitute 5h for c in the second equation
[tex]c + h = 168[/tex]
[tex]5h + h = 168[/tex]
[tex]6h= 168[/tex]
Solve for h
[tex]h = 168/6[/tex]
[tex]h = 28[/tex]
Recall that:
[tex]c = 5h[/tex]
[tex]c = 5 * 28[/tex]
[tex]c = 140[/tex]
Hence, there are 28 horses and 140 cows
pls answer this pls i’m gonna die
It 's an isosceles triangle if you look carefully. 2 Sides of the triangle are equal which is denoted by those marks. The angles opposite to the equal sides are always equal, so: [tex]m\angle FST = 64^\circ[/tex]
By angle sum property, [tex]m\angle TFS = 180 - 2 * 64 = 180 - 128 = 52^\circ[/tex]
52 degrees is the answer: Option D :D
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[tex]
FT = FS \: \: → \: \: angle \: \: T = angle \: \: S \\ [/tex]
Thus ;
[tex]angle \: \: S = 64°[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Sum of the interior angles of any triangle is 180° .
Thus ;
[tex]T + F + S = 180°[/tex]
[tex]64° + F + 64° = 180°[/tex]
[tex]F + 128° = 180°[/tex]
Subtract sides 128°
[tex]F + 128° - 128° = 180° - 128° \\ [/tex]
[tex]F = 52°[/tex]
So :
[tex]TFS = F = 52°[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The correct answer is Option four .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
4y - 9 - 6y = 2(y + 5) - 3 solve for y
What is the equation of the line that has a slope of -6/5 and goes through the point (5, -4)?
I need help on this question
Answer:
105 [tex]cm^{2}[/tex]
Step-by-step explanation:
Rectangle 2 is 3 times rectangle 1. We know this because one side of rectangle 2 is 3 times the same side of rectangle 1. Area of rectangle 1 × 3 = area of rectangle 2: 35 × 3 = 105 [tex]cm^{2}[/tex]I hope this helps!
Answer:
B- 105 cm
Step-by-step explanation:
4. Sasha sells t-shirts. Each day she earns a set amount, plus a
commission. Write a linear function fto determine Sasha's pay.
T-shirts 1 2 3 4 5
Total Pay 68 71 74 77 80
Answer:
The linear function is: p(x) = 3x+65The linear function is: p(x) = 3x+65
Step-by-step explanation:
Let x be the number of t-shirts and y be the total pay
As we can clearly see in the table that there is a linear relationship between x and y
A linear function is given as:
[tex]y = mx+b[/tex]
Here m is the gradient of the function then
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Taking any two pairs of x and y
(1,68) and (2,71)
[tex]m = \frac{71-68}{2-1}\\m = 3[/tex]
Putting in equation
[tex]y = 3x+b[/tex]
Putting a pair (1,68) in the equation to find the value of b
[tex]68 = 3(1) + b\\68 = 3+b\\b = 68-3\\b = 65[/tex]
Putting the value of b
[tex]y = 3x+65[/tex]
Let p(x) be the linear function
Hence,
The linear function is: p(x) = 3x+65
Answer:
y=3x+65
Step-by-step explanation:
Help asap
A local hamburger shop sold a combined total of 555 hamburgers and cheeseburgers on Saturday. There were 55 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
Answer:
There were 250 hamburgers sold on Saturday.
Step-by-step explanation:
∵ A local hamburger shop sold a combined total of 555 hamburgers
and cheeseburgers on Saturday
→ Assume that the shop sold x hamburgers
∵ The shop sold x hamburgers
∵ There were 55 more cheeseburgers sold than hamburgers
→ That means the number of cheeseburgers is greater than the
number of hamburger by 55
∴ The shop sold x + 55 cheeseburgers
∵ The shop sold 555 burgers
→ Add the two types of burgers and equate the sum by 555
∴ x + x + 55 = 555
∴ 2x + 55 = 555
→ Subtract 55 from both sides
∴ 2x + 55 - 55 = 555 - 55
∴ 2x = 500
→ Divide both sides by 2 to find x
∵ [tex]\frac{2x}{2}[/tex] = [tex]\frac{500}{2}[/tex]
∴ x = 250
∵ x represents the number of hamburgers
∴ There were 250 hamburgers sold on Saturday.
what calculates the slope of a line from two coordinate points from that line?
Answer:
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
solve this question and help save my life!
The next two term is 13 and 16 respectively.
Step-by-step explanation:
here,
a1 = -2
a2 = 1
a3 = 4
a4 = 7
a5 = 10
So, d = a2 - a1 = 1 - (-2) = 3
= a3 - a2 = 4 - 1 = 3
Here, Common difference is same everywhere and the value of d is 3
Then,
To find 6th term of this sequence
a6 = a5 + d
= 10 + 3
a6 = 13
To find 7th term of this sequence
a7 = a6 + d
= 13 + 3
a7 = 16
Thus, The next two term is 13 and 16 respectively.
-TheUnknownScientist
