Answer: 1.4286 gallons
Step-by-step explanation: the equation would be:
0.9*5+0x=0.7(5+x)
then you can shorten it down to:
4.5=3.5+0.7x
subtract both sides by 3.5 and you end up with:
1=0.7x
divide both sides by 0.7 and you get 1.4286 gallons
The chemist needs to add approximately 1.43 gallons of distilled water to 5 gallons of acid to obtain a 70% pure tannic acid solution.
Here, we have,
To solve this problem, we can use a mixture equation that equates the amount of pure tannic acid in the initial solution to the amount of pure tannic acid in the final solution.
Let's denote the amount of distilled water to be added as "x" gallons.
The initial solution contains 5 gallons of acid at 90% purity. This means it contains 0.90 * 5 = 4.5 gallons of pure tannic acid.
When the distilled water is added, the total volume of the solution becomes 5 + x gallons.
The goal is to obtain a 70% pure solution, which means it should contain 0.70 * (5 + x) gallons of pure tannic acid.
According to the mixture equation, we can set up the following equation:
4.5 = 0.70 * (5 + x)
Now, let's solve for x:
4.5 = 0.70 * 5 + 0.70 * x
4.5 = 3.5 + 0.70x
0.70x = 4.5 - 3.5
0.70x = 1
x = 1 / 0.70
x ≈ 1.43
Therefore, the chemist needs to add approximately 1.43 gallons of distilled water to 5 gallons of acid to obtain a 70% pure tannic acid solution.
To learn more on equation click:
brainly.com/question/24169758
#SPJ2
Each year, the number of students taught by Mr. Wright increases by 2. The first year, he taught 18 students. The total number of students taught after 25 years can be represented using the expression . How many students has Mr. Wright taught in 25 years?
450
500
1,050
2,100
Answer:
Mr. Wright taught 1,050 students in 25 years.
Step-by-step explanation:
Given,
The number of students Mr. Wright taught = 18,
Also, every year the number of student is increased by 2,
So, in second year, the number of students = 18 + 2 = 20,
In third year = 20 + 2 = 22,
In fourth year = 22 + 2 = 24,
.............., so on,
Hence, we get an A.P. that shows the given situation,
18, 20, 22, 24, ............. till 25 years.....
First term, a = 18,
Common difference, d = 2,
And, number of terms, n = 25,
Hence, the total number of students that have been taught by him are,
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{25}=\frac{25}{2}[36+(25-1)2][/tex]
[tex]=\frac{25}{2}[36+24\times 2][/tex]
[tex]=\frac{25}{2}[36+48][/tex]
[tex]=\frac{25}{2}(84)[/tex]
[tex]=\frac{2100}{2}[/tex]
[tex]=1050[/tex]
Third option is correct.
(((FIND THE MEASUREMENT INDICATED IN EACH PARALLELOGRAM)))
Help please
Thanks
Answer:
LM=12
V =90
Step-by-step explanation:
4. If it is a parallelogram, the two sides have to be equal.
2x-6 = x+3
Subtract x from each side
2x-x -6 = x+3-x
x-6 =3
Add 6 to each side
x-6+6 = 3+6
x=9
LM =2x-6
= 2*9 -6
= 18-6
= 12
5.
<U + < T = 180 Adjacent corners in a parallelogram are supplementary
11x+2 + 12x-6 = 180
Combine like terms
23x -4 = 180
Add 4 to each side
23x-4+4 = 180+4
23x = 184
Divide by 23
23x/23 = 184/23
x=8
<V = <T Opposite corners in a parallelogram are equal.
<V = 12x-6
<V = 12(8) -6
<V = 96-6
<v =90
The question involves solving algebra and geometry problems related to parallelograms, focusing on transformations, coordinates, and area calculations to find the equation for y.
Explanation:The student is asked to solve a series of algebra and geometry problems related to the properties of a parallelogram. These include finding coordinates, proving algebraic expressions, computing distances, and determining areas. The goal is to find the equation for y given a series of transformations and conditions on a square that becomes a parallelogram. Important concepts include the area of a parallelogram, vector addition using the parallelogram rule, and the determinant relating to a change of basis in vectors.
For example, part (e) involves finding the area of the parallelogram by computing twice the area of triangle PQO, using PQ as the base of the triangle. Solving for y in part (f) by setting this area equal to 1 involves understanding the effects of transformation on geometrical shapes and employing algebra to arrive at the desired equation.
PLEASE HELP ME !! Carter has 3 statues of various sizes in his garden. Statue A is one foot taller than statue B. Statue is one-half of a foot taller than statue B. A) write an algebraic expression for the total combined height of statue A and c. (equations for statues A and C) B) If the total combined height of the 3 statues is 10 feet, find the height of statue B in inches.
Answer:
Step-by-step explanation:
Find the value of the permutation.
8P1 ?
Answer:
8P1 = 8
Step-by-step explanation:
Permutation
The number of elements can be selected from a set of elements.
Let r be the number of elements want to select and n be the set of elements.
It can be written as nPr
nPr = n!/(n - r)!
To find 8P1
n= 8 and r = 1
8P1 = 8!/(8-1)! = 8!/7! = (8 x 7!)/7! = 8
Therefore 8P1 = 8
On a car trip Sam drove m miles Kara drove twice as many miles as Sam and Darin drove 20 fewer miles than Kara in terms of m many miles did Darin drive
Answer:
Darin drove '2m - 20' miles.
Step-by-step explanation:
We are given that Sam drove 'm' no. of miles.
As, it is also given that Kara drove twice as many miles as Sam. Therefore we get that Kara drove '2m' no. of miles.
Now, it is given that Darin drove 20 miles fewer than Kara .i.e. Darin drove '2m - 20' no. of miles.
Hence, in terms of m, Darin drove '2m - 20' miles.
Huma, Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother such that Seema gets 12 of what Huma gets and Hubna gets 123 times Seema’s share. How much money do the three sisters get individually?
i need correct answer no signs used
Answer:
Huma's share =Rs x = Rs. 1.35392881
Seema's share =Rs. 12x = Rs (12 * 1.35392881) = Rs. 16.2471457
Hubna's share =Rs. 123*12x = Rs. (123*16.2471457) = Rs. 1998.39892
Step-by-step explanation:
Given :
Huma , Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother.
Seema gets 12 of what Huma gets
Hubna gets 123 times Seema’s share
To find : How much money do the three sisters get individually?
Solution :
Let Huma's share be Rs. x.
Since we are given that Seema gets 12 of Huma's share
⇒ Seema's share = Rs 12x.
Since we are given that Hubna gets 123 times Seema’s share
⇒Hubna's share = Rs. (123 * 12x) = Rs. 1476x.
We are given that they received together Rs. 2016 in total .
⇒[tex]x+12x+1476x= 2016[/tex]
⇒[tex]1489x= 2016[/tex]
⇒[tex]x = \frac{2016}{1489}[/tex]
⇒[tex]x = 1.35392881[/tex]
Thus Huma's share =Rs x = Rs. 1.35392881
Thus Seema's share =Rs. 12x = Rs (12 * 1.35392881) = Rs. 16.2471457
Thus Hubna's share =Rs. 123*12x = Rs. (123*16.2471457) = Rs. 1998.39892
Find the value of x such that PQ = QRwhere P, Q and Rare the pints (2, 5), (x, -3) and (7, 9) respectively.
Answer: x = 12.5
Step-by-step explanation:
P = (2, 5)
Q = (x, -3)
R = (7, 9)
[tex]d_{PQ}=d_{QR}[/tex]
[tex]d_{PQ}=\sqrt{(2-x)^2+(5+3)^2}, \quad d_{QR} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex]\sqrt{(2-x)^2+(5+3)^2} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex](2-x)^2+(5+3)^2 = (x-7)^2+(-3-9)^2[/tex]
[tex]4-4x+x^2+64 = x^2-14x+49+144[/tex]
[tex]4x+68 = -14x+193[/tex]
[tex]10x+68 = 193[/tex]
[tex]10x= 125[/tex]
x = 12.5
Which inequality best represents that ice cream at −3°C is cooler than ice cream at 1°C?
A. −3°C > 1°C
B.−3°C < 1°C
C. 1°C > 3°C
D. 1°C < −3°C
Answer: Choice B
"ice cream at -3 degrees C is cooler than ice cream at 1 degree C"
-3 is smaller than 1
-3 < 1
Keep the order the same even though 1 > -3 is also possible, but fortunately this isn't listed.
These triangles are similar. find Y and X
It these triangles are similar, then the sides of the triangles are in proportion:
[tex]\dfrac{y}{10}=\dfrac{y+4}{15}[/tex] cross multiply
[tex]15y=10(y+4)[/tex] use distributive property
[tex]15y=10y+40[/tex] subtract 10y from both sides
[tex]5y=40[/tex] divide both sides by 5
[tex]\boxed{y=8}[/tex]
[tex]\dfrac{x}{4}=\dfrac{6}{8}[/tex] cross multiply
[tex]8x=(4)(6)[/tex]
[tex]8x=24[/tex] divide both sides by 8
[tex]\boxed{x=3}[/tex]
Please explain your answer.
Answer:
x=4.4
Step-by-step explanation:
To get from A to B, the scale factor is 2.5, since 4*2.5 = 10
So, to get from B to A, you divide by 2.5.
11/2.5 = 4.4
Jian’s family sells honey from beehives. They collected 3,311 ounces of honey from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars. Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each. Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311 / 4 =827 R3. That rounds up to 828, and 828 multiplied by $5 is $4,140. Part A-Explain the error that Jian made when finding the amount of money his family could make if they use only 4-ounce jars. Enter your explanation in the space provided. Part B- Explain how to determine the money Jian’s family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation. Enter your answers and your explanation in the space provided.
Answer:
A. Jian rounded the number of 4-ounce jars to 828 which is wrong. There are only 827 jars that can be completely filled.
B. Total number of 6-ounce jars = 551
Total money earned from 6-ounce jars = $4408
Step-by-step explanation:
A. Jian's family's collection = 3311 ounces
Number of 4-ounce jars = [tex]\frac{3311}{4}[/tex]
= 827.75
Jian rounded it to 828 which is wrong. There are 827 jars that can be completely filled.
Cost per 4-ounce jar = $5.
Total cost = 827 × 5 = 4135
B. Now, number of 6-ounce jars = [tex]\frac{3311}{6}[/tex]
= 551.83
≅ 551 jars
Cost per 6-ounce jar = $8
Total cost = 551 × 8 = 4408
Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 50% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution? Gabe needs 30 liters for a 50% solution .
He also needs a ___ for a 70% solution . whats __?
Answer:
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Step-by-step explanation:
Equation:
acid + acid = acid
0.40x + 0.70(60-x) = 0.60*60
40x + 70*60 - 70x = 60*60
-30x = -10*60
x = 20 liters
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
In combining like terms, what do these equations equal?
1: 5+6(2x+3)-2x
2: 3(4x+8) + 3(2x-6)
3: (32-8x)
____
4
4: 24x+18
____
6
If you can, please explain it! Thanks!
Answer:
Look below. The answers are bolded!
Step-by-step explanation:
1. 10x + 23
5+6(2x+3)-2x
Distribute first!
5 + 12x + 18 -2x.
Now you can combine like terms.
23 + 10x
2. 18x + 6
3(4x+8) + 3(2x-6)
Distribute first!
12x + 24 + 6x - 18
Now you can combine like terms.
18x + 6
3. -2x + 8
(32-8x)
____ ___
4
Divide 32 and -8x by 4.
32/4 = 8
-8x/4 = -2x
-2x + 8
4. 4x + 3
24x+18
______
6
Divide 24x and 18 by 6
24x/6 = 4x
18/6 = 3
4x + 3
Find the value of
[tex] {x}^{i} [/tex]
for all x belongs to Real Numbers and i = √(-1).
Answer: cis (ln x) ; x > 0
Step-by-step explanation:
[tex]x^i[/tex]
[tex]= e^{ln(x^i)}[/tex]
[tex]=e^{i \ln(x)}[/tex]
= cos (ln x) + i sin (ln x)
AKA: cis (ln x)
NOTE: I found this following formula which you may find useful:
[tex]A^i = x + iy[/tex]
a train travels 160 km in 2 h what is the trains average speed in km/h
Answer:
80km/h
Step-by-step explanation:
we know that the train is 160 km in 2 hours we need to find how much is in 1 hour you divide 160÷2= 80 so it means that there is 80 km in 1 hour which is "80 km/h"
use the diagram to answer the questions
1. which ray is a bisector of ABC
A. BC
B. BD
C. BA
D. BF
2. what is GH
A. 5
B. 10
C. 15
D. 25
3. what is the value of y
A. 2
B. 4
C. 16
D. 20
Answer:
1. B. BD
2. C. 15
3. A. 2
Step-by-step explanation:
1. From the figure,
∠DAB = ∠DAC
Therefore, BD is the bisector of ∠ABC.
2. From the figure, IG = GH
3x = 5x - 10
10 = 5x - 3x
2x = 10
x = 5
So, GH = 5x - 10
= 5(5) - 10
= 25 - 10
= 15
Therefore, GH = 15.
3. From the figure,
∠DAB = ∠DAC
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 2
Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1
It's a vertical line. The slope of vertical line is undefined.
The equation of a vertical line is x = a (a - any real number).
Answer: Slope = undefinedEquation of line: x = -1Answer:
Slope = undefined
Step-by-step explanation:
A vertical STRAIGHT line that represents a slope is undefined.
you are a plumber installing a pipe the ratio of the outside diameter to the inside diameter is 1.5 to 1. you use a pipe with a 0.5 inch inside diameter what is the smallest diameter that you will need to drill to allow the pipes to pass through the wall
The smallest diameter needed to drill through the wall is 0.75 inches, which is calculated by multiplying the inside diameter of the pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). Always measure and plan ahead to avoid mistakes.
Explanation:The subject matter of this question is mathematics, specifically ratios. To find the smallest diameter you would need to drill into the wall, you would need to multiply the inside diameter of your pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). So, 0.5 inches * 1.5 = 0.75 inches.
This means, to allow the pipes to pass through the wall, you will need to drill a hole at least 0.75 inches in diameter. This is assuming the wall is thin enough that the entire length of the pipe that needs to pass through the wall is less than the thickness of the wall.
Remember, it's always better to pre-measure and plan ahead to avoid unnecessary work and potentially costly mistakes.
Learn more about Ratio here:https://brainly.com/question/32531170
#SPJ3
At the popular restaurant Fire Wok,
55% of guests order the signature dish.
What fraction of guests order the signature dish?
Answer:
11/20
Step-by-step explanation:
Answer: [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.
Step-by-step explanation:
Since we have given that
Percentage of guest who order the signature dish = 55%
Total percentage = 100
We need to find the fraction of guests order the signature dish.
So, Fraction of guests order the signature dish is given by
[tex]\dfrac{\text{Percentage of guest order the signature dish}}{\text{Total percentage}}\\\\=\dfrac{55}{100}\\\\=\dfrac{11}{20}[/tex]
Hence, [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.
Dianna earns $8.50 an hour working as a lifeguard write an equation to find Dianna’s money earned?
An equation that expresses a mathematical rule or relationship is a ___.
proportion
conversion factor
formula
ratio
Answer:
formula
Step-by-step explanation:
3rd option is correct which is formula.
What is a formula ?
A mathematical relationship or rule which expressed only in symbols and which is the connection between two or more variable.
What is the correct option ?An equation that expresses a mathematical rule or relationship is a formula.
Learn more about Formula here :
https://brainly.com/question/11853945
#SPJ2
Your parents are renting an apartment for you when you go away to college. An annual contract is $502.00/month with a 2-month penalty if you break the lease. The month-to-month contract is $615.00/month. How much is the difference in payments if you stay the whole year?
Answer:
The month-to-month contract will cost an extra $1356.
Step-by-step explanation:
"An annual contract is $502.00/month with a 2-month penalty if you break the lease."
If you stay the whole year, and you pay $502 per month, you pay 12 * $502 = $6024 for the entire year.
"The month-to-month contract is $615.00/month."
If you stay the entire year, you pay 12 * $615 = $7380.
The difference is $7380 - $6024 = $1356
the sum of two numbers is 76. The difference is 24. Find the two numbers doing the elimination method
Answer:
50 and 26
Step-by-step explanation:
Make an equation! That makes it much simpler and has helped me a lot.
x+x-24=76
Combine like terms
2x+24=76
Add 24 on both sides
2x=52
Divide both sides by 2
x=26
72-26=50
To check that their difference is correct, subtract 26 from 50
50-26=24
Hope this helps!
A jet plane can travel 567 miles per hour. How many mile can it travel in 4hour
Answer: 2268 miles
Step-by-step explanation: 1 hour = 567 miles
4 hours= n miles
multiply 567 miles by four hours
= 2268 miles
Answer:
2304
Step-by-step explanation:
567 x 4
2t + 15 = 40 – 3t please solve
Answer:
t=5
Step-by-step explanation:
Add 3t to the other side to cancel it out
2t+3t+15=40
Subtract 15 to the other side to cancel it out
2t+3t=40-15
Simplify
5t=25
t=5
How do I do this please dumb this down
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept fprm is
y = mx + b ( m is the slope and b the y-intercept )
y = [tex]\frac{5}{4}[/tex] x - 4 is in this form
with m = [tex]\frac{5}{4}[/tex] and b = - 4
Plot the point (0, - 4)
using the slope add 5 to the y-coordinate and 4 to the x-coordinate
(0, - 4 ) → (0 + 4, - 4 + 5) → (4, 1) ← point on the line
Plot the points (0, - 4) and (4, 1) and draw a straight line through them to obtain a sketch of the graph
What is the geometric mean of 5 and 4
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Geometric mean of two numbers of the square root of their product:
[tex]\sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}[/tex]
The geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
What is the geometric mean of two numbers?The Geometric mean of the two numbers formula is defined as the square root of the product of 2 numbers.
The following formula is used to calculate the geometric mean;
[tex]\rm Geometric \ mean = \sqrt{a \times b}[/tex]
Where a is the first term and b is the second term.
Therefore,
The geometric mean of 5 and 4 is;
[tex]\rm Geometric \ mean = \sqrt{a \times b}\\\\a=5 \ and \ b=4\\\\\rm Geometric \ mean = \sqrt{5 \times 4}\\\\\rm Geometric \ mean = \sqrt{20}\\\\\rm Geometric \ mean = 2\sqrt{5}[/tex]
Hence, the geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
To know more about the Geometric mean click the link given below.
https://brainly.com/question/23483761
Mr. Geyer dog weighs 32.01 pounds if he goes on a die and loses 5.89 pounds how much will he weigh
Answer: 27.12
Step-by-step explanation:
32.01
-5.89
27.12
Name the angle in 2 different ways and name the 2 rays from the diagram below please show work
Answer:
3) TB and NT
4) ∠KLM and ∠MLK
Step-by-step explanation:
3) those two rays intersect to form the angle shown in the diagram
4) an angle can always be named from left to right or right to left as long as the middle letter is always the vertex of the angle
What is the LCD of 4/7 and 1/2 ? get this right you will be marked brainlest dont put random anwsers!
Answer:
14
Step-by-step explanation:
The LCD is the LCM of the denominators, 7 and 2. Since these numbers have no common factors, their LCM is simply their product:
... 7·2 = 14