A = 10% alcohol solution
B = 55% alcohol solution
we know we have 75 mL of A, that means A itself since it's 10% alcohol, really only has 75 * (10/100) = 7.5 mL of alcohol, likewise the B solution has say "x" mL, so alcohol wise it only has "x" * (55/100) = 0.55x, and we have a final mixture we need of say "y" mL at 30% alcohol.
[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{mL of }}{amount}\\ \cline{2-4}&\\ A&75&0.10&7.5\\ B&x&0.55&0.55x\\ \cline{2-4}&\\ mixture&y&0.30&0.3y \end{array}~\hfill \begin{cases} 75+x=y\\\\ 7.5+0.55x=0.3y \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\stackrel{\textit{using the 1st equation}}{75+x=y}\hspace{12em}\stackrel{\textit{substituting on the 2nd equation}}{7.5+0.55x=0.3(75+x)} \\\\\\ 7.5+0.55x=22.5+0.3x\implies 0.55x=15+0.3x\implies 0.25x=15 \\\\\\ x=\cfrac{15}{0.25}\implies {\Large \begin{array}{llll} x=60 \end{array}} ~mL[/tex]
The PTA prepared 10 gallons of punch to serve at their first meeting. If each serving is eight ounces, how many people can be served?
Based on mathematical operations, the number of people that 10 gallons of punch can serve is 192 persons.
How is the number determined?The number of people can be determined using mathematical operations of multiplication based on converting the gallons to ounces and division.
The number of gallons of punch to serve at the first meeting = 10 gallons
The quantity of punch per serving = 8 ounces
1 gallon = 153.722 ounces
10 gallons = 1537.22 ounces
The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).
Thus, mathematically, from the 10 gallons of punch, the PTA can serve 192 persons.
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Write as an inequality. Do not solve.
Yellow Cab charges a flat rate of $3.00 plus $0.50 per mile. Raven
has $20.00 to spend on a cab ride. Write an inequality that expresses how
many miles Raven can travel under her limit.
The product of 8 and y is less than 21.
Raven can travel 5.71 miles or less under her limit.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions. If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
Let x b the number of miles Raven travels, we can write an expression relating the amount he spends. So there:
3.00 + 0.50= 3.50
Consider that total cost per mile be less than equal to the amount the Raven can spend:
3.50x ≤ 20
We can determine x;
x ≤ 5.71
Therefore, Raven can travel 5.71 or less under her limit.
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PLEASE HELP ME ! due tonight , Will make you a brainlist if you give me the correct answer .
Answer:
y=3/2x+3
Step-by-step explanation:
gradient is dy/dx
so up 3 and across 2
3/2
crosses at 3
Answer:
y=-3/2x+3
Step-by-step explanation:touches y axis at 3 and negative 3/2 slope
Draw the graph of each circle given its equation below.
Step 1:
First, write the general equation of a circle
[tex]\begin{gathered} (x-a)^a+(y-b)^2=r^2 \\ r\text{ is the radius} \\ (a,\text{ b) is the center} \end{gathered}[/tex]Step 2:
Question 1
[tex]\begin{gathered} x^2+y^2\text{ = 121} \\ x^2+y^2=11^2 \\ \text{radius r = 11} \\ \text{center = (0 , 0)} \end{gathered}[/tex]Question 2
[tex]\begin{gathered} (x-2)^2+y^2\text{ = 64} \\ (x-2)^2+y^2=8^2 \\ \text{Center = (2, 0)} \\ r\text{ = 8} \end{gathered}[/tex]Question 3
[tex]\begin{gathered} (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = 36} \\ (x\text{ + }\frac{3}{2})^2\text{ + (y + }\frac{5}{8})^2\text{ = }6^2 \\ \text{Center = (-}\frac{3}{2}\text{ , -}\frac{5}{8}) \\ r\text{ = 6} \end{gathered}[/tex]Question 4
[tex]\begin{gathered} (x-1)^2+(y+7)^2\text{ = 9} \\ (x-1)^2+(y+7)^2\text{ = }3^2 \\ \text{Center = (1, -7)} \\ r\text{ = 3} \end{gathered}[/tex]Question 5
[tex]\begin{gathered} (x+8)^2+(y-3)^2\text{ = 7} \\ (x+8)^2+(y-3)^2\text{ = (}\sqrt[]{7})^2 \\ \text{Center = (-8, 3)} \\ \text{radius r = }\sqrt[]{7} \end{gathered}[/tex]solve the following equation 23 + 23 = 5y + 11
Answer:
7
Step-by-step explanation:
Since 23 + 23 = 46
We just have to multiply 5 by something. 11 + 5 x 7 = 46
Y is = 7
btw im in middle school
your answer could be 72
i did a lot of math
and if you have what y means to me its y = 3 so i did 5*3
b/c=a solve for c b nb
Answer:
b = ca
c = ba
Step-by-step explanation:
The larger of two numbers is 1 more than 3 times the smaller. Their sum is 65. Find the numbers.
The larger number is 49 and the smaller number is 16.
What are the numbers?The first step is to form a linear expression that represents the larger number.
Let the smaller number be represented with y
The larger number is represented with this linear expression : 1 + 3y
The sum of the two numbers : 1 + 3y + y = 65
Take the following steps to determine the value of the smaller number:
Combine similar terms: 65 - 1 = 3y + y
Add similar terms together: 64 = 4y
Divide both sides by 4: y = 64 / 4
y = 16
Larger number = 1 + 3(16)
1 + 48 = 49
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Alvin's
age Is three times Elga's age. The sum of their ages Is 96. What Is Elga's age?
years old
Answer: Elga is 16 years old
Step-by-step explanation: so first you divide 96 by 2 and get 48, 48 divided by 3=16,
please mark brainliest if this helps :)
Work Shown:
x = Elga's age
3x = Alvin's age since he is 3 times older
x+3x = 4x = sum of their ages
4x = 96
x = 96/4
x = 24 is Elga's age
3x = 3*24 = 72 is Alvin's age
Check: 24+72 = 96 which confirms the answer.
please help asap
during a snow storm the temperature drops from 0 degress f to - 12 degress f in 3 hour. on averge by how many degress is the temperature changing per hour?
A, -4f
B. 12f
C. 15f
D. -9f
The average change per hour is: -4 F/h
So the temperature decreases by 4 degrees Fahrenheit each hour.
How to get the average change in temperature?
To get the average change in degrees per hour, we need to take the quotient between the change in temperature and the number of hours in which this happens.
We know that initially the temperature is 0F
The final temperature is -12F
and this happens on an interval of 3 hours, then the average change per hour is:
(-12F - 0F)/3h = -12F/3h = -4 F/h
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A water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. To monitor this, they take 2 oz. Of water at 37 locations every hour, measure the ph at each of those locations, and find their average. If the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8. 5 and a standard deviation of 0. 22. If the ph level of the reservoir is ok, what is the probability that the sample average is less than 8. 42?.
P(X < 8.4)
= P(Z < (8.4 - 8.5) / (0.22 / sqrt(37)))
= P(Z < -2.76 ) = 0.0029
So the probability is 0.0029
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Math To Do, -Ready
Interactive Practice: Work with Scientific Notati
-) Multiply. Write your answer using scientific notation.
(2 × 10 ) × (3.1 × 10¹⁰) = ||
X ?
6.2 × [tex]10^{11}[/tex] is the result after multiplying the terms (2 × 10 ) × (3.1 × 10¹⁰).
We are provided with the equation mentioned below:
(2 × 10 ) × (3.1 × 10¹⁰) equation 1
We were asked to multiply the terms mentioned in the above equation using scientific notation. The steps to simplify the above mentioned equation are written below;
(2 × 10 ) × (3.1 × 10¹⁰)
Separately write similar terms first as shown below,
= ( 2 × 3.1 ) × ( [tex]10^{1}[/tex] × [tex]10^{10}[/tex] )
Now multiply the similar terms as written below;
= 6.2 × [tex]10^{(1 + 10)}[/tex]
Add powers of 10, we get
= 6.2 × [tex]10^{11}[/tex]
Thus, the solution of the given equation is 6.2 × [tex]10^{11}[/tex].
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Read the following actions and decide if they are responsible (R) or irresponsible(IR).
1. checking my credit score:
2. paying a credit card bill one day late:
3. listing expenses in a budget:
4.making decisions without all of the information:
5.purchasing something because it is on sale:
6.writing some goals:
7.researching what a mutual fund is:
8.making financial decisions without discussing it with your spouse:
9.finding a savings account with a great interest rate:
10. looking for the cheapest price for an item:
HELP ME PLEASE!!!!!!
Answer:
1. R
2. IR
3. R
4. IR
5. IR
6. R
7. R
8. IR
9. R
10. R
Step-by-step explanation:
Note on #5: purchasing something on sale that you were already going to buy would be responsible, but not simply BECAUSE the item is on sale and you were not already needing to purchase it.
a high school has 48 players on the football team. the summary of the players' weights is given in the box plot. approximately, what is the percentage of players weighing greater than or equal to 232 pounds?
The proportion of players weighing more than or equatable to 220 pounds is 50%.
What is termed as the quartile?The dataset is divided into four groups by dividing the data into three points: lower quartile, midpoint, and upper quartile.The quartiles, along with the data set's minimum and maximum values, divide a collection of observations in to the four sections, each chosen to represent 25% of the observations.Based on the information provided
There are 48 players in total.
Based on the box plot;
158 pounds is the minimum weight.
Q1 = 185, which represents 25% of the information below 185 pounds.
The second quartile Q2 = 220 pounds, which represents 50% of the information below 220 pounds.
The third quartile (Q3) = 232, representing 75% of the information below 232 pounds.
248 pounds is the maximum weight.
In this case, 220 is the middle number and represents the median.
50% of the information are located on both the left and right sides of the median.
As a result, the proportion of players weighing more than or equatable to 220 pounds is 50%.
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how does y sqaured eqaul 169
Answer:
13
Step-by-step explanation:
A number squared is just a number multiplied by itself.
13 x 13 is 169.
Answer is 13.
Hope this helps!
P.S, Brainliest, please, thanks!
Two planes left the same airport traveling in opposite directions. The
lirections. The first plane left at 9:00 a.m. and 2.25 hours later, the two planes
were 1825 miles apart. The second plane left at 10:00 a.m. and its average
average rate. Let x represent the first plane's average rate.
rate was 108 miles per hour slower than the first plane's
What was the first plane's average rate?
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the first plane's average rate in the second box.
Answer: x=560 miles per hour
Step-by-step explanation:
[tex]\displaystyle\\2.25=\\\\2\frac{1}{4}= \\\\\frac{2*4+1}{4}=\\\\\frac{8+1}{4}=\\\\\frac{9}{4}\ hours[/tex]
The second plane left at 10:00 a.m. so, him fly was 1.25 hours:
[tex]\displaystyle\\1.25=\\\\1\frac{1}{4}=\\\\\frac{1*4+1}{4}=\\\\\frac{4+1}{4} =\\\\\frac{5}{4} \ hours[/tex]
Let x represent the first plane's average rate
Hence, (x-108) represent the second plane's average rate
So,
[tex]\displaystyle\\\frac{9}{4}x+\frac{5}{4} (x-108)=1825\ \ \ \ (1)\\[/tex]
Multiply both parts of the equation by 4:
[tex]9x+5(x-108)=7300\\\\9x+5x-540=7300\\\\14x-540+540=7300+540\\\\14x=7840[/tex]
Divide both parts of the equation by 14:
[tex]x=560\ miles/hour[/tex]
Eric orders 3 large cheese pizzas. There is a $2 delivery fee for each pizza. He pays a total of $42. Which equation can be used to find the price, r, of each pizza?
we have that he paid 4 dollars due the delivery. So each pizza costs
[tex]\frac{38}{2}=19[/tex]so the equation to find the price r is
[tex]r=\frac{42-4}{2}[/tex]PLEASE HELP FASTTT ILL MARK BRAINLIEST
Answer:
[tex]2\sqrt{2}[/tex]
Doing RSM I see... lol gl. (tell me if this is wrong, I'll correct it if it is) :]
Step-by-step explanation:
h(6)=2
g(2) = [tex]\sqrt{2\\}[/tex]
f(sqrt2) = [tex]2\sqrt{2}[/tex]
:]
WILL GIVE BRAINLY
PLS ANSWER QUICK
Use properties to evaluate [tex]-5x14 ÷ \frac{3}{4} x 15[/tex]
A. -350
B. -1400
C. 350
D. 1400
The expression has a value of -1400 when evaluated
How to evaluate the expression?From the question, the expression is represented as
-5 x 14 ÷ 3/4 x 15
Start by evaluating the product of -5 and 14
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 ÷ 3/4 x 15
Next, we rewrite the quotient as products
So, we have the following equation represented as
-5 x 14 ÷ 3/4 x 15 = -70 x 4/3 x 15
Divide 15 by 3
So, we have
-5 x 14 ÷ 3/4 x 15 = -70 x 4 x 5
Continue by evaluating the product of -70 and 4
So, we have the following equation
-5 x 14 ÷ 3/4 x 15 = -280 x 5
Lastly, we have
-5 x 14 ÷ 3/4 x 15 = -1400
Hence, the value of the expression is -1400
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five hundred feet of fencing is available for a rectangular pasture alongside a river, the river serving as one side of the rectangle (so only three sides require fencing). find the dimensions yielding the greatest area
The dimensions yielding the greatest area (125*250).
What is a dimensions?
The minimal number of coordinates required to specify any point within a dimensional vector space (or object) is known as the dimension in physics and mathematics. Because only one coordinate is required to specify a point on a line, such as the point at 5 on the a number line, a line is said to have one dimension (1D). Because two coordinates are required to specify a point on a surface, such as the perimeter of a sphere or cylinder, it is referred to as having a dimension of two (2D). For instance, a point on the a sphere's surface requires both a latitude and a longitude to be located. A two-dimensional space just on plane is referred to as a Euclidean space.
The perimeter is 2a+b = 500
b= 500-2a
Max are is A = ab
A= a(500-2a)
= 500a - 2[tex]a^{2}[/tex]
for max value
a = -y/2x
= -500/2(-2)
= 125 feet
and b = 250 feet
Greatest area (125*250) = 31250 feet²
Hence dimensions yielding the greatest area (125*250).
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given the quadratic equation below, evaluate f(-1):f(x)=(x-2)^2+3
The evaluation of f(-1) given the quadratic equation f(x)=(x-2)^2 + 3 gives 12
What will the value of the function be?Given the quadratic equation f(x)=(x-2)^2 + 3. To evaluate to f(-1), we will substitute x = -1 into the equation:
Since f(x)=(x-2)^2 + 3
Therefore f(-1) = (-1 - 2)^2 + 3
= (-3)^2 + 3
= 9 + 3 = 12
Therefore, the value of c is 12. This shows the concept of functions and equations.
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Is √3 rational?
I’m trying to figure out is the question above rational
Answer:
The square root of 3 is an irrational number if that's what you were asking
Suppose Alex wants to kick a ball over a 10-foot fence. Assuming that gravity has no effect, at what angle would he have to kick the ball if he were standing 6 feet away from the fence?
a.
36.9°
c.
53.1°
b.
59.0°
d.
31.0°
You would take Alex's distance from the fence, which is 10 feet, and the length of the fence to get the angle.
Finding the angle using the right triangle's trig formulas, sine, cosine, or tangent
neighboring side = 6 feet
obverse side = 10 feet
employ a tangent because
[tex]tan^{-1}\frac{opposite}{adjacent} = tan^{-1}\frac{10}{6} = 59.0[/tex]
About Right triangle's
The formula for a right triangle's area, perimeter, and hypotenuse length are all included in the formula for a right triangle.
In geometry, there are several figure kinds that are distinguished from one another by their unique characteristics. A triangle is one of the shapes they frequently use. A triangle is a closed, three-sided polygonal shape. It has three vertices and three sides that contain the triangle's three interior angles. A triangle's three inner angles always add up to 180 degrees.
Equilateral, isosceles, scalene and right-angled triangles are the most typical triangle types we examine. The right triangle formula, commonly known as the right-angled triangle formulae, will be discussed in this section.
Any interior angle that is 90 degrees in length is said to be in a right triangle. It should be remembered that only one of the three angles may be a right angle because the total interior angle of a triangle is 180 degrees.
Continue reading: Right Angle Triangle
The triangle is referred to as an isosceles right-angled triangle if the other two angles are equal, or 45 degrees each. A scalene right-angled triangle, on the other hand, results from the other two angles being uneven.
Trigonometry is where right-angled triangles are used the most frequently. In reality, trigonometry's foundation is the relationship between its angles and sides.
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12. x=lyl with inputs x = 1, x = 2, and x
3
If x=lyl with inputs x = 1, x = 2, and x = 3 then y = ±1, y = ±2, and y = ±3.
To solve this problem we have to learn about the modulus operator and absolute value.
What is absolute value?
Absolute value is the distance of a number from zero.
Example: for -12, the distance from 0 is 12. Therefore 12 is the absolute value of -12.
What is the mod operator?
A Mod operator is a mathematical device that converts all types of integers into a positive integer or it finds the absolute value.
Now, we have to find values.
x=lyl Or, 1 = |y| or, we can say the absolute value of y is 1. y may be ±1x=lyl Or, 2 = |y| or, we can say the absolute value of y is 2. y may be ±2x=lyl Or, 3 = |y| or, we can say the absolute value of y is 3. y may be ±3To know more about absolute values visit,
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Choose the best initial step in solving the following system by substitution.
2x + 3y = –12
6x + y = 18
Answers:
1.Solve the first equation for x.
2.Solve the first equation for y.
3.Solve the second equation for x.
4.Solve the second equation for y.
Answer:
I think you have to first solve the first equation for y.
Answer choice: 3.
Step-by-step explanation:
Hope this helps! :)
division of fractions and mixed numbers in the real world the local preservation group is cleaning up a 3 3/5 km hiking trail twelve members sign up to help. to make the work easier, the leader of the group splits the trail into equal sections, one for each member. what length of trail is each member responsible for cleaning?
The length of trail is each member responsible for cleaning is 0.3.
Given,
In the real world the local preservation group is cleaning up a 3 3/5 km hiking trail twelve members sign up to help.
To find the length of trail is each member responsible for cleaning.
(Division of fractions)
Now, According to the question:
Based on the given condition
= [tex]3\frac{3}{5}[/tex] ÷ 12
= 18/5 ÷ 12
Convert into decimal
= 3.6 x 1/12
= 0.3
Hence, The length of trail is each member responsible for cleaning is 0.3.
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Connor left his house for work and was gone 4 hours. He spent a total of
hour driving to and from work and didn't go anywhere else. How long was he
at work?
A. 4 hours
B. 3 hours
c. 4 hours
D. 3 hours
HELP FAST GIVING HIGHEST AMOUNT OF POINT
Answer:
4 hours
Step-by-step explanation:
he was gone for 5 hours, he spent an hour driving.
5 - = 4 hours at work.
Answer:
4 hours
Step-by-step explanation:
says he was gone 4 hours, he was at work
Vistaprint offers the first 500 business cards for free. Then each additional set of 500 cards cost $9.99.
A. Write an equation that gives the total cosr (in dollars) of cards, C, in terms of the number (in groups of 500) of business cards, b, ordered.
B. Find the cost of buying 3500 business cards.
If the Vistaprint offers the first 500 business card for free and each additional set of 500 card cost $9.99
Part A
The equation that gives the total cost (in dollars) of card C, in terms of the number(in group of 500) of business cards b ordered is C = 9.99×b -9.99
Part B
The cost of buying 3500 business cards is $59.94
The Vistaprint offers the first 500 business cards for free
The cost of each additional set of 500 cards = $9.99
Part A
Consider the total cost of the card = C
Number of business card in group of 500 = b
Then the equation of the total cost of cards
C = 9.99×b -9.99
Part B
Total number of cards = 3500
Number of cards in group of 500 = 3500/500
= 7
The cost of buying 3500 business card = 9.99×7-9.99
= 69.93-9.99
= $59.94
Hence, If the Vistaprint offers the first 500 business card for free and each additional set of 500 card cost $9.99
Part A
The equation that gives the total cost (in dollars) of card C, in terms of the number(in group of 500) of business cards b ordered is C = 9.99×b -9.99
Part B
The cost of buying 3500 business cards is $59.94
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Is it possible for consecutive interior angles to be congruent?
No, It is not possible for consecutive interior angles to be congruent.
If the transversal line crosses the two lines as parallel to one another, the consecutive interior angles are supplementary rather than congruent and add up to 180 degrees.
Parallel internal angles are additional (the consecutive interior angles postulate) External angles that follow each other are supplemental (the consecutive exterior angles theorem) Congruent alternate interior angles (the alternate interior angles theorem)
What are consecutive interior angles?The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles. The term "consecutive" describes events that take place side by side. On the internal side of a transversal, two consecutive interior angles are situated next to one another.
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Find the average rate of change:
Input
1
2
3
4
5
Output
11
13
15
17
19
Average rate of change = 2
How to find the average rate of change?
Given:
Input(x) = 1, 2, 3, 4, 5
Output(y)= 11,13,15,17,19
We know,
Average rate of change = change in output/change in input
[tex]=\frac{y_1-y_2}{x_1-x_2}\\\\=\frac{11-13}{1-2} \\\\ =\frac{-2}{-1} \\\\=2[/tex]
What is average rate of change?
The average rate of change is a typical indicator of change over a period of time given in a function. It is equal to the difference between the function's input and output as a whole. It is a measurement of the average amount of change in the function per unit throughout that time. On the graph of the function, it is calculated from the slope of the straight line joining the interval's ends.To learn more about average rate of change, refer:
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rearrange the following so g is the main subject:
f+4(g-h)=x
Answer:
g=x-f+4h/4
Step-by-step explanation:
change of subject of formula
f+4(g-h)=x
f+4g-4h=x
4g-4h=x-f
4g=x-f+4h
g=x-f+4h/4
rate as brainliest