A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the teacher mix together to get 105 ML of 60% sugar solution for an experiment
70 ML of the 50% solution and 35 ML of the 80% solution
35 ML of the 50% solution and 70 ML of the 80% solution
70 ML of the 50% solution and 70 ML of the 80% solution
35 ML of the 50% solution and 35 ML of the 80% solution
the length of a rectangle is given by 2t+1 and its height is t^(1/2), where t is time in sec. Find the rate of change of the area with respect to time
What is the maximum number of intersection points a hyperbola and a circle could have?
A. 4
B. 3
C. 1
D. 2 ...?
Answer: A. 4
Step-by-step explanation:
The characteristic equation of a circle is
[tex]x^2+y^2=r^2[/tex]
The characteristic equation of a hyperbola is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
The intersection points will be obtained as the solution of the both characteristic equations.
[tex]x^2+y^2=r^2[/tex].......(1)
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex].............(2)
⇒[tex]y^2=r^2-x^2[/tex].....(from 1)
put this in (2)
[tex]\frac{x^2}{a^2}-\frac{r^2-x^2}{b^2}=1[/tex]
⇒[tex]y^2=r^2-x^2\\\frac{x^2}{a^2}+\frac{-x^2}{b^2}=1+\frac{r^2}{b^2}[/tex]
⇒[tex]y^2=r^2-x^2\\x^2(\frac{1}{a^2}+\frac{1}{b^2})=1+\frac{r^2}{b^2}[/tex]
⇒[tex]y^2=r^2-x^2\\x^2(\frac{a^2+b^2}{a^2b^2})=\frac{b^2+r^2}{b^2}[/tex]
[tex]\Rightarrow\ x^2=\frac{a^2(b^2+r^2)}{a^2+b^2}\\y^2=\frac{b^2(r^2-a^2)}{a^2+b^2}[/tex]
So there are 2 different values of x and two different values of y, thus the maximum number of intersection points is 4.
Convert 11-4x=(3x-2)^2 1 to standard form?
Mark and John were sharing the $10 cost to rent some video games with another friend. Mark paid $3, John paid of the total, and their friend paid the rest. Who paid the most towards the rental?
John paid the most towards the rental.
Explanation:To determine who paid the most towards the rental, we need to find out how much each person paid. Mark paid $3 and John paid <percentage> of the total. Their friend paid the remaining amount. Since the total cost to rent the video games was $10, we can calculate how much John paid by subtracting what Mark paid from $10 and finding the percentage of that remaining amount.
Subtracting $3 from $10 gives us $7. Since John paid the majority, we can say that he paid 70% of the total. Therefore, John paid the most towards the rental.
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What is the greatest common factor of 84 and 108?
Hello. Im having problems in Geometry programming and I was wondering if there is anyway for someone to help me
Number 7. I need to write a ladder diagram
A-Team Corporation issued 1,000 shares of $5 par value stock for land. The stock is actively traded at $9 per share. The land was advertised for sale at $10,500. The land should be recorded at:
A.$4,000.
B.$5,000.
C.$9,000.
D.$10,500.
543,982 rounded to the nearest thousand
AB is tangent to the circle at B m< A = 14 and mBC = 112 (The figure is not drawn to scale.
a.Find x
b.Find y.
a. The value of x ≈ 60°
b. The value of y ≈ 93°
The relevant relations are ...
external angle A is half the difference of intercepted arcs BC and BD
inscribed angle y° is half the measure of intercepted arc CD
the sum of arcs of a circle is 360°
Using these relations, we have ...
(a) A = (BC -x°)/2
x° = BC -2A = 112° -2(27°)
x° = 58°
(b) y° = CD/2 = (360° -BC -BD)/2 = (360° -112° -60°)/2
y° = 91°
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Which must be true in order for the relationship △ZYV ~ △XWV to be correct?
∠Z ≅ ∠X and ∠W ≅ ∠Y is the correct answer
D
Answer correct for brainliest and also a thanks ! Don't answer if you don't know it please . CHOOSE ALL THAT ARE CORRECT .
Answer choices :
A. QP
B. EJ
C. PR
D. RA
E. TQ
2. A bowling alley charges $3.00 to rent shoes and $1.50 per game bowled.
if Jane has 5 pairs of pants and 7 shirts, how many different combinations of pants and shirts are possible?
What is 2840 divided by 6 in long division
PLLEEAASSEE HELP ME!!!!! 20 POINTS AND BRAINLIEST ANSWER
Holly made fruit punch for an office party a few months ago; she used 1 gallon of strawberry juice and 3 gallons of watermelon juice, which cost her a total of $8. For today’s party, she used 3 gallons of strawberry juice and 2 gallons of watermelon juice, spending a total of $10. How much does a gallon of each type of juice cost? Write a system of equations to describe the situation and solve using elimination. (use x for strawberry juice and y for watermelon juice)
What is the volume of a rectangular prism that has a length, width, and height of 1/2 m, 1/4 m, and 2/3 m, respectively?
A young equestrian loved to ride her horse all day long, dreaming of the day she would ride in the Kentucky Derby. One day in early April, she left home at 10:00 am and rode her stallion at a nice, steady 10 miles per hour away from her house. At noon a call came in from the Derby saying she was in! Her father immediately jumped on his scooter to try and track her down and tell her the good news. Riding at a breezy 15 miles per hour, at what time will her father catch up to her?
The equestrian's father will catch up to her at 2:00 pm by using the concept of relative speed and calculating the time it will take for him to close the gap between them.
Explanation:The student's father will catch up to the equestrian at 2:00 pm. To solve this problem, we can use the concept of relative speed. The equestrian starts riding away from the house at 10 miles per hour (mph) at 10:00 am. By noon, when the father starts chasing her on his scooter at 15 mph, the equestrian is already 20 miles away (2 hours × 10 mph).
Since the father's speed is 15 mph and the equestrian's speed is 10 mph, the father is closing the gap at a speed of 15 mph - 10 mph = 5 mph. To cover the 20 miles gap, the father will need 20 miles / 5 mph = 4 hours. Therefore, if the father starts at noon, he will catch up to her at 4 hours later, which is 2:00 pm.
Gina invests $1,677 in an account paying 8.61% simple interest annually. How much interest has Gina gained after six years? a. $668.65 b. $240.65 c. $866.34 d. $2,543.34
Answer:
Option (c) is correct.
The interest gained by Gini in 6 years is $ 866.34
Step-by-step explanation:
Given: Gina invests $1,677 in an account paying 8.61% simple interest annually for 6 years.
We have to calculate the interest gained by Gina in 6 years.
Using formula for simple interest
[tex]S.I.=\frac{P\times I\times T}{100}[/tex]
Where,
S.I = simple interest
P is principal
R is interest rate
T is time
Given : P = $ 1677
R = 8.61%
T = 6 years
Substitute, we get,
[tex]S.I.=\frac{1677\times 8.61\times 6}{100}[/tex]
Simplify, we get,
S.I. = $ 866.3382
Rounding off to nearest hundred we get, Interest is $866.34
Thus, the interest gained by Gini in 6 years is $ 866.34
Gina has gained $866.34 in interest after six years.
To find the interest gained, we can use the formula: Interest = Principal * Rate * Time. In this case, the principal is $1,677, the rate is 8.61%, and the time is 6 years. Plugging these values into the formula, we get: Interest = $1,677 * 0.0861 * 6 = $866.34. Therefore, Gina has gained $866.34 in interest after six years.
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The price of a coat is $114 before sales tax . The sales tax is 7%. Find the total cost of the coat
Final answer:
To calculate the total cost of the coat with a 7% sales tax, multiply the cost of the coat by 0.07 to get the sales tax amount of $7.98, then add it to the original cost for a total of $121.98.
Explanation:
To find the total cost of a coat that costs $114 with a 7% sales tax, you first need to calculate the amount of sales tax by converting the percentage to a decimal. Then multiply the decimail by the price of the coat to get the sales tax amount.
Here is the calculation for sales tax:
$114 × 0.07 = $7.98
Next, add the sales tax to the original price to find the total cost:
$114 + $7.98 = $121.98
So, the total cost of the coat, including sales tax, is $121.98.
Which expressions are equivalent to the one below? Check all that apply.
10x
A. 50x/5x
B. 10 • 10x - 1
C. 10 • 10x + 1
D. 50x/5
E. (50/5)x
F. x5
The answer is A, B, and E.
Just plot write the equation in a graphing calculator which shows they are the same.
Mary and tom were buying a present for their mother on mothers day. mary spent $12 and tom spent $28 if they wanted to share the cost equally, how much money does mary owe tom?
The solution set for -p^2 − 11p = 0 is
Answer:
the solution set is {0,-11}
Step-by-step explanation:
The equation is [tex]-p^2-11p=0[/tex]
The GCF of the left hand side of the expression is -p. Hence, factored out the GCF
[tex]-p(p+11)=0[/tex]
Now, apply the zero product property, we get
[tex]-p=0,p+11=0[/tex]
Now, solve the equations for p
[tex]p=0,p=-11[/tex]
Thus, the solution set is {0,-11}
The total fare for two adults and three children on an excursion boat is $14. If each childs fare is one half of each adults fare, what is the adult fare ...?
Answer:
$4
Step-by-step explanation:
In order to solve this problem you just have to create an equation, and it´s very simple, each kid ticket will be represented by the letter "x", and as we know a kid´s ticket is worth half what is worth an adult ticket, so the adult ticket = 2 kids tickets=2x
So we know that there are 2 adults and three kids, and the totla was $14, we create our equation:
[tex]2 adults+3kids=14\\2(2x)+3x=14\\4x+3x=14\\7x=14\\x=\frac{14}{7}\\ x=2[/tex]
Now we know that the kids ticket is $2, so the adult ticket would be twice that, $4 is the price of the adult ticket.
What does 4.87×10^12 equal?
Sally went into the local dollar store because they have so many deals .the following deal that she was debating is 4 bars of soap that cost $5 .what would 8 bars cost her
use the remainder theorem to divide 3x2+10x-8 by x-2 what is the remainder
Answer:
Remainder is 24.
Step-by-step explanation:
Given dividend = 3x² + 10x - 8
and divisor = x - 2
To find: Remainder using Remainder theorem.
Remainder Theorem states that let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).
Let p(x) = 3x² + 10x - 8
using remainder theorem,
Remainder = p(2) = 3 × 2² + 10 × 2 - 8
= 3 × 4 + 20 - 8
= 12 + 12
= 24
Therefore, Remainder is 24.
solve the seperable equation:
dy/dx= (sec^2)y/1+x^2
Factor 25x2 – 16.
A. (5x – 4)2
B. (5x + 1)(5x – 1)
C. (5x + 4)2
D. (5x + 4)(5x – 4)
Answer:
D. (5x + 4)(5x – 4)
Step-by-step explanation:
This is the difference of two squares
[tex]a^{2} - b^{2} = (a-b)(a+b)\\[/tex]
Following from above,
25[tex]25x^{2} -16[/tex]
Taking the elements of the expression
[tex]25x^{2} = 5^{2}x^{2}[/tex]
Using the law of indices,
[tex]a^{2} b^{2} = (ab)^{2}[/tex]
[tex]25x^{2} = (5x)^{2}[/tex]
[tex]16 = 4^{2}[/tex]
Therefore,
[tex]25x^{2} -16[/tex] = [tex](5x)^{2} - 4^{2}[/tex]
=[tex](5x-4)(5x+4)[/tex]
Hence the correct answer is Option D.