To obtain a 35% antifreeze solution, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze.
Explanation:To obtain a 35% antifreeze solution, you need to add a certain amount of water to 1 gallon of pure antifreeze. Let's assume that x gallons of water should be added. In a 35% antifreeze solution, the amount of antifreeze is 35% of the total solution. So, we can set up the following equation:
1 gallon of antifreeze = (35/100) * (1 + x) gallons of solution
Simplifying this equation, we get:
1 = 0.35 * (1 + x)
Now, let's solve for x:
Divide both sides of the equation by 0.35:
1/0.35 = 1 + x
2.857 = 1 + x
Subtract 1 from both sides of the equation:
2.857 - 1 = x
x = 1.857 gallons of water
Therefore, you need to add approximately 1.857 gallons of water to 1 gallon of pure antifreeze to obtain a 35% antifreeze solution.
Final answer:
To obtain a 35% antifreeze solution from 1 gallon of pure antifreeze, approximately 1.857 gallons of water needs to be added. This calculation is based on a simple concentration equation, resulting in the given ratio.
Explanation:
To calculate the amount of water to be added to 1 gallon of pure antifreeze to obtain a solution that is 35% antifreeze, we need to perform a simple concentration calculation.
We are starting with pure antifreeze, so it's 100% antifreeze. We want to end with a solution that is 35% antifreeze. Let's denote the amount of water added as x gallons. Because we are diluting the antifreeze, the total volume of the solution after adding water will be 1 gallon (the initial volume of the antifreeze) plus x gallons (the volume of water added).
The concentration of antifreeze after adding water is the volume of antifreeze divided by the total volume of the solution:
Concentration of antifreeze = Volume of antifreeze / Total volume of solution
Thus, 0.35 = 1 / (1 + x)
Multiplying both sides by (1 + x) and then by 0.35 we get:
1 = 0.35 * (1 + x)
Dividing by 0.35 and then subtracting 1:
x = 1 / 0.35 - 1
After calculating:
x ≈ 1.857 gallons
To obtain a 35% antifreeze solution, approximately 1.857 gallons of water should be added.
What is the justification for each step in solving the inequality?
−2(x+1)≥3x+8−2(x+1)≥3x+8
Select from the drop-down menus to correctly justify each step.
2nd picture is the dropdown box answers
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3427 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 65.75 feet per second and Plane B is gaining altitude at 35.5 feet per second.
How many seconds will pass before the planes are at the same altitude?
What will their altitude be when they're at the same altitude.
Three consecutive integers have a sum of 297 . Find the integers.
297 /3 = 99
99-1 = 98
99 +1 = 100
98 + 99 + 100 = 297
the numbers are 98, 99 , 100
Read the following statement: Line segment CD is congruent to line segment XY.
Which of the following is an equivalent statement?
-CD overbar is similar to XY overbar
- CD overbar is congruent to XY overbar
-CD overbar equals XY overbar
-CD overbar is an element of XY overbar
SOMEONE PLEASE HELP I HAVE A TEST IN 5 MIN!!
The statement which is equivalent to line segment CD is congruent to line segment XY is CD overbar is congruent to XY overbar.
What is a line?A line is made up of an infinite no. of points it can extend in both directions indefinitely.
We know a line has two subsets they are a ray and a line segment.
A ray is a type of line that has one initial point and the other end can extend indefinitely and a line segment is a type of line which has two endpoints.
Given a line, segment CD is congruent to line segment XY.
∴ [tex]\overline{CD}[/tex] ≅ [tex]\overline{XY}[/tex].
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Find the probability that the person is frequently or occasionally involved in charity work.
(a) The probability is [tex]\[\boxed{0.464}\][/tex]. (b) The probability is [tex]\[\boxed{0.763}\][/tex]. (c) The probability is [tex]\[\boxed{0.585}\][/tex]. (d) The probability is [tex]\[\boxed{0.921}\][/tex]. (e) No, because 205 females are frequently involved in charity work. The option (A) is correct.
To address the given questions based on the provided table, let's go through each question step-by-step:
(a) Find the probability that the person is frequently or occasionally involved in charity work.
First, we need the total number of people who are frequently or occasionally involved in charity work. This is the sum of people in the "Frequently" and "Occasionally" columns.
[tex]\[\text{Total frequently or occasionally involved} = 432 + 904 = 1336\][/tex]
Now, we divide this by the total number of people surveyed:
[tex]\[P(\text{frequently or occasionally involved}) = \frac{1336}{2881} \approx 0.464\][/tex]
So, the probability is [tex]\[\boxed{0.464}\][/tex].
(b) Find the probability that the person is female or not involved in charity work at all.
To solve this, we need to find the number of females and those not involved in charity work at all.
[tex]\[\text{Total females} = 1402\][/tex]
[tex]\[\text{Total not involved at all} = 1545\][/tex]
We need to subtract the overlap (females not involved in charity work) to avoid double-counting. From the table, the number of females not involved at all is 747.
[tex]P(\text{female or not involved at all}) = \frac{\text{Total females} + \text{Total not involved at all} - \text{Females not involved}}{\text{Total}}[/tex]
[tex]= \frac{1402 + 1545 - 747}{2881} = \frac{2200}{2881} \approx 0.763[/tex]
So, the probability is [tex]\[\boxed{0.763}\][/tex].
(c) Find the probability that the person is male or frequently involved in charity work.
[tex]\[\text{Total males} = 1479\][/tex]
[tex]\[\text{Total frequently involved} = 432\][/tex]
We need to subtract the overlap (males frequently involved) to avoid double-counting. From the table, the number of males frequently involved is 227.
[tex]P(\text{male or frequently involved}) = \frac{\text{Total males} + \text{Total frequently involved} - \text{Males frequently involved}}{\text{Total}}[/tex]
[tex]= \frac{1479 + 432 - 227}{2881} = \frac{1684}{2881} \approx 0.585[/tex]
So, the probability is [tex]\[\boxed{0.585}\][/tex].
(d) Find the probability that the person is female or not frequently involved in charity work.
[tex]\[\text{Total females} = 1402\][/tex]
[tex]\[\text{Total not frequently involved} = 2881 - 432 = 2449\][/tex]
We need to subtract the overlap (females not frequently involved) to avoid double-counting. From the table, the number of females not frequently involved is 1197 (450 + 747).
[tex]P(\text{female or not frequently involved})=\frac{1402 + 2449 - 1197}{2881} = \frac{2654}{2881} \approx 0.921[/tex]
So, the probability is [tex]\[\boxed{0.921}\][/tex].
(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive?
Two events are mutually exclusive if they cannot occur at the same time.
From the table, 205 females are frequently involved in charity work.
Since there are females who are frequently involved in charity work, the events "being female" and "being frequently involved in charity work" are not mutually exclusive.
So, the answer is A. No, because 205 females are frequently involved in charity work.
The complete question is:
The table below shows the results of a survey that asked 2881 people whether they are involved in any type of charity work. A per selected at random from the sample. Complete parts (a) through (e).
(a) Find the probability that the person is frequently or occasionally involved in charity work.
P(being frequently involved or being occasionally involved) - (Round to the nearest thousandth as needed.)
(b) Find the probability that the person is female or not involved in charity work at all.
P(being female or not being involved) (Round to the nearest thousandth as needed.)
(c) Find the probability that the person is male or frequently involved in charity work.
P(being male or being frequently involved) (Round to the nearest thousandth as needed.)
P(being male or being frequently involved) - (Round to the nearest thousandth as needed.)
(d) Find the probability that the person is female or not frequently involved in charity work.
P(being female or not being frequently involved) = (Round to the nearest thousandth as needed.)
(e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain.
A. No, because 205 females are frequently involved in charity work.
B. Yes, because no females are frequently involved in charity work.
C. Yes, because 205 females are frequently involved in charity work.
D. No, because no females are frequently involved in charity work.
A store sells toaster ovenstoaster ovens for $4646 each, retail price. The wholesale cost to stock the ovensovens is $ 28$28 each. The fixed cost associated with acquiring the ovensovens, storing them in inventory, using shelf space, and advertising the ovensovens for sale is $25002500. a. Write a function for the total cost of stocking the ovensovens for sale. b. Write a function for the total revenue received from selling the ovensovens. c. Write a system of equations and determine the number of ovensovens that must be sold to break even.
a cell phone company charges a monthly fee of $0.25 for each text. message the monthly fee is $30.00 and you owe $59.50. how many text messages did you have
Mr. Small, the store manager for Jay's Appliance, is having a difficult time placing a selling price on a refrigerator that cost $410. Mr. Small knows his boss would like to have a 45% markup based on cost. The selling price should be
Answer:
$594.50
Step-by-step explanation:
1. Divide markup into decimal form
45/100 = .45
2. multiply by cost of Refrigerator
.45 x 410 = $184.50
3. Add markup cost to original Refrigerator cost.
184.50 + 410 = $594.50
Solve for x.
x−1/4=38
Enter your simplified answer in the box.
Find the point in the first octant where the tangent plane to x2+116y2+14z2=1 is parallel to the plane x+y+z=10
Look at the triangle what is the value of sin X ?
Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. assume boys and girls are equally likely. is the result the same as the probability of getting sall boys among four children
The probability of having a baby boy on the fourth child, given that the first three children were all boys, is 0.5. This result is not the same as the probability of getting all boys among four children, which is 0.0625. The conditional probability accounts for the information about the first three births.
To solve this probability problem, let's break it down step by step.
Probability of Having a Boy on the Fourth Child:
Assuming boys and girls are equally likely, the probability of having a boy or a girl is 1/2 or 0.5. When considering each child's gender independently, the probability of having a boy on the fourth child is 0.5, regardless of the genders of the previous children.
However, the question specifies that the first three children were all boys. This information is crucial for the conditional probability calculation.
Conditional Probability:
The probability of having a boy on the fourth child given that the first three children were all boys is denoted as [tex]\( P(B_4 | B_1, B_2, B_3) \)[/tex].
Since the events are assumed to be independent (the gender of one child does not affect the gender of another), the conditional probability is the same as the probability of having a boy on any single birth: 0.5.
Comparison with Getting All Boys:
The probability of getting all boys among four children [tex](\( P(B_1 \cap B_2 \cap B_3 \cap B_4) \))[/tex] is the product of the probabilities of having a boy for each birth.
[tex]\[ P(B_1 \cap B_2 \cap B_3 \cap B_4) = P(B_1) \times P(B_2) \times P(B_3) \times P(B_4) \][/tex]
Given that [tex]\( P(B_4) = 0.5 \)[/tex] and the previous births are all boys, [tex]\( P(B_1 \cap B_2 \cap B_3 \cap B_4) = (0.5)^4 = 0.0625 \)[/tex].
The question probable may be:
Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. Assume boys and girls are equally likely. Is the result the same as the probability of getting all boys among four children?
For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≥ −1.
The vertex is (3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1.
The vertex is (−3, −1), the domain is all real numbers, and the range is y ≥ −1.
Answer:
C. The vertex is [tex](-3,-1)[/tex], the domain is all real numbers, and the range is [tex]y\leq -1[/tex].
Step-by-step explanation:
We have been given a function [tex]f(x)=-2(x+3)^2-1[/tex]. We are asked to identify the vertex, domain and range of the given function.
We can see that our given parabola is in vertex form [tex]y=a(x-h)^2+k[/tex], where [tex](h,k)[/tex] represents vertex of parabola.
We can rewrite our given equation as:
[tex]f(x)=-2(x-(-3))^2-1[/tex]
Therefore, the vertex of our given parabola would be [tex](-3,-1)[/tex].
We know that parabola is a quadratic function and the domain of a quadratic function is all real numbers.
We know that range of a quadratic function in form [tex]f(x)=a(x-h)^2+k[/tex] is:
[tex]f(x)\leq k[/tex], when [tex]a<0[/tex] and,
[tex]f(x)\geq k[/tex], when [tex]a>0[/tex]
Upon looking at our given function, we can see that [tex]a=-2[/tex], which is less than 0, therefore, the range of our given function would be [tex]y\leq -1[/tex].
what is the approximate value of the square root of 8
Answer:
2.828427
Step-by-step explanation:
I looked it up
a jar of jelly beans that weigh 4.25 ounces costs 2.89. what is the cost of one ounce of jelly
A girl is now one-third as old as her mother. In three years, she will be two-fifths as old as her mother will be. What are their present ages?
A girl is 9; mom is 27
B girl is 18; mom is 54
C girl is 25; mom is 75
Option: A is the correct answer.
A girl is 9; mom is 27
Step-by-step explanation:A girl is now one-third as old as her mother.
i.e. if x is the present age of girl.
and y is the present age of her mother.
Then,
[tex]x=\dfrac{1}{3}y[/tex]
i.e.
[tex]y=3x-----------(1)[/tex]
In three years, she will be two-fifths as old as her mother will be.
This means after three years.
The age of girl will be: x+3
and the age of her mother will be: y+3
This means that:
[tex](x+3)=\dfrac{2}{5}\times (y+3)[/tex]
[tex]5(x+3)=2(y+3)\\\\i.e.\\\\5x+15=2y+6[/tex]
i.e.
[tex]5x+15=2\times 3x+6[/tex]
( since on using equation (1) )
i.e.
[tex]5x+15=6x+6\\\\i.e.\\\\6x-5x=15-6\\\\i.e.\\\\x=9[/tex]
and the value of y from equation (1) is:
[tex]y=27[/tex]
The formula for any arithmetic sequence is a n = a 1 + d(n - 1), where a n represents the value of the nth term, a 1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the arithmetic sequence -7, -3, 1, 5, ...?
Plz help
The student body of a large university consists of 60% female students. a random sample of 8 students is selected. what is the probability that among the students in the sample at least 7 are female?
The probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
To solve this problem, we'll use the binomial probability formula, which calculates the probability of a certain number of successes (in this case, selecting female students) in a fixed number of trials (the sample size).
Given:
Probability of selecting a female student (success), ( p = 0.60 )
Probability of selecting a male student (failure), ( q = 1 - p = 0.40 )
Sample size, ( n = 8 )
We need to calculate the probability of selecting at least 7 female students from the sample.
Calculate the probability of selecting exactly 7 female students:
[tex]\[ P(X = 7) = \binom{8}{7} \times (0.60)^7 \times (0.40)^{8-7} \][/tex]
[tex]\[ = \frac{8!}{7!(8-7)!} \times (0.60)^7 \times (0.40)^{1} \][/tex]
[tex]\[ = 8 \times 0.60^7 \times 0.40 \][/tex]
[tex]\[ = 8 \times 0.0279936 \times 0.40 \][/tex]
[tex]\[ = 0.1119744 \][/tex]
Calculate the probability of selecting exactly 8 female students:
[tex]\[ P(X = 8) = \binom{8}{8} \times (0.60)^8 \times (0.40)^{8-8} \][/tex]
[tex]\[ = (0.60)^8 \][/tex]
[tex]\[ = 0.60^8 \][/tex]
[tex]\[ = 0.16777216 \][/tex]
Add the probabilities from Step 1 and Step 2 to get the final probability:
[tex]\[ P(X \geq 7) = P(X = 7) + P(X = 8) \][/tex]
[tex]\[ = 0.1119744 + 0.16777216 \][/tex]
[tex]\[ = 0.27974656 \][/tex]
So, the probability of selecting at least 7 female students from the sample of 8 students is 0.2797.
A sample of 12 measurements has a mean of 8.5 and a sample of 20 measurements has a mean of 7.5. Find the mean of all 32 measurements.
The distance of planet Mercury from the Sun is approximately 5.8 ⋅ 107 kilometers, and the distance of planet Venus from the Sun is 1.1 ⋅ 108 kilometers. About how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun? (1 point)
Select one:
a. 5.2 ⋅ 107 kilometers
b. 4.7 ⋅ 108 kilometers
c. 5.2 ⋅ 108 kilometers
d. 5.7 ⋅ 109 kilometers
Answer:
a) 5.2 *10^7 km
Step-by-step explanation:
If we could describe our Solar System, in order of appearance nearer the Sun, it would be like this:
Sun --- Mercury --- Venus --- Earth
Sun --------------------- Venus
1.1 * 10^8 km
Sun -------Mercury
5.8 * 10^7 Km
To find out how many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun, all we have to do is simply subtract the distance Sun ---Venus minus Sun ---Mercury
So,
1.1 * 10^8 - 5.8 * 10^7 =
Adjusting the first distance to the same power
110*10^7- 5.8*10^7 =
Subtracting the factors
5.2 * 10^7
Choose all the doubles facts that can help you solve 8+7
Answer: 7 + 7 = 14
8 + 8 = 16
Step-by-step explanation: doubles facts are simply additions where a number is added to it self. The strategy sums up two consecutive numbers when they are next to each other to give their result as given by the question above (8 + 7). We simply add the smaller number together then add one (double-plus-one) OR add the larger number together then subtract one (double-minus-one)
All doubles that can be used in solving 8 + 7 are:
A) 8 + 7 = 7 + (7 + 1) = (7 + 7) + 1 = 14 + 1 = 15 [double-plus-one]
B) 8 + 7 = (8 + 8) - 1 = 16 - 1 = 15 [double-minus-one]
The doubles fact makes use of the associative property of addition —changing the grouping of addends does not change the sum.
tina wants to save money for school. tina invests 1100 in an account that pays an interest of 7.25%. how many years will it take the account to reach 6600?
It would take approximately 19 years for Tina's investment to grow from $1100 to $6600 with an annual interest rate of 7.25% if the interest is compounded annually.
Explanation:This problem deals with the concept of compound interest. To find out how many years it will take for Tina's investment to grow from $1100 to $6600 with an interest rate of 7.25%, we would use the formula for compound interest: A = P(1 + r/n)_(nt), where A is the final amount, P is the principal amount (initial investment), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per time unit (year), t is the time the money is invested for in years.
In Tina's case, she does not make additional contributions, so we assume the interest is compounded once per year (n=1). Our formula becomes A = P*(1 + r)_t. Arranging for t, we get t = log(A/P) / log(1+r).
Using these values: A=$6600, P=$1100, r=7.25/100=0.0725, we can find t = log(6600/1100) / log(1+0.0725). Calculating this, you would get around 19 years.
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The Leukemia and Lymphoma Society sponsors a 5k race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race.
Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
The degree of the Boolean function given by f(x,y,z,w) = xy + yz + zw is........
a law firm charges $100 per hour plus a $300 origination fee for its services find a function notation
The required function notations for the total law firm charges is expressed as f(t) = 100t + 300
Given the following
Law firm charges = $100 per hour
The amount of charge for "t" hours will be 100t hours
Also, the original fee = $300
In other to get the total charge using function notation;
f(t) = Law firm charges for "t" hours + Original fee
f(t) = 100t + 300
The required function notations for the total law firm charges is expressed as f(t) = 100t + 300
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Determine the inverse of f(x) = x^3 - x^2 - 2x show steps
Switch the x and y values to find the inverse.
y=x−3x+2
The inverse is given by
x=y−3y+2
Solve for y now:
x(y+2)=y−3
xy+2x=y−3
2x+3=y−xy
2x+3=y(1−x)
2x+31−x=y
The inverse, f−1(x), is given by f−1(x)=2x+31−x.
The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).
For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).
Find the saving plan balance after 4 years with an apr of 7% and monthly payments of 100
Solve the Pythagorean Theorem for the variable a.
c²=a²+b²
Find the slope of a line that passes through the points (-3,-1) and (0,-5)