Final answer:
The inequality representing "a cat weighs no more than 8 pounds" is expressed as w ≤ 8, where w symbolizes the cat's weight in pounds. This concept illustrates how inequality symbols are applied in algebra to represent the relationship between quantities, applicable in various real-world scenarios.
Explanation:
The question asks which inequality represents "a cat weighs no more than 8 pounds." In mathematical terms, this statement can be translated using an inequality symbol that indicates the cat's weight is either equal to or less than 8 pounds. The appropriate symbol for this is “≤”, which stands for “less than or equal to.” Therefore, the inequality that represents this statement is w ≤ 8, where w represents the weight of the cat in pounds.
Using inequality symbols to show how two metric measurements are related is a foundational concept in algebra, and it is crucial when working with real-world scenarios where quantities have upper or lower bounds. For instance, understanding this concept can apply to various situations such as determining the weight of a dog, or comparing soda in a can to ensure it does not exceed a certain weight limit. It's important to grasp how these symbols convey relationships between quantities.
Which coin have a diameter with a 5 in a hundredths place
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.
Find the saving plan balance after 4 years with an apr of 7% and monthly payments of 100
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]
a jar of jelly beans that weigh 4.25 ounces costs 2.89. what is the cost of one ounce of jelly
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
Deon is riding his bicycle. He rides for 7 hours at a speed of 22.4 kilometers per hour. For how many kilometers does he ride
A cyclist rides his bike at a rate of 21 miles per hour. What is this rate in miles per minute? How many miles will the cyclist travel in 2 minutes? Do not round your answers.
Look at the triangle what is the value of sin X ?
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
Solve for x.
x−1/4=38
Enter your simplified answer in the box.
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?
Solve the Pythagorean Theorem for the variable a.
c²=a²+b²
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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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.
what are the coordinates of a p;point on the unit circle if the angle formed by the positive x axis and the radius is 60 degrees
HELP WILL GIVE HIGHEST RATING!!!
36 POINTS TO CORRECT ANSWER Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets. What is the practical domain of the function?
Answer:
The answer is all integers from 1 to 10, inclusive
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Find then selling price per liter of a mixture made from 70 L of cranberry juice which cost $1.20 per liter and 130 L of apple juice which cost $0.80 per liter
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
what is the approximate value of the square root of 8
Answer:
2.828427
Step-by-step explanation:
I looked it up
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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0.00000002 in scientific notation
Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?
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.
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.
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.
Can someone walk me through the steps in solving this question
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
What is the minimum number of degrees that a hexagram can be rotated so that it is carried onto itself?
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