Jason started with 72 baseball trading cards. To find out how many baseball trading cards Jason started with, let's break down the information given step by step.
1. Jason bought 8 new baseball trading cards: This implies that Jason's collection increased by 8 cards.
Let's denote the number of cards Jason had before buying the new ones as X . After buying the new cards, Jason would have X + 8 cards.
2. The next day his dog ate half of his collection: If his dog ate half of his collection, this means that the number of cards left after the incident is half of what Jason had before. So, after the dog ate half of the collection, Jason would have [tex]\( \frac{1}{2} \times (X + 8) \)[/tex] cards remaining.
3. There are now only 40 cards left: This information tells us that the number of cards left after the incident is 40. So, we have the equation:
[tex]\[ \frac{1}{2} \times (X + 8) = 40 \][/tex]
Now, let's solve for X:
[tex]\[ \frac{1}{2} \times (X + 8) = 40 \][/tex]
[tex]\[ X + 8 = 40 \times 2 \][/tex]
X + 8 = 80
X = 80 - 8
X = 72
So, Jason started with 72 baseball trading cards.
To verify, let's check the steps:
1. Jason initially had 72 cards.
2. He bought 8 new cards, totaling 72 + 8 = 80 cards.
3. After his dog ate half of his collection, he was left with [tex]\( \frac{1}{2} \times 80 = 40 \)[/tex] cards, which matches the given information.
Therefore, Jason started with 72 baseball trading cards.
The complete question is:
Jason bought 8 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 40 cards left. how many cards did jason start with?
describe how to find the number of $4 train tickets you can buy with $32.
A graduate student is studying bacteria known to have a growth rate of 15% per day. If the population of a bacterial sample is currently 29,000 bacteria, then how many bacteria will there be in 3 days?
The population of bacteria in 3 days will be approximately 44,503 bacteria.
Explanation:To calculate the future population of bacteria, we can use the formula P = P0(1+r)t, where P0 is the initial population, r is the growth rate, and t is the time in days. In this case, P0 is 29,000 bacteria, r is 15% or 0.15, and t is 3 days. Plugging in these values, we get:
P = 29000(1+0.15)3
Calculating this expression, we find that P is approximately 44,503 bacteria
Final answer:
The population of bacteria will be approximately 44,076 in 3 days, given an initial population of 29,000 and a growth rate of 15% per day.
Explanation:
To calculate the population of bacteria in 3 days, we need to use the formula:
P = P0 * (1 + r)^t
Where P is the final population, P0 is the initial population, r is the growth rate per day (expressed as a decimal), and t is the time in days.
In this case, the initial population is 29,000 and the growth rate is 15% per day (0.15). Plugging these values into the formula, we get:
P = 29,000 * (1 + 0.15)³
Simplifying the equation gives:
P = 29,000 * 1.15³
P = 29,000 * 1.520875
P ≈ 44,076
Therefore, there will be approximately 44,076 bacteria in 3 days.
A customer is withdrawing $890 and wants as many $50 bills as possible. How many $50 bills should the Teller give her?
Will upvote!
I just need two or three points on the graph
Graph −7y+8=21x−6
A survey was given and here are the results "Number responding less than 1 week"
Gender - X N
Males - 71 411
Females - 64 253
a) Construct a 95% confidence interval for the difference in the proportions of males and females at this university. Who would respond less than one week?
b) does there appear to be evidence of a difference in the proportions of men and women at this university who would respond less than 1 week. Provide statistical justification
What are all the factor pairs for 30?
On a certain day, the company took 88 people on whale watching trips. There were 44 children aged twelve and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day?
(44 + x)35 + (88 – (44 + x)) ∙ 46 = C
(88 - x)35 + (88 – 44) ∙ 46 = C
(44 – x)35 + (88 – 44) ∙ 46 = C
(88 + x)35 + (88 – (44 + x)) ∙ 46 = C
Please explain why? ...?
Answer with explanation:
Total number of People who were on Whale Watching Trip =88 People
Number of People (Children ) who was 12 and under ,and some children who were under three years old=44
Number of three year and less old Children = x
Amount of Money charged for three year and less= $ 0
Amount Charged for Children who were above 12 years and less than or equal to 3 years=(44-x) = $ 35
Total Number of Adults =88-44
Amount charged for each Adult = $46
Total amount of money collected from tickets on that day=$ C
Writing the Above Statements in terms of Equation
⇒ (44 -x)×35+(88-44)×46=C
Option C
The equation to find the number of children under three years of age during a whale watching trip is (44 - x)35 + (44)46 = C, accounting for different ticket costs for children and adults.
The correct equation to find the value of x, which represents the number of children under three years, is (44 - x)35 + (88 - 44) \46 = C. This equation takes into account the cost of tickets for the children under three and those above three but under thirteen, as well as adults and older children, given that the cost of tickets might be different.
To explain, the total number of children is 44, and if we subtract the number of children under three (x), we have the number of children between the ages of four and twelve left.
We multiply this number by the ticket price for children in this age group, which is $35. The remaining passengers are adults, totaling 88 passengers minus the 44 children, which gives us the number of adult tickets sold. This number is then multiplied by the adult ticket price, which is $46. Finally, the sum of these two products gives us the total amount of money collected, C.
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + 7 k S is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 6
To find the flux of the vector field F across the boundary of the described cylindrical region, the surface integral must be computed with outward normals, parameterizing each surface portion, setting appropriate bounds, and summing all contributions.
Explanation:The student has asked to evaluate the surface integral (flux) of the vector field F(x, y, z) = x i + y j + 7 k across the boundary of a cylindrical region defined by x2 + z2 = 1 and the planes y = 0 and x + y = 6. To solve this problem, we first define a consistent outward orientation for the surface normals.
It is important to carefully determine the components of the vector field that contribute to the flux through the various portions of the boundary surface - the curved cylindrical surface, the bottom plane at y = 0, and the slanted plane at x + y = 6.
We compute the surface integral by parameterizing each portion of the surface, setting up and evaluating the integrals for each, and summing these contributions.
This involves finding the antiderivatives with respect to both dimensions defining the surface area, considering the appropriate bounds derived from the region described.
To evaluate the surface integral of the given vector field F across the oriented surface S, parameterize the surface S as a combination of two surfaces and evaluate the surface integral of F · dS for each surface separately. Then, calculate the total flux of F across the surface S.
Explanation:To evaluate the surface integral of the given vector field F across the oriented surface S, we need to find the flux of F across S. The vector field F is given as F(x, y, z) = x i + y j + 7 k. The surface S is the boundary of the region enclosed by the cylinder x^2 + z^2 = 1 and the planes y = 0 and x + y = 6.
To evaluate the surface integral, we can use the formula Φ = ∫∫ F · dS, where F is the vector field, dS is the area element, and the integral is taken over the surface S. In this case, the surface S is the boundary of the region enclosed by the cylinder and the planes. We can parameterize the surface S and then use the formula to evaluate the integral.
By parameterizing the surface S as a combination of two surfaces, we can evaluate the surface integral of F · dS for each surface separately. The total flux of F across the surface S is the sum of the fluxes across the two surfaces. Using the formula and the parameterization, we can calculate the flux of F across the surface S.
The complete question is:content loaded
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + 7 k S is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 6 is:
Which of the following best represents the average speed of a fast runner?
10 meters per second
10 miles per minute
10 centimeters per hour
10 kilometers per second
Answer:
D
Step-by-step explanation:
kilo is faster than meters
Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=−3x+12y=−6x+2
The system of equations given is y=-3x+12 and y=-6x+2. Comparing their slopes and y-intercepts, the slopes are different and the y-intercepts are different too. Hence, the system is consistent.
Explanation:The system of equations given is y=-3x+12 and y=-6x+2. To determine whether these equations are inconsistent, consistent, or consistently coincident, we must compare their slopes and y-intercepts. If the slopes are the same (-3 and -6 are not similar) and the y-intercepts are different (12 and 2 are not equal), then the system is inconsistent. If the slopes and the y-intercepts are identical, then the system is consistent and coincident. Otherwise, if the slopes are different, which is the case in this scenario, the system is consistent.
Learn more about system of equations here:https://brainly.com/question/21620502
#SPJ12
write an equation in point-slope form for the line through the given point with the given slope.
(8,3);m=6
a. y+3=6(x-8)
b. y-3=6(x-8)
c. y-3=6(x+8)
d. y+3=6(x+8)
Find the slope of the line tangent to the
graph of ln(xy)-2x=0 when x= -1
answer choices..
1. slope = 3/2e^-2
2. slope= 3/2e^2
3. slope= 3e^-2
4. slope= -3e^2
5. slope= -3/2e^2
6. slope= -3e^-2
Answer:n
Step-by-step explanation:
How many times does 6 go into 87?
An isosceles trapezoid has shorter base of measure a, longer base of measure c, and congruent legs of measure b. The perimeter of the trapezoid is 58 inches. The average of the bases is 19 inches and the longer base is twice the leg plus 7. Find the lengths of the sides.
2x + 7y + 3x − 4y simplify
How do you find the perimeter and area?
The area of a trapezoid is given by the formula A =1/2 (b 1 + b 2)h, where base b 1 is parallel to base b 2 and h is the height. Solve the formula for b 2. Show your work.
Find the slope the line that contains (2,4) and (4,4)
MRS. FARLY WANTS TO BUY A PENCIL FOR EACH OF HER 23 STUDENTS. PENCILS COME IN BOXES OF 5 PENCILS EACH. WHAT IS THE LEAST NUMBER OF BOXES SHE MUST BUY TO HAVE A PENCIL FOR EACH STUDENT. A. 2, B3, C4, OR D 5
An angle measures 41 degrees. What is the measure of its complement?
Jina's earnings vary directly with the number of hours she works. Suppose that she worked 8 hours yesterday and earned $88 . How much will she earn today if she works 11 hours?
Which inequality models this problem?
The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?
A.
2w + 2 • (5w) ≤ 96
B.
2w + 2 • (5w) ≥ 96
C.
2w + 2 • (5w) < 96
D.
2w + 2 • (5w) > 96
Answer:the answer is A
Step-by-step explanation:took the test and got it right
Suppose you are determining the growth rate of two species of plants. Species A is 12 cm tall and grows 2 cm per month. Species B is 10 cm tall and grows 3 cm per month. Which system of equations models the height of each species H(m) as a function of months m.
H(m ) = 12 + 2m
H(m ) = 3 + 10m
H(m ) = 2 + 12m
H(m ) = 3 + 10m
H(m ) = 12 + 2m
H(m ) = 10 + 3m
H(m ) = 2 + 12m
H(m ) = 10 + 3m
2x -3 =6
Value of x
Help_
help me please tryna finish
Tess has 2 1/2 cups of fruit. how many 3/4 cup servings can she make?
Multiply (2 – 7i)(9 + 5i)
To multiply complex numbers, use the distributive property and combine like terms.
Explanation:To multiply (2 - 7i)(9 + 5i), you can use the distributive property. Multiply the first terms, then multiply the outer terms, the inner terms, and finally the last terms. Then combine the like terms and simplify.
(2 - 7i)(9 + 5i) = 2 * 9 + 2 * 5i - 7i * 9 - 7i * 5i
= 18 + 10i - 63i - 35i²
= 18 + 10i - 63i + 35
= 53 - 53i
So, (2 - 7i)(9 + 5i) = 53 - 53i
Jill Barkely obtained a 25-year, $460,000 mortgage loan from University Savings and Loan Association with 6% interest. The monthly payment is $2,962.40. For the first payment, find the interest to the nearest cent.
A sneaker store salesman had $4,125 in total monthly sales last month. he made $165 in commission from those sales. what is the salesman's commission as a percent of his total monthly sales?
There are ten shirts in your closet, four blue, three green, and three red. You randomly select a different shirt each day. You wear a blue shirt Monday, Tuesday, and Wednesday.