3,868,000,000 in scientific notation
The number 3,868,000,000 in scientific notation is 3.868 x [tex]10^9[/tex].
We have,
Scientific notation is a way to express large or small numbers in a concise format. It consists of two parts:
a coefficient and a power of 10.
In the given number 3,868,000,000, we can express it in scientific notation by moving the decimal point to the left until there is only one non-zero digit to the left of the decimal point.
Count the number of places you moved the decimal point, and that becomes the exponent of 10.
Starting with 3,868,000,000, we can move the decimal point 9 places to the left to get 3.868.
The original number has been divided by [tex]10^9[/tex], so the exponent is 9.
Putting it all together,
We express 3,868,000,000 in scientific notation as
= 3.868 x [tex]10^9[/tex]
Where the coefficient is 3.868 and the exponent is 9.
Thus,
The number 3,868,000,000 in scientific notation is 3.868 x [tex]10^9[/tex].
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Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horses whose combined weight is 6,240 pounds. Let t represent the average weight of tack per horse. Which of the following inequalities could be used to determine the weight of tack Cari can allow for each horse?
To determine the weight of tack Cari can allow for each horse, use the inequality 6,240 + 5t ≤ 8,000, where 't' is the average weight of tack per horse. Solve for 't' to find that the maximum average weight of tack per horse is 352 pounds or less.
Explanation:The inequality to determine the weight of tack per horse that Cari can allow would be based on the maximum weight the trailer can transport, which is 8,000 pounds, minus the combined weight of the horses. The combined weight of the horses is given as 6,240 pounds. Let t represent the average weight of tack per horse. Since Cari travels with 5 horses, the total weight of the tack for all horses would be 5t. The inequality would therefore be:
6,240 + 5t ≤ 8,000
To find the maximum average weight of tack per horse that Cari can allow, we should solve the inequality for t as follows:
5t ≤ 8,000 - 6,240
5t ≤ 1,760
t ≤ 1,760 / 5
t ≤ 352
So, the weight of tack per horse must be 352 pounds or less for Cari to safely transport the horses and the tack in the trailer.
The inequality that could be used to determine the weight of tack Cari can allow for each horse is: [tex]\[ 5t + 6,240 \leq 8,000 \][/tex]
Step 1
To determine the weight of tack Cari can allow for each horse, we can set up an inequality based on the total weight limit of the trailer. The total weight limit includes the weight of the horses and the weight of the tack.
Let [tex]\( t \)[/tex] represent the average weight of tack per horse.
The total weight of the horses and tack should not exceed the weight limit of the trailer, which is 8,000 pounds.
Step 2
The weight of the horses is given as 6,240 pounds.
Therefore, the weight of the tack can be represented as [tex]\( 5t \)[/tex] (5 horses each with an average weight of tack [tex]\( t \))[/tex].
Putting this all together, the inequality that represents this situation is:
[tex]\[ 5t + 6,240 \leq 8,000 \][/tex]
Complete correct question:
Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horses whose combined weight is 6,240 pounds. Let t represent the average weight of tack per horse. Which of the following inequalities could be used to determine the weight of tack Cari can allow for each horse?
6240+t≤ 8000
8000≥ 6240t
6240+5t≤ 8000
8000+6240≤ 5t
8000-6240≥ 5t
What is missing for the following quantity to be true? 2x*5a*7 = 5a*2x*__
A. 5a
B. 2x
C. 7
D. 14
Thanks guys!
both sides have 2x & 5a, so both sides need 7
answer is C. 7
What is the unit rate for 501.9 mi in 21 h? Enter your answer, as a decimal, in the box
The required unit rate is given as 23.9 mi per h.
Given that,
To determine the unit rate of the given 501.9 mi in 21 h,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Unit rate is given as,
Rate = 501.9/21 = 23.9 mi per h
Thus, the required unit rate is given as 23.9 mi per h.
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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 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.
Show your work.
race entry costs 55, they use 15 of it to cover costs so they get 55-15 = 40 per entry
x = race entries
equation becomes 55000>= 40x +10000
45000>= 40x
x >= 45000/40 >= 1125
they need at least 1125 race entries to make $55,000
Vivian bought 6 bottles of cooking oil. She gave the cashier $40 and expected $y change. (a) express the cost of 1 bottle of cooking oil in terms of y. (b) if y=10, find the cost of 1 bottle of cooking oil. (c) if y=1, find the cost of 1 bottle of cooking oil.
Answer:
Part (a) The required equation is [tex]y=40-6x[/tex].
Part (b) If y=10, the cost of 1 bottle of cooking oil is $5.
Part (c) If y=1, the cost of 1 bottle of cooking oil is $6.5.
Step-by-step explanation:
Consider the provided information.
Let the cost of each bottle of cooking oil is $x.
Vivian bought 6 bottles of cooking oil.
Thus the cost of 6 bottles of cooking oil is 6x.
She gave the cashier $40 and expected $y change.
This can be written as:
[tex]y+6x=40[/tex]
Part (a) express the cost of 1 bottle of cooking oil in terms of y.
[tex]y+6x=40[/tex]
Subtract both sides by 6x.
[tex]y=40-6x[/tex]
The required equation is [tex]y=40-6x[/tex].
Part (b) if y=10, find the cost of 1 bottle of cooking oil.
Substitute the respective values in the above equation.
[tex]10=40-6x[/tex]
[tex]-30=-6x[/tex]
[tex]x=5[/tex]
If y=10, the cost of 1 bottle of cooking oil is $5.
Part (c) if y=1, find the cost of 1 bottle of cooking oil.
Substitute the respective values in the above equation.
[tex]1=40-6x[/tex]
[tex]-39=-6x[/tex]
[tex]x=6.5[/tex]
If y=1, the cost of 1 bottle of cooking oil is $6.5.
Adam has $300 to donate.For the next five weeks he donates $60 each week to a different charity. His remaining donation money can be shown by a sequence.
At a store, 4 pairs of pants cost $90.00 and 4 pairs of jeans cost $78.00. How much would it cost to buy 3 pairs of pants and 5 pairs of jeans?
Final answer:
To calculate the total cost, find the individual costs of the pants and jeans, multiply them by the required quantity, and sum the resulting amounts. It costs $165.00 to buy 3 pairs of pants and 5 pairs of jeans.
Explanation:
To calculate the cost of buying 3 pairs of pants and 5 pairs of jeans, we first need to find the cost of one pair of pants and one pair of jeans. Given that 4 pairs of pants cost $90.00, the price per pair of pants is $90.00 ÷ 4 which equals $22.50. Similarly, 4 pairs of jeans cost $78.00, so the price per pair of jeans is $78.00 ÷ 4 which equals $19.50.
We then multiply the cost per pair of pants by the number of pants we want to buy, which is 3, and do the same for the jeans by multiplying the cost per pair by 5. Therefore, the total cost for the pants is 3 × $22.50 = $67.50, and the total cost for the jeans is 5 × $19.50 = $97.50.
Finally, we add these two amounts together to get the total cost: $67.50 + $97.50 = $165.00. So, it would cost $165.00 to buy 3 pairs of pants and 5 pairs of jeans.
At a school, 20% of the sixth-grade students are in the band. There are 22 sixth-grade students in the band. How many sixth-graders are in the school?
This is a mathematics problem about percentages. It tells us that 20% of the total number of sixth-grade students equals 22 students who are in the band. By setting up and solving a simple equation, we find that there are 110 sixth-grade students in the school.
Explanation:The subject of your question is Mathematics. This problem is about percentages and can be solved by setting up an equation based on the given information.
It says that 20% which is (0.20 in decimal form) of the total number of sixth-grade students equals the 22 students who are in the band. Let's denote the total number of sixth-grade students by X.
Your equation will look like this: 0.20 × X = 22
To solve for X, divide both sides of the equation by 0.20:
X = 22 / 0.20
Therefore, X = 110.
So, there are 110 sixth-grade students in the school.
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20 points
please help
in return brainliest and special thanks
Luis bought stock at $75.40. The next day, the price increased $19.25. The new price changed by -5 3/4% the following day. What was the final stock price, rounded to the nearest cent? Is your answer reasonable?
How to divide 2.07 by 0.9
A rectangle is dialated using a scale factor of 6. The image is then dilated using a scale factor of one thirds. What scale factor could you use to dilate the original rectangle to get the final rectangle? Explain
Answer:
If this rectangle is dilated using a scale factor of One-half through point B, what is the result?
Point B is the bottom left corner of rectangle X.
Step-by-step explanation:
Point Z is equidistant from the vertices of ΔTUV.
Which must be true?
TA=TB
AZ=BZ
BTZ=BUZ
TZA= TZB
Consider right triangles BTZ and BUZ.
ZB = ZB (Common)
ZT = ZU (Given)
Therefore, ΔBTZ ≅ ΔBUZ (By RHS theorem)
Hence, by CPCTC,
∠BTZ = ∠BUZ
Answer:
(C)
Step-by-step explanation:
It is given that Point Z is equidistant from the vertices of ΔTUV, therefore ZT=ZU=ZV.
Now, from ΔBTZ and ΔBUZ, we have
ZT=ZU (Given)
BZ=ZB (common)
therefore, by RHS rule of congruency,
ΔBTZ≅ΔBUZ
Thus, by corresponding parts of congruent triangles, we have
∠BTZ=∠BUZ
Thus, option C is correct.
Also, it is not necessary that TA=TB and AZ=BZ because there is no information given regarding these equalities.
Jordan has 5.48 milliliters of liquid in one test tube and 9.63 milliliters in another. Luke's test tube has 17.24 milliliters of liquid.
How much more liquid is in Luke's test tube than the liquid in Jordan's two test tubes combined?
2.13 mL
4.15 mL
7.61 mL
15.11 mL
Which of the following is an equivalent form of the mixed number -12 3/4
Answer: - 51/4
Step-by-step explanation:
When light energy meets the surface of your sunglasses, what is the evidence that some of it has been: transmitted, reflected and absorbed?
When light energy meets the surface of sunglasses, some of it is transmitted, some are reflected, and some are absorbed.
What is light energy?Light energy is a form of electromagnetic radiation that is visible to the human eye.
It is a type of kinetic energy that travels in the form of waves at a speed of 299,792,458 meters per second in a vacuum.
We have,
The evidence that light has been transmitted through your sunglasses is that you can see through them.
The amount of light that is transmitted depends on the type of sunglasses and the properties of the lens material.
Sunglasses with darker lenses will transmit less light than those with lighter lenses.
The evidence that light has been reflected is that you can sometimes see reflections on the surface of your sunglasses.
This can be from the front surface of the lens or the back surface, depending on the design of the sunglasses.
Reflected light can also cause glare, which is why many sunglasses have anti-reflective coatings.
The evidence that light has been absorbed is that the lens of your sunglasses appears to be a different color.
The color of the lens is determined by the type of material used and the specific dyes or pigments added to the lens during manufacturing.
Different colors of lenses are designed to absorb different wavelengths of light, which can be useful for different activities such as driving or skiing.
Overall, the combination of transmission, reflection, and absorption of light in sunglasses helps to reduce the amount of light that reaches your eyes and can improve your visual comfort and clarity in bright environments.
Thus,
When light energy meets the surface of sunglasses, some of it is transmitted, some are reflected, and some are absorbed.
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A poster is 8 1/2 inches by 11 inches you enlarge the poster by increasing each dimension by a factor of 2 1/2 what is the area of the new poster
Answer:
Area of the new poster = 584.375 inch²
Step-by-step explanation:
Length of old poster = 8 1/2 inches = 8.5 inches
Breadth of old poster = 11 inches
Scale factor = 2 1/2 = 2.5
Length of new poster = 8.5 x 2.5 = 21.25 inch
Breadth of new poster = 11 x 2.5 = 27.5 inch
Area of new poster = 21.25 x 27.5 = 584.375 inch²
Area of the new poster = 584.375 inch²
Mary wants to go on a trip to Washington D.C which will cost $800. She has saved $48 so far. What percentage of the total amount needed has she saved?
Heidi stops at three water stations during the running race. She drinks 0.25 liters of water at the first stop, 0.3 liters at the second stop, and 0.37 liters at the third stop. How much water does she consume throughout the race?
(3c + 2) + 4(1.3c - 5)
Madvi was playing a card game with her friends. Each time she played Madvi Lost 13 points. If Madvi played 5 rounds, how many points did she lose overall?
suppose you pay $15 per hour to go horseback riding you ride 2 hours today and plan to ride for more hours this weekend
a: write two more different expressions to find the total cost of horseback riding
b: find the total cost
about 3/4 of the students on the track team are girls. about 3/4 of these girls are in grade 8. what fraction on the track team are grade 8 girls?
Given that 3/4 of a track team are girls and 3/4 of these girls are in 8th grade, we can multiply the two fractions to find the fraction of the whole track team that are 8th-grade girls, which is 9/16.
Explanation:The question involves two instances of finding 3/4 of a group. Initially, we are given a track team and we are told that 3/4 of the team are girls. If we let the total number of students in the team equal 1 (or 100%), then the fraction representing the girls is 3/4. Further, 3/4 of these girls are in 8th grade. Therefore, to find the fraction of 8th-grade girls out of the whole team, we multiply the two fractions together as follows: 3/4 * 3/4 = 9/16. This means that 9 out of 16 students are 8th-grade girls, assuming that the track team consists of 16 students. If the track team doesn't consist of 16 students, we can interpret the 9 out of 16 as a ratio.
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The fraction of the track team that are grade 8 girls is [tex]\(\frac{9}{16}\)[/tex].
To find the fraction of the track team that are grade 8 girls, we need to multiply the fraction of the team that are girls by the fraction of those girls who are in grade 8.
Let's denote the total number of students on the track team as [tex]\(T\)[/tex]. According to the information given:
- About[tex]\(\frac{3}{4}\)[/tex] of the students on the track team are girls. So the number of girls on the track team is [tex]\(\frac{3}{4}T\)[/tex].
- About [tex]\(\frac{3}{4}\)[/tex] of these girls are in grade 8. Therefore, the number of grade 8 girls is [tex]\(\frac{3}{4} \times \frac{3}{4}T = \frac{9}{16}T\)[/tex].
Thus, the fraction of the track team that are grade 8 girls is [tex]\(\frac{9}{16}\)[/tex]. This is found by dividing the number of grade 8 girls by the total number of students on the track team:
[tex]\[ \frac{\text{Number of grade 8 girls}}{\text{Total number of students on the track team}} = \frac{\frac{9}{16}T}{T} = \frac{9}{16} \][/tex]
Therefore, the fraction of the track team that consists of grade 8 girls is[tex]\(\frac{9}{16}\)[/tex].
1. Marco and Drew stacked boxes on a shelf. Marco lifted 9 boxes and Drew lifted 14 boxes. The boxes that Drew lifted each weighed 8 lb less than the boxes Marco lifted.
Let m represent the weight of the boxes that Marco lifted.
Which expression represents the total number of pounds Drew lifted?
A. 9(m+8)
B. 112m
C. m−8
D. 14(m−8)
2. Two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator’s price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal.
Let p represent the refrigerator’s original price.
Which equation models this situation?
A. 0.15p=p−150
B. 0.15p=p+180
C. 0.85(p−150)=p
D. 0.85p=p−150
3. Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A.
How fast did Car B travel?
(The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)
Enter your answer for the box.
? mph
4. Louann and Carla received equal scores on a test made up of multiple choice questions and an essay. Louann got 14 multiple choice questions correct and received 24 points for her essay. Carla got 16 multiple choice questions correct and received 14 points for her essay.
How many points was each multiple choice question worth?
Enter your answer in the box.
? points
5. In May, Liam and Charlie had the same amount of money in their savings accounts. In June, Liam deposited $140 into his account. Charlie said he increased the money in his account by 5%. When they compared their balances, they found that they were still equal.
How much money did they both have in their accounts in May?
Enter your answer in the box.
$?
Question 1
14 (m−8)
Question 2
0.85p = p-150
Question 3
60 mph
Question 4
5 points
Question 5
2800
I got all of these answers from doing the same test, and getting all of the questions correct. You are in UTVA right?
Which of the following masses is the smallest? 400 milligrams 55 grams .9 centigrams .65 kilogram
One tray holds eight sandwiches if there are 30 sandwiches in all, how many trays are needed?
Which Function rule matches the graph below?
a. f(x) = x
b. f(x) = x-2
c. f(x) = x+2
d. f(x) = 2x
Answer:
Step-by-step explanation:
Last week, Chen bought 812 gallons of gas at $2.30 per gallon. This week, he bought 4310 gallons of gas at $2.70 per gallon.
What was his total cost?
The total cost for the gas that was bought by Chen is $13504.60.
How to calculate the cost?Chen bought 812 gallons of gas at $2.30 per gallon. The cost for the gas will be:
= $2.30 × 812
= $1867.60
This week, he bought 4310 gallons of gas at $2.70 per gallon. The cost will be:
= $2.70 × 4310
= $11637
The total cost will be:
= $1867.60 + $11637
= $13504.60
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what is 1.75t-4.5=7.75