To estimate the product or quotient, round numbers to the nearest whole or compatible number: 5 multiplied by 2 3/5 is about 15; 25 7/8 divided by 2 8/9 is about 9; and the total pizzas eaten by all classes is about 11.
Estimation with Rounding and Compatible Numbers
The estimation of products or quotients using rounding or compatible numbers involves adjusting values to simpler, more manageable numbers before performing the calculation. Here's how to estimate each of the provided examples:
For estimating the product of 5 by 2 3/5, you can round 2 3/5 to 3, which is a compatible number since 5 times 3 equals 15. Hence, the estimated product is about 15.To estimate the quotient of 25 7/8 divided by 2 8/9, round 25 7/8 to 26 (as 7/8 is close to a whole) and 2 8/9 to 3 (since 8/9 is close to 1), resulting in an estimated quotient of about 9 when you divide 26 by 3.For the total pizzas eaten by all three classes, use benchmarks: 3 2/3 rounds to 4, 4 1/8 rounds to 4, and 3 1/4 rounds to 3. Adding these gives 4+4+3 which equals 11. So, the total estimated number of pizzas is about 11.These estimations use the concept of rounding to the nearest whole number or to a fractions compatibility and demonstrate the importance of not over-representing the precision in your answer. Moreover, estimations are especially useful in mental math and when an approximate answer is sufficient.
What is the number in standard form?
5.8×10^-10
0.00000000058
A: 0.00000000005008
B: 0.0000508
C: 0.00000005008
D: 0.0000000508
E: 0.0000058
please help this is a unit test due today. thank you
The number 0.00000000058 in standard form is equal to [tex]58\times10^{-11}[/tex].
In Mathematics and Statistics, any numerical data (number) can be written in scientific notation as shown below:
a × [tex]b^{n}[/tex]
Where
a represent a real number.b represent an integer.Based on the information provided above, the numerical data (number) is given by 0.00000000058. When expressed in decimal notation, it can be computed as follows;
Numerical data = 0.00000000058
Numerical data = [tex]5.8\times10^{-10}=58\times10^{-11}[/tex]
Note: The number of zeros must be equal to ten (10).
Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?
The equation that could be used to solve the number of hours Ben ran during each half of the race will be y = 5x + 3 and y = 5.5x + 2
During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. Therefore, the number of miles covered will be:
y = 5x + 3
During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. Therefore, the number of miles covered will be:
y = 5.5x + 2
Then using both equations will be:
y = 5x + 3
y = 5.5x + 2
Subtract the equations
0.5x = 1
x = 1/0.5 = 2
Therefore, the value of y will be:
y = 5x + 3 = 5(2) + 3 = 13
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The circle in the diagram is moved from Quadrant IV to the shaded region in Quadrant II. How does this affect the probability that a dart that hits the rectangular region lands in the circle?
The probability that a dart hits the circle when moved from Quadrant IV to Quadrant II stays the same if the size of the circle and the rectangular region remain unchanged, as it is dependent on the area ratio of the circle to the rectangle.
Explanation:When the circle is moved from Quadrant IV to the shaded region in Quadrant II, the probability that a dart hitting the rectangular region lands in the circle depends on whether the size of the circle or its position relative to the overall dartboard (the rectangle) changes. The probability is determined by the ratio of the area of the circle to the area of the rectangle. If the circle remains the same size and merely shifts positions, the probability does not change. However, if moving the circle changes its size or if it overlaps differently with the rectangular region, then the probability will be affected. To calculate the probability, you would divide the area of the circle by the area of the rectangle. Provided there are no changes to the size of the circle or rectangular area, the probability remains constant despite the move.
What is the justification for each step in solving the inequality?
−5(4x+6)<−18x+6+4x
Select from the drop-down menus to correctly justify each step. *Answer choices are in parentheses*
−5(4x+6)<−18x+6+4x Given
−20x−30<−18x+6+4x (Combine like terms) (Distributive Property) (Subtraction Property of Order)
−20x−30<−14x+6 Combine like terms
−6x−30<6 (Addition Property of Order) (Division Property of Order) (Multiplication Property of Order)
−6x<36 (Addition Property of Order) (Division Property of Order) (Multiplication Property of Order)
x>−6 Division Property of Order
Answer:
Step-by-step explanation:
−5(4x 6)<−18x 6 4x given
−20x−30<−18x 6 4x distributive property
−20x−30<−14x 6 combine like terms
−6x−30<6 addition property of order
−6x < 36 addition property of order
x>−6 division property of order
Mr. Gonzalez bought 5 pounds of grapes for $15.How much did he spend per pound?
Use the figure to find the measures of the numbered angles
The blanket is 2.25 meters long and 1.8 meters wide.What is the area of the blanket?Write the answer in centimeters
To calculate the area of the blanket, multiply the length (2.25 meters) by the width (1.8 meters) to get 4.05 square meters. Then convert this to square centimeters by multiplying by 10,000 (since 1m^2 is 10,000 cm^2), resulting in an area of 40500 square centimeters.
The area of the blanket can be calculated by multiplying its length by its width. We start with the measurements in meters and then convert the result into centimeters.
First, we find the area in square meters:
Area = length × width = 2.25 m × 1.8 m = 4.05 m²
Since there are 100 centimeters in a meter, we need to convert each dimension from meters to centimeters before we can find the area in square centimeters. This means we multiply each meter by 100 to get the dimension in centimeters:
Length in centimeters = 2.25 m × 100 cm/m = 225 cmWidth in centimeters = 1.8 m × 100 cm/m = 180 cmArea in square centimeters = length in cm × width in cm = 225 cm × 180 cm = 40500 cm²So, the area of the blanket is 40500 cm².
Four gallons of gas cost $16.80. what is the unit rate?
Jocelyn has 6 birds. Their mean age is 10. The mode is 8. What might their ages be?
total ages = 60
Generally, if the mode is 8 would mean there are more than one age of 8
suppose there are two with age 8,
leaving 44 for the other 4
(11 for the average of the remaining 4)
could have 9 and 13, and 8 and 14
so we could have:
8,8,8,9,13,14
or we could have:
8,8,9,10,12,13
check:of the 1st answer
mean = (8+8+8+9+13+14)/6 = 10
the mode is 8
you check the 2nd case
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.
−2(x+1)≥3x+8−2(x+1)≥3x+8 :Given
−2x−2≥3x+8−2x−2≥3x+8 :
−2x≥3x+10−2x≥3x+10 :
−5x≥10−5x≥10 :
x≤−2x≤−2 :
The speed of light is 3 x 10^8 meters/seconds. If the sun is 1.5 x 10^11 meters from earth, how many seconds does it take light to reach the earth? Express your answer in scientific notation.
The sunlight takes about 8 minutes and 20 seconds to reach earth.
We have given that,
The speed of light is 3 x 10^8 meters/seconds.
D = r x t distance is equal to the rate of speed multiplied by time.
What is the formula for time?Thus t = d ÷ r
This is the relationship we'll use to solve this problem.
Now, let's organize our data
r = 300,000,000 m/s
Let's write this using scientific notation
r = 3 x 108 m/s
d = 1.5 x 1011 m
t = d ÷ r ⇒ t = 1.5 x 1011 ÷ 3 x 108 or
t = 0.5 x 103
That is 500 seconds or about 8.3 minutes so basically the answer is the sunlight takes about 8 minutes and 20 seconds to reach earth.
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Select the sets that are not functions.
Choose all that apply.
A = {(1, 2), (2, 3), (3, 4), (4, 5)}
B = {(1, 2), (2, 1), (3, 0), (4, -1)}
C = {(-1, 3), (0, 3), (1, 3), (2, 3)}
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
E = {(6, 2), (7, 3), (6, -1), (5, 4)}
Answer with Step-by-step explanation:
A function is a map from a set A to another set B such that
the image of any point in a has a unique image in set B.
A = {(1, 2), (2, 3), (3, 4), (4, 5)}
It is a function since image of 1,2,3 and 4 is unique.
B = {(1, 2), (2, 1), (3, 0), (4, -1)}
It is a function since image of 1,2,3 and 4 is unique.
C = {(-1, 3), (0, 3), (1, 3), (2, 3)}
It is a function since image of -1,0,1 and 2 is unique.
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
It is not a function since image of 1 is not unique.
E = {(6, 2), (7, 3), (6, -1), (5, 4)}
It is not a function since image of 6 is not unique.
Hence, sets that are not functions are:
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
E = {(6, 2), (7, 3), (6, -1), (5, 4)}
A blueprint for a house shows the height of the house to be inches. The actual house is feet tall. What is the unit rate in feet per inch?
Every day, Jason's burrito stand uses 2 bags of tortillas. For how many days will 3/4 of tortillas last?
To find out how many days 3/4 of the tortillas will last, we can set up a proportion using the given information. By solving the proportion, we find that 3/4 of tortillas will last for 8 days.
Explanation:To find out how many days 3/4 of the tortillas will last, we can set up a proportion using the given information.
Let's assume that the total number of tortillas is represented by 'x'.
We know that 2 bags of tortillas are used every day, so in 'x' number of days, 2x bags of tortillas will be used.
According to the question, 3/4 of tortillas should last 'x' number of days. So, we can set up the proportion: 2x / x = 3/4.
To solve this proportion, we can cross multiply: 2x * 4 = x * 3. Simplifying, we get 8x = 3x. Dividing both sides by 3, we get x = 8.
Therefore, 3/4 of tortillas will last for 8 days.
Molly buys a scooter for $26.99. Robert buys a basketball for $12.89. How much more does Molly spend more money than Robert?
Ken went to the store for his mother. He spent $2.37 on groceries. In addition, his mother said he could spend $0.35 on candy. What was his change from a five dollar bill? Enter one digit in each box below.
$[______] [______] [_____]
2.37 + 0.35 = 2.72 total spent
5.00 - 2.72 = $2.28 change back
Round 38,237 to nearest ten thousand
Simplify. 8u+9v+3u−5v
What is the answer?
11u + 14v
15uv
5u + 4v
11u + 4v
To simplify the expression 8u + 9v + 3u - 5v, combine the u terms and the v terms separately to get 11u + 4v.
Explanation:To simplify the expression 8u + 9v + 3u - 5v, we can combine like terms. Like terms have the same variables raised to the same power. Combining the u terms and the v terms separately, we have (8u + 3u) + (9v - 5v), which simplifies to 11u + 4v. Therefore, the answer is 11u + 4v.
Susie bought 4 3/4 pounds of cherries at the store. She ate 5/8 of a pound on the way home.
How many pounds of cherries does Susie have left?
Enter your answer in the box as a mixed number in simplest form.
round 0.05468 to 2 significant figures
please explain.
The rate 165 ounces and 11 boxes describes the relationship between the number of boxes and the weight of the crackers in the boxes. What is the weight, in ounces, of one box?
11 ounces per box
12 ounces per box
15 ounces per box
16 ounces per box
Answer:11 boxes
Step-by-step explanation:
In a certain card game , For every four blue cards, there are three yellow cards. There are a total of 84 blue and yellow cards in the game how many blue cards are in the game
Answer:
It is 48
Step-by-step explanation:
Select the best answer for the question. 3. 9⁄11 = ?⁄22 A. 9 B. 4 C. 12 D. 18
what is the relationship between "2ab and a+b"
Elizebeth wants to challenge you to a toothpicks and tiles game using exactly 6 tiles solve her
find a pattern where the number of toothpicks is more than double the number of tiles
answer and explain
To solve Elizebeth's challenge, we can arrange 6 tiles in different ways to find a pattern where the number of toothpicks is more than double the number of tiles. The pattern is that the number of toothpicks is the same as the number of tiles when the tiles are arranged in a straight line.
Explanation:To solve Elizebeth's challenge, we need to find a pattern where the number of toothpicks is more than double the number of tiles. Let's start with 6 tiles. We can arrange these tiles in various ways and count the number of toothpicks:
Using all 6 tiles in a straight line, we would have 6 toothpicks.Using 5 tiles in a straight line and leaving one tile out, we would have 5 toothpicks.Using 4 tiles in a straight line and leaving two tiles out, we would have 4 toothpicks.Using 3 tiles in a straight line and leaving three tiles out, we would have 3 toothpicks.Using 2 tiles in a straight line and leaving four tiles out, we would have 2 toothpicks.Using 1 tile alone, we would have 1 toothpick.So, for 6 tiles, the number of toothpicks is either 1, 2, 3, 4, 5, or 6. The pattern we can observe is that the number of toothpicks is the same as the number of tiles when the tiles are arranged in a straight line.
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Eric's goal is to walk 2.75 miles to and from the park every day for an entire year. If he meets his goal' how many miles will Eric walk?
Eric will walk 1003.75 miles in a year if he meets his goal.
Further ExplanationEric goal is 2.75 miles/day
How many miles in one year?
[tex]\boxed {1 year = 365 days }[/tex]
so in a year, Eric will walk:
[tex]\boxed {2.75 miles \times 365 days }\\ \boxed {= 1003.75 miles }[/tex]
Here is how to do decimal numbers multiplication using standard algorithm (You can see in the attachment below how to multiply using the area model)
2.75 ⇒ 2 decimal place
365 x ⇒ 0 decimal place (a whole numbers)
1375
1650
825 +
1003.75 ⇒ 2 decimal place
Here how to determine where the decimal point, from the calculation above
First factor has 2 decimal place
Second factor has no decimal place,
so the result would have 2 decimal place (2+0)
In doing decimal numbers multiplication we don't need to line the decimal place.
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Keywords: multiplication, decimal multiplication, three digits number additional, additional, multiplication, three digit numbers, subtraction decimal numbers
Note that if Eric meets his goal, he will walk approximately 1003.75 miles in a year
How to compute the distance Eric will walkNote that the distance walked to and from the park every day = 2.75 miles
Number of days in a year = 365 days
Total miles walked in a year = Distance walked every day x Number of days in a year
Total miles walked in a year = 2.75 miles x 365 days
= 1003.75 miles
So , if Eric meets his goal, he will walk approximately 1003.75 miles in a year.
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In Nathan’s baseball card collection, 58% of the cards are players form the national league. He has 702 baseball cards. About how many baseball cards are players form the national league? Use a rate per 100 to estimate
SHOW WORK PLEASE THANKYOU!
Answer: 406
Step-by-step explanation:
Given : In Nathan’s baseball card collection, 58% of the cards are players form the national league.
We can write 58% as 0.58 [To convert percent into decimal we divide it by 100]
If he has 702 baseball cards, then the number of baseball cards are players that form the national league will be :
[tex]0.58\times702\approx 0.58\times700=406[/tex]
Hence, about 406 baseball cards are players form the national league.
Louise bought 114 pounds of roast beef at $2.00 per pound and 212 pounds of turkey at $1.50 per pound. What was her total cost? Enter your answer in the box. $
It took a cheetah 45 minutes to run from Jungle A to Jungle B. The average speed for the trip was 80 km/h. Find the distance between the two jungles.
Total distance cover from Jungle A to B is 60 km
Given that;
Time taken to cover distance = 45 minutes
Speed of trip = 80 km/h
Find:
Total distance cover from Jungle A to B
Computation:
Distance = Speed × Time
Total distance cover from Jungle A to B = Time taken to cover distance × Speed of trip
Total distance cover from Jungle A to B = [45/60] × 80
Total distance cover from Jungle A to B = [0.75] × 80
Total distance cover from Jungle A to B = 60 km
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which is true about the functional relationship shown in the graph
Answer:
D) it shows the functional relationship , the cost of the apples is a function of weight.
Step-by-step explanation:
Given : Graph between cost of the apples and the weight of apples.
To find : Which is true about the functional relationship shown in the graph.
Solution : We can see from the graph is showing the relation between cost of an apple and weight of apple .
Therefore, D) it shows the functional relationship , the cost of the apples is a function of weight.