Analyzing the climbing pattern of the turtle for four days shows that it climbed 15 meters which is halfway to the top, thus the entire depth of the well is 30 meters.
The question asks for the determination of the depth of a well based on a pattern observed in a turtle's attempt to climb out of it. To do this, we need to analyze the climbing and slipping pattern for four days until the turtle is halfway out of the well.
On the first day, the turtle climbed up 2 meters and slipped back 1 meter, netting a 1 meter gain. On the second day, the distance climbed is double that of the previous day (2 meters x 2 = 4 meters), but the turtle loses half of it while resting, which means a gain of 2 meters for the second day (4 meters / 2 = 2 meters). Following the pattern:
Day 1: +2 - 1 = +1 meterDay 2: +(2 x 2) - (4 / 2) = +2 metersDay 3: +(4 x 2) - (8 / 2) = +4 metersDay 4: +(8 x 2) - (16 / 2) = +8 metersThe total distance climbed after four days is 1 + 2 + 4 + 8 = 15 meters. Since this is halfway to the top, the entire depth of the well would be 15 meters imes 2 = 30 meters.
Five cans for six dollars or eight cans for cans $10
The question is about comparing the ratios or rates of the number of cans to cost. This mathematical analysis can help you determine which option offers the best value for money. The same method can be used to compare prices of different types of fruits.
Explanation:The subject of the problem concerns the unit cost for purchasing cans or apples, bananas, grapes, and raspberries. It's essentially a comparison between two ratios or rates in mathematics. In this case, we have the ratio of cans to cost (either 5 cans for $6 or 8 cans for $10). For the first ratio, the price per can is $6 ÷ 5 cans = $1.2 per can. In the second scenario, the price per can is $10 ÷ 8 cans = $1.25 per can. Therefore, the option of 5 cans for $6 has a lower cost per can compared to the option of 8 cans for $10.
With the same method, you can compare prices of different types of fruits (apples, bananas, grapes, and raspberries), determining which fruit gives you the best value for your money based on the price per unit.
Through this kind of mathematical analysis, you can make informed decisions about value for money, which is a useful skill not only in performing school assignments but also in real-world situations such as grocery shopping.
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Marsha practiced the flute for double the minutes Sílvio practiced. Together they practiced for 90 minutes. How long did each student practice?
To find out how long Marsha and Sílvio practiced, we set up the equation x + 2x = 90, where x is the time Sílvio practiced. Solving the equation, we found that Sílvio practiced for 30 minutes and Marsha for 60 minutes.
The question asks us to solve for the amount of time Marsha and Sílvio each practiced their instruments given that Marsha practiced for twice the time that Sílvio did and together they practiced for a total of 90 minutes.
Let's denote the time Sílvio practiced as x minutes. This means Marsha practiced for 2x minutes. We know that the sum of their practice times is 90 minutes, which gives us the equation:
x + 2x = 90
Combining like terms, we have:
3x = 90
Dividing both sides by 3 to solve for x gives:
x = 30
Therefore, Sílvio practiced for 30 minutes and Marsha practiced for 60 minutes (double the time of Sílvio).
a bowling ball has a mass of 5.54 kg. A bowling pin has a mass of 1.58 kg. About how many pins are equal in mass to one ball
To find the number of bowling pins equal in mass to one bowling ball, divide the mass of the ball by the mass of one pin. Approximately 4 pins are equal in mass to a 5.54 kg bowling ball.
To find how many bowling pins are equal in mass to one bowling ball, we divide the mass of the bowling ball by the mass of a single pin. This gives us the number of pins that would have a combined mass equal to the mass of the ball.
Mass of bowling ball = 5.54 kg
Mass of one pin = 1.58 kg
We calculate the number of pins as follows:
Number of pins = Mass of bowling ball / Mass of one pin
Number of pins = 5.54 kg / 1.58 kg
Number of pins ≈ 3.51
Since the number of pins must be a whole number, we would say that approximately 4 pins are equal in mass to one bowling ball.
In 1980, when the consumer price index (CPI) was 82.4, Ivan purchased a house for $71,900. Assuming that the price of houses increased at the same rate as the CPI from 1970 to 1980, approximately how much would the house have cost in 1970, when the CPI was 38.8?
Answer:
$33,856
Step-by-step explanation:
We have been given that in 1980, when the consumer price index (CPI) was 82.4, Ivan purchased a house for $71,900. The CPI in 1970 was 38.8. We are asked to find the cost of house in 1970.
[tex]\text{Past dollars in terms of recent dollars}=\text{Dollar amount}\times \text{Ending-period CPI}\div\text{ Beginning-period CPI}[/tex]
Substitute the given values:
[tex]\text{Cost of house in 1970}=\$71,900\times 38.8\div 82.4[/tex]
[tex]\text{Cost of house in 1970}=\$71,900\times 0.470873786407767[/tex]
[tex]\text{Cost of house in 1970}=\$33,855.825242718[/tex]
[tex]\text{Cost of house in 1970}\approx \$33,856[/tex]
Therefore, the cost of house in 1970 was $33,856.
Determine the missing information in the paragraph proof.
Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.
Prove: Parallel lines have the same slope.
Since slope is calculated using the formula , the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.
Answer:
The answer should be A) v-z w-x
Step-by-step explanation:
between which two consecutive whole numbers is square root 95
Answer:
81..........................................................................................
Step-by-step explanation:
3x+2y+4+9y=
Plz answer
what is the value of b in the equation brainly (y^-9)^b=y^45?
a. -405
b. -5
c. 5
d. 405
Answer:
its -5 just took the test
Step-by-step explanation:
Answer:
The correct answer is option B, - 5
Step-by-step explanation:
2. [02.06] Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3? (1 point)
−5x − 7 < −22 and −5x − 7 ≥ −3
−5x − 7 > −22 and −5x − 7 ≥ −3
−5x > −22 and −7 ≥ −3
−5x − 7 < −22 and −5x − 7 ≤ −3
Answer:
−5x − 7 < −22 and −5x − 7 ≥ −3 (the first one)
Step-by-step explanation:
22 is bigger than -5x and 7
-5x-7 is equal to or less than 22
and negative 3 is just negative 3
hope this helps!
The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 is -5x - 7 < -22 and -5x - 7 ≥ -3.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
We can subtract 7 from all parts of the inequality to get:
-29 > -5x ≥ -10
Then we can divide all parts by -5 (and remember to reverse the direction of the inequality signs because we are dividing by a negative number) to get:
5.8 < x ≤ 2
So, an equivalent form of the compound inequality -22 > -5x - 7 ≥ -3 is:
-5x - 7 < -22 and -5x - 7 ≥ -3
Therefore, the equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 is -5x - 7 < -22 and -5x - 7 ≥ -3.
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0.561 rounded to the nearest hundredth is what
Six people share 3/5 pound of peanuts equally. What fraction of a pound of peanuts does each person receive?
Mr.Ramirez divides 12 frogs equally into 6 groups for students to study.how many frogs are in each group?Label known and unknown information on the tape diagram to help you solve.
If Mr.Ramirez divides 12 frogs equally into 6 groups for students each group will have 2 frogs.
What is unitary method?Unitary method is a mathematical technique for first obtaining the value of a single unit then deriving the required units by multiplying it with the single unit.
This type of question can be solved using the unitary method where we can obtain how many frogs each group gets.
Given, Mr.Ramirez divides 12 frogs equally into 6 groups for students to study.
∴ Each group will have the total number of frogs upon the total number of groups which is,
= (12/6).
= 2 frogs.
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Suppose there are 20 questions on a multiple-choice test. If 25% of the answers are choice B, how many of the answers are not choice B?
What is the x and y intercept for 4x-5y=-20
What is a perfect square between 81 and 121
Diane serves breakfast to two groups of children at a daycare center. One box of Oaties contains 12 cups of cereal. She needs 1/3 cup for each younger child and 3/4 for each older child. Today’s group includes 11 younger children and 10 older children. Is one box of oaties enough for everyone
Answer:
Yes, one box of Oaties is enough for everyone.
Explanation:
To find out if one box of Oaties is enough for everyone, let's calculate the total amount of cereal needed for each group and then sum them up.
For the younger children:
Number of younger children = 11
Amount of cereal needed for each younger child = 1/3 cup
Total cereal needed for younger children = Number of younger children × Amount of cereal needed for each younger child
Total cereal needed for younger children = 11 × 1/3 = 11/3 cups
For the older children:
Number of older children = 10
Amount of cereal needed for each older child = 3/4 cup
Total cereal needed for older children = Number of older children × Amount of cereal needed for each older child
Total cereal needed for older children = 10 × 3/4 = 30/4 = 7.5 cups
Now, let's sum up the total cereal needed for both groups:
Total cereal needed = Total cereal needed for younger children + Total cereal needed for older children
Total cereal needed = 11/3 + 7.5
To add fractions, we need a common denominator, which is 3 in this case:
Total cereal needed = (11/3) + (7.5 × 3/3)
Total cereal needed = (11/3) + (22.5/3)
Total cereal needed = (11 + 22.5) / 3
Total cereal needed = 33.5/3
Now, 33.5/3 cups of cereal are needed for everyone.
Since one box of Oaties contains 12 cups of cereal, let's check if it's enough:
1 box = 12 cups
So, 12 cups > 33.5/3 cups
Yes, one box of Oaties is enough for everyone.
You purchase a car using a 20,000 loan with a 5% interest rate suppose you pay the loan off after 4 years how much interest do you pay on your loan suppose you pay the loan off after 2 years how much interest do you save by paying the loan off sooner
A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/3 miles. At this rate , how many miles can the vehicle travel per gallon of gasoline? Show your work.
Answer:
13 1/3 miles = 40/3 miles
Step-by-step explanation:
1 1/8 gallons of gasoline = 9/8 gallons of gasoline
(40/3) / (9/8)
= 40/3 x 8/9
= 320 /27
= 11 23/27 miles gallon of gasoline
the tallest tree a redwood name Hyperion measures 379 feet tall and the average NBA player is 80 inches. how many NBA players would it take to equal the height of the tree?
3.2 ÷ 10.261
Dividing decimal
Which is a correct definition for an obtuse angle? A. an angle with a measure that equals the measure of a square corner B. an angle with a measure that is less than the measure of a square corner C. an angle with a measure that is greater than the measure of a square corner D. an angle that looks like a line
A square kitchen floor has an area of 500 ft.² estimate the length of one wall to the nearest 10th of a foot
To estimate the length of one wall of the square kitchen, take the square root of the area of 500 square feet, which gives approximately 22.4 feet, rounded to the nearest tenth.
Explanation:The student is asking how to estimate the length of one wall in a square kitchen that has an area of 500 square feet. To find the length of the wall, you need to take the square root of the area because the area of a square is equal to the side length squared. Using a calculator, the square root of 500 is approximately 22.36 feet. Therefore, the length of one wall of the square kitchen is approximately 22.4 feet, rounded to the nearest tenth of a foot.
Is 19/7 irrational or rational??
Answer: It is a rational number.
Step-by-step explanation:
Sine we know that Rational numbers are those numbers which can be written in the form of p/q where, q is not equal to zero.
Here p denotes the numerator and q denotes the denominator.
So, According to question,
p = 19 and q = 7
Hence, it is written in p/q form.
Therefore, it is a rational number.
tom ate 1/4 of a pizza. He divided the leftover pizza into pieces each equal to 1/12 of the Original Pizza. After he gave some friends one piece each 1/6 of the Original Pizza remained. How many friends got pizza?
The radius of a circular Frisbee is 9.8 centimeters. Using rounding to the nearest whole number, what is an estimate for the circumference of this circle?
A. 50 cm B. 60 cm C. 65 cm D. 72 cm
math question down below
Help please. I don’t understand.
On a shopping trip, Peter spent 1/3 of his money for a jacket and another $5 for a hat. If peter still had 1/2 of his money left, how much money did he have originally ??
Side a = 4
Side b = 3
Side c = 5
How would you find the sine of Angle B?
Divide 3 by 90 degrees.
Divide 5 by 3.
Divide 3 by 5.
Divide 3 by 4.
Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars.
Number of crates 2 4 6 8
Cost ($) $25 $45 $65 $85
Which equation represents this situation, where x is the number of crates and y is the cost? A)y−2=−10(x−25) B) y−85=10(x−8) C)y−65=−10(x−6) D)y−4=10(x−45)
The equation representing the Manuel's situation is -
y = 10x + 5
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following problem -
Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars -
Number of crates (n) 2 4 6 8
Cost ($) $25 $45 $65 $85
We can write the equation as -
y = mx + c
y = {(45 - 25)/(4 - 2)}x + c
y = 10x + c
c = 25 - 10 x 2
c = 5
Therefore, the equation representing the Manuel's situation is -
y = 10x + 5
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