On solving the provided question, we can say that number 12 is the smallest natural number is abundant
What is natural number?Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.
number 12 is the smallest natural number is abundant
factor of 12 = 1,2,3,4,6,12,
1~1
2>1
3>1
4>2+1
.............
10> 1+2+5
11>1
therefore, number 12 is the smallest natural number is abundant
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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?
the monthly cost for 43 min is $17.96 and the monthly cost for 94 min is $24.72 what is the monthly cost for 88 min
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
y = mx + b
(50,13.98)(78,17.06)
slope = (17.06 - 13.98) / (78 - 50) = 3.08 / 28 = 0.11
slope(m) = 0.11
use either of ur points...(50,13.98)...x = 50 and y = 13.98
now sub into the formula and find b, the y int
13.98 = 0.11(50) + b
13.98 = 5.5 + b
13.98 - 5.5 = b
8.48 = b
so our equation is : y = 0.11x + 8.48.......for 94 minutes...sub in 77 for x
y = 0.11(94) + 8.48
y = 8.47 + 8.48
y = 16.95 <=== this is the cost for 94 minutes
Therefore , the solution to this problem of equation is y = 16.95 cost for 94 minutes.
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During a sale, a store offered a 20% discount on a tablet computer that originally sold for $490. After the sale, the discounted price of the tablet computer was marked up by 20%. What was the price of the tablet computer after the markup? Round to the nearest cent.
Step-by-step explanation:
I think you have to change 20% to a fraction
Fatuma recently hired a roofer to do some necessary work. On the final bill, Fatuma was charged a total of $1449. $315 was listed for parts and the rest for labor. If the hourly rate for labor was $63, how many hours of labor was needed to complete the job?
(A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation.
The equation is
(B) Solve your equation in part (A) to find the number of labor hours needed to do the job.
Answer: The number of labor hours was
(A) The equation is:
$63[tex]x[/tex] = $1449 - $315
(B) The labor hours needed to complete the job was 18 hours.
STEPS TO FIND TIME OF THE COMPLETE JOBS(A) To find the number of labor hours needed to complete the job, we can set up an equation using the information given in the problem.
We know that the total bill was $1449, and $315 of that was for parts. So the remaining amount, $1449 - $315 = $1134, was for labor.We also know that the hourly rate for labor was $63. To find the number of hours needed for labor, we can divide the amount for labor by the hourly rate:$63[tex]x[/tex] = $1449 - $315
[tex]x[/tex] = ($1134 / $63)
Solving this equation gives us the number of hours needed for labor, which is 18 hours. We can check this by multiplying 18 hours by the hourly rate, which should give us the same amount for labor:[tex]x[/tex] = ($1134 / $63)
= 18 hours
Double check for:18 hours × $63 = $1134
This confirms that 18 hours is the correct number of labor hours needed to complete the job.
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Write an equation in slope-intercept form of the line that passes through the points (-5,-12) and 2,9) .
The equation is y=
Answer:
y=3x+3
Step-by-step explanation:
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.
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Yolanda spends 8 2/3 hours per month playing soccer. approximately how many hours does she play soccer in a year?
Answer:
[tex]8 \frac{2}{3} \times 12 = 104[/tex]
Therefore, she spends 104 hours a year playing soccer.
Answer:
104 hours
Step-by-step explanation:
1 year = 12 months
Since 1 year equals 12 months, we multiply the time she spends in 1 month by 12 to calculate the time she spends in 1 year.
8 2/3 hours × 12
= (8 + 2/3) hours × 12
= (8 × 12 + 2/3 × 12) hours
= (96 + 8) hours
= 104 hours
The sum of ages of a woman and her daughter is 46 years. In 4 years time, the ratio of their ages will be 7:2. Find their present ages?
Step-by-step explanation:
Given ,The sum of the ages of a woman and her daughter is 46 years.In 4 years time,the ratio of their ages will be 7:2.To Find : Their present ages
Solution :Consider,
Present age of woman = x yearsPresent age of Daughter = y yearsAccording to the 1st condition :-The sum of the ages of a woman and her daughter is 46 years.[tex]x + y = 46\\x = 46 -y[/tex]
According to the 2nd condition :-In 4 years time,the ratio of their ages will be 7:2.After 4 years,Age of woman = (x+4) yearsAge of daughter = (y+4) years→ (x+4) : (y +4) = 7:2
→ x+4/y+4 = 7/2
→ 46-y+4/y+4 = 7/2
→ 50-y/y+4 = 7/2
→7y +28 = 100-2y
→ 7y +2y = 100 -28
→ 9y = 72
→ y = 8
Present age of Daughter = 8 yearsNow put y = 8 in eq(1) .
→ x = 46 - y
→ x = 46 - 8
→ x = 38
Present age of woman = 38 years.Mark Me Brainliest
What should be added to 7x^2 5x 1 to get 3x^2 4x 7?
The value should be added will be [tex]y = -4x^{2} +9x+6[/tex]
Now, According to the question:
Let the value y be added to [tex]7x^2-5x+1[/tex] to give [tex]3x^2+4x+7[/tex]
y = [tex]3x^2+4x+7[/tex] - ( [tex]7x^2-5x+1[/tex])
y = [tex]3x^{2} +4x+7-7x^{2} +5x-1[/tex]
Combine like terms:
y = [tex]3x^{2} -7x^{2} +4x+5x+7-1[/tex]
Calculate the subtraction and addition.
[tex]y = -4x^{2} +9x+6[/tex]
Hence, The value should be added will be [tex]y = -4x^{2} +9x+6[/tex].
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The complete question is this:
What should be added to [tex]7x^2-5x+1[/tex] to get [tex]3x^2+4x+7[/tex] ?
Find the volume of given solid figure.
Answer:
48cm3
Step-by-step explanation:
Volume of a rectangular box = a.b.c
The volume of the solid figure: (2.2.5) + (7.2.2) = 20 + 28 = 48 cm3
help for 100 points please please
Answer:
Step-by-step explanation:
Take the percentages for both 1992 and 2000 and make the average. that is your answer
Find the missing values in the ratio table then write the equivalent ratios in the order they appear in the table 3/4 1/3 2/3 3 1
The missing values in the ratio table are given as follows:
8 meters -> 1/3 minutes.4 meters -> 1/6 minutes.6 meters -> 1/4 minutes.10 meters -> 5/12 minutes.Hence the equivalent ratios are given as follows:
8 : (1/3).4 : (1/6).6 : (1/4).10 : (5/12).What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
The input and output variables for this problem are given as follows:
Input: time.Output: meters.Hence the constant of proportionality is obtained as follows:
k = 8/(1/3) = 24.
Hence the equation is given as follows:
y = 24x.
The time for 4 meters is given as follows:
4 = 24x
x = 4/24
x = 1/6.
The distance for 1/4 minutes is given as follows:
y = 24 x 1/4
y = 6 meters.
The distance for 5/12 minutes is given as follows:
y = 24 x 5/12
y = 120/12
y = 10 meters.
The equivalent ratios for each case are given as follows:
y = y : x.
Missing InformationThe problem is given by the image presented at the end of the answer.
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4ft 5 ft 3ft 5ft please help me i dont know
the answer
83.2 square feet is the area of the figure.
What is Three dimensional shape?A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The given figure is a cone with radius 3 ft and height 5 ft.
We need to find the area of cone=A=πrl+πr²
where l is √r²+h²
A=πr(r+√r²+h²)
=π×3(3+√3²+5²)
=3π(3+√34)
=3×3.14(3+5.83)
=3×3.14(8.83)
=83.2 square feet
Hence, 83.2 square feet is the area of the figure.
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Aiko bakes croissants for a community center bake sale. She already has a number
of batches baked from the day before. After 2.5 hours, Aiko has a total of 8 batches.
After 4 hours, she has a total of 11 batches. Determine the number of batches Aiko
baked per hour.
Answer:
Aiko baked 2 batches per hour.---------------------------------
Find the difference in time and the difference in the number of batches.
The two numbers will help to find the rate of change in that time interval.
This is same as finding the slope of a line with points (2.5, 8) and (4, 11):
m = (11 - 8)/(4 - 2.5) = 3/1.5 = 2Mrs. Hana paid for 30 tickets that cost $7 and $5 with $200. She was given $14 in charge. How many $7 movie tickets did she buy?
Solve it in Singapore Math-Using Models
Answer:
18 tickets at $7
Step-by-step explanation:
You want a "Singapore Math" model solution to the number of $7 tickets Mrs. Hana bought if she got $14 change from $200, and she received a total of 30 tickets, some of which cost $5 each.
ModelThe attachment shows the model we decided upon. Starting from $200, we subtract $14 in change, then divide the remainder into tickets costing $7 each and tickets costing $5 each. The point where the total number of tickets is 30 is the point that identifies the solution.
Mrs. Hana bought 12 tickets at $5 each, and 18 tickets at $7 each.
__
Additional comment
Most illustrations of Singapore Math models are solving for a single variable. Here, we must choose values for two variables (the numbers of $5 and $7 tickets) so the intended model isn't clear.
The model we have used is adequate for the purpose, but tedious to construct. It requires us to identify the point at which the count of $7 tickets (top bar) and the count of $5 tickets (bottom bar) has a sum of 30.
please help: find the value of x
What will make the expression x² 4x+ a perfect square trinomial?
In order for an expression, such as x² + 4x + , to become a perfect square trinomial, it must be in the form of a² + 2ab + b².
What is perfect squares?Perfect squares are whole numbers that are the result of multiplying a given number by itself. For example, 4 is a perfect square because it is the result of multiplying 2 by itself. Similarly, 9 is a perfect square because it is the result of multiplying 3 by itself. Other examples of perfect squares include 16 (4x4), 25 (5x5), 36 (6x6), and so on.
To do this, you must factor the expression. In this case, the expression can be factored into (x + 2)².
Once the expression has been factored into a perfect square trinomial, it can be written as (x + 2)².
This is a perfect square trinomial because it represents the area of a square, as the length of each side is equal to (x + 2).
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Order the following number from greatet to leat. When entering fraction pleae ue "/". For example 1/2 or 3 2/3
-0. 44, -3/8, -0. 5, -2/5
The order from greatest to least is -3/8> -2/5>-0.44>-0.5
To compare all the numbers, we first convert the numbers to their fractional equivalent.
Therefore, -0.44= -44/100
And -0.5= -5/10
Now, we covert all the numbers to get the same denominator in all the numbers, therefore, let the denominator be 100
Therefore, we multiply -3/8 with 12.5 in both numerator and denominator to get, -37.5/100
Then, we multiply -2/5 with 20 in both numerator and denominator to get, -40/100
and, we multiply -5/10 with 10 in both numerator and denominator to get -50/100
Therefore, with these resultant value we can say that, -37.5/100> -40/100 >-44/100> -50/100
Thus, -3/8> -2/5>-0.44>-0.5
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HELP!! Find the value of… (picture)
Answer:
C. 94
Step-by-step explanation:
|A| = [tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
det(A) = a * [tex]\left[\begin{array}{ccc}e&f\\h&i\\\end{array}\right][/tex] - b * [tex]\left[\begin{array}{ccc}d&f\\g&i\\\end{array}\right][/tex] + c * [tex]\left[\begin{array}{ccc}d&e\\g&h\\\end{array}\right][/tex]
OR
det(A) = aei - afh - bdi + bfg + cdh - ceg
|A| = [tex]\left[\begin{array}{ccc}-2&-2&-5\\2&7&-3\\8&9&9\end{array}\right][/tex]
det(A) = -2 * [tex]\left[\begin{array}{ccc}7&-3\\9&9\\\end{array}\right][/tex] - (-2) * [tex]\left[\begin{array}{ccc}2&-3\\8&9\\\end{array}\right][/tex] + (-5) * [tex]\left[\begin{array}{ccc}2&7\\8&9\\\end{array}\right][/tex]
OR
det(A) = (-2)(7)(9) - (-2)(-3)(9) - (-2)(2)(9) + (-2)(-3)(8) + (-5)(2)(9) - (-5)(7)(8)
det(A) = 94
Please answer #6a and 6b
The possible values of x for the given triangle ABC are 0.75<x<8.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, m∠A < m∠B < m∠C.
a) From triangle ABC,
BC<AC<AB
2x+3<6x<5x+8
Now, 2x+3<6x
Subtract 2x on both the sides of an inequality, we get
3<4x
Divide 4 on both the sides of an inequality, we get
0.75<x
Here, 6x<5x+8
Subtract 5x on both the sides of an inequality, we get
x<8
So, possible values of x are 0.75<x<8
b) From triangle ABC,
BC<AC<AB
3x+1<4x+8<7x+2
Now, 3x+1<4x+8
Subtract 3x on both the sides of an inequality, we get
1<x+8
Subtract 8 on both the sides of an inequality, we get
-7<x
Here, 4x+8<7x+2
Subtract 4x on both the sides of an inequality, we get
8<3x+2
Subtract 2 on both the sides of an inequality, we get
6<3x
Divide 3 on both the sides of an inequality, we get
2<x
So, possible values of x are -7<x<2
Therefore, the possible values of x for the given triangle ABC are 0.75<x<8.
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Let Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).
(a) Using the distribution method, find the pdf of U = Z 2. (We proved this in class by using the MGF method. )
(b) Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution. Write down the corresponding parameters for each
On using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2
What is the Gamma Distribution ?
A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.
Given,
Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).
Using the distribution method, find the pdf of U = Z 2.
And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.
Suppose e Z ∼ N (0, 1), then
mZ (t) = 1√2πetxe−x2/2dx
= et2/21/√2π
[tex]e ^ {-(x-t)^{2} /2[/tex] dx
= [tex]e ^ {t^{2}[/tex]/ 2
hence, on using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2
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A club plans to sell tote bags. The club members estimate they will sell 100 tote bags when the bags are priced at $11 each. For every price increase of $1, they estimate they will sell 10 fewer bags.
What is the estimated revenue, in dollars, when the bags are priced at $13 each?
(revenue = price × number sold)
1) 1,300
2) 1,100
3) 1,040
4) 880
The estimated revenue, in dollars, that the club will generate when the bags are priced at $13 each is 3) 1,040.
What is the revenue formula?The revenue formula is the multiplication of the number of units sold and the price per unit.
To determine the total revenue, we must first ascertain the unit price and the quantity sold.
We know that market forces and the competitive environment determine the quantity sold or supplied.
The demand for tote bags at $11 = 100 units
Decrease in demand for every $1 price increase = 10 units
When the price is $13 each, the units to be sold = 80 (100 -10 x 2)
The total revenue at $13 each = $1,040 (80 x $13)
Total revenue at $12 each = $1,080 (90 x $12)
Total revenue at $11 each = $1,100 (100 x $11)
Thus, we can conclude that the club generates less revenue when it increases its price per tote bag from $11 to $13, justifying the interactions between supply, demand, and cost.
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Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Let p be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p?
In order to use the Normal approximation for the sampling distribution of p
the sample should have at least 10 successes and at least 10 failures.
What is sampling distribution?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or the mode of a variable.
What are statistics?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
For a sample of size n = 125,
The condition for the sample size to be large enough is that both np and n(1-p) should be greater than or equal to 10. This means that the sample should have at least 10 successes and at least 10 failures. If this condition is met, we can use the Normal approximation for the sampling distribution of p.
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Help please with this maths
The radius of the sphere is 9 centimeters.
What is the surface area of a sphere?The area of the outer surface of a sphere is the surface area of a sphere.
And its formula:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
Given:
The surface area of the sphere is 4πr².
Where r is the radius of the sphere.
So,
surface area of the sphere = 4πr²
324π cm² = 4πr²
Simplifying,
r² = 324π/4π
r² = 324/4
r² = 81
r = 9
Therefore, the radius is 9 centimeters.
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Is the interval 0 1 Infinite?
Therefore, the interval (0, 1) must be countless and infinite. Since the interval (0, 1) is as large as R, R is also infinite.
Interval:
In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing (0, 1), and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).
Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.
Open Interval:
Open intervals do not include endpoints and are indicated by parentheses. For example, (0, 1) means greater than 0 and less than 1. This is (0, 1) = {x | 0 This interval can also be expressed as ]0, 1[ . Please refer to the following.
Closed Interval:
A closed interval is an interval that contains all boundary points and is indicated by square brackets. For example, [0, 1] means greater than or equal to 0 and less than or equal to 1.
Half- Open Interval:
A half-open interval contains only one of its endpoints and is represented by a combination of open and closed interval notation. Example: (0, 1) means greater than 0 and less than or equal to 1, [0, 1) means greater than or equal to 0 and less than 1.
Complete Question:
II. Identify the following terms described in each item. Quantitative & Quaeritated. It can be separated into different categories that are distinguished by some nonnumeric characteristics. 2. It consists of numbers representing counts or measurements. Quantitative Quantitative 3. The result from either a finite number of possible values or countable number of possible values as 0, or 1, or 2, and so on 4. The result from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions 5. It is characterized by data that consist of names, labels, or categories only. 6. It involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. 7. It involves meaningful amounts of differences between data. It has no true zero point or absolute zero. 8. It contains all the properties of the interval level but has true zero point or absolute zero. 9. It is a complete collection of all elements to be studied. 10. It is a branch of Mathematics that deals with the collection, organization presentation, analysis, and interpretation of data.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
2nd choice: -3x - 5 = 10
Step-by-step explanation:
10 - x = -5
-x = -5 - 10 = -15
-3x - 5 = 10
-3x = 10 + 5
x = 15/-3 = -5
Pls help this is math work
Answer:
∠ R = 35° , ∠ T = 45°
Step-by-step explanation:
since the triangles are similar then corresponding angles are congruent, so
∠ R = ∠ U = 35°
∠ T = ∠ Q = 45°
Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides 5 times as fast as Bella walks. The distance between their houses is 2 miles, which is 10,560 feet, and Bella covers $2\frac{1}{2}$ feet with each step. How many steps will Bella take by the time she meets Ella
Since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
To determine this:
We can start by using the information given to find out how long it takes Bella and Ella to meet.
Since Ella rides 5 times faster than Bella walks, we can use the following equation to find out how long it takes each of them to cover the 2-mile distance:
Time (Ella) = Time (Bella) / 5
We can also use the distance formula to find out how long it takes Bella to cover the 2-mile distance:
Distance = Speed x Time
We know that Bella's speed is [tex]$2\frac{1}{2}$[/tex] feet per step, and the distance between their houses is 10,560 feet. So:
10,560 feet = [tex]$2\frac{1}{2}$[/tex] feet/step x Time (Bella)
Solving for Time (Bella), we get:
Time (Bella) = 10,560 feet / [tex]$2\frac{1}{2}$[/tex] feet/step = 4,224 steps
Now we can use this information to find out how long it takes Ella to meet Bella:
Time (Ella) = Time (Bella) / 5 = 4,224 steps / 5 = 844.8 steps
And since Bella takes 4,224 steps, and Ella takes 844.8 steps, they meet at 4,224 steps.
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The point A (1,1) and the point B(5,-1) lie on the line L. Find the equation of the line L
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
-1, 0, 4
Step-by-step explanation:
2f - 8 ≤ 6f + 4
-4f ≤ 12
f ≥ 12/-4 **flip the inequality when you divide by a negative number
f≥ -3
Check all the answers that are ≥ -3
Two vehicles start from the same point traveling in the same direction. One vehicle travels 55.5 miles per hour (mph) and the other 45 ¼ mph. When will the two cars be 350 miles apart?
The number of hours after which the cars will be 350 miles apart is 34 hours.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Vehicle 1.
Speed = 55.5 mph
Distance(1) = 55.5 x Time
Vehicle 2.
Speed = 45(1/4) mph
Distance(2) = 45(1/4) x Time
The difference in the distance = 350 miles.
Distance(1) - Distance(2) = 350
55.5 x Time - 45(1/4) x Time = 350
55.5 x Time - (181/4) x Time = 350
(55.5 - 181/4) x Time = 350
Time = 350 / (55.5 - 45.25)
Time = 350 / 10.25
Time = 34 hours.
Thus,
The car will be 350 miles apart after 34 hours.
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