The error interval for a number x rounded to 12.3 is 12.25 ≤ x < 12.35, indicating the range that x could be before rounding to one decimal place.
Explanation:If a number x, rounded to 1 decimal place, is 12.3, the error interval for x defines the range of values that x could be in order to round to 12.3. Since the value is rounded to one decimal place, we consider half of a tenth (0.05) on either side of 12.3 to find the error interval. Hence, the lower bound of the error interval would be just below 12.3 (12.25), and the upper bound would be just before it would round up to the next tenth (12.35).
The error interval for x can be written as: 12.25 ≤ x < 12.35.
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Error interval for [tex]\( x \)[/tex] rounded to 1 decimal place as 12.3 is from 12.25 to 12.35.
To find the error interval for the number [tex]\( x[/tex], rounded to 1 decimal place as 12.3, we need to consider the possible range of values that [tex]\( x \)[/tex] could have been before rounding.
1. Lower Bound: To find the lower bound, we need to consider the smallest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The smallest value that would round up to 12.3 is 12.25.
2. Upper Bound: Similarly, to find the upper bound, we need to consider the largest value [tex]\( x \)[/tex] could have been that would round to 12.3 when rounded to 1 decimal place. The largest value that would round down to 12.3 is 12.35.
So, the error interval for [tex]\( x \)[/tex] is from 12.25 to 12.35.
What is the surface area of a cone, to the nearest whole number?
a.221 cm^2
b.240 cm^2
c.304 cm^2
d.620cm^2
The surface area of a cone is b. 240 cm^2.
What is surface area of a cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r^2 + π L r .
where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.
Here, we have,
from the given figure,
we get,
L= 12.5 cm
r=9/2
=4.5cm
by using the formula, we get,
the surface area of a cone is = 240.33 cm^2
Hence, the surface area of a cone is b. 240 cm^2.
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Which situation is represented by the equation? 9x + 90 = 6x + 120
A) Jake has $90 and Mike has $120. Jake saves $6 per week and Mike saves $9 per week. How long will it be before Jake has more money than Mike?
B) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake has more money than Mike?
C) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Mike has more money than Jake?
D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?
Answer:
D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?
Step-by-step explanation:
The answer is D, because it make them equal
How many numbers between 50 and 250 (inclusive) are not perfect squares?
During a dig, an archaeological team starts at an elevation of −512 feet. At a rate of 234 feet per hour, the team digs deeper into the surface for 312 hours. For the next 412 hours, the team digs at a rate of 1512 feet per hour. Then the team quits for the day.How many feet did the archaeological team dig after 312 hours? feetWhat was the team's elevation at the end of the day?
Choose the correct answer. two cars leave phoenix and travel along roads 90 degrees apart. if car 1 leaves 30 minutes earlier than car 2 and averages 42 mph and if car 2 averages 50 mph, how far apart will they be after car 1 has traveled 3.5 hours? miles.
The answer is 210 miles.
select the values of r, below, that represent a low or no correlation
0.8
0.3
0.1
-0.2
-0.5
1
-0.001
Please help please please
\Omega=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9;\ 10\}\\\\|\Omega|=10\\\\A=\{1;\ 3;\ 6;\ 7\};\ B=\{2;\ 3\}\\\\A\ \cup\ B=\{1;\ 2;\ 3;\ 6;\ 7\}\\\\|A\ \cup\ B|=5\\\\P(A\ \cup\ B)=\dfrac{|A\ \cup\ B|}{|\Omega|}\to P(A\ \cup\ B)=\dfrac{5}{10}=\dfrac{1}{2}=0.5=0.50
Toss a coin three times. what is the probability of getting a head on the first toss
Find three consecutive odd integers such that six times the second decreased by twice the first is equal to twenty more than the sum of the second and third
Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides. Question 8 options: A six-sided figure can have four sides congruent. A rectangle has four sides. Some triangles have all sides congruent. A square has four congruent angles.
Answer:
1. The six-sided figure can have 4 sides congruent but is not a square.
Step-by-step explanation:
We are given the statement,
'A square is a figure with four congruent sides'.
It is required to find the statement which is the counter-example for the above statement.
For the counter-example, the statement should hold:
1. The figure has 4 congruent sides
2. The figure is not a square.
According to the options, we see that,
The six-sided figure can have 4 sides congruent but is not a square.
Thus, option 1 is true.
A counterexample to the faulty definition will be that A six-sided figure can have four sides congruent.
It should be noted that a rectangle has four sides while there are some triangles that have all their sides congruent and a square has four congruent angles as well.The statement that a six-sided figure can have four sides congruent is the correct option.In conclusion, the correct option is A.
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On a island, the population of flamingos is currently 400, and this population doubles every 3 years. Which of the following functions will correctly model this situation? Assume t is measured in years.
F f(t)= 2 x 400^3t
G f(t)= 400 x 3^t/2
H f(t)= 400 x 2^t/3
J f(t)= 400 x 2^3t
A runner is participating in a 10.3 mile race. If the runner stopped at a water station that is twice as far from the starting line as from the finish line, how far is the runner from the finish line?
Answer:
6.86
Step-by-step explanation:
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs
20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in
pounds can be represented by f x( ) = 20x + 4.
What is the range of the function for this situation?
Please explain.
The range of the function is the distance from the maximum of the function to the minimum of the function. The minimum amount of pairs of plates that you can add to the bar (x) is 0, meaning you add no plates. The maximum amount of plates that you can add to the bar is 6, because this is how many plates come in one weight set. The range of the function is y values, and 0 and 6 are x values, so we must plug these values into the function to find the range values.
f(x) = 20x + 4 = 20(0) + 4 = 0 + 4 = 4
f(x) = 20x + 4 = 20(6) + 4 = 120 + 4 = 124
Therefore, the range of the function is 120 pounds, or from [4, 124].
Hope this helps!
The range of a function is the possible output values of the function. The range of [tex]f(x) =20x + 4[/tex] is [4,124]
Given that:
[tex]f(x) =20x + 4[/tex]
To determine the range of the function, we simply determine the value of f(x) using the input values
When no pair is added (this means x = 0).
So, we have:
[tex]f(0) =20 \times 0 + 4[/tex]
[tex]f(0) = 0 + 4[/tex]
[tex]f(0) = 4[/tex]
When 4 pairs are added (this means x = 4).
So, we have:
[tex]f(4) = 20 \times 4 + 4[/tex]
[tex]f(4) = 84[/tex]
When 6 pairs are added (this means x = 6).
So, we have:
[tex]f(6) = 20 \times 6 + 4[/tex]
[tex]f(6) = 124[/tex]
f(6) is greater than f(4).
i.e. [tex]124 > 84[/tex]
So, the range of the function is: [0,124] or [tex]4 \le x \le 124[/tex]
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How do I factorise
28x-4
Use the x-intercept method to find all real solutions of the equation. x^3-10x^2+29x+-20=0
Answer:
C. is the answer 1,4 or 5
Step-by-step explanation:
Please help with easy math problem.
What is the value of d to the nearest tenth?
A. 11.2
B. 13.8
C. 16.7
D. 17.5
Answer:
Option B is correct
d = 13.8
Step-by-step explanation:
Definition:
If two secant segments are drawn to a circle from the same external point(P),
the product of the length of one secant segment and its external part is equal to product of the length of the other secant segment and its external part.
As per the statement:
Labelled the diagram:
then;
PA = 14 units , AB = 20 units, PC = 16 units and CD = d units
Find PB and PD:
PB = 14+20 = 34 units
PD = 16+d units
then by above definition we have;
[tex]PA \cdot PB = PC \cdot PD[/tex]
⇒[tex]14 \cdot 34 = 16 \cdot (16+d)[/tex]
⇒[tex]476=16 \cdot (16+d)[/tex]
Divide both sides by 16 we have;
[tex]29.75 = 16+d[/tex]
Subtract 16 from both sides we have;
13.75 = d
or
d = 13.75 units
Therefore, the value of d to the nearest tenth is, 13.8
4/10= heeeeeeellllllppppppppppppp
Two runners ran as a team in a 5,000-m relay race. the first runner ran 500 m farther than the second runner. how many meters did each run?
Max recorded the math scores of five of his classmates in the table. What is the range of their test scores? 16 24 88 89
Math Scores98761008882
Answer:
B. 24
Step-by-step explanation:
We have been given a data set that represents the math scores of five of Max's classmates. We are asked to find the range of the given data set.
Math score: 98, 76, 100, 88, 82.
Since we know range is the difference between the largest and smallest values of the data set.
[tex]\text{Range}=\text{The largest value of data set - The smallest value of data set}[/tex]
We can see that largest score is 100 and smallest score is 76.
[tex]\text{Range}=100-76[/tex]
[tex]\text{Range}=24[/tex]
Therefore, the range of the given test scores is 24 and option B is the correct choice.
Find the number of sides when:
a. The measure of each interior angle of a regular polygon is 156 degrees.
b. The measure of each exterior angle of a polygon is 36 degrees.
Final answer:
To find the number of sides of a polygon, one can use the relations between interior or exterior angles and the number of sides. For an interior angle of 156 degrees, the polygon has 15 sides. For an exterior angle of 36 degrees, the polygon has 10 sides.
Explanation:
The question is about finding the number of sides of a polygon based on the interior and exterior angles. For part (a), where the measure of each interior angle of a regular polygon is 156 degrees, and for part (b), where the measure of each exterior angle is 36 degrees, we can use specific formulas to find the number of sides.
Part A: Interior Angle 156 Degrees
For a regular polygon, the formula connecting the number of sides (n) to an interior angle (A) is A = [(n-2) * 180] / n. Solving for n when A = 156 degrees gives us:
156 = [(n-2) * 180] / n
Solving this equation yields n = 15, meaning the polygon has 15 sides.
Part B: Exterior Angle 36 Degrees
The measure of each exterior angle of a polygon (E) is related to the number of sides (n) by the formula E = 360 / n. When E = 36 degrees:
36 = 360 / n
Solving for n gives us n = 10. Therefore, the polygon has 10 sides.
A bookstore marks up the cost of a book from $6 to $10. What was the percent increase?
Final answer:
To find the percent increase from $6 to $10, subtract the initial cost from the final cost, divide by the initial cost, and multiply by 100. The percent increase is 66.67%.
Explanation:
To find the percent increase, you need to calculate the difference between the final cost and the initial cost, and then divide that difference by the initial cost. Finally, multiply by 100 to get the percentage.
Given that the initial cost is $6 and the final cost is $10, the difference is $10 - $6 = $4.
To find the percent increase, divide $4 by $6: $4/$6 = 0.6667 (rounded to four decimal places).
Multiply by 100 to get the percentage: 0.6667 * 100 = 66.67% (rounded to two decimal places).
The scale drawing of a baby blanket has the dimensions of 6 inches by 10 inches. the dimensions of the actual baby blanket are 30 inches by 50 inches. what is the scale factor that is used to make the drawing?
the fish aquarium holds 150 liters of water. How many milliliters dose the aquarium holds?
Larry has taken out a loan for college. He started paying off the loan with a first payment of $150. Each month he pays, he wants to pay back 1.3 times as the amount he paid the month before. Explain to Larry how to represent his first 15 payments in sigma notation. Then explain how to find the sum of his first 15 payments, using complete sentences. Explain why this series is convergent or divergent.
A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?
Help me..... please.....
What is the sum of this geometric series?5 + 25 + 125 + 625 + 3,125 + 15,625?
The sum of the given geometric series (5 + 25 + 125 + 625 + 3,125 + 15,625) is -78120.
Explanation:The question is asking for the sum of a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the first term (a) is 5 and the common ratio (r) is 5 (since we get each term by multiplying the previous one by 5).
The sum (S) of the first n terms of a geometric series can be calculated using the formula S = a * (1 - r^n) / (1 - r). In this case, there are n=6 terms in the series, so we will plug these values into the formula.
Therefore, S = 5 * (1 - 5^6) / (1 - 5). So, the sum of this geometric series is -78120.
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square root of 75 plus square root of 3
Text messages cost $.15 each. You can spend no more than $10. How many text messages can you send? Show Working
If each text message costs $.15, and you have $10, you can send a maximum of 66 text messages after rounding down.
Explanation:To figure out how many text messages you can send with $10, given that each text message costs $.15, we need to divide the total amount of money ($10.00) by the cost of each text message ($.15).
It's a simple division problem: $10.00 ÷ $.15 = 66.67.
However, you can't send a fraction of a message, so we need to round down to the nearest whole number. So, you can send a total of 66 text messages for $10.
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A rectangular prism measures 6.7 in. by 4.2 in. by 2.5 in. Round each measure to the nearest whole number to estimate the volume.