If 3 < a < 4 and 4 then, 3 < a ≤ 4 is the relationship.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, A number 'a' which is 3 < a < 4 and 4.
This implies that the number 'a' is less than or equal to 4.
∴ 3 < a ≤ 4.
Q. Suppose 3 < a < 4 and a is also equal to 4, write this statement in inequality form.
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Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish.
Which of the following is the best reason for the random assignment of a treatment level to an experimental unit?
A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects. B. Randomization will make up for improper experimental design, data collection, and analysis.
C. Randomization makes the analysis easier since the data can be entered into the computer in any order. D. Randomization is required by statistical consultants before they will analyze the experiment.
E. Randomization means that the experiment would not need to be replicated.
In order to prevent such factors from influencing the treatment's outcomes, randomization tends to reduce the impact of uncontrollable variables like water temperature.
What are variables?
A variable in mathematics is a symbol that designates a mathematical object. A variable can represent any of the following: a number, a vector, a matrix, a function, its argument, a set, or an element of a set. An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed. Because they make up a significant portion of mathematics, variables are crucial.
The impact of water pH on moon jellyfish mating behavior is being studied by researchers. In a scientific experiment, the water in the tanks containing the jellyfish will be randomly assigned to one of three treatments: low pH, medium pH, or high ph.
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3. draw the circuit for an sr flip-flop given the characteristic table, equation and state diagram. (8pts)
The logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)
What is SR flip-flop?A gated set-reset flip-flop is an SR flip-flop.
The flip-flop is controlled by the S and R inputs when the clock pulse changes from LOW to HIGH.
Till the clock pulse is on a rising edge, the flip-flop won't alter.
There is a chance that the outputs will be HIGH or LOW when S and R are both HIGH at the same time.
A global flip flop with two inputs, the JK flip flop has the letters "J" and "K."
While J and K are not the reduced abbreviated letters for Set and Reset in the SR flip flop, S and R are.
SR flip-flop equation: Qn+1 = S + QnR'
(Refer to the images attached below)
Therefore, the logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)
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10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x+y=8
-x-3y=-12
O 3y + 12
O-3y + 12
O 3y - 12
-3y - 12
The expression that we can use to substitute into the first equation is
x = - 3y + 12.
Substitution Method:
The algebraic approach to solving linear equations is known as the substitution method. This procedure involves substituting a variable's value from one equation into the other. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Here we have
2x + y = 8 ---- (1)
- x - 3y = -12 ----- (2)
We can isolate x in the second equation as given below
=> - x - 3y = -12
Add 3y on both sides
=> - x - 3y + 3y = - 12 + 3y
=> - x = - 12 + 3y
Multiply by -1 on both sides
=> -(- x) = - (- 12 + 3y)
=> x = + 12 - 3y
=> x = - 3y + 12
Therefore,
The expression that we can use to substitute into the first equation is
x = - 3y + 12.
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Tom received a $75 gift certificate for the local sporting goods store. He
bought two baseballs for $1.79 each, a baseball glove for $49.99, and a
baseball bat for $12.19. About how much of his gift certificate will he have
left?
Answer:
He has $9.24 left of his gift certificate
Step-by-step explanation:
Given that,
He bought two baseballs for $1.79
Baseball= 1.79+1.79 or 1.79 × 2 (because there are two baseballs.
= $3.58
Baseball Glove = $49.99
Baseball Bat = $12.19
Altogether = $3.58 + $49.99 + $12.19
= $65.76
So you subtract $65.76 from the Original amount in the gift certificate,
=> $75 - $65.76
= $9.24
In a sale, normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20 Work out the normal price of the pen.
Answer:
The normal price of a pen is £8
Step-by-step explanation:
let p be the normal price.
The statement : “normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20”
Means
[tex]p \times \frac{15}{100} = 1.20[/tex]
Then
[tex]p = 1.20 \times \frac{100}{15} = \frac{120}{15} = 8[/tex]
Answer:
The normal price of the pen is £8
Step-by-step explanation:
Reduced by 15%
Reduced by £1.20
Meaning that 15% is £1.20
To find the 100% or the normal price of the pen we find the 1% first then the 100%
So, 1% = £1.20/15
100% =£1.20/15 x 100
= 8
Checking..
If normal price was 8 and reduction is 15%
8(1- R/100) {R = %}
8(1 -15/100) = 6.8 (Reduced price)
8 - 6.8 = £1.20 ( Reduction price aka the 15%)
Therefore, the normal price of the pen is £8.
Here are summary statistics for the weights of Pepsi in randomly selected cans: n=36, x=0.82412 lb, s=0.00573 lb.
Use a confidence level of 90% to complete parts (a) through (d) below.
a. Identify the critical value ta/2 used for finding the margin of error.
¹a/2=
(Round to two decimal places as needed.)
The critical value is given as 1.69
The margin of error is 0.00161
How to solve for the critical valueWe are to find the critical value ta/2 used for finding the margin of error
T∝ / 2 = 1 - 0.10 / 2
1 - 0.05 = 0.95
The critical value at the level if we use the critical value table is 1.69
2. Next we would have to solve for the margin of error
When comparing your results to the actual population value, a margin of error indicates how many percentage points they will deviate.
ME= [tex]z * \frac{s}{\sqrt{n} }[/tex]
z is the critical value = 1.69
s = standard deviation = 0.00573
n = sample size
where z = 1.69
s = 0.00573
n = 36
We would have to put these values in the formula above to get the margin of error
[tex]1.69 * \frac{0.00573}{\sqrt{36} }[/tex]
Margin of error = 0.00161
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Find the missing side length
Answer:
8
Step-by-step explanation:
x+7=15 so x=15-7 which is x=8
Answer:
8 ft
Step-by-step explanation:
The length of the shape is 15 ft. The length on the bottom is equal to the length on the top.
We are given 2 "sides" or lines on the bottom. One of them is 7 ft. Find the other "side" length.
x + 7 =15
x = 15 - 7
x = 8
Evaluate the function for the given values of a and b then use the intermediate value theorem to determine which of the statements below is true.
a=-1 and b =0
f(x)=6x^3-9x^2-7x+3
a).f(-1) and f(0) have the same sign, therefore the function f has a real zero between -1 and 0
b.)f(-1) and f(0) have opposite signs, therfore the function f does not have a real zero between -1 and 0
c.) f(-1) and f(0) have the opposite sign, therefore the function f has a real zero between -1 and 0
d.) f(-1) and F(0) have the same sign, therefore intermediate value theorem cannot be used to determine wheter the function f has a real zero between -1 and 0
The function f has a real zero between -1 and 0. Therefore, statement c) is true.
To evaluate the function for the given values of a and b, we can plug in the values of a and b into the function and solve.
For a=-1, we get:
f(-1) = 6(-1)^3 - 9(-1)^2 - 7(-1) + 3 = 6 - 9 + 7 - 3 = 1For b=0, we get:
f(0) = 6(0)^3 - 9(0)^2 - 7(0) + 3 = 3Therefore, f(-1) and f(0) have opposite signs (one is positive and one is negative).
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Simplify: 0÷(x−1/3), where x≠1/3.
Answer:
0
Step-by-step explanation:
0 divided by any nonzero quantity is zero.
Write a linear inequality to represent the information given. Shanley would like to give $5 gift cards and $8 teddy bears as party favors. Shanley has $144 to spend on party favors. Enter an inequality to find the number of gift cards x and teddy bears y Shanley could purchase. Give one solution to the inequality.
Can someone evaluate these
1 × ( –6 × – 18 – 8) ÷ 4
–4 – –20 + –5 ×( –11 – –18)
13 – –10 × 16 ÷(14 + –16)
1– –9 × 12 × (–19 + 20)
Answer:
1 × ( –6 × – 18 – 8) ÷ 4=[tex]\frac{1}{404}[/tex]
–4 – –20 + –5 ×( –11 – –18)=[tex]18[/tex]
13 – –10 × 16 ÷(14 + –16)=[tex]173[/tex]
1– –9 × 12 × (–19 + 20)=[tex]110[/tex]
Please help this is percentages.
The percentage of boys in the class is 60% and the percentage of girls in the class is 40%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Total number of students in class = 45
Total number of boys in the class = 27
Then, the percentage of boys in the class will be,
Let the percentage of boys be x.
x% Of 45 = 27
x = (27 × 100)/45
x = 2700/45
x = 60%
Then, total number of girls in the class = 45 - 27 = 18
Assume the percentage of girls in the class be y.
y% Of 45 = 18
y = (18 × 100)/45
y = 1800/45
y = 40%
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1. Anya is at camp and walks 2km due north and then turns and walks another 3km at a bearing angle of 35° . Find her distance back to camp and the bearing angle from her starting point.
Anya her distance back to camp and the bearing angle from her starting point is 4.78 km North 26.3° West.
Define direction ?
Direction gives the information about the way towards which an object moves or tends.
The angle formed by the 2 km and 3 km is the supplement of the 35 ° angle west of north;
180°- 35° = 145°
We know that the length of two sides and one angle.
The opposite side know angle is the direct distance between the starting and ending points.
Using the law of cosines.
[tex]a^{2} = b^{2} + c^{2} - 2bc (cosA)[/tex]
[tex]a^{2} = 2^{2} + 3^{2} - 2(2)(3)(cos 145)[/tex]
[tex]a^{2} = 4 + 9 - 12 (-0.8192)[/tex]
[tex]a^{2} = 22.83[/tex]
a = 4.78 km
To determine the bearing from the starting point , we must determine the angle between the first leg and the direct path.
Using the law of sines
[tex]\frac{4.78}{sin(145)} = \frac{3}{sin C}[/tex] sin(145°)
4.78 sin C = 3 sin 145°
sin C = [tex]\frac{3 sin (145^ 0)}{4.78}[/tex]
sin C = 0.4438
C = 26.3°
Therefore, the distance and bearing of the end point from the starting point is 4.78 km North 26.3 ° West.
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Kara is flying to Hawaii. If her packed suitcase weighs more than 50 pounds
when she checks in at the airport, she will have to pay a fee. Her empty suitcase
weighs 11.3 pounds, and she has to pack all her camera equipment, which
weighs 14.25 pounds. To stay under the weight limit, what is the maximum
possible weight of her other packed items?
at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t
At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6], so the bug is neither speeding up nor slowing down.
The instantaneous velocity of a bug at any particular moment in time is the rate at which the bug is changing its position. The average velocity of the bug over a particular interval (in this case, [0,6]) is the average rate at which the bug changes its position over the entire interval. To compare the instantaneous velocity to the average velocity, the two velocities need to be measured at the same time.
At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6]. That means that the bug is neither speeding up nor slowing down.
The Complete the question is :
at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t = 0.6
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The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply. The sample needs to be random but we don’t know if it is. The actual count of drivers is too small. The actual count of those who do not drive to campus is too small. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.
The statements that apply to the given random sample situation are:
(A) Despite the idea that the sample must be random, we are unsure of this.
(C) It is underreported how many pupils don't drive to school.
(D) n(1p) is not greater than 10.
What is a Simple random sample?A simple random sample, also known as an SRS, is a smaller group of individuals (also known as a sample) chosen randomly and with equal probability from a larger population.
This technique involves picking a sample at random.
The probability of being chosen from any subset of k persons in SRS is the same as that of being chosen from any other subset of k people.
A simple random sample is an objective sampling approach.
A basic sampling method that can be used in conjunction with other, more advanced sampling techniques is simple random sampling.
So, statements that apply in the given situation are:
- We don't know if the sample is random, despite the fact that it must be.
- The number of students who don't drive to school is undercounted.
- n(1−^p) does not exceed 10.
Therefore, the statements that apply to the given random sample situation are:
(A) Despite the idea that the sample must be random, we are unsure of this.
(C) It is underreported how many pupils don't drive to school.
(D) n(1p) is not greater than 10.
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Correct question:
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of drivers is too small.
c. The actual count of those who does not drive to campus is too small.
d. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.
27 POINTS!! The price of 2 items in P and Q come to a ratio of 4:5. When the price of P is increased of $12 and the price of Q is reduced by $6,the items have the same price. Find the original price of P
The original price P will be $72
To find the ratiosIf we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.
4 × y =?
5 × y =?
We need to input a value in for y.
Let's put 9.
4 × 9 = 36 (P)
5 × 9 = 45 (Q)
Now adding 12 to P, and take away 6 from Q.
36 + 12 = 48
45 - 6 = 39
The numbers aren't the same yet.
Let's use a different value for y.
y = 18
The equations will now look like this:
4 × 18 = 72 (P)
5 × 18 = 90 (Q)
Let's add 12 and 6 to the numbers again.
72 + 12 = 84
90 - 6 = 84
The numbers are now equal
Therefore, the original price of P = $72
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PLEASE HELP ASAP
Three key features of a linear function are described as shown.
• The graph of the function has a y-intercept of (0, 3) .
• The function is increasing over its entire domain.
• The x-intercept of the function is (-4, 0).
Answer:
y = 3/4 x + 3
Step-by-step explanation:
slope of the line :
(0-3)/(-4-0)
-3/-4
3/4
y = 3/4 x + 3
what is 10+40-11+100=
Answer:139 is the answer
Step-by-step explanation:
There are various mathematical equations that help us understand the structures of the ear and how they contribute to hearing. the decibel equation, expressed as db
The decibel equation is used in many different contexts, including acoustics, audiology, and engineering, to measure and compare the intensity of sounds.
The decibel equation is a measure of sound intensity, which is a way to describe the strength or magnitude of a sound. It is expressed as dB, and it is defined as the ratio of the intensity of a sound to a reference intensity. The reference intensity is usually set at a level that is the minimum intensity that a person can hear, which is approximately 0 dB.
The decibel equation is typically written as:
dB = 10 × log10(I / I0)
where I is the intensity of the sound being measured and I0 is the reference intensity. The log10 part of the equation is used to express the ratio of the two intensities on a logarithmic scale, which allows the decibel value to be more easily interpreted.
The decibel scale is logarithmic, which means that a small change in decibel value corresponds to a much larger change in sound intensity. For example, a sound with a decibel value of 60 dB is much louder than a sound with a decibel value of 50 dB, even though the difference between the two values is only 10 dB.
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7. (85D) Richards Park charges an admission fee of
$10 plus an hourly fee for each sport that you
choose to participate in. Which equation
represents the cost C, in terms of the number of
hours, h, you pay to sled?
HELP PLEAAASEEE 20 POINTS
Answer:
C. C = $10 +$5h
Step-by-step explanation:
The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.
CostThe cost is ...
cost = admission fee + hourly charge
The hourly charge is the product of the cost per hour ($5) and the number of hours (h).
C = $10 +$5h
The length of a rectangle is 1 7/9 inches and its width is 3/4 of its length. Find the area of this rectangle.
Answer:
Area = 2 10/27 inch²
Step-by-step explanation:
Length: 1 7/9 inches
Width: (3/4)(1 7/9 inches)
Area = Length × Width
Area = (1 7/9 inches) × (3/4)(1 7/9 inches)
Area = 16/9 inches × 16/9 inches × 3/4
Area = 768/324 inch²
Area = 256/108 inch²
Area = 128/54 inch²
Area = 64/27 inch²
Area = 2 10/27 inch²
What is the solution and how do I solve this step by step?
Suppose continuous random variable Y has cumulative distribution function FY (y), and density
function fY (y) > 0. Let random variable U = FY (Y ), find the density function of U, and identify its
distribution (name and parameter(s)) if possible.
Since, U = FY(Y) is uniform distribution (i.e. U(0, 1)).
In the given question, suppose continuous random variable Y has cumulative distribution function FY (y), and density function fY (y) > 0.
Let random variable U = FY (Y ).
We have to find the density function of U, and identify its distribution (name and parameter(s)) if possible.
A random variable Y has cumulative distribution function FY (y).
A random variable Y has density function f(y).
Let U = FY(Y)
Now we have to find the density function of U using cumulative distribution function method
FU(u) = P(U≤u)
FU(u) = P(FY(Y) ≤ u)
FU(u) = P(Y ≤ F (u))
FU(u) = FY(F (u))
FU(u) = u
fU(u) = F'U(u).1
fU(u) = 1
fU(u) = 1, 0<u<1
Here U = FY(Y) is uniform distribution (i.e. U(0, 1)).
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A researcher performs three independent hypothesis tests each at the 5% significance level.
Determine the probability of observing at LEAST one Type I Error. (Round your final answer to the nearest hundredth of a percent)
The probability of observing at least one Type I Error is 16.67%.
What is probability?Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. It is a measure of how likely it is that something will happen, given the conditions and information available. Probability is the foundation of statistics, which is the science of making decisions when faced with uncertainty. Probability can be used to make predictions about future events and to help us understand how likely various outcomes are.
A Type I Error, also known as a false positive, occurs when an experiment incorrectly rejects a true null hypothesis. This probability can be calculated by multiplying the probability of a Type I Error occurring in each test (0.05) three times, yielding 0.125 (or 12.5%).
We then add 1 minus that probability, which yields 0.167 (or 16.67%). In other words, the probability of observing at least one Type I Error in the three tests is 16.67%.
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HELPPPPPPPP PLEASESEEEEEEEE
Answer: 7/3 or 2.333
Step-by-step explanation:
the formula for slope is y2-y1 over x2-x1
so if you apply the formula here its going to be
4-(-3) over 5-2
which is 7 over 3 therefore your slope will be
7/3
Answer:
[tex]m=\frac{7}{3} =2.33333... = 2.\overline{3}[/tex]
Step-by-step explanation:
in a survey of 1,000 adults in a country, 722 said that they had eaten fast food at least once in the past month. create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month. use excel to create the confidence interval, rounding to four decimal places.
To create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month, we need to first calculate the sample proportion.
The sample proportion is calculated by dividing the number of adults who ate fast food at least once in the past month (722) by the total number of adults surveyed (1000). This gives us a sample proportion of 0.722.
To calculate the confidence interval, we can use the following formula:
Sample proportion +/- 1.96 * sqrt((Sample proportion * (1 - Sample proportion)) / Sample size)Plugging in the values, we get:
0.722 +/- 1.96 * sqrt((0.722 * (1 - 0.722)) / 1000)This gives us a 95% confidence interval of (0.6901, 0.7539). Rounded to four decimal places, the confidence interval is (0.6901, 0.7539).
Note: To calculate the confidence interval using Excel, you can use the following formula:
=CONFIDENCE.NORM(alpha, standard_dev, size)Where "alpha" is the desired confidence level (e.g., 0.95 for a 95% confidence interval), "standard_dev" is the standard deviation of the sample, and "size" is the sample size. To calculate the standard deviation, you can use the STDEV.P function.
For example, to calculate the lower and upper bounds of the 95% confidence interval, you could use the following formulas:
Lower bound: =CONFIDENCE.NORM(0.95, STDEV.P(A1:A1000), 1000) - (1.96 * STDEV.P(A1:A1000))Upper bound: =CONFIDENCE.NORM(0.95, STDEV.P(A1:A1000), 1000) + (1.96 * STDEV.P(A1:A1000))Where A1:A1000 is a range containing the values "1" for those adults who ate fast food at least once in the past month and "0" for those who did not. This will give you the same result as the manual calculation above.
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If the area of square and rectangle is same and the side of the square is 40cm and width of rectangle is 25cm. So what is the total area of rectangle?
Answer:
s² = lw
s = 40 w= 25cm
s² = lh
(40cm)² = (25cm)
1 600 cm² = 25cm L
L = 64 cm
The length is 64 cm
Area of Rectangle = length(width)
Area = 64cm(25cm)
Area = 1 600 cm²
Which is correct because the statement is, the area of a square ( 1 600 cm²) is equal to area of the rectangle ( 1 600 cm²)Therefore the area of rectangle is 1 600 cm²Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
The area of a rectangle is 9/10 square meter. The width is 2/5 meter. b. How many times greater is the length than the width? Write your answer in simplest form.
Using the area of rectangle formula, w = A/l, determine the width of the rectangle first before determining its length.
How do you find the length and width of a rectangle when given the area?In conclusion, you must divide a rectangle's area by its known width in order to determine its length.If you have an area A and a width w, you can calculate the length w using the formula h = A/w.
If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w.
Given a diagonal (d) and a width (w), its length is given by h = (d2w2).The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape.
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By first rounding Both number to 1 significant figure estimate the answer to 13 x 378
The solution is A = 4000
The equation after rounding up numbers is A = 10 x 400 = 4000
What is rounding up numbers?
There are basically two rules while rounding up numbers
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Leading zeros are never significant
Trailing zeros are only significant if the number contains a decimal point
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be = p
The value of p = 13
Let the second number be = q
The value of q = 378
Rounding the number p to 1 significant figure , p = 10
Rounding the number q to 1 significant number q = 400
So , the equation is A = p x q
Substituting the values in the equation , we get
A = 10 x 400
The value of A = 4000
Hence , The equation after rounding up numbers is A = 10 x 400 = 4000
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