0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
In mathematics, the decimal representation of numbers allows for the use of trailing zeros after the decimal point. When a decimal number has trailing zeros, such as in the case of 0.8 and 0.80, they are considered equivalent because they represent the same value.
The trailing zeros after the decimal point do not change the numerical value of the number. The number 0.8 represents eight tenths, and adding a trailing zero to make it 0.80 does not change its value; it still represents eight tenths. The zero after the decimal point in 0.80 is simply a placeholder, indicating that there are no hundredths or smaller fractional parts.
It is common to use trailing zeros in decimal representations to indicate the precision or accuracy of a measurement. For example, if a measurement is known to be accurate to two decimal places, it is common to represent it as 0.80 rather than 0.8 to indicate the level of precision.
Therefore, mathematically speaking, 0.8 and 0.80 are equivalent representations of the same value, with the latter including a trailing zero for precision or clarity.
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2. When a large truckload of mangoes arrives at a packing plant, a random sample of 150 is selected and examined for
bruises, discoloration, and other defects. Suppose 15 mangoes do not meet the required standards.
(a) Estimate with 90% confidence the percent of all mangoes on the truck that fail to meet the standards.
(b) What was the margin of error associated with your estimate. Explain its meaning.
(c) Explain the meaning of “90% confidence” in the context of this application.
(d) What would be the most conservative sample size necessary to estimate the true percent of mangoes that fail to
meet standards within 3% at 90% confidence?
a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).
b) The margin of error is: 2.45%.
c) The 90% confidence is the level of confidence that the true population percentage is in the interval.
d) The needed sample size is: 271.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The variables are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.
The sample size and the estimate are given as follows:
[tex]n = 150, \pi = \frac{15}{150} = 0.1[/tex]
The margin of error is of:
[tex]M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%[/tex]
The interval is given by the estimate plus/minus the margin of error, hence:
The lower bound is: 10 - 2.45 = 7.55%.The upper bound is: 10 + 2.45 = 12.45%.For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}[/tex]
[tex](\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2[/tex]
n = 271 (rounded up).
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12. Use the coordinate grid below to answer the question.
What are the coordinates of Point A?
Answer: (7, 12)
Step-by-step explanation:
The x-coordinate is 7.
The y-coordinate is 12.
Thus, the coordinates are (7, 12).
What is the image of (12,-12) after a dilation by a scale factor of 1/4 centered at the origin?
The image of (12, -12) after a dilation by a scale factor of 1/4 centered at the origin would have these coordinates (3, -3).
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object based on the scale factor applied, but not its shape.
Next, we would dilate the coordinates of the preimage (12, -12) by using a scale factor of 1/4 centered at the origin (0, 0) as follows:
Coordinate A (12, -12) → Coordinate A' (12 × 1/4, -12 × 1/4) = Coordinate A' (3, -3).
In conclusion, the coordinates of the image after a dilation by using a scale factor of 1/4 are (3, -3).
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carolina and her friends are training for a kayaking competition. the average distance and time traveled by each is shown in the table below. if the distance kayaked in the competition is 3 miles, predict who will win based on the rates shown. predict how long it will take the winner to complete the race if their rate remains constant
Carolina, 7/8 mi in 1/2 hr
Leslie, 1 mi in 1/3 hr
Bryan 3/4 mi in 3/4 hr
Javier 1 mi in 2/3 hr
The winner of the race among the friends would be Leslie.
Who would win the race?The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.
Average speed = total distance / total time
Carolina's average speed = 7/8 ÷ 1/2
7/8 x 2 = 7/4 = 1 3/4 miles per hour
Leslie's average speed = 1 ÷ 1/3
1 x 3 = 3 miles per hour
Bryan's average speed = 3/4 ÷ 3/4
3/4 x 4/3 = 1 mile per hour
Javier's average speed = 1 ÷ 2/3
1 x 3/2 = 1 1/2 miles per hour
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A doll sold for $209 in 1977 and was sold again in 1989 for $467. Assume that the growth in the value V of the collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V0=209
b) Find the Exponential growth function in terms of t, where t is the number of years since 1977
c) Estimate the value of the doll in 2009.
d) What is the doubling time for the value of the doll to the nearest tenth of a year?
e) Find the amount of time after which the value of the doll with be $2221
Step-by-step explanation:
the exponential growth function is
f(t) = v0 × (1 + k)^t
1977 to 1989 is 12 years (t).
a)
so, we have
467 = 209 × (1 + k)¹²
467/209 = (1 + k)¹²
12th root(467/209) = 1 + k = 1.069295033...
k = 0.069295033...
b)
f(t) = 209 × 1.069295033...^t
c)
2009 = 32 years after 1977
f(32) = 209 × 1.069295033...³² = $1,783.478472... ≈
≈ $1,783.48
d)
double the value of 209 is 418.
418 = 209 × 1.069295033...^t
2 = 1.069295033...^t
t = log1.069295033...(2) =
= log(2)/log(1.069295033...) = 10.34554457... ≈
≈ 10.3 years
e)
2221 = 209 × 1.069295033...^t
2221/209 = 1.069295033...^t
t = log1.069295033...(2221/209) =
= log(2221/209)/log(1.069295033...) =
= 35.27452616... years ≈
≈ 35.3 years
35 years would mean end of 2012. so, 35.3 years would be early 2013.
help please, right answers only
Part a: p gets closer to 0, the number of T-shirt purchased increases.
Part b: p gets larger, the number of T-shirt purchases decreases: so it is a decreasing function.
What is defined as the decreasing function?As we approach towards the right side of the x-axis, the graphs of increasing and decreasing functions, respectively, shift upward and downward. A function is considered to be decreasing on to an interval I if it has the value f(x) ≥ f(y). for any two values in the interval I that are such that x < y.For the given function;
The relation of the number of T-shirt and the price of the T-shirt are given by the function; n(p) = 800/p.
The graph of the function is given as; y = n(p)
From, the graph it is clear that when, the value on x axis increases, the value on y-axis decreases.
Thus, the function is decreasing function.
Part a: p gets closer to 0,
Now, when, p gets closer to 0, the number of T-shirt purchased increases as the there is a reduction of the price of T-shirt.
Part b: p gets larger.
When p gets larger, the number of T-shirt purchased decreases, as there is a increase in the price of the T-shirt.
Thus, the T-shirt purchased will be reduced.
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11/7 Thursday Math Math Hw. Fractions
Answer:
96, $ 144
Step-by-step explanation:
WHat is 5/1 x 4/5 This is a hard one
4
Step-by-step explanation:
[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]
[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]
[tex]{ \tt{ = \frac{20}{5}}} [/tex]
[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]
Im giving 20 points for this
Answer:
(B)={8,10,15,18,20}
Step-by-step explanation:
Identify the values of the variables. Give your answers in simplest radical form. Help!
Considering the right angle triangle given the values of the variables are
n = 2√3k = 4√3How to determine the values of the variablesInformation from the question
right angle triangle
The values of the variables is worked using SOH CAH TOA
The right angle triangle of sides as described below
hypotenuse = k
opposite = n
adjacent = 6
The variable n is solved using tan, TOA, the angle is 30
tan 30 = Opposite / Adjacent
tan 30 = n / 6
tan 30 * 6 = n
n = 2√3
The variable k is solved using cos, CAH, the angle is 30
cos 30 = Adjacent / Hypotenuse
cos 30 = 6 / k
k = 6 / cos 30
k = 4√3
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16. Use the number line to help you decide which statement is true.
Answer: The answer is D ( 2/5 < 1/2
Step-by-step explanation:
Chang will run at least 21 miles this week. So far, he has run 12 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
Using an inequality to represent the problem, Chang must run at least an additional 9 miles or greater than 9 miles
What is an InequalityIn Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
To find the number of additional miles he will run, let's set the unknown number equals t
12 + t > 21
t > 21 - 12
t >9
Chang will need to run at least 9 miles
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Find the measure of the exterior angle. (hint: find x first, then plug it in to the exterior angle)
Answer:
[tex]3x - 10 = 25 + x + 15[/tex]
according to theorem
[tex]3x - x = 40 + 10 \\ 2x = 50 \\ x = 25[/tex]
Hopefully this will help u
Michel is taking 4 credit hours of courses at his local community college. Each credit hour costs $110.50. He is also to pay three technology fees of $19.25. Determine the total amount that he will pay in tuition.
Total: 499.75
Step-by-step explanation:
4 × 110.5 = 442
3 × 19.25 = 57.75
442 + 57.75 = 499.75
I’m doing my geometry homework and don’t remember the formula or way to solve the lengths of a triangle side with graph points. How do I solve both parts of #1?
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }[/tex]
From ratio proportion for the following using
2 different way
45 members of Glee Club to 30 members of Dance
Club
Answer:
see explanation
Step-by-step explanation:
this can be expressed in ratio form and fractional form , that is
45 : 30 ( divide each part by 15 )
= 3 : 2 ← in simplest form
= [tex]\frac{3}{2}[/tex]
Luis has $80 in his checking account. He makes a deposit of $100, and the write a check for $40
Answer: 140 is the answer
Step-by-step explanation: Luis adds 100 to his account so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account
A website got 4 × 10^9 views on Saturday and 8 × 10^6 views on Sunday. How many times more views were on Saturday than Sunday?
There were 500 times more views were on Saturday than Sunday
In this question, we have been given a website got 4 × 10^9 views on Saturday and 8 × 10^6 views on Sunday.
We need to find the number of times more views were on Saturday than Sunday.
We need to divide 4 × 10^9 by 8 × 10^6
( 4 × 10^9) / (8 × 10^6)
= (4/8) * 10^(9 - 6) ..............(rule of exponents)
= 0.5 * 10^3
= 500
Therefore, there were 500 times more views were on Saturday than Sunday.
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Question 6
The functions g is defined on the real numbers by g (x) = (x² + 1) (3x - 5). What is the value
of g(4) ?
-51
63
119
175
Answer: 119
Step-by-step explanation:
(4^2+1)(3*4-5)
=(16+1)(12-5)
=17*7
=119
Answer:
g(4) = 119
Step-by-step explanation:
g(x) = (x² + 1) (3x - 5)
Substitute x for 4 in the equation
g(4) = (4² + 1) (3(4) - 5)
g(4) = (16 + 1) (12 - 5)
g(4) = (17) (7)
g(4) = 119
Hence, the value of g(4) is 119
Expand and simplify 5(x + 7) + 3(x–2)
Answer:
8x + 29
Step-by-step explanation:
[tex]5(x + 7) + 3(x–2) \\ 5 \times x + 5 \times 7 + 3 \times x - 3 \times 2 \\ 5x + 35 + 3x - 6 \\ 5x + 3x + 35 - 6 \\ 8x + 29[/tex]
For which equation would x = 5 be a solution?
3x+6=21
12-2x = 13
7+ 6 x = 27
4x-7=27
A chemist is mixing a 30% salt solution with a 15% salt solution to make 60 L of a new solution that will contain 20% salt. How much of the 30% solution
should the chemist use?
20 amount of 30% salt solution
How to find the salt solution percentage?
Divide the solute's gram weight by the total weight of the solution, then multiply the result by 100 to get the mass/mass percent of the solution. The amount of solute (measured in grams) per milliliter of solution is known as the mass/volume percent.
Let x be the amount of 30% salt solution
Then, 60-x = amount of 15% salt solution
Salt content of the first solution + salt content of second solution = salt content of the mixture
∴ 0.30x + 0.15(60-x) = 0.20*60
0.30x + 9 - 0.15x = 12
0.15x = 3
x = 20
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India's hourly wage is $10.50. If she
regularly works 40 hours per week, what is
her regular weekly pay?
Step-by-step explanation:
10 hours per week: $10.50 x 10 = $105.00
20 hours per week: $105.00 x 2 = $210.00
40 hours per week: $210.00 x 2 = $420.00
1. Which expression has a whole-number product?
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
C (-6+ i)(3- i)
D(-4+3i)(4-3i)
Option (B) (3 + 2i) (3 - 2i) is the expression that has the whole number product.
Whole number:
Whole number refers the numbers without fractions and it is a collection of positive integers and zero and represented by the symbol “W” and the set of numbers are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.
Given,
Here we have the following expression:
(A) (4- 2i) (4 - 2i)
(B) (3 + 2i) (3 - 2i)
(C) (-6+ i)(3- i)
(D) (-4+3i)(4-3i)
Now, we need to find the whole number product.
In order to find the solution we have to perform the multiplication on the given expression,
First expression will gives the following,
(A) (4 - 2i) (4 - 2i)
When we apply the (a-b)² formula in it then we get,
=> 4²+ (2i)² - (2 x 4 x 2i)
=> 16 - 4 - 16i
=> 12 - 16i
Which is not a whole number product.
Second expression,
(B) (3 + 2i) (3 - 2i)
Apply the (a + b)(a - b) formula in it,
Then we get,
=> 3² - (2i)²
=> 9 + 4
=> 13
Therefore, this one is the whole number product.
Third expression,
(C) (-6 + i) (3 - i)
When we perform the multiplication on it, then we get,
=> -18 + 6i +3i -i²
=> -18 + 9i + 1
=> -17 + 9i
his one is not a whole number product.
Final expression,
(D) (-4 + 3i) (4 - 3i)
When we perform the multiplication on it, then we get,
=> -16 + 12i + 12i - (3i)²
=> -16 + 24i + 9
=> -7 + 24i
This one is also no the whole number product.
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Given: m//n
Prove: angle 1 and angel 4 are supplementary
⇒ Supplementary angles are angles that add up to 180°
⇒ ∠1+∠2=180°(angles on a straight line)
∠2=∠4( Corresponding angles are equal m||n)
⇒*NOTE THE FOLLOWING STATEMENT IS TO MAKE YOU UNDERSTAND,IT MUST NOT BE INCLUDED IN YOUR ANSWERBOOK)
If ∠2=∠4
in the place of ∠2 in the equation ∠1+∠2=180° we can substitute ∠4 since the two angles (∠2 and ∠4) are equal by corresponding angles
______________________________________________________
⇒You may include this step now as you now know how ∠4 came up.
∴∠1+(∠4)=180°
∠1+∠4=180°
Now from the above equation we can see that ∠1 and ∠4 are supplementary angles as they both add up to 180°
Can someone please help me solve this, I’m so stressed
Answer:
3a. $8493.42
3b. 139.0 months
4a. 10
4b. 10.2 years
Step-by-step explanation:
Given exponential equations, you want values for specific times, and you want times for specific values.
In part (a), the value is found by substituting an appropriate value for t and doing the arithmetic.
In part (b), logarithms will be involved in solving for t.
3. Investment(a) Use t=12, the number of months in one year. You want the value of ...
S = 8000·1.005^12 ≈ 8493.42
The amount after 1 year is $8493.42.
(b) The time it takes to double the investment is the value of t such that ...
16000 = 8000·1.005^t
2 = 1.005^t . . . . . . divide by 8000
log(2) = t·log(1.005) . . . . . take logarithms
t = log(2)/log(1.005) ≈ 138.976
The investment will double in about 139.0 months.
4. Otters(a) Use t=0 and evaluate.
y = 2500 -2490e^(-0.1·0) = 2500 -2490 = 10
The population of otters was 10 when they were reintroduced.
(b) The time it takes for the population to reach 1600 is the value of t such that ...
1600 = 2500 -2490e^(-0.1t) . . . . use 1600 for y
-900 = -2490e^(-0.1t) . . . . . . . . . subtract 2500
900/2490 = e^(-0.1t) . . . . . . . . . divide by -2490
ln(900/2490) = -0.1t . . . . . . . . . take natural logs
t = ln(900/2490)/-0.1 . . . . . . . . divide by the coefficient of t
t ≈ 10.176 ≈ 10.2
It will be 10.2 years before the otter population reaches 1600.
Please help ASAP will mark brainliest
Plot the points ( -3, 7 ) and ( 9, 0)
Find the distance between the points and the midpoint of the line segment joining the points.
Answer: 13.89 units
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
help please only have till 12
y=mx+b
Answer:
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
The frequency table gives information about the numbers of mice in some nests
answer:
we need the table.
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be kilograms.
According to the scatter plot provided, the weight for someone who is 1.5 meters tall is predicted to be 45.45 kilograms.
What is a line of best fit?A line of best fit is also referred to as a trend line and it can be defined as a statistical and analytical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.
In this scenario, the weight (in kilogram) would be plotted on the y-axis of the scatter plot while the height (M) would be plotted on the x-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear function for the line of best fit is given by:
Weight, kg = -114.3 + 106.5M
When M = 1.5 meters, we have:
Weight, kg = -114.3 + 106.5(1.5)
Weight, kg = -114.3 + 159.75
Weight, kg = 45.45 kg.
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Complete Question:
According to the graph provided, the weight for someone who is 1.5 meters tall is predicted to be ____ kilograms.
