volumes from liters (L) to milliliters (mL), you can use the conversion factor that 1 L is equal to 1000 mL.
How to convert the volumes from liters (L) to milliliters (mL)?Knowing the relationship between the two units will make converting between litres and millilitres simple. Both litres and millilitres are measurements of a liquid's volume.
The basic measure of liquid capacity is the litre. The liquid volume can also be measured in millilitres, centilitres, and kilolitres. All of these units have different values from one another.
Similar to millilitres, litres also denote volume, however one litre is equivalent to one thousand millilitres (1 L = 1000 mL).
To convert the given volumes from liters (L) to milliliters (mL), you can use the conversion factor that 1 L is equal to 1000 mL. Here are the conversions:
4.27 L = 4.27 x 1000 mL = 4270 mL
0.35 L = 0.35 x 1000 mL = 350 mL
0.06 L = 0.06 x 1000 mL = 60 mL
9.05 L = 9.05 x 1000 mL = 9050 mL
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In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 30, there is a .5034 probability of obtaining a sample mean within +/- $500 of the population mean. A. What is the probability that the sample mean is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?
B. What is the probability that the sample mean is within $500 of the population mean if a sample of size 120 is used (to 4 decimals)?
A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611
B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362
The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.
The formula for calculating the standard error of the mean is
SE = σ/√n
where SE is the standard error, σ is the population standard deviation, and n is the sample size.
For n = 30, SE = 4,000/√30 = 729.16
A. For a sample size of n = 60, SE = 4,000/√60 = 516.40
To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error.
For a range of +/- $500, the z-scores are
z = ($51,300 - $51,800) / 516.40 = -0.969
z = ($52,300 - $51,800) / 516.40 = 0.969
Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.
B. For a sample size of n = 120, SE = 4,000/√120 = 368.93
Following the same steps as above, the z-scores for a range of +/- $500 are
z = ($51,300 - $51,800) / 368.93 = -1.364
z = ($52,300 - $51,800) / 368.93 = 1.364
Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.
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Your friend in college decides to purchase textbooks using his credit card, which has an APR
(Annual Percentage Rate) of 12.5% compounded continuously. He charges $500 for the
textbooks. Without making any payments, after how many years will his credit card balance be
$1360? Round your answer to the nearest year.
If your friend in college decides to purchase textbooks using his credit card. The number of year his credit card balance be $1360 is 8 years.
How many years will his credit card balance be?We can use the continuous compounding formula to solve this problem:
A = Pe^(rt)
where A is the ending balance, P is the initial balance, e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time in years.
In this case, we want to solve for t when P = 500 and A = 1360. The interest rate is given as 12.5% compounded continuously, which means r = 0.125. Substituting these values into the formula, we get:
1360 = 500e^(0.125t)
Dividing both sides by 500, we get:
e^(0.125t) = 2.72
Taking the natural logarithm of both sides, we get:
0.125t = ln(2.72)
Solving for t, we get:
t = ln(2.72)/0.125 ≈ 8
Rounding to the nearest year, we get that it will take 8 years for the credit card balance to reach $1360 without making any payments.
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The population of Log Village is 1800 in 2010, and the population increases each year by 9%. What equation is used to determine the population, y, of Log Village x years after 2010?
The equation that will be used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ
What is equation?
An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.
The population of Log Village is 1800 in 2010, and the population increases each year by 9%.
Initial population(p)= 1800
rate of increase(r)= 9%
Time(t)= x years.
The formula for the population after n years is p(1+r/100)ⁿ.
To determine the equation for the population after x years we have to put the values in the above expression.
So putting all the values we get,
The population, y, of Log Village x years after 2010 is
y= 1800( 1+9/100)ˣ
y= 1800(1.09)ˣ
Hence, The equation that will be used to determine the population, y, of Log Village x years after 2010 is y= 1800(1.09)ˣ
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a one-hectare forest community is sampled in early august. the sample yields 12 small trees, 4 types of vines, as well as 17 native shrubs that represent 10 species. what can be estimated from the sample for the shrubs in the forest community?
Based on the sample of a one-hectare forest community in early August, an estimate can be made for the total number and diversity of shrub species present in the community.
From the sample of the one-hectare forest community, several estimates can be made for the shrubs in the forest community:
Abundance: The abundance of shrubs in the one-hectare forest community can be estimated by multiplying the number of shrubs in the sample by 10 (the number of species represented by the sample). Therefore, an estimate of the total number of shrubs in the one-hectare forest community would be 17 x 10 = 170 shrubs.
Species richness: The sample contained 10 species of shrubs. This can be used as an estimate of the total number of shrub species in the one-hectare forest community.
Diversity: The diversity of the shrub community in the one-hectare forest can be estimated using the data on species richness and abundance. The most commonly used metric for estimating diversity is the Shannon-Wiener diversity index, which takes into account both the number of species and their relative abundance.
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The wheels on a bike have a diameter of 26 inches. How many full revolutions will the wheels need to make to travel 100 feet?
Answer:
Step-by-step explanation:
distance traveled by one revolution = circumference of the wheel
= 2πr = 2π(13 inches) = 26π inches
number of revolutions = distance traveled / distance traveled by one revolution
100 feet = 1200 inches
= 1200 inches / 26π inches
≈ 45.91 full revolutions
If you have a polygon with a number of sides, n, that does not have a special name like triangle or nonagon, what do you call it?
A polygon with n sides is simply referred to as an n-gon.
A polygon with n sides is simply referred to as an n-gon. This naming convention allows for any polygon to be easily identified based on the number of sides it has, without the need for a specific name for every possible number of sides.
For example, a polygon with 3 sides is called a triangle, a polygon with 4 sides is called a quadrilateral, while a polygon with 5 sides is called a pentagon. However, for polygons with sides greater than 12, the names become less commonly used, and n-gon is often used instead as a general term to describe any polygon with n number of sides.
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A polygon with a number of sides, n, that does not have a special name is typically referred to as an "n-gon".
A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges. Vertex or corners refer to the intersection of two line segments, where an angle is created. Having three sides makes a triangle a polygon. A circle is a plane figure as well, but it isn't regarded as a polygon because it's curved and lacks sides and angles. So, while all polygons are two-dimensional shapes, not all two-dimensional figures are polygons.
For example, a polygon with 5 sides would be called a pentagon, but a polygon with 7 sides would simply be called a heptagon or a 7-gon.
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The histogram below shows the results of a survey on the number of traffic tickets received by a random group of drivers. 3 86 76 51 Number of People A 1 9 2 Traffic Tickets 10 8 6 Number of Traffic Tickets Step 6: How many people received either 4 or 5 traffic tickets? 12
In reference to the given histogram, an absence of bars signifying either 4 or 5 traffic tickets implies that no one from the selection had accumulated this amount.
How to explain the histogramIt should be noted that to make sure our point is accurate, we can sum the heights of the separate bars for 3, 6 and 8 tickets which demonstrate the total people included within the survey who have acquired the relevant number of traffic citations.
The height of the bar for three violations measures out at 1.
Conversely, a measurement of 2 denotes the bar for six infringements.
An assessment of 1 has been given to the bar with regards to eight offences.
Due to the lack of representation mentioned in the histogram concerning both 4 and 5 transgressions, it confirms our inference: nobody from the selection received four or five traffic tickets.
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4. One of the players scored 13. 7 points per game with 4. 1 free throw attempts per game. How does this compare to what the model predicts for this player?
The model predicts that the player should score around 17.47 points per game based on their 4.1 free throw attempts per game. However, the player's observed score of 13.7 points per game suggests that they may be underperforming compared to what would be expected based on this relationship.
Let us assume that the model predicts a linear relationship between points per game and free throw attempts per game, we can calculate the predicted value of points per game for this player using the regression equation
points per game = slope * free throw attempts per game + intercept
From the given data, we know that the slope of the regression line is 2.6 and the intercept is 7.1. Plugging in the values for this player, we get:
points per game = 2.6 * 4.1 + 7.1 = 17.47
So the model predicts that this player should score approximately 17.47 points per game, which is higher than the observed value of 13.7 points per game. This suggests that this player may be underperforming compared to what would be expected based on their free throw attempts per game.
However, just one player and there may be other factors that could affect their performance beyond just free throw attempts per game.
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Sue and 4 friends share half a pizza. Each piece of pizza is the same size. Sue believes each piece of pizza has an angle measure of 30º. Is Sue correct? Explain.
Sue statement that each piece of pizza has an angle measure of 30º is incorrect
Stating if Sue's statement is correctAssuming the pizza is circular, we know that the total angle measure of a circle is 360 degrees.
If we cut the pizza into halves, we have two equal pieces, each with an angle measure of 180 degrees.
If Sue and her 4 friends share half a pizza, they are sharing one of these equal pieces.
If we divide the 180 degree angle of the piece of pizza by 5 (Sue and her 4 friends plus Sue herself), we get an angle measure of 36 degrees, which is what Sue believes.
Therefore, Sue is incorrect.
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please help asap this is for geometry its R.4
The value of k is given as follows:
k = 2.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that the parameters are given as follows:
k is the hypotenuse.The side length adjacent to the angle of 45º is of [tex]\sqrt{2}[/tex].Hence the equation to obtain k is given as follows:
[tex]\sin{45^\circ} = \frac{\sqrt{2}}{k}[/tex]
[tex]\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{k}[/tex]
k = 2.
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What is the sum and the product of x^2-9x+8
The sum of the roots of x² - 9x + 8 is 9. The product of the roots of x² - 9x + 8 is 8.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
According to question:The expression x² - 9x + 8 can be factored as follows:
x² - 9x + 8 = (x - 1)(x - 8)
To check that this factorization is correct, you can expand the expression using the distributive property:
(x - 1)(x - 8) = x² - 8x - x + 8 = x² - 9x + 8
So the factorization is indeed correct.
The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -9, and c = 8, so the sum of the roots is:
-sum of roots = -b/a = -(-9)/1 = 9
Therefore, the sum of the roots of x² - 9x + 8 is 9.
The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a. In this case, c = 8 and a = 1, so the product of the roots is:
product of roots = c/a = 8/1 = 8
Therefore, the product of the roots of x² - 9x + 8 is 8.
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175% of what number is 31
Step-by-step explanation:
To find the number that is 175% of 31, we can use the following formula:
175% of X = 31
Mathematically, we can represent 175% as 1.75 (since percentage is a ratio out of 100).
So, the equation becomes:
1.75 * X = 31
To solve for X, we divide both sides of the equation by 1.75:
X = 31 / 1.75
Using a calculator, we can evaluate the right-hand side to find the value of X:
X ≈ 17.714
So, 175% of approximately 17.714 is equal to 31.
Answer:
17.714
Step-by-step explanation:
BigDecimal gives you control over how values are rounded. By default:
a. all calculations are approximate and no rounding occurs.
b. all calculations are approximate and rounding occurs.
c. all calculations are exact and no rounding occurs.
d. all calculations are exact and rounding occurs.
BigDecimal gives you control over how values are rounded. By default option(d) all calculations are exact and rounding occurs.
BigDecimal is a Java class that provides a way to perform exact calculations on decimal numbers with a high degree of precision and control over rounding. Unlike primitive data types, such as double and float, which are prone to rounding errors due to their binary representation, BigDecimal stores numbers using a base-10 representation, allowing for more precise calculations.
Additionally, it allows the programmer to specify rounding rules, such as rounding up or down to a certain number of decimal places, ensuring that the results of calculations are accurate and consistent. This makes BigDecimal a useful tool for applications that require precise numerical calculations, such as financial and scientific applications.
Therefore, the correct option is (d) all calculations are exact and rounding occurs
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Rafi downloads a song from an online service. A few minutes later, a customer in another city searches for a song on the same site. Are these two events dependent or independent?
These two events are independent. The action of Rafi downloading a song does not affect the probability of another customer in another city searching for a song on the same site.
Explaing if these two events are dependent or independent?The two events, Rafi downloading a song and a customer searching for a song, are independent because the occurrence of one event does not affect the probability of the other event occurring.
In other words, the actions of Rafi do not affect the actions of the customer in another city, and vice versa. The two events are unrelated and can occur simultaneously without affecting each other.
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please help would be amazing
Answer:
(9,8)
Step-by-step explanation:
Solve the first equation
then solve the second equation with the substitute number from the first equation.
Corey buys 27 inches of trim for a craft project
If Corey buys 27 inches of trim for a craft project, Corey bought 3/4 of a yard of trim for the craft project.
To determine what fraction of a yard Regina buys, we need to know how many inches are in a yard. There are 36 inches in a yard.
To convert 27 inches to yards, we need to divide by 36:
27 ÷ 36 = 0.75 yards
So Corey bought 0.75 yards of trim for the craft project.
To find the fraction of a yard, we need to express 0.75 as a fraction with a denominator of 1:
0.75 = 75/100 = 3/4
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Complete question is:
Corey buys 27 inches of trim for a craft project. What fraction of a yard does Regina buy?
I need to know how to do these and if I got the one right
23. The value for x in triangle is 11.14
24. The value for x in the triangle is 18.3
25. The value for x = 30.4
27 The value for x = 63.413 degrees
Sine, Cosine and Tangent23
Cos θ= adj/ hyp
cos 42= x/15
x = 15 cos 42
x = 11.14
24
tan θ= opp/ adj
tan 31= 11/ x
x(tan 31)= 11
x = 11/tan 31
x = 18.3
25
cos θ= adj/ hyp
cos 18= 29/x
x(cos 18) = 29
x = 29/ cos 18
x = 30.4
27
sin x = opp/ hyp
sin x = 17/19
sin x = 0.8947
x = 63.413 degrees
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Look at this set of 5 numbers:
32 52 29 32 25
Which value would change the most if the number 80 replaced the number 25 in the set?
The measure of central tendency that will change the most in the data set is: Mean
How to find the measure of central tendency?The mean is defined as the average value of a distribution which is obtained by dividing the sum of the values by the frequency.
The median is defined as the number at the middle of the distribution. It is obtained by arranging the values in ascending order and picking the mid value.
The mode is defined as the value which has the most number of occurrences in the distribution.
The set of numbers can be arranged as:
25, 29, 32, 32, 52
The mean = 34
Mode = 32
Median = 32
If we replace 25 with 80, we will have:
Mean = 45
Mode = 32
Median = 32
Thus, the mean will change the most
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Select the correct answer.
The graph of function f is shown.
Function g is represented by the equation.
g(x) = 4(1/4)^x +2
Which statement correctly compares the two functions?
A. They have different y-intercepts but the same end behavior.
B. They have different y-intercepts and different end behavior.
C. They have the same y-intercept and the same end behavior.
D. They have the same y-intercept but different end behavior.
Answer:
A. They have different y-intercepts but the same end behavior.
Step-by-step explanation:
From the shape of f we see that its a descending exponential fnction, so the factor taken to the power x will be a fraction, and from the points the eqation is
f(x) = 2(1/4)^x + 2
and the y-intercept is 4
g(x) has y-intercept of 4(1/4)^0 + 2 = 6 so they are different.
As x approaches infinity both f and g approach 2 so the end behavior s the same.
Help on this pls due tmrw
5. The value of x in the figure is
C. 6√77. Length of arc AD is 125 degrees
8. Angle ROT is 36.87 degrees
How to find the length of chord xThe length of chord x is solved using Pythagoras theorem as follows
5.
let x/2 = y then we have
y² = 12² - 9 ² = 144 - 81 = 63
y = √63 = 3√7
and x/2 = y = 3√7. so x = 6√7
7. BD is the diameter hence arc BAD = 180 degrees
if arc ABC is 110 then arc BA = 110 /2 = 55
Arc AD = arc BAD - arc BA
Arc AD = 180 - 55
Arc AD = 125 degrees
8. Angle ROT = arc sin (3/5)
Angle ROT = 36.87 degrees
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Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
The correct answer is: The IQR of 13 is the most accurate to use, since the data is skewed. (Option B).
The correct answer is: Together, Streetcar and Cable Car are the preferred transportation for 168 residents. (Option A).
The correct answer is: The IQR is the best measure of variability, and it equals 6.
How to Solve the Problem?1. Since the data is skewed, it is not appropriate to use the range as a measure of variability. The range is sensitive to extreme values and can be misleading in skewed data. The interquartile range (IQR) is a better measure of variability for skewed data since it is not affected by extreme values. Therefore, the charity should use the IQR of 13 as the measure of variability for this data.
2. From the circle graph, we can draw the following conclusion:
Together, Streetcar and Cable Car are the preferred transportation for 27% + 15% = 42% of the residents. 42% of 400 is 168 residents.
3. The line plot shows that the data is discrete and not continuous. Also, the data is not normally distributed and is skewed. Therefore, the range is not an appropriate measure of variability. The interquartile range (IQR) is a better measure of variability for skewed data. The IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data.
From the plot, we can see that Q1 is 2 and Q3 is 8. Therefore, the IQR is 8 - 2 = 6.
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Estefanía has 2,593 euros and Rocío has 3,238 euros. How much money does Rocío have more than Estefanía?
The amount of money with Rocio has 645 euros more than Estefania.
Total amount of money with Estefania has = 2,593 euros
Total amount of money with Rocio has = 3,238 euros
When we compare the amount of money of both Estefania and Rocio
Rocio has more amount of money than Estefania .
3,238 Euros is greater than 2,593 Euros
To find out how much money Rocio has more than Estefania,
= Subtract Estefania's amount of money from Rocio's amount of money.
= 3,238 euros (Rocio's money) - 2,593 euros (Estefania's money)
= 645 euros
Therefore, Rocio has 645 euros more amount of money than Estefania.
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Which of these nets can be folded to form a square prism?
in which one of the four scenarios would you consider a non-parametric test? group of answer choices when we are dealing with time series when we have numeric data and want to plot a regression line when we want to perform multiple regression when we only have ordered data
Non-parametric tests are statistical tests that do not require specific assumptions about the population distribution, such as normality or equal variances. They are useful in situations where the data does not meet the assumptions of parametric tests, or when the variables are ordinal or categorical.
There are some additional examples of non-parametric tests.
When the data is skewed or has outliers: If the data is not normally distributed, non-parametric tests such as the Wilcoxon rank-sum test or the Kruskal-Wallis test can be used instead of the t-test or ANOVA.When the sample size is small: If the sample size is small, it may be difficult to determine if the data is normally distributed or if variances are equal. In this case, non-parametric tests such as the Mann-Whitney U test or the Wilcoxon signed-rank test may be more appropriate.When the data is categorical or ordinal: If the data is categorical or ordinal, non-parametric tests such as the Chi-square test or Spearman's rank correlation coefficient can be used instead of parametric tests.When the data violates assumptions of independence: If the data is not independent, non-parametric tests such as the Friedman test or the McNemar's test may be used.Hence, non-parametric tests offer a flexible alternative to traditional parametric tests and can be useful in a variety of situations.
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6. Justin listed these items on his deposit slip: (bills) 8 one-hundreds, 27 fifties, 83 fives, 141 ones; (coins) 13 quarters, 117 nickels; (checks) $317.94, $57.89, $527.24, $77.49. He received cash back of 30 twenties and 11 tens. What total deposit did he make?
Justin made a total deposit of $1985.66.
What is deposit?A deposit is a sum of money that is added to an account or made available for use in a financial transaction. It can refer to money that is placed into a bank account, such as a savings or checking account, or to a payment made in advance for goods or services. Deposits are often required when b accounts, taking out loans, or making large purchases.
In the context of banking, deposits can earn interest, which can increase the amount of money in the account over time.
Let's start by adding up the bills:
Total amount of bills = 8 x 100 + 27 x 50 + 83 x 5 + 141 x 1
Total amount of bills = 800 + 1350 + 415 + 141
Total amount of bills = 1706
Next, let's add up the coins:
Total amount of coins = 13 x 0.25 + 117 x 0.05
Total amount of coins = 3.25 + 5.85
Total amount of coins = 9.10
Now, let's add up the checks:
Total amount of checks = 317.94 + 57.89 + 527.24 + 77.49
Total amount of checks = 980.56
Finally, let's add up the cash back:
Total amount of cash back = 30 x 20 + 11 x 10
Total amount of cash back = 600 + 110
Total amount of cash back = 710
To find the total deposit, we need to add up all the amounts:
Total deposit = Total amount of bills + Total amount of coins + Total amount of checks - Total amount of cash back
Total deposit = 1706 + 9.10 + 980.56 - 710
Total deposit = 1985.66
Therefore, Justin made a total deposit of $1985.66.
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Solve for x. Round your answer to the nearest tenth, and type it in the blank without units.
X is the adjacent side and is 50 inches long.
Right angle triangleUsing the trigonometric ratio of cosine:
cos(60 degrees) = adjacent / hypotenuse
cos(60 degrees) = 1/2 (cosine of 60 degrees is 1/2)
So, we can solve for the X, the adjacent:
adjacent = cos(60 degrees) x hypotenuse
adjacent = (1/2) x 100 inches
adjacent = 50 inches
Therefore, the length of the adjacent is 50 inches.
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the mean of a normal probability distribution is 480; the standard deviation is 12. a. about 68% of the observations lie between what two values?
The difference between two observation concerning the values are 68% of observation lie in between 468 and 492 , then 95% of observation lie in 456 and 504.
The normal distribution is considered a continuous probability distribution that has a different bell-shaped probability density function. Therefore, the mean of a normal distribution is the center of its symmetric bell-shaped curve.
Therefore it is given , a normal distribution with mean of 480 and standard deviation 12
Lower limit = Mean - Standard deviation = 480 - 12 = 468
Upper limit = Mean + Standard deviation = 480 + 12 = 492
Following the same procedure then the results to evaluate for 95%
The difference between two observation concerning the values are 68% of observation lie in between 468 and 492 , whereas 95% of observation lie in 456 and 504.
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Sarah is turning 27 today. In the mail, she received 14 envelopes, and each envelope included $2. 70. How much money did she receive in the mail?
If in the mail, she received 14 envelopes, and each envelope included $2. 70,Sarah received a total of $37.80 in the mail.
Sarah received a total of 14 envelopes, and each envelope had $2.70. To find out how much money she received in total, we can multiply the number of envelopes by the amount of money in each envelope:
Total money = 14 × $2.70
We can simplify the expression by first multiplying the whole number, 14, by the tenths value of $2.70, which is $0.70:
Total money = $37.80
This amount of money is the sum of all the money in the 14 envelopes she received. It can be useful to double-check the answer by adding up the amounts in each envelope manually, but in this case, it is not necessary since we have already calculated the total.
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1. Calculate the area of the following parallelogram:
28 in²
26 in²
40 in²
30 in²
Option D is correct, the area of given parallelogram is 30 square inches
Parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Area of parallelogram =bh
=10×3
=30 square inches
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An electrician is running wire from the electric box on a house to a utility pole 85 feet away. The angle of elevation to the connection on the pole is 17°. How much wire does the electrician need? (Round your answer to two decimal places.)
The electrician needs approximately 296.26 feet of wire.
What is trigonometry?The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).
According to question:The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.
Using trigonometry, we can write:
sin(17°) = opposite / hypotenuse
where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:
hypotenuse = opposite / sin(17°)
To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:
tan(17°) = opposite / 85
Solving for the opposite side, we get:
opposite = 85 tan(17°)
Substituting this into the formula for the hypotenuse, we get:
hypotenuse = (85 tan(17°)) / sin(17°)
hypotenuse ≈ 296.26 feet
Therefore, the electrician needs approximately 296.26 feet of wire.
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