The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to 2 decimal places
Answers
Answer:
Step-by-step explanation:
We'Re looking at a normal distribution here- let's start by drawing it out to the mean me- is 315 grams standard. Deviation is 16 point. We want to know the weight corresponding to each of these events and we can use either the appendix which i assume is a z, school table or excel so the first 1. We want the highest 20 percent up here somewhere. This is what we would call the 80 percent. It separates the bottom 80 percent from the highest 20 percent. So how do we work the well? We need to start by getting the z score for it. So how do we get that, while in excel you're going to use the norm inverse function which looks like this? So it's calls norm and then in here you just put in x, where x is your percentage and that will spit out the z score and i'm using this rather than a table, because it will give me a more exact value. So we're going to do that, and so here the percent is the 80, so it's not .8 and that spits out the z score of nort .8416 to 4 decimal places. But i'm always going to this exact score, because we now have to turn it from a z score to a piece of real data. Z score is a measure of how many standard deviations away from the mean a value is so we're. Looking for the value not .84 standard deviations, above the mean or if we write it like this x, is equal to z, sigma plus mu. So here we take our exact zedscore, because we can still just use excels, multiply it by 16 and add it on to the mean and we'll get our value of 328.447328 .47 grams to 2 decimal places for part b. We want to be middle 60 percent. Now we need to cut off points and within here where, in this interval we have 60 percent of values, which means we have 40 percent of values, not in here. So we can label our 3 sections. These 2 add up to 40 percent, so they have to be 20 percent. Each are called nor .2 and not .2, and then this middle bit here is nor .6 for the total of 100 percent point. So we need these cut off points when you, the z, scores first, and because these are equal distances away from a mine they're going to have the same z score. Just 1 is going to be positive or negative, so z is going to be equal to plus and minus. Let'S look at the lower 1. This is the 20 percent here so into this excel command. We put 20 percent nor .2 and out of it we get the z score of minus, not .8416. So it's actually very similar to the top question, because the top question asked you for the 80 percent be 80 percent. Is the upper cut off point here? 20? Is below cutoff point, so we already have the up 1, let's just calculate below 1, so we've got to be minus, nor .8416 multiplied by 16, but the standard deviation and on to the mean- and we get 301.53 and the upper cut off point is from part A so that's the middle 60 percent makes more space a part c. We want to be highest 80 percent. So now what we want is the cut off between the lowest 20 and the highest 80, which we've just got from part c part b. It'S this lower 1, here, 301.53 grams. That'S an easy! 1! Now we want the lowest 15 percent, so the lowest 15 percent is the 15 percent. So we go to our exylgamant put in the 15 for percent, so that would be no .15 and it's a z score of minus 1.036 keeping the exact value put into this formula. We multiply our z by 16, as on 315, to get 298.42 grams.
The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.
What is normal distribution?To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:
z = (x - μ) / σ
where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).
Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:
x = μ + z * σ
where z is the z-score that corresponds to the desired probability.
Event 1: The weight is less than 345 grams.
z = (345 - 360) / 9 = -1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.
x = 360 + (-1.67) * 9 = 344.03 grams
Therefore, the weight that corresponds to this event is approximately 344.03 grams.
Event 2: The weight is between 355 and 365 grams.
First, we need to find the z-scores that correspond to the two boundaries:
z1 = (355 - 360) / 9 = -0.56
z2 = (365 - 360) / 9 = 0.56
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:
0.7123 - 0.2123 = 0.5
x1 = 360 + (-0.56) * 9 = 355.16 grams
x2 = 360 + (0.56) * 9 = 364.84 grams
Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.
Event 3: The weight is greater than 375 grams.
z = (375 - 360) / 9 = 1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.
x = 360 + (1.67) * 9 = 375.97 grams
Therefore, the weight that corresponds to this event is approximately 375.97 grams.
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Related Questions
What is the probability that a 43% free-throw shooter will miss her next free throw?
Answers
Answer:
57%
Step-by-step explanation:
Answer:
.57 or 57%
Step-by-step explanation:
If a basketball player has a free-throw shooting percentage of 43%, it means that she makes 43% of her free throws on average. Therefore, the probability that she will miss her next free throw is equal to the complement of her shooting percentage, which is 1 minus 0.43. This simplifies to 0.57 or 57%. So, the probability that she will miss her next free throw is 57%.
Use the Law of Cosines to solve the problem. You must solve for BC first. Solve this order
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173 miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it turn when it changed direction? Show you Work.
Answers
answer: 175
Step-by-step explanation:
Answer:
71.9 degrees
Step-by-step explanation:
The find the value of x on the given diagram, we must first find the included angle between the two line segments labelled 94 mi and 119 mi in the triangle. To do this, we can use the Law of Cosines.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
The values to substitute into the formula are:
a = 119b = 94c = 173Solving for the angle C:
[tex]\begin{aligned}173^2&=119^2+94^2-2(119)(94)\cos C\\\\29929&=14161+8836-22372\cos C\\\\29929&=22997-22372\cos C\\\\6932&=-22372\cos C\\\\-\dfrac{6932}{22372}&=\cos C\\\\C&=\cos^{-1}\left(-\dfrac{6932}{22372}\right)\\\\C&=108.0502874...^{\circ}\end{aligned}[/tex]
As angles on a straight line sum to 180°, the value of x can be calculated by subtracting the found value of C from 180°:
[tex]x=180^{\circ}-108.0502874...^{\circ}[/tex]
[tex]x=71.9497125...^{\circ}[/tex]
[tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the ship turned 71.9 degrees north of west when it changed direction.
20/8as a mixed number in its simplest form
Answers
Answer:
2 1/2
Step-by-step explanation:
20/8=2r4
2r4= 2 4/8
2 4/8 = 2 1/2
Answer:
2 1/2
Step-by-step explanation:
Step 1:
We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
20/8= 2.5 = 2
Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.
Step 2: Get the new numerator
To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:
20 - (8 x 2) = 4
Step 3: Our mixed fraction
We've now simplified 20/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:
2 4/8
Step four: Convert it by simplifying
2 4/8 = 2 1/2
HELP MEHHHH! I WILL MARK YOU BRAINLIEST! I NEED AN EXPLANATION
Answers
This illustrates the rule of large numbers, according to which the sample mean approaches the population mean as the sample size rises.
what is probability ?The likelihood or chance of an occurrence occurring is measured by probability. It is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the occurrence. Additionally, probabilities can be stated as percentages, with 0% denoting an improbable event and 100% denoting a specific event. By dividing the number of favourable outcomes by the total number of potential outcomes, the probability of an occurrence is determined.
given
Since there are six potential outcomes and only one of them is a 5, the theoretical probability of rolling a 5 on a fair die is 1/6.
Mya's experimental chance of rolling a 5 after 100 trials is 25/100, which can be expressed as 1/4. Her experimental probability after 200 attempts is 30/200, which can be expressed as 3/20.
This implies that the experimental probability moves closer to the theoretical probability as the number of trials rises.
In other words, Mya's experimental findings get closer to the anticipated theoretical probability the more times she rolls the die.
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The complete question is :- Communicate and Justify Mya rolls a fair die and counts the number of times she rolls a 5. She rolls a 5 on 25 of the first 100 trials. She rolls a 5 on 30 of the first 200 trials. Compare the experimental probability to the theoretical probability after 100 trials and 200 trials. What do you notice? Explain.
Tell me which brand or which size is a better buy.
Answers
Answer:
The answer is brand B
Step-by-step explanation:
You divide $14.88 by 24 which equals 68 cents per item.
Then brand B is 60 cents per item which is the better buy!
Graph to solve the system: y=-3/2 and y=(1/2) × -1 At what x-values are the equations equal?
Answers
the x-value that makes the two equations equal is x = -1. and x=0.
equation defineAn equation consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), connected by an equals sign (=). The LHS and RHS may contain one or more variables, which are values that can change or vary.
The first equation, y = -3/2, is a horizontal line with a y-intercept of -3/2. This means that no matter what x-value we plug in, the corresponding y-value will always be -3/2.
The second equation, y = (1/2) x - 1, is the equation of a line with slope 1/2 and y-intercept -1. To find the x-value(s) where this equation equals -3/2, we can set the two equations equal to each other:
-3/2 = (1/2) x - 1
Adding 1 to both sides, we get:
-1/2 = (1/2) x
Multiplying both sides by 2, we get:
-1 = x
At x=0, two equation satisfy the condition.
Therefore, the x-value that makes the two equations equal is x = -1 and 0.
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how many inches are in 1 1/2 yards
Answers
Answer:54 inches
Step-by-step explanation:
type the correct words in the blanks. two radicals are said to be radicals if they have the same and the radicand.
Answers
Two radicals are said to be radicals if they have the same indices and the radicand.
In mathematics, a radicand is an expression, a number, or a variable that is enclosed in a root symbol. The factor for which we are determining the root is quantity. As we study exponents and roots, the word "radicand" is utilised. Therefore, the radicand in 2 has a value of 2. Following are some radicand examples:
3√(pq) → pq is the radicand
√(a+b) → a + b is the radicand
4√15 → 15 is the radicand
A radical is a symbol used to represent a number's root. It is symbolised as. The word or phrase that appears after the radical symbol is known as the radicand. Hence, it may be claimed that the radical represents the radicand. Alternatively said, the radicand sign is √.
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Complete question:
Type the correct words in the blanks:
Two radicals are said to be radicals if they have the same and the radicand.
Daniel opens a new savings account and makes an initial deposit of $1,200.
If the account earns 2.5%
annual interest, which equation shows how much money is in the account in 9
months?
Responses
A x=1,200+1,200(0.25)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 0 point 7 5
B x=1,200+1,200(0.025)(0.75)
x is equal to 1 comma 200 plus 1 comma 200 0 point 0 2 5 0 point 7 5
C x=1,200+1,200(0.25)(9)
x is equal to 1 comma 200 plus 1 comma 200 0 point 2 5 9
D x=1,200+1,200(0.025)(9)
Answers
Answer:
D) x = 1,200 + 1,200(0.025)(9)
In this equation, 1,200 is the initial deposit, 0.025 is the decimal representation of the annual interest rate, and 9 represents the time period in months. The multiplication of 0.025 and 9 gives the proportion of interest earned in 9 months, which is then multiplied by the initial deposit and added to it to give the total amount in the account after 9 months.
Simplifying the equation:
x = 1,200 + (1,200)(0.025)(9)
x = 1,200 + 270
x = 1,470
Therefore, there would be $1,470 in the account after 9 months
I really need help and there also is a part c and d
Answers
Part A: The probability of rolling a 5 is 1/6 or approximately 0.167. Part B: the probability of rolling an even number is 3/6 or 1/2 or 0.5.
Describe probability ?Probability is a branch of mathematics concerned with measuring the likelihood or chance of an event occurring. It is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability is expressed as a number between 0 and 1, where 0 means that the event will not occur and 1 means that the event will definitely occur. For example, if the probability of an event is 0.5, it means that the event has an equal chance of occurring or not occurring. Probability is used in various fields, such as science, engineering, finance, and statistics, to make predictions and make decisions based on uncertain events.
Part A:
The number cube has six faces, and each face has an equal chance of landing face-up. Therefore, the probability of rolling a 5 is 1/6 or approximately 0.167.
Part B:
The even numbers on a number cube are 2, 4, and 6. There are three even numbers out of a total of six possible outcomes. Therefore, the probability of rolling an even number is 3/6 or 1/2 or 0.5.
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Last weekend, Mrs. Nelson earned $132 selling rings. She earned $6 for each ring she sold.
How many rings did she sell?
Answers
Hi!
Let's think about this really quick.
Each ring is $6. She made $132.
In order to find the solution, we need to divide the total from the original price of the ring, making the equation: 132÷6.
132÷6= 22.
So, she sold 22 rings. To verify that answer, we'll multiply 6 to 22.
6x22=132.
22 Is your answer.
Hope this helps!
Appreciated if you mark brainliest <3
~~~PicklePoppers~~~
Answer:
22 rings :)
Step-by-step explanation:
By diving 132 by 6 we can determine the number of rings she sold.
After dividing, we get 22 rings!
May I please have a brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!
26. Paul, Raul, and Saul had a competition to see who could pick the greatest amount of strawberries
in three minutes. Paul picked 1 pounds of strawberries, Raul 1 pounds, and Saul 1 pounds.
Who came in second? Show your work.
Answers
There is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.
What is probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It is the measure of the likelihood or chance that an event will occur. Probability is expressed as a number between 0 and 1, where 0 indicates that the event will not occur and 1 indicates that the event will occur with certainty.
According to the given information:The problem states that each of the three competitors picked 1 pound of strawberries. Since all of them picked the same amount, there is no way to determine who came in second. All three competitors can be considered tied for first place. If the problem had given different weights of strawberries picked by each competitor, then we could have compared the weights and determined who picked the second greatest amount of strawberries. But since all three competitors picked the same amount, there is no way to determine a second place winner.
Therefore, there is no second place winner. all three competitors picked the same amount of strawberries, so there is a tie for first place.
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Calculate the bearing of G from H.
Answers
The bearing of G from H at the given point location is determined as 155⁰.
What is bearing?
Bearing as a direction refers to the direction or angle of an object or location relative to a reference point, usually measured in degrees. For example, a compass can be used to determine the bearing of a landmark or to navigate in a particular direction.
The bearing of G from H is calculated by applying the following principle;
Let the bearing of G from H = θ
θ = 360 - 205 ( sum of angles in a circle )
θ = 155⁰
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when a certain number is doubled and then decreased by 9, the result is not more than 19. Find the range of values of the number
Answers
Answer:
The number must be at most 10.
If the number is doubled and then decreased by 9, the result is 2x - 9.
2x - 9 ≤ 19
2x ≤ 28
x ≤ 14
Therefore, the range of values of the number is 0 to 10.
Question
Jaq rode their bike for 3 1/3
hours at 15 miles per hour. How far did they ride?
✪
Answers
Answer:
Step-by-step explanation:
We can use the formula distance = rate x time to solve the problem.
The rate is 15 miles per hour and the time is 3 1/3 hours.
To work with the time, we need to convert it to an improper fraction:
3 1/3 = (3 x 3 + 1)/3 = 10/3
Now we can plug in the values:
distance = 15 x 10/3
distance = 50 miles (rounded to the nearest mile)
Therefore, Jaq rode 50 miles.
Determine the interval(s) over which the graph of f left parenthesis x right parenthesis equals short dash x to the power of 6 minus 6 x to the power of 5 plus 12 x minus 2 is concave up or concave down.
Answers
Answer:
gdiduusuehfuehvv
Step-by-step explanation:
bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it
PLEASEE help!!!! Urgent!!!!!
Answers
Answer:
Step-by-step explanation:
Solve for x
(x-14)+(2x+8)= 180
3x-14+8=180
3x-6=180
3x=186
x=62degrees
Solve for y
(7y-15)+62=180
7y+47=180
7y=180-47
7y=133
y=19degrees
PLS HELP ME with all 4 questions!!
Answers
By answering the presented question, we may conclude that so by SAS congruency property we have said that all these triangles are similar.
What precisely is a triangle?A triangle is a closed, a double geometric shape made up of three line segments known as sides that connect at three parameters known as vertices.
Triangles are differentiated by their angles and their sides. Triangles can be collinear (all sides equal), angles, or scalene dependent on their sides.
Triangles are classed as acute (all angles just under 90 degrees), right (one angle of approximately to 90 degrees), or ambiguous (all angles greater than 90 degrees).
The area of a triangle may be determined with the formula A = (1/2)bh, where A is the surface, b is really the right triangle base, and h is the triangle's height
here, from the figure, we have
Two sides of the triangle are equal.
And also all angles are also same.
Therefore, so by SAS congruency property we have say that all these triangles are similar.
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g suppoe x follows a distribution with pdf given by...show that the moment generating function of x is mx(t)
Answers
The distribution of Z=X+Y is gamma(1,10), which has a probability density function f(z) = 10 × e^(-10z), 0 ≤ z.
The moment generating function (mgf) of Z=X+Y can be found by taking the product of the mgfs of X and Y
Mz(t) = Mx(t) × My(t) = (e^(-4+4t))×(e^(-6+6t)) = e^(-10+10t)
We recognize that Mz(t) is the mgf of the gamma distribution with shape parameter k=1 and rate parameter λ=10. Therefore, Z=X+Y follows a gamma distribution with shape parameter k=1 and rate parameter λ=10.
In summary, the distribution of Z is gamma(1,10), which has a probability density function f(z) = λ^k × z^(k-1) × e^(-λz) / Γ(k) where k=1 and λ=10. Therefore, the probability density function of Z is f(z) = 10 × e^(-10z), 0 ≤ z.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
What is the distribution of Z and the value of the parameter?
please help asap!!!!!!!
Answers
To remove the y-term in the given linear equation in two Variable multiply the equation by 4 then add these two equations.
What is linear equation in two Variable;
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. Yet, there are two solutions to a linear equation with two variables.
According to given question;
5X+8y=5 ……..eqn 1.
3x-2y=3 ………eqn 2.
Multiply by 4 in the eqn 2.
We get
12x-8y=12 ……..eqn 3 .
When we add eqn 1 and eqn 3 we get ;
17x =17
X =1
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After eliminating the y-term in the given equations i.e 5x+8y=5 and
3x-2y=3, The solution to the system of equations is x = 1, y = 0.
What is elimination method?The elimination method is the technique used to solve systems of linear equations. It involves adding or subtracting equations in a system to eliminate one variable and find the value of the other variable.
To eliminate the y-term in these equations, you can multiply the second equation by 4, which will give you:
12x - 8y = 12
Now, you can add this equation to the first equation:
5x + 12x + 0y = 5 + 12
Simplifying the left side gives you 17x, and simplifying the right side gives you 17. So, you have the equation:
17x = 17
Solving for x gives you x = 1.
Now that you have found the value of x, you can substitute it into one of the original equations to solve for y. Using the first equation, you get:
5(1) + 8y = 5
Simplifying this equation gives you:
8y = 0
Solving for y gives you y = 0.
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Divide 18a6b2 by 9a3b.
2a9b3
2a2b2
2a3b2
2a3b
Answers
Answer: Choice D) [tex]2a^3b[/tex]
Work Shown:
[tex]\frac{18a^6b^2}{9a^3b}=\frac{18a^6b^2}{9a^3b}\\\\\frac{18a^6b^2}{9a^3b}=\frac{18}{9}*\frac{a^6}{a^3}*\frac{b^2}{b}\\\\\frac{18a^6b^2}{9a^3b}=2a^{6-3}b^{2-1}\\\\\frac{18a^6b^2}{9a^3b}=2a^3b\\\\[/tex]
The formula used on the 3rd line was (a^b)/(a^c) = a^(b-c). We subtract the exponents when dividing exponential expressions with the same base.
When a stone is dropped from the top of a tower, the distances metres it falls in t seconds is given by s = 10?. Find how far it falls in 3 seconds?
Answers
Answer: 45 meters
Step-by-step explanation:
The given equation is:
s = (1/2) * g * t^2
Where,
g = acceleration due to gravity = 10 m/s^2 (approximate value)
To find the distance it falls in 3 seconds, we can substitute t = 3 in the above equation:
s = (1/2) * g * t^2
s = (1/2) * 10 * 3^2
s = (1/2) * 10 * 9
s = 45 meters
Therefore, the stone falls 45 meters in 3 seconds.
Jason invested $5,500 in an account paying an interest rate of 1 7/8 % compounded quarterly. Kayden invested $5,500 in an account paying an interest rate of 1 3/8 % compounded annually. After 8 years, how much more money would Jason have in his account than Kayden, to the nearest dollar?
Answers
Using compounding we know that the additional amount Jason has more than Kayden is $249.48.
What is compounding?Calculating interest on the principal borrowed as well as any prior interest.
In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one.
So, the amount of Jason after 8 years:
Amount: $5500
Interest: 1.875%
Compounded: Quarterly
Using a compounding calculator:
Amount after 8 years: $6,387.85
The amount of Kayden:
Amount: $5500
Interest: 1.375%
Compounded: Quarterly
Using a compounding calculator:
Amount after 8 years: $6,138.37
The additional amount Jason got: 6,387.85 - 6,138.37 = $249.48
Therefore, using compounding we know that the additional amount Jason has more than Kayden is $249.48.
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Answer:253
Step-by-step explanation:
Please help !!!! Given m∥n, find the value of x.
(3x+5) (x-25) = 180 degrees
Answers
Answer:
Step-by-step explanation:
[tex](3x+5)+(x-25)=180 \text{ \ (angles on a straight line are supplementary)}[/tex]
[tex]4x-20=180[/tex]
[tex]4x=200[/tex] (+20 both sides)
[tex]x=50[/tex] (÷4 both sides)
4x-20=180
4x-20+20=180+20
4x=200
Divide both sides by the same factor
Cancel terms that are in both the numerator and denominator
Divide the numbers
4
x
4
=
200
4
4
4
=
2
0
0
4
x
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A baseball diamond is shaped like a square. The perimeter is 360 feet. What is the length of each side?
Answers
Answer: 90 feet
Step-by-step explanation:
Since the baseball diamond is shaped like a square, all sides are equal in length.
Let's denote the length of each side by x.
The perimeter of a square is the sum of the lengths of all four sides, so we can write:
4x = 360
Dividing both sides by 4, we get:
x = 90
Therefore, each side of the baseball diamond is 90 feet long.
Do not put any punctuation (other than a necessary decimal place) or spaces into your answer.
When Claudia borrowed $6400 at 11% compounded semiannually for three years, the value of the rate per period was
Answers
Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.
What is compound interest?
compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.
Capital(p) = $6400
Rate of interest(r) = 11%
Years(n) = 3
The general formula of compound interest is [tex]A= p(1+\frac{r}{100}})^n[/tex].
Now
[tex]A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384[/tex]
The entire amount (Capital+interest) is equal to $8752.8384.
If we take 1 year as a period then Claudia needs to pay [tex]\frac{8752.8384}{3}\\=2917.6128[/tex]
Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.
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Question 6 of 10
Ashlee is purchasing a $125,000 home and her bank is offering her a 30-year
mortgage at a 4.75% interest rate. In order to lower her monthly payment,
Ashlee will make a 20% down payment and is considering a purchase of 2
points. How much lower will her monthly payment be if she purchases the
points?
A. $16.69
B. $15.98
C. $12.09
D. $14.96
SUBMIT
Answers
Answer:
D
Step-by-step explanation:
First, let's calculate the initial monthly payment without purchasing any points.
The amount of the mortgage after the 20% down payment is:
$125,000 x 0.8 = $100,000
To calculate the monthly payment, we can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = Monthly payment
P = Principal (loan amount)
i = Interest rate (per month) = 4.75% / 12 = 0.0039583
n = Number of payments = 30 years x 12 months per year = 360
So, plugging in the values:
M = $100,000 [ 0.0039583(1 + 0.0039583)^360 ] / [ (1 + 0.0039583)^360 – 1]
M = $522.12 (rounded to the nearest cent)
Now, let's calculate the new monthly payment if Ashlee purchases 2 points. Each point costs 1% of the loan amount, so for a $100,000 loan, each point is $1,000.
By purchasing 2 points, Ashlee would pay an additional $2,000 upfront (2 x $1,000). This will lower the interest rate on the loan by 0.5%, from 4.75% to 4.25%.
Using the same formula as before, but with the new interest rate of 4.25% / 12 = 0.0035417, we get:
M = $100,000 [ 0.0035417(1 + 0.0035417)^360 ] / [ (1 + 0.0035417)^360 – 1]
M = $505.16 (rounded to the nearest cent)
The difference in monthly payments is:
$522.12 - $505.16 = $16.96
Rounding to the nearest cent, the answer is option D, $14.96.
you are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative? select all.OP1Op 1 - 2Standard errorCritical valueLower bound of the confidence intervalUpper bound of the confidence interval
Answers
For the computation of confidence interval for the difference in two population proportions following are negative,
p₁(cap) - p₂(cap)
Lower bound of the confidence interval
Upper bound of the confidence interval
For the computation of confidence interval,
The difference in two population proportions,
p₁ - p₂, can be negative or positive.
This implies,
The sample estimate of the difference in proportions,
p₁(cap) - p₂(cap), can also be negative or positive.
The standard error and critical value are always positive values and cannot be negative.
The lower and upper bounds of the confidence interval can be negative or positive.
Depending on the sample estimate and the margin of error.
So, both the lower and upper bounds can be negative.
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The above question is incomplete, the complete question is:
You are computing a confidence interval for the difference in 2 population proportions. which of the following could be negative?
Select all.
a. p₁
b. p₁(cap) - p₂(cap)
c. Standard error
d. Critical value
e. Lower bound of the confidence interval
f. Upper bound of the confidence interval
At age 39, you start saving for retirement. If your investment plan pays an APR of 4% and you want to have $0.8 million when you retire in 26 years, how much should you deposit monthly?
Answers
Answer:
Step-by-step explanation:
TRUE/FALSE. Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" Ris a linear transformation. If Ic.B = Tç, e then B = E = C.
Answers
Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.
The above statement is True.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.
A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.
Sometimes the term linear function has the same meaning as linear map, but not in analysis.
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