Answer:
So the payoff balance of the car loan after 4 years will be approximately $22,169.73.
Step-by-step explanation:
payoff balance after 4 years can be calculated using the following formula:
Payoff balance = Principal * (1 + APR/n)^(nt) - [(Principal * (1 + APR/n)^(nt) * (APR/n)) / (1 + APR/n - 1)]
Where:
Principal is the loan amount, which is $28,550 in this case.
APR is the annual percentage rate, which is 8% in this case.n is the number of times per year that interest is compounded, which is usually 12 for monthly compounding.t is the number of years for which the loan is taken, which is 4 years in this case.
Plugging in the values, we get:
Payoff balance = $28,550 * (1 + 0.08/12)^(124) - [($28,550 * (1 + 0.08/12)^(124) * (0.08/12)) / (1 + 0.08/12 - 1)]
Payoff balance = $28,550 * 1.006669^48 - [$28,550 * 1.006669^48 * 0.006669] / 0.006669Payoff balance = $22,169.73
reported the results of a study on the occurrence of sodium and chloride in surface streams in central rhode island. the following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).
The study found that as the percentage of roadway area in the watershed increases, the concentration of chloride in the surface streams also increases.
| Roadway Area (x) | Chloride Concentration (y) |
|--------------------|--------------------------|
| 10.7 | 28.2 |
| 11.3 | 28.3 |
| 11.7 | 28.4 |
| 11.8 | 28.5 |
| 12.6 | 28.8 |
| 13.2 | 29.2 |
The study found that as the percentage of roadway area in the watershed increases, the concentration of chloride in the surface streams also increases. Specifically, there was a statistically significant positive correlation between the two variables, with the chloride concentration increasing by an average of 0.3 mg/L for every 1% increase in the roadway area in the watershed.
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A chemical plant manufactures fertilizer. A particular fertilizer recipe calls for 2 units of potash for every 3 units of urea. The potash is shipped to the plant in modular pallets with dimensions (x+6) by (x-2). The urea is shipped to the plant in modular pallets with dimension (x-2) by (x+1). Assuming equal molar density in each product, calculate x such that there is no material left over after manufacturing the fertilizer.
The value of x such that no meterial left over after manufacturing the fertilizer is 1
How to calculate for x?The area of a place is the floor space occupied by an object. we are to determine the value of x in the length and width of the floor to be used by the manufacturer
The givn parameters are the use of
2 units of potash and
3 units of urea.
Recall that the area of a rectangular floor space is (L*W).
This implies that (x+6)(x-2)=2
x²-2x+6x-12=2
x²+4x-10=0 .......................... (1)
Also, for the urea
Area= (x-3)(x+1)=3
x²+x-2x-2=3
x²-x-2-3=0
This implies that
x²-x-5=0 .............................(2)
Assuming equal molar density in each product,
equations 1 and 2 are equal
x²+4x-10=x²-x-5
Collecting like terms
x²-x+4x+x-10+5=0
5x-5=0
5x=5
x=1
Therefore, assuming equal molar density in each product the value of x=1
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Chee is ordering a taxi from an online taxi service. She has to pay a flat charge just to
order the taxi, and then has to pay per mile, depending on how far she travels. She
wrote an equation to represent her total cost, y = 1.3x + 5, where y represents the
total cost in dollars and cents, and a represents the number of miles she travels.
What is the meaning of the y-value when x = 1?
A) The flat charge to order the taxi.
B) How far Chee can ride for $1.
C) The total charge for 1 mile.
D) The change in the total cost for every one additional mile traveled.
Answer: c?
Step-by-step explanation:
this is a guess :)
consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. the possible outcomes of the sample space s are listed as follows, where in each case the die on the left is blue and the one on the right is gray. s = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} Write the following event as a set. (Enter your answer in roster notation. Enter EMPTY or o for the empty set.) The event that the sum of the numbers showing face up is at least 9. E Compute its probability.
consider the sample space given below. a die is a cube with six sides on which each side contains one to six dots. Suppose probability a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded.a fraction in lowest terms. 21/36
The sample space given in the question is the set S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66} The event that the sum of the numbers showing face up is at least 9 is represented by the set E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}.
To compute the probability of this event, we need to count how many elements are in the set E and divide this number by the total number of elements in the set S. There are 18 elements in the set E and 36 elements in the set S. Therefore, the probability of the event is 18/36, which can be simplified to 21/36.
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[tex]3-2\sqrt3\\[/tex]
Answer:
=3−√3 (Decimal: 1.267949)
Step-by-step explanation:
3−√3
=3−√3 (Decimal: 1.267949)
This is the best I could do! hope it helps!!
Ralf and Susie share$57 in the ratio 2:1.Calculate the amount Ralf rec
eive
Step-by-step explanation:
since the fraction is a ratio, we know that the whole amount of $57 consists of 2+1 = 3 equally sized parts.
Ralf gets 2 of these parts, Susie one part.
each part is
57 / 3 = $19
so, Ralf gets
19×2 = $38
Susie gets
19×1 = $19
an article in neurology (1998, vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. the investigators measured an intelligence score of 10 pairs of twins, and the data follow: pair birth order: 1 (first) birth order: 2 (second) 1 6.08 5.73 2 6.22 5.80 3 7.99 8.42 4 7.44 6.84 5 6.48 6.43 6 7.99 8.76 7 6.32 6.32 8 7.60 7.62 9 6.03 6.59 10 7.52 7.67 (a) State the appropriate hypotheses. (b) Create a Paired- T test at α=0.05 in Minitab and find the P-value. Do you reject the null?
The p - value of the given hypothesis is P(2<x<6.75) is 0.49974
How to calculate p - value?
In statistics, p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve.
Here we have given that an article in neurology (1998, vol. 50, pp. 1246-1252) discussed that monozygotic twins share numerous physical, psychological, and pathological traits. the investigators measured an intelligence score of 10 pairs of twins, and the data.
And we need to find the value of p from it.
Here we have the following sample data,
=>2,5.73,5.80,6.08,6.22,7.99,7.44,6.48,7.99,6.32,7.60,6.03,7.52,8.42,6.84,6.43,8.76,6.32,7.62,6.59,7.67
Through the sample data we ahve identified the following values,
Standard Deviation, σ: 1.3737491940207
Count, N: 21
Sum, Σx: 141.85
Mean, μ: 6.7547619047619
Variance, σ2: 1.8871868480726
in order to find the p-value, we have to calculate the z score for the given data,
Z score = (x - μ)/σ
=> (2 - 6.75)/ 1.37
=> -3.46715
P-value from Z-Table:
=> P(x<2) = 0.000263
=> P(x>2) = 1 - P(x<2) = 0.99974
=> P(2<x<6.75) = 0.5 - P(x<2) = 0.49974
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can someone help me figure out how to solve this problem
Answer:
In an arithmetic sequence, each term is obtained by adding the common difference to the previous term. In this case, the common difference is 3, so the formula for the nth term of the sequence can be written as:
a^n = a^1 + (n-1) * d
where a^1 is the first term of the sequence, and d is the common difference.
Since the first term of the sequence is -25 and the common difference is 3, we can plug these values into the formula to find the 30th term of the sequence:
a^30 = (-25) + (30-1) * 3
= (-25) + 29 * 3
= (-25) + 87
= 62
Therefore, the 30th term of the sequence is 62.
Step-by-step explanation:
Select all the equations that are NOT equivalent to p – 7 = 22.
Answer:
I'm sorry but this question isnt do-able without the multiplechoice
Step-by-step explanation:
Empirical Rule 06
IQ scores can be described using a Normal distribution with a mean of 100 and a standard deviation of 15.
Using the Empirical '68-95-99.7' Rule, what percent of IQ scores are above 130?
Answer:
The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data lies within one standard deviation of the mean, 95% lies within two standard deviations, and 99.7% lies within three standard deviations.
In this case, the mean is 100 and the standard deviation is 15, so approximately 95% of the data lies within two standard deviations of the mean. Since two standard deviations of 100 is 30 (15 * 2), this means that approximately 95% of the data lies within the range of 70 to 130. Therefore, approximately 5% of the data lies outside of this range, with 2.5% lying below 70 and 2.5% lying above 130.
Therefore, the percent of IQ scores that are above 130 is approximately 2.5%.
Suppose you are designing and conducting a poll to see which of the Congressional candidates are popular in your area. Use the terminology and concepts that we are learning in Lesson 1 - population, sample, sampling methods, representative sample, and presentation of data....
1. Discuss the following in your own words :
the population that you are trying to predict,
where and how are you selecting your sample,
what sampling method would you use,
how would you assure that you are selecting a representative sample, and
show an example of how you would present your data.
The population we're trying to predict is the population that is going to be Voters in our area, the where should probably be well as above our area, and the how now, generally speaking, we want to do a simple, random, or a random sample of some sort, random sample.
For instance, what you could do would be something like choose: random addresses in the area and send a survey, but sending a survey could introduce self-selection bias. So it would be ideal to visit in person basically and ask a few questions making sure the representative sample or how to ensure that we're getting a representative sample would be to, for instance, filter the random results and make sure that we have an even distance.
Ensure that there's an equal number within each quadrant of the town, basically split up the town. Split towns into regions of populations or population densities and make sure we get the same proportion from each region. However, we end up splitting the town into different regions. We show the proportion or show who is the most popular candidate in each 1 of the regions, so it could be something like this. That was supposed to be an alternative to a bar graph. The number of results for each different candidate depends on whether or not there's a sort of well-defined districts or areas in the town, but most sorts of relatively large cities have things like that. So the idea would be to represent not just the location, but also the information that you gain separately.
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Split up the town so that there are an equal amount in each of its four quadrants. Make sure we receive the same proportion from each region by dividing towns into population or population density regions. But ultimately, we divide the town into many parts. It might look something like this since we display the percentage or the candidate who is most supported in each location. That was meant to be a bar graph substitute. Whether or not a town has clearly defined districts or areas affects the amount of results for each candidate, although this is true of most types of moderately large cities.
explain how to use the multiplication table to solve 5 x 4
Answer:
Go and look up your tables and read below
Step-by-step explanation:
To solve the problem 5 x 4 using the multiplication table, you would look up the corresponding entries in the table for the numbers 5 and 4. In the row labeled 5 and the column labeled 4, you would find the product 20, which is the answer to the problem 5 x 4.
answer
Step-by-step explanation:
the diagrqam shows an object with a mass of 1.0 kiolgram attached to a string 0.50 merer long. the object is moving at a constant speed of 5.0 meters per second in hporizontal circular path with center at point o
The object is undergoing uniform circular motion. The radius of the circular path is equal to 0.50 meters. The centripetal force, F, acting on the object can be calculated using the equation F= mv^2/r in hporizontal circular path
m is the mass of the object, v is the velocity of the object and r is the radius of the circular path.
F = (1.0 kg) (5.0 m/s)^2 / 0.50 m
F = 50.0 kg m/s^2
The object is undergoing uniform circular motion, which means it is moving at a constant speed in a circular path with its center at point O. The radius of the circular path is equal to 0.50 meters. The force acting on the object is known as the centripetal force, and can be calculated by using the equation F= mv^2/r. This equation requires the mass of the object (m), its velocity (v), and the radius of the circular path (r). In this case, the mass is 1.0 kg, the velocity is 5.0 m/s, and the radius is 0.50 m. Plugging these values into the equation gives the centripetal force acting on the object as 50.0 kg m/s^2.
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the sampling distribution of the sample mean is close to normal distribution a. only if the parent population is unimodal, not badly skewed, and does not have outliers.
C) The Central Limit Theorem states that the sample mean's sampling distribution is very similar to a normal distribution.
The central limit theorem is founded on what?The idea of a sampling distribution, which is the probability distribution of a statistic for a large number of samples taken from a population, is the foundation of the central limit theorem.
What are the central limit theorem's two main tenets?To summarize, the following two distributions are linked by the central limit theorem: The population's distribution of the variable. The testing dissemination of the mean.
What is As far as possible Hypothesis?The CLT is a statistical theory that holds that the mean of all samples taken from a population with a finite level of variance will roughly match the population mean if a sufficient number of samples are taken from that population.
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Full Question = The sampling distribution of the sample mean is close to the normal distribution
A. only if the parent population is unimodal, not badly skewed, and does not have outliers.
B. no matter what the distribution of the parent population of what the value of n.
C. if n is large, no matter what the distribution of the parent population.
D. if the standard deviation of the parent population is known.
E. only if both n is large and parent population has a normal distribution.
Use inductive reasoning to predict the most probable next number in the list.
8, 15, 1, 8, −6, 1, −13, −6, −20, ?
Answer:
-13
Step-by-step explanation:
the pattern goes +7 - 14, so -20 + 7 = 13
find $m\angle1$ .two triangles a b c and q r s are drawn. angles b and q are labeled with a single arc. angles a and s are marked with a double arc. angles a and b are labeled 45 degrees and 80 degrees respectively. angle r is labeled 1.
The measure of angle 1, m∠1, found using the congruency of the angles and the angle sum property of a triangle is 55°
What is the angle sum property of a triangle?The angle sum property of a triangle specifies that the sum of the interior angles of a triangle is 180°
Please find attached the presentation of the details of the question as a drawing of the triangles created with MS Word
The parameters of the question are;
The number of arcs on angles b and q = Single arcs
Therefore, based on the arc markings indicating congruency of the angles, we get;
Angle b is congruent to angle q ∠b ≅ ∠q
Therefore, ∠b = ∠q, by the definition of congruency
The number of arcs on angle a and angle s = Double arcs
Therefore, angle a is congruent to angle s based on the arc markings, which indicates;
∠a ≅ ∠s
∠a = ∠s by the definition of congruency
The label on angle ∠a = 45°
The label on angle ∠b = 80°
∠a = ∠s, therefore, ∠s = 45°, by substitution property
∠b = ∠q, therefore, ∠q = 80° by substitution
∠s + ∠q + ∠1 = 180° Angle sum property of a triangle
45° + 80° + m∠1 = 180°
m∠1 = 180° - (45° + 80°) = 55°
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WILL GIVE BRAINLIST! The story is "I, Too, Have a Dream" by Brittany Taylor.
Directions: Use your planning in Part 1 to write your two body paragraphs in the box below. The box will expand. Use complete sentences, proper grammar and punctuation, and transitions to develop your body paragraphs. Each body paragraph should have a transition at the beginning of the topic sentence and at least two within each paragraph.
Body paragraph 1: Topic Sentence: Brittany Taylor states people's dream to keep DACA up, so the editor can let DACA stay in the U.S.
Example from text to support topic sentence: “Yes, Areliss is a DREAMer. But I, too, have a dream. My dream is that DACA will be reinstated. My dream is that Areliss will be invited to stay in the country she was born in and live out her dreams in the country she loves.”
Explanation of how the example serves purpose: Brittany states that she has a dream to keep the DACA in the U.S. so that her befriend, Areliss can stay to live her dreams and stay in the country as well.
Example from text to support topic sentence: “DACA recipients have a dream: they dream that their lifelong contribution to the United States will one day be recognized, and they will be permitted to stay in the country they have always called home.”
Explanation of how the example serves purpose: Brittany is trying to convince the editor that DACA has a dream to be recognized and stay around and not get shut down.
Body paragraph 2:
Topic Sentence: Brittany Taylor uses figurative language such as metaphors and similies to tell the audience why DACA should be reinstated.
Example from text to support topic sentence: “But, I know their words were bullets to Areliss’s heart.”
Explanation of how the example serves purpose: She uses a metaphor in the sentence to show how she knew her best friend felt when the protesters were saying awful things.
Example from text to support topic sentence: “These protesters couldn’t have known what Areliss felt as they shouted and waved pamphlets in our faces like tattered flags.”
Explanation of how the example serves purpose: She uses simile in the sentence to show how hard and rudely they were waving the pamphlets in their faces as if it was a ripped flag.
Brittany Taylor employs some figurative language in her letter to the editor titled "I, Too, Have a Dream." She employed personification and metaphors. In order to persuade her audience to support the reinstatement of DACA, she makes her ideas by presenting a problem and a solution. According to Brittany Taylor's letter, she used personal experience and official government documents like the DACA to prove that deportation is cruel.
What was the literary work about?Brittany Taylor expresses the desire for DACA to continue so that the editor will permit its continuation in the United States. In order for her friend Areliss to continue living her dreams and remaining in the country, Brittany says she has a dream to keep DACA in the United States.
DACA recipients have a dream: they hope that one day their lifetime of service to the US will be acknowledged and they will be able to remain in the place they have always called home. An explanation of how the example achieves its objectives Brittany is attempting to persuade the editor that DACA has a dream to be acknowledged, remain operational, and not be terminated.
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Answer:
An idea to help: In “I, Too, Have A Dream”, Brittany Taylor, the author, uses a metaphor to help emphasize an objective in the minds of the audience
U KICKED ME OUT HOPE THIS HELPS KATEEEEE!
Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind. To rewrite the sentence.
What is rewrite?
The term rewrite sentence refers to the sentence was the written in the sentence but in the different style. It was to describe the sentence meaning was the similar, but the wittering style was the different. The rewrite the sentence was the but not the copy to the sentence.
According to the given, the sentence are the rewrite. There was the sentence is the different but, the meaning was the same. The sentence was the "Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind."
As a result, the sentence was the Brittany Taylor, the author, employs metaphor in her "I, Too, Have A Dream" letter to explain a notion in the audience's mind. To rewrite the sentence.
¿Do you think that Mexico is transitioning to a green economy? why?
Answer:
Step-by-step explanation:
yes probaly
im doing this for point
Personally, he considered that Mexico is indeed transitioning to a green economy, because the economy is adjusting towards the sustainable and adequate use of resources.
¿What is the green economy?It is a type of economy that is based on developing sustainable and sustainable processes in all its processes and activities, this in favor of caring for the planet and its natural elements.
¿Does Mexico seek to have a green economy?It can be said that Mexico is transitioning to a green economy, this can be observed, for example:
In the implementation of sustainable and sustainable strategies of companies.In the appropriate and increasingly efficient use of many natural resources.¡Hope this helped!
2. A local manufacturing firm produces four different metal products, each of which must be machined, polished and assembled. the specific times requirements ( in hours) for each products are as follows
Machining hours Polishing hours Assembling hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Pruduct IV 4 3 1
Step-by-step explanation:
To find the total time required to produce each product, we can add up the machining, polishing, and assembling hours for each product. For example, for Product I, the total time required would be:
Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours
We can do this for each product to find the total time required for all four products:
Total time for Product I = 3 hours + 1 hour + 2 hours = 6 hours
Total time for Product II = 2 hours + 1 hour + 1 hour = 4 hours
Total time for Product III = 2 hours + 2 hours + 2 hours = 6 hours
Total time for Product IV = 4 hours + 3 hours + 1 hour = 8 hours
So, the total time required to produce all four products is 6 hours + 4 hours + 6 hours + 8 hours = 24 hours.
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The value of the other points in each of the number line is;
a) M = -2¹/₂; N = -1; R = 4
b) M = -1; P = 1; R = 1.6
c) M = -125; P = 125; N = -50
d) N = -6; P = 15; R = 24
How to interpret Number Lines?a) The point P = 2¹/₂
The distance from point 0 of the number line to point P is 5 units and therefore;
Each unit = 2¹/₂/5 = ¹/₂
Thus;
M = -2¹/₂
N = -1
R = 4
b) The point N = -0.4
The distance from point 0 of the number line to point N is 2 units and therefore;
Each unit = 0.4/2 = 0.2
Thus;
M = -1
P = 1
R = 1.6
C) The point R = 200
The distance from point 0 of the number line to point R is 8 units and therefore;
Each unit = 200/8 = 25
Thus;
M = -125
P = 125
N = -50
D) The point M = -15
The distance from point 0 of the number line to point N is 5 units and therefore;
Each unit = 15/5 = 3
Thus;
N = -6
P = 15
R = 24
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Read the following prompt and type your response in the space provided.
The perimeter of Dawna's new flat screen television is 70 inches. The ratio of its length to width is 4:3. Write and solve an algebraic equation to determine the dimensions of the television.
Answer:4*3+70=840
Step-by-step explanation:
Perimeter = 2(Length + Width)
length = 4x ; width = 3x ; perimeter = 70
SOLUTION:Perimeter = 2(Length + Width)
70 = 2(4x + 3x)
70 = 2(7x)
70 = 14x
x = 5
Length = 4x = 4(5) = 20 inchesWidth = 3x = 3(5) = 15 inchesCHECKING:Perimeter = 2(Length + Width)
70 = 2(20 + 15)
70 = 2(35)
70 = 70
We proved and checked the answer.Therefore, the length of the screen television is 20 inches while the width is 15 inches.CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-
bob had 612 qt of paint. he used 323 qt to paint a room how much paint does bob have left? hint: you might have to re-group! enter your answer in the box as a mixed number in simplest form. qt
The quantity of paint left with Bob after painting a room from the quantity of 6 1/2 is equal to 2 5/6 qt.
As given in the question,
Quantity of paint Bob had is equal to 6 1 / 2 qt
Quantity of paint used by Bob to paint a room is equal to 3 2 / 3 qt
Quantity of paint left with Bob after painting is equal to :
= Total quantity - Used quantity
= ( 6 1 / 2 ) - ( 3 2 / 3 )
= ( 13 / 2 ) - ( 11 / 3 )
= ( 39 - 22 ) / 6
= 17 / 6
= 2 5/6 qt
Therefore, the quantity of paint left with Bob from 6 1/2 qt after painting the room is equal to 2 5/6 qt.
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Let A be a square matrix. Assume that the following statement is true: If B is an invertible matrix then rank BA = rank A. (a) Show that if B is an invertible matrix then rank AB = rank A. Hint: What is rank(AB)" ? (b) Show that for any invertible matrix P, rank(P-'AP) = rank A. (c) If P is invertible then nullity P-'AP = nullity A.
We proved the expression rank(AB)=rank(B) and rank(BA)=rank(B),
where A and B are the two matrices of same order.
Given, A is a square matrix.
If A is invertible and a n×n square matrix of full rank.
Since both AB and BA exist, where B is also a n×n square matrix.
rank(B)=rank(BT)
On using the rank–nullity theorem, we get
nullity of a matrix be n minus the rank of the matrix.
So let U be a matrix whose columns are a basis for the nullspace of AB, so that ABU = 0.
Pre-multiplying both sides by A−1 , we obtain BU=0,
As B and AB have the same rank.
Similarly, let V be a matrix whose columns are a basis for the null space of ATBT, so that ATBTV=0 .
Pre-multiplying both sides by (A−1)T , we get
BTV=0.
Since rank(BT)=rank(B) and rank(ATBT)=rank((BA)T)=rank(BA)
we get rank(AB)=rank(B) and rank(BA)=rank(B).
So, rank(AB)=rank(B) and rank(BA)=rank(B).
Hence, rank(AB)=rank(B) and rank(BA)=rank(B).
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what is the square root of 81
Answer: I hope this is helpful
Step-by-step explanation:
The square root of 81 is 9 and you can say -9
We can find the square root of 81 using prime factorization method, or repeated subtraction method.
81 is a perfect square number and it is the fourth power of 3. we will calculate the square root of 81 by repeated subtraction method and solve a few interesting problems.Square Root of 81: √81 = 9
The square root of a number is the number that when multiplied to itself gives the original number as the product. Finding the square root of a number is the inverse of squaring a number. 81 = a × a = a2 Thus, a = √81= √(9 × 9)9 × 9 = 81 or -9 × -9 = 81. Therefore √81= ± 9This shows that 81 is a perfect square.
Nicole has saved $120 toward the purchase of a new bike. She gets a job that pays $12 an hour. She saves 25% of her hourly wage to purchase the new bike. She uses the equation y=(0.25)(12)x+ 120 to determine how much money she has saved toward the purchase of the new bike. What is the slope of the line represented by Nicole's equation?
A. 120
B. 0.25
C. 12
D. 3
Answer: The correct answer is B.
Step-by-step explanation:
The slope of a line in the form of y = mx + b is represented by the coefficient m. In this case, the slope of the line represented by Nicole's equation is:
y = (0.25)(12)x + 120
The coefficient m is 0.25.
a movie production company is releasing a movie with the hopes that many viewers will return to see the movie in the theater for a second time. their target is to have 40 million viewers, and they want more than 40% of the viewers to want to see the movie again. they show the movie to a test audience of 140 people, and after the movie they asked them if they would see the movie in theaters again. of the test audience, 66 people said they would see the movie again.
Answer: the test is 47 percent
Step-by-step explanation: 66 out of 140 is 47 percent so it would work
one period of a sine function or cosine function is called one amplitude incorrect: your answer is incorrect. of the sine curve or cosine curve.
The correct answer is cycle. A sine or a cosine function represent periodic functions where the value of the function is repeats after a definite interval.
What do you mean by periodic function?
A periodic function can be defined as:
A function returning to the same value at regular intervals. Though periodic motion and oscillatory motion sound the same, not all periodic motions will be oscillatory motion.
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If a function has a repeating pattern like sine or cosine, it is called a periodic function. The period is the length of the smallest interval that contains exactly one copy of the repeating pattern.
A motion that repeats itself at regular intervals is termed periodic motion. 1. A motion that does not repeat itself at regular intervals is termed non-periodic motion. 2. After a certain period of time, an object exhibiting periodic motion returns to its original position.
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find the least positive integer $n$ such that the set of $1000$ consecutive integers beginning with $1000\cdot n$ contains no square of an integer.
The difference between consecutive integral squares must be greater than 1000. (x+1)^2-x^2>=1000, so x>=999/2 implies x>=500. x=500 does not work, so x>500. Let n=x-500. The sum of the square of n and a number a little over 1000 must result in a new perfect square. By inspection, n^2 should end in a number close to but less than 1000 such that there exists 1000N within the difference of the two squares. Examine when n^2=1000. Then, n=10sqrt(10). One example way to estimate sqrt(10) follows.
3^2=9, so 10=(x+3)^2=x^2+6x+9. x^2 is small, so 10=6x+9. x=1/6 implies sqrt(10)\approx 19/6. This is 3.16.
Then, n approx 31.6. n^2<1000, so n could be 31. Add 500 to get the first square and 501 to get the second. Then, the two integral squares are 531^2 and 532^2. Checking, 531^2=281961 and 532^2=283024. 282,000 straddles the two squares, which have a difference of 1063. The difference has been minimized, so N is minimized N=282000 implies 282
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refer to exhibit 1-3. based on the data provided in this table, what type of relationship exists between variables x and y?
Based on the data provided in the table, an inverse relationship exists between variables x and y. (Option A)
An inverse relationship refers to a relationship between two variables that changes in opposite directions. In other words, an increase in one variable results in a decrease in the other variable and vice versa. An inverse relationship is represented in the form of y = k/x, where x and y are two variables and k is the constant value. Based on the data provided in the table, as the value of x increases, the value of y decreases by a constant value. Hence, the relationship that exists between variable x and y is inverse.
Note: The question is incomplete as it is missing options which are A) inverse B) direct C) independent d) there is no relationship between variable x and y.
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christopher is working two summer jobs, making $7 per hour babysitting and making $10 per hour washing cars. in a given week, he can work no more than 16 total hours and must earn a minimum of $130. if xx represents the number of hours babysitting and yy represents the number of hours washing cars, write and solve a system of inequalities graphically and determine one possible solution.
Christopher can work average 9 hours babysitting and 7 hours washing cars in a given week to meet the minimum wage requirement and not exceed the maximum hours he can work.
Christopher is working two summer jobs and has a maximum of 16 hours to work in a given week. He is making $7 per hour babysitting and $10 per hour washing cars. To meet the minimum wage requirement of $130, he needs to make a total of $130 in a week. We can represent this using a system of inequalities. The first inequality is 7xx + 10yy ≥ 130, which means that the total wages (7 times the hours babysitting plus 10 times the hours washing cars) must be greater than or equal to $130. The second inequality is xx + yy ≤ 16, which means that the total hours (babysitting plus washing cars) must be less than or equal to 16. Graphically, we can solve this system of inequalities to find the possible solutions. One possible solution is x = 9 and y = 7, meaning Christopher can work 9 hours babysitting and 7 hours washing cars in a given week to meet the minimum wage requirement and not exceed the maximum hours he can work.
Graphically:
7xx + 10yy ≥ 130
xx + yy ≤ 16
7xx + 10yy = 130
xx + yy = 16
Therefore, the solution is x = 9 and y = 7.
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