Solve for the equation for all x values by completing the square x^2 - 27= 67
Answer:
The solutions for the equation [tex]x^2\:-\:27=\:67[/tex] are [tex]x=\sqrt{94},\:x=-\sqrt{94}[/tex].
Step-by-step explanation:
To find the solutions for the equation [tex]x^2\:-\:27=\:67[/tex] you must:
[tex]\mathrm{Add\:}27\mathrm{\:to\:both\:sides}\\\\x^2-27+27=67+27[/tex]
[tex]\mathrm{Simplify}\\\\x^2=94[/tex]
[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{94},\:x=-\sqrt{94}[/tex]
Solve similar triangles (advanced)
Write a recursive rule an explicit rule for the arithmetic sequence 15,22.5,30,37.5
Answer:
[tex]a_n = a_o +(n-1) d[/tex]
[tex] 22.5 = 15 +(2-1) d[/tex]
[tex] d = 22.5-15 =7.5[/tex]
The general expression is:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
Step-by-step explanation:
For this case we have the following arithmetic sequence given:
15, 22.5, 30,37.5
In order to fidn the recursive rule for this sequence we need to take in count that the general formula for an arithmetic sequence is given by:
[tex]a_n = a_o +(n-1) d[/tex]
Where [tex]a_n[/tex] is the nth term [tex]a_o[/tex] the initial value for the sequence and d the common difference. For this case we have that [tex]a_o =15[/tex]
And for the first term we have:
[tex] 15= 15 +(1-1)d[/tex]
For the second term we have this:
[tex] 22.5 = 15 +(2-1) d[/tex]
And solving for the value of d we got:
[tex] d = 22.5-15 =7.5[/tex]
And for the 3th term we have:
[tex] a_3= 15 +(3-1)*7.5 =30[/tex]
And for the 4th term
[tex]a_4 =15 +(4-1)*7.5 =37.5[/tex]
So then our expression is correct and would be given by:
[tex] a_n = 15+ (n-1)*7.5 , n \geq 1[/tex]
Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula Vuxe - x0) + (V2 = 1
(2 √21)
(
23)
Answer:
its 2,21
Step-by-step explanation:
The only point that is in the circle of radius 5 is option A: (2, √21).
What is Polynomial?A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.
The distance between a point (x, y) and the origin is:
d = √(x² + y²).
Of the given options, the only one that meets this condition is the one in option A. (2, √21).
If we find the distance to the origin, we get:
d = √(2² + √21²) = √(4 + 21) = 5.
So that is the correct option.
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Complete question:
Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
A. (2, StartRoot 21 EndRoot)
B. (2, StartRoot 23 EndRoot)
C. (2, 1)
D. (2, 3)
Malaya wrote a survey question in the newspaper about changing the school colors. Ninety percent of those who responded in an e-mail said they should be changed. She concludes that 90% of the student body wants the colors changed *
Riley planted 10 flowers.five of the flowers are purple.three are pink , and the rest are red.what fraction of the flowers is red?
Answer:
2/10 or simplified, 1/5
Step-by-step explanation:
5 are purple out of 10 flowers so 5/10. 3 are pink so 3/10. That leaves 2/10 left, and depending on what your teacher prefers, the simplified answer is 1/5. I hope this helps.
A bag contains 10 marbles: 3 are green, 5 are red, and 2 are blue. Karen chooses a marble at random, and without putting it back, choose another one at
random. What is the probability that both marbles she chooses are red? Write your answer as a fraction in simplest form
Answer:
don't bother commenting im a bot
Step-by-step explanation:
Answer:
5/18 I believe
Step-by-step explanation:
1
The slope of a vertical line is:
(a) o
(b) Undefined
R
(c) 1
(d) -1
Find the value of x in each of the following
a)2x-7 = 13
b)3x+4 = 25
Sorry, I'm bad at maths.
The membership of a student group is expressed by the equation y = 14x + 10, where x represents the number of years since the group was formed and y represents the number of members. How many years will it take for the group to have 290 members? If the group was formed in the year 2000, in what year would you expect the group to have 290 members?
Answer:
1: 20
2: 2020
Step-by-step explanation:
just got it man so ima go yeet
The group will have 290 members in the year 2020
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, the equation is y = 14x + 10 and we are required to have 290 members thus, 290=14x + 10
x= 280/14
x = 20 years
Hence the number of years required to achieve 290 members is equal to 20 years.
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Determine Whether The Sides Make A Right Triangle
24,18,30
Right Triangle Or Not?
Answer:
Yes
Step-by-step explanation:
Since we want to test if it is a right triangle, we can use the Pythagorean Theorem
a^2+b^2=c^2
where a and b are the legs (shortest sides) and c is the hypotenuse (longest side)
We have the sides: 24,18 and 30
24 and 18 are the shortest, therefore they are the legs. 30 is the longest, so it is the hypotenuse.
So, a is 24, b is 18 and c is 30
24^2+18^2=30^2
Evaluate the exponents
576+324=900
Add 576 and 324
900=900
This statement is true, so this is a right triangle
in a basketball game, sally was the top scorer woth 30% of the teams points. If sally scored 15 points, how many total points did the team score
Answer:
The team scored 50 points
Step-by-step explanation:
Let the points scored by team be x
We are given that sally was the top scorer woth 30% of the teams points
So, Sally scored points = [tex]30\% \times x[/tex]
Sally scored points = [tex]\frac{30}{100}x[/tex]
We are given that Sally scored 15 points
So, [tex]\frac{30}{100}x=15[/tex]
[tex]30x=1500[/tex]
[tex]x=\frac{1500}{30}[/tex]
x=50
Hence The team scored 50 points
What is (x^2+3x-10)/(x-2)
The simplified expression is x+5.
To simplify the expression x^2 +3x−10 /x−2, you can use polynomial long division or factorization.
Here's how to do it by factorization:
Factor the numerator
x^2 +3x−10:
x^2 +3x−10=(x+5)(x−2)
Rewrite the expression with the factored form of the numerator:
(x+5)(x−2)/ x−2
Cancel out the common factor of x−2:
(x−2) /(x+5) /x−2
The simplified expression is x+5.
So, x^2 +3x−10/ x−2 =x+5.
Evaluate the function. Find f(5). f(x)=2x2-1. The second 2 is a exponent
Answer:
[tex]f(x)=2x^2-1\\f(5)=2(5)^2-1\\f(5)=2(25)-1\\f(5)=50-1\\f(5)=49[/tex]
Step-by-step explanation:
a hospital did a ten year study on patients who used its services. one thousand patients were randomly selected and followed over a period of ten years to determine the average number of visits per year. by the end of the year period some of the patients had left the area. identify the problem with the pool
Option A is the correct answer. That is a nonresponse occurred.
Given that, a hospital did a 10-year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year.
What is a poll in statistics?An opinion poll, often simply referred to as a poll or a survey, is a human research survey of public opinion from a particular sample.
Look at the explanation given below for the options:
Option A:
We understand that in the span of 10 years, 1000 patients were monitored, and among those were some individuals who had moved. These certain individuals are not responsive anymore, and can not be a source of data, and the poll would be incorrect if the hospital decided to switch out the patients in the midst of the decade. Therefore we are to assume a nonresponse occurred. (To define nonresponse, it is simply a failure to respond, which is indeed what is defined for those who had moved.)
Option B:
It is not B for the two variables have no correlation.
Option C:
It is not C for all patients were at first patrons and the problem did not explicitly state there was missing info.
Option D:
It is incorrect for it said the sample group was selected at random.
Therefore, with the process of elimination, option A would still be the correct answer.
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A hospital did a 10-year study on patients who use his services. 1000 patients were randomly selected and followed over a period of 10 years to determine the average number of visits per year. By the end of the 10 years. Some of the patients had left the area. Identify the problem with the poll.
A) A nonresponse occurred
B) The relationship between two variables implies one causes the other
C) Some of the sample data are missing
D) The conclusion is based on a voluntary response sample
The rectangle has an area of 198 square millimeters. The length is 9 millimeters. What is the width of the rectangle?
Answer:
22 millimetres
Step-by-step explanation:
[tex]width \: of \: rectangle \\ = \frac{area}{length} \\ = \frac{198}{9} \\ = 22 \: millimeters \\ [/tex]
The speeds of a car and a train after they activate their emergency brakes are represented by the following tables:
Car
Time (seconds) Speed (m/s)
0 69.4
2 34.0
4 16.7
6 8.2
8 4.0
Train
Time (seconds) Speed (m/s)
0 88.9
2 50.1
4 28.1
6 15.8
8 8.5
Determine whether the data for cars is best modeled as a linear function or an exponential fuction.
Determine whether the data for train is best modeled as a linear function or an exponential function
Answer:
Car: Exponential Function
Train: Exponential Function
Step-by-step explanation:
The consecutive differences are quite far from being constant. However, the consecutive ratios are quite close to being constant, being approximately 0.49 for every increase in 2 seconds.Therefore, the speed of the car is best modeled by an exponential function. The consecutive ratios for the trains are quite close to being constant, being approximately 0.56 for every increase in 2 seconds. Therefore, the speed of the train is best modeled by an exponential function.
The data of car is exponential function.
The data of truck is exponential function.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
As, the difference between two consecutive terms is not constant.
but the ratios are quite close to being constant, approximately 0.49 for every increase in 2 seconds.
The consecutive ratios for the trains are 0.56 for every increase in 2 seconds.
Thus, the speed of the car and truck is an exponential function.
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Which scenarios have a negative correlation? Check all that apply. the number of calories consumed and the amount of weight lost by a person the temperature outside and the number of pool guests the number of children assigned to a class and the number of desks the price of rice and the number of penguins at the South Pole the thickness of the ice on a lake and the likelihood of falling through the ice
Answer:
A. the number of calories consumed and the amount of weight lost by a person.
E. the thickness of the ice on a lake and the likelihood of falling through the ice.
Step-by-step explanation: This is the correct answer on Edge 2021, just did the assignment. Hope this helps ^-^.
An example of negative correlation is;the number of calories consumed and the amount of weight lost by a person.
What is a correlation?The term correlation has to do with the way in which two quantities are related. If there is a positive correlation between two quantities, they tend to have a positive slope when plotted.
Two examples of negative correlation are;
the number of calories consumed and the amount of weight lost by a person. the thickness of the ice on a lake and the likelihood of falling through the ice.Learn more about correlation:https://brainly.com/question/6563788
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If a circle has a diameter of 91 units how many units is the radius
Answer:
r =45.5 units
Step-by-step explanation:
The diameter is twice the radius, or the radius is 1/2 the diameter
r = d/2
r = 91/2
r =45.5 units
Answer: 45.5
Step-by-step explanation: 91/2 because to find the diameter you have to multiply the radius by 2 and now we need to reverse it
What is the absolute value of -7.95
Is it
A- -7.95
B- 7.95
C- not known
Answer:
7.95.
Step-by-step explanation:
Absolute value is the positive version of that number.
The expression 3(1.5)^t models the number of bacteria in a culture as a function of the number of hours since the cultures was created.
What does 3 represent in this expression?
A. The culture was created 3 hours ago.
B. There were initially 3 bacteria in the culture.
C. The number of bacteria is multiplied by 3 each hour.
Answer:
3 would be the initial value so B
Step-by-step explanation:
Answer:
The answer is There were initially 3 bacteria in the culture.
Step-by-step explanation:
Jake drew a kite the sketch below of a kite that he wants to make.
Part A
Which of the following expression can be used to find the area of the kite?
Part B
What is the area of Jakes kite?
area= ??
a) The area of a kite is given by [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals. So the answer is [tex]\frac{1}{2} (40 \times 60)[/tex].
b) Evaluating the expression from part (a), we get the area to be [tex]\boxed{1200 \text{ cm}^{2}}[/tex]
For a hypothesis test of H0 : μ = 8 vs. H0 : μ > 8, the sample mean of the data is computed to be 8.24. The population standard deviation is unknown; the sample standard deviation is computed, and its value is 0.29. These sample statistics are based on a sample size of 19. It is assumed that the underlying population is normally distributed. Which of the following would be the distribution of the test statistic in this scenario?a) The t-distribution with 8 degrees of freedomb) The standard normal distributionc) The t-distribution with 19 degrees of freedomd) The t-distribution with 18 degrees of freedom
Answer:
d) The t-distribution with 18 degrees of freedom
Step-by-step explanation:
If we have the population standard deviation, we use the standard normal distribution.
Otherwise, if we only have the standard deviation for the sample, we use the t-distribution.
The number of degrees of freedom is the sample size subtracted by 1.
In this problem:
Sample size of 19, we have the standard deviation for the sample.
So the t-distribution will be used to solve this question, with 19-1 = 18 degrees of freedom.
So the correct answer is:
d) The t-distribution with 18 degrees of freedom
In a hypothesis test where the population standard deviation is unknown and estimated by the sample standard deviation, we use the t-distribution with degrees of freedom equal to the sample size minus one. In this case, the distribution of the test statistic would follow a t-distribution with 18 degrees of freedom.
Explanation:In this particular case, the sample size is 19, and the population standard deviation is unknown and estimated by the sample standard deviation. Because of these conditions, the t-distribution would be used to determine the test statistic. Specifically, we would use the t-distribution with degrees of freedom equaling the sample size minus one, i.e., 18. Therefore, the correct answer among the options given is 'The t-distribution with 18 degrees of freedom'.
For example, suppose we have a set of samples from an unknown population, we compute the sample standard deviation and use it as an estimator of the actual unknown population standard deviation. In such cases, we use the t-distribution with (n-1) degrees of freedom, where n is our sample size. Here, it would be the t-distribution with 18 degrees of freedom because our sample size is 19.
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According to a report by Scarborough Research, the average monthly household cellular phone bill is $73. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of $11.
a. What is the probability that a randomly selected monthly cell phone bill is less than $95?
Answer:
The probability that a randomly selected monthly cell phone bill is less than $95 is 0.9772
Step-by-step explanation:
The average monthly household cellular phone bill is $73.
[tex]\mu = 73[/tex]
Local monthly household cell phone bills are normally distributed with a standard deviation of $11.
[tex]\sigma = 11[/tex]
We are supposed to find the probability that a randomly selected monthly cell phone bill is less than $95 i.e.P(x<95)
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{95-73}{11}[/tex]
Z=2
Refer the z table for p value
So,p value = 0.9772
Hence the probability that a randomly selected monthly cell phone bill is less than $95 is 0.9772
Compare each set of data. Determine which set shows greater variability.
Set A
5, 8, 9, 10, 12, 15, 16, 20
Set B
24, 34, 37, 42, 56, 57, 65
Answer:
Which set shows greater variability? Set B
Which measure provides greater variability for the set you chose? Range
Answer:
Set B
Range
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
Mike runs for the president of the student government and is interested to know whether the proportion of the student body in favor of him is significantly more than 50 percent. A random sample of 100 students was taken. Fifty-five of them favored Mike. At a 0.05 level of significance, it can be concluded that the proportion of the students in favor of Mike:
a.is significantly greater than 50 percent because 55 percent of the sample favored him.
b.is not significantly greater than 50 percent.
c.is significantly greater than 55 percent.
d.is not significantly different from 55 percent.
Using the z-distribution, it is found that the correct option is:
b. is not significantly greater than 50 percent.
At the null hypothesis, it is tested if the proportion is not significantly greater than 50%, that is:
[tex]H_0: p \leq 0.5[/tex]
At the alternative hypothesis, it is tested if the proportion is significantly greater than 50%, that is:
[tex]H_1: p > 0.5[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]n = 100, \overline{p} = \frac{55}{100} = 0.55, p = 0.5[/tex].
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.55 - 0.5}{\sqrt{\frac{0.5(0.5)}{100}}}[/tex]
[tex]z = 1[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, using the z-distribution with a significance level of 0.05, is of [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that the proportion is greater than 50%, hence, option b is correct.
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Which opening sentence goes best with the details in the above paragraph?
A.
Recycling programs have become popular.
B.
Pollution from burning of fossil fuels causes acid rain.
C.
Canada is a land rich in mineral resources.
D.
The United States is rich in resources.
People have often acted as though these resources were unlimited. In recent years, however, the people of the United States have started to understand that they must use their resources more wisely than in the past.
Answer:
The United states is rich in resources
Step-by-step explanation:
Got it right on study island:))
Final answer:
The opening sentence that best fits the paragraph's context is 'The United States is rich in resources,' as it introduces the theme of resource consumption and sustainability within the U.S.
Explanation:
The best opening sentence that goes with the details in the paragraph provided is option D: The United States is rich in resources. This opening sentence sets the context for discussing how the people in the United States have historically acted as if their resources were unlimited. It leads into the realization that there must be a more prudent approach to using resources going forward, as indicated in the paragraph. The passage indicates a shift in understanding within the United States regarding resource consumption and the necessity for wiser use, aligning well with the recognition of resource richness and the implication of historical abundance.
A market researcher for Eric’s Electronics wants to study TV viewing habits of residents in Chicago. The individuals in the survey are asked to keep track of their weekly TV viewing time. A random sample of 50 respondents is selected, and the average viewing time per week for the 50 individuals in the sample is 17.5 hours. The population standard deviation is known to be 5.0 hours. Assume that TV viewing is a normally distributed random variable. (7 points) Construct a 90% confidence interval estimate for the mean amount of television watched per week by individuals in Chicago. Interpret your result.
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
1) x = 17.5
σ = 5
n = 50
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, confidence level of 90% is 1.645
Margin of error = 1.645 × 5/√50 = 1.16
Confidence interval = 17.5 ± 1.16
Which lines have a y-intercept at (0,4)?
Answer:
Is there any picture ?
Step-by-step explanation:
Jada buys a bottle of laundry detergent that contains 6 cups of detergent . She uses 1/8
cup in each load of laundry she does.
How many loads of laundry can Jada do with her bottle of laundry detergent
Answer:
Jada can do 48 loads of laundry.
Step-by-step explanation:
There are 6 cups of detergent in the bottle. If Jada uses 1/8 cup of detergent each load you would have to find out how many 1/8 cups are in 6 cups. There are 8, 1/8 cups in 1 cup. So you would do 6 time 8, which equals 48 loads.
Answer: I literally gust took the the test and the answer is 112.
Your welcome!!