Answer:
O х= -8/3 or x = 7/2
Step-by-step explanation:
6x² - 5x - 56 = 0
6x² - 21x + 16x - 56 = 0
3x(2x - 7) + 8(2x - 7) = 0
(2x - 7)(3x + 8) = 0
x = 7/2, -8/3
The solutions of the equation 6x² - 5x + 56 using the zero product property is x = -8/3 or x = 7/2.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given is a quadratic expression,
6x² - 5x = 56
We have to find the solutions using zero product property.
Zero product property states that, if a.b = 0, the either a = 0 or b = 0.
Let 6x² - 5x = 56
6x² - 5x - 56 = 0
Dividing throughout by 6,
x² - 5/6 x - 56/6 = 0
We can factorize it as (x + p)(x + q) such that pq = -56/6 and p + q = -5/6.
We know that,
8/3 × -7/2 = -56/6
8/3 - 7/2 = 16/6 - 21/6 = -5/6
So,
x² - 5/6 x - 56/6 = 0
(x + 8/3) (x - 7/2) = 0
Using zero product property,
(x + 8/3) = 0 or (x - 7/2) = 0
x = -8/3 or x = 7/2
Hence the solutions are x = -8/3 or x = 7/2.
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Which of the following is NOT true of using the binomial probability distribution to test claims about a proportion? Choose the correct answer below. A. One requirement of this method is that npgreater than>5 and nqgreater than>5. B. In a left-tailed test, the P-value is the probability of getting x or fewer successes among the n trials. C. In a right-tailed test, the P-value is the probability of getting x or more successes among the n trials. D. This method uses the binomial probability distribution with the P-value method and uses the value of p assumed in the null hypothesis.
Answer:
The correct option is;
D. This method uses the binomial probability distribution with the P-value method ans uses the value of p assumed in the null hypothesis
Step-by-step explanation:
Here we have the binomial probability distribution is used to test claims about a proportion then the requirement is np > 5 and nq >5
In a left-tailed test, the P value is the probability of getting x or fewer successes among n trials while in a right tailed test, the P-value is the probability of getting x or more successes among n trials
However, the P-value where a binomial distribution is used to test a claim about a proportion is derived from the z score of the parameters of the statistic and not from the p assumed in the null hypothesis.
The incorrect statement is option B. A left-tailed test in binomial probability distribution does not correspond to the probability of getting x or fewer successes among n trials.
Explanation:The statement among the given options that is NOT true of using the binomial probability distribution for testing claims about a proportion is option B. A left-tailed test does not entail the probability of getting x or fewer successes in the n trials. Instead, it approximates the probability of observing a value as extreme as the test statistic or even more extreme, which leans to the left or lower end of the distribution. Thus, the P-value in a left-tailed test corresponds to the total probability of the shaded region of the curve that falls to the left of observed value or test statistic. The remainder of the options (A, C, and D) are accurate statements.
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A bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls. Tony removes for tennis balls, without replacement from the bucket shown. What is the probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball?
Answer:
The probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball is 0.0039.
Step-by-step explanation:
We are given that a bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls.
As we know that, Probability of an event = [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]
Number of green tennis balls = 5
Number of yellow tennis balls = 2
Number of red tennis balls = 6
Number of blue tennis balls = 8
Total number of tennis balls = 5 + 2 + 6 + 8 = 21
{Now it should be notes that Tony removes for tennis balls, without replacement from the bucket means that every time the total number of remaining balls available for selecting will be one less}.
Now, Probability that Tony removes one yellow = [tex]\frac{2}{21}[/tex]
Probability that Tony removes one green = [tex]\frac{5}{20}[/tex]
Probability that Tony removes one blue = [tex]\frac{8}{19}[/tex]
Probability that Tony removes one blue again = [tex]\frac{7}{18}[/tex]
SO, final probability is = [tex]\frac{2}{21} \times \frac{5}{20} \times \frac{8}{19} \times \frac{7}{18}[/tex]
= [tex]\frac{2}{513}[/tex]
= 0.0039
Economist: The price of tap water in our region should be raised drastically. Supplies in local freshwater reservoirs have been declining for years because water is being used faster than it can be replenished. Since the price of tap water has been low, few users have bothered to adopt even easy conservation measures. The two sections in boldface play which of the following roles in the economist's argument?(A) The first is a conclusion for which support is provided, and which in turn supports the main conclusion; the second is the main conclusion.(B) The first is an observation for which the second provides an explanation; the second is the main conclusion but not the only conclusion.(C) The first is a premise supporting the argument's main conclusion; so is the second.(D) The first is the only conclusion; the second provides an explanation for the first.(E) The first is the main conclusion; the second is a conclusion for which support is provided, and which in turn supports the first.
Answer:
(C) The first is a premise supporting the argument's main conclusion; so is the second.
Step-by-step explanation:
The two sections in boldface are "Supplies in local freshwater reservoirs have been declining for years" and "few users have bothered to adopt even easy conservation measures"
In the economist's argument, both highlighted sections are premises giving the reason why the price of tap water should be drastically raised.
The conclusion of the argument is that the supply of water be drastically raised, the two boldfaced sections are just premises on which the conclusion is based.
Last month, Belinda worked 160 hours at a rate of $10.00 per hour. If her employer retains 9% of her gross salary, is $1,500 a reasonable estimate of her net salary?
We have been given that last month, Belinda worked 160 hours at a rate of $10.00 per hour.
Let us find amount earned by Belinda last month as:
[tex]\text{Amount earned in 160 hours}=\$10\times 160[/tex]
[tex]\text{Amount earned in 160 hours}=\$1600[/tex]
We are also told that Belinda's employer retains 9% of her gross salary. This means that Belinda's net income will be 91% of $1600. [tex](100\%-9\%=91\%)[/tex].
[tex]\text{Belinda's net income would be}=\$1600 \times \frac{91}{100}[/tex]
[tex]\text{Belinda's net income would be}=\$16\times 91[/tex]
[tex]\text{Belinda's net income would be}=\$1456[/tex]
Upon rounding $1456 to nearest hundred, we will get:
[tex]\text{Belinda's net income would be}\approx \$1500[/tex]
Therefore, $1500 is a reasonable estimate of her net salary.
Final answer:
After calculating the gross salary at $1,600 and then determining the tax retained, Belinda's net salary would be $1,456. Hence, $1,500 is not a reasonable estimate for her net salary.
Explanation:
Let's first calculate the gross salary that Belinda earned. She worked for 160 hours at a rate of $10.00 per hour, so her gross salary can be calculated by multiplying the number of work hours by the rate per hour:
Gross Salary = 160 hours * $10.00 per hour = $1,600
The employer retains 9% of her gross salary, so let's find out how much that amounts to:
Tax = 9% of $1,600 = 0.09 * $1,600 = $144
Now, to obtain the net salary, we subtract the tax from the gross salary:
Net Salary = Gross Salary - Tax = $1,600 - $144 = $1,456
Therefore, $1,500 is not a reasonable estimate of her net salary, as the exact calculation shows that her net salary is $1,456.
Consider the following data set:
7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9
Work out the IQR.
Answer:
Population size:8
Lower quartile (xL): 0.925
Upper quartile (xU): 5.85
Interquartile range (xU-xL): 4.925
Step-by-step explanation:
Answer:
4.65
Step-by-step explanation:
7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9
Sort the data
0.6, 0.7, 1.6, 1.9, 5, 5.7, 5.9, 7.8
Q1: (0.7+1.6)/2
= 1.15
Q3: (5.7+5.9)/2
= 5.8
IQR = 5.8 - 1.15
= 4.65
HELP THIS IS DUE IN 5 MINSSSSS! Mr. Viviano would like to report to the principal the smaller measure of center between the mean and the median for the distribution of test scores of his AP Calculus class.
The test scores are as follows: 60, 65, 70, 75, 80, 80, 85, 85, 90, 95, 100.
What is the number that he will report?
Answer:
The median. 80 because the mean is 80.454545
Step-by-step explanation:
(x+4y=5
- 1-2x + 5y = 16
Answer:
x,y( 27/13 ,43/13)
Step-by-step explanation:
x=5-4y
•1-2x+5y=16
1-2(5-4y)+5y=16
y=27/13
x=5-4y
x=5-4×27/13
x=-43/13
Need help ASAP for this question 15 points
Answer:
D
Step-by-step explanation:
If you plug it into desmos, this is the answer.
Mark knows that his yard is 214 times as long as it is wide. Which equation shows the length, in feet, of the fence that goes all the way around the yard if Mark measures the width as w feet?
Answer:
Length in feet is equal to [tex]\frac{2P}{6.5}[/tex], where P is the perimeter
Step-by-step explanation:
Let the width (W) of the yard be "X"
[tex]W = w[/tex]
Then the length(L) of the yard will be
[tex]2\frac{1}{4} * w[/tex]
[tex]L = \frac{9}{4} *w[/tex]
The perimeter of the yard will be equal to the sum of twice the length and width of the yard
Thus,
[tex]P = 2 W + 2L\\[/tex]
Substituting the given values in above equation, we get -
[tex]P = 2 w + 2 (\frac{9}{4})w\\P = 2w + 4.5 w\\P = 6.5w[/tex]
Thus, width in terms of perimeter is equal to
[tex]w = \frac{P}{6.5}[/tex]
Length in feet is equal to [tex]\frac{2P}{6.5}[/tex]
What is the reasonable estimate of the probability that ragin Cajun score 30 more points in their next football game
Answer:
Step-by-step explanation:
A recipe called for using 2 6/8 cups of flour before baking the another 3 1/2 cups after baking what is the total amount for flour needed in the recipe
Final answer:
To calculate the total flour needed, simplify 2 6/8 cups to 2 3/4 cups and add it to 3 1/2 cups. Convert to a common denominator and sum up to get the total of 6 1/4 cups of flour.
Explanation:
To find the total amount of flour needed in the recipe, we will have to add the two quantities of flour given: 2 6/8 cups and 3 1/2 cups. First, we can simplify 2 6/8 cups to 2 3/4 cups by dividing the numerator by the denominator's GCD (Greatest Common Divisor), which is 2 in this case. Then, we can add the simplified amount to the 3 1/2 cups.
Adding the two amounts together, we have:
2 3/4 cups + 3 1/2 cups
= (2 + 3) + (3/4 + 1/2) cups
= 5 + (3/4 + 1/2) cups
To add fractions, we need a common denominator. Multiply the second fraction by 2/2 to get the same denominator:
5 + (3/4 + 2/4) cups
= 5 + (5/4) cups
= 5 + 1 1/4 cups
= 6 1/4 cups
Therefore, the total amount of flour needed for the recipe is 6 1/4 cups.
Annie spent $70 at a clothing store and $35 at a pet store. What percent of the money did she spend? Check all that apply. 1) 33 1/3% at the pet store 2) 35% at the pet store 3) 50% at the pet store 4) 66 2/3% at the clothing store 5) 70% at the clothing store 6) 100% at the two stores 7) 105% at the two stores
Answer:
1, 4 and 6 are correct
Step-by-step explanation:
In answering this question, we shall be evaluating the validity of the options.
1 is correct
the total amount of money is 70+35 = 105
The percentage spent at pet store = 35/105 * 100 = 33 1/3 %
2. is wrong since 1 is correct
3 is wrong since 1 is correct
4. is correct
since she spent 33 1/3 at pet shop, what is spent at clothing store will be 100 - 33 1/3 = 66 2/3 %
5 is wrong
6 is correct
7 7 is wrong
Answer:
1) [tex]33\frac{1}{3}\%[/tex] at the pet store4)[tex]66\frac{2}{3}\%[/tex] at the clothing store6) 100% at the two storesStep-by-step explanation:
Amount of Money spent by Annie
At clothing store=$70At pet store=$35Total Amount Spent= 70+35=$105
Percentage Spent at each place
Clothing Store
[tex]\frac{70}{105}X100=66\frac{2}{3}\%[/tex]
Pet Store
[tex]\frac{35}{105}X100=33\frac{1}{3}\%[/tex]
Therefore the following applies:
1) 33 1/3% at the pet store4)66 2/3% at the clothing store6) 100% at the two storesWhich statement is true about the values of the ones and tenths digit in 346.68? A. The value of the ones digit is 6 more then the value of the tenths digit. B. The value of the ones digit is the same as the value of the tenths digit. C. The value of the ones digit is 6 times as many as the value of the tenths digit. D. The value of the ones digit is 10 times as many as the value of the tenths digit,
Answer:
B. The value of the ones digit is the same as the value of the tenths digit.
Step-by-step explanation:
346.68
From the above digit, the value of one is 6 and the value of tenth is 6.
3 = hundred
4 = ten
6 = unit
6 = tenth
8 = hundredth
The unit is the same for ones.
From the above we can see that unit and tenth have the same value.
So, therefore, the answer is:
B. The value of the ones digit is the same as the value of the tenths digit.
Estimate the perimeter of the figure to the nearest whole number. PLZ SOLVE PLZ
Answer:
The perimeter is approximately 19.
Step-by-step explanation:
Three of the sides are roughly four segments long and two are around three and a half.
4 + 4 + 4 + 3.5 + 3.5 = 19
Answer:
Approximately 19 units.
Step-by-step explanation:
The question asks for an estimate, so this is an estimate.
The bottom side has a length of 4.
The two sides that go up from the bottom are diagonals in 1 by 3 rectangles.
Each side is between 3 and 4 units long. Call it approximately 3.5 units long each.
The two upper sides are diagonals in 3 by 3 rectangles.
Each side is approximately 4 units long.
4 + 3.5 + 3.5 + 4 + 4 = 19
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 732 hours. A random sample of 28 light bulbs has a mean life of 704 hours. Assume the population is normally distributed and the population standard deviation is 65 hours. At alphaequals0.05, do you have enough evidence to reject the manufacturer's claim?
Answer:
[tex]z=\frac{704-732}{\frac{65}{\sqrt{28}}}=-2.279[/tex]
[tex]p_v =P(z<-2.279)=0.0113[/tex]
If we compare the p value and the significance level given for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and the the true mean is significantly lower than 732 hours so we have enough evidence to reject the claim
Step-by-step explanation:
Data given and notation
[tex]\bar X=704[/tex] represent the sample mean
[tex]\sigma=65[/tex] represent the standard deviation for the population
[tex]n=28[/tex] sample size
[tex]\mu_o =732[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to determine if the true mean is at least 732 or no, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 732[/tex]
Alternative hypothesis:[tex]\mu < 732[/tex]
We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{704-732}{\frac{65}{\sqrt{28}}}=-2.279[/tex]
Calculate the P-value
Since is a one-side lower test the p value would be:
[tex]p_v =P(z<-2.279)=0.0113[/tex]
Conclusion
If we compare the p value and the significance level given for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and the the true mean is significantly lower than 732 hours so we have enough evidence to reject the claim
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ ≥ 732
For the alternative hypothesis,
µ < 732
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = lifetime of the bulb
µ = mean lifetime
σ = standard deviation
n = number of samples
From the information given,
µ = 732
x = 704 hours
σ = 65 hours
n = 28
z = (704 - 732)/(65/√28) = - 2.28
Looking at the normal distribution table, the probability corresponding to the z score is 0.011
Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is enough evidence to reject the manufacturer's claim
Keith opened an investment account where he is paid 8% annual interest, compounded semi-annually. He wants to have $7,000 in the investment account in 3 years. What is the number of periods for this investment?
Answer:
6 periods
Step-by-step explanation:
The investment is compounded semi-annually which means it is compounded twice in a year. Period of investment is 3 years. So, number of periods compounded is 3 multiplied by 2 that is 6 periods.
Rate would be 8% divided by 2 that is 4%.
Initial investment can be calculated usinf spreadsheet function as =PV(rate,nper, pmt, FV)
Where,
rate is 0.04
nper is 6
pmt is 0
FV is 7,000
So, initial investment is $5,532.20.
It is negative as it is a cash outflow.
Bargain Bikes is having a 50%-off sale. The original price of the bicycle Gillian wants to buy is $72. Find 50% of $72.
50% is equivalent to the unit fraction
To find 50% of $72, divide 72 by
50% of $72 is
Answer:
50% is equivalent to the unit fraction .answer:1/2
To find 50% of $72, divide 72 by . answer: 2
50% of $72 is .answer: $36
Step-by-step explanation:
just answered :) good luck everyone
The sales price of the Bikes are obtained by finding the percent value as $36.
What is percentage?A percentage is a value that indicates 100th part of any quantity. It can be converted into a fraction or a decimal by dividing it by 100. The percent value is useful in representing the large data into a two digit number.
The sales percent is given as 505
And, the original price is $72.
The value of sales price is given as follows,
50% × Original price
⇒ 50/100 × 72
⇒ 1/2 × 72
⇒ 36
Hence, the sales price is obtained as $36.
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The average of a list of 4 numbers is 90. 0.A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth numberin the list is 80, and the fourth number in the new list is 96. What is the average of this new list of numbers.
Answer:
New Average of New List = 87.5
Step-by-step explanation:
Average is the arithmetic mean (M) of observations.
M = ΣX / N
where ΣX = sum of all observations , N = number of observations
Given : M = 90 ; N = 40
M = ΣX / N
90 = ΣX / 4
ΣX = 90 x 4
ΣX = 360 [ Of Old List of 4 numbers ]
New ΣX of new list of 4th new number = Old ΣX - Old 4th No. + New 4th No.
New ΣX = 360 - 90 + 80
New ΣX = 350
New Average (Mean M) = New ΣX / N
New M = 350 / 4
New M = 87.5
Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula: V = 999.87 − 0.06426T + 0.0085043T² − 0.0000679T³ Find the temperature at which water has its maximum density.
Answer:
[tex]T \approx 3.967\,^{\textdegree}C[/tex]
Step-by-step explanation:
The density of water is given by the following definition:
[tex]\rho = \frac{m}{V(T)}[/tex]
[tex]\rho = \frac{1000\,g}{999.870.06426\cdot T + 0.0085043\cdot T^{2}-0.0000679\cdot T^{3}}[/tex]
The density is maximum when volume is minimum, which can be found by First and Second Derivative Tests:
First Derivative
[tex]V' = -0.06426 +0.0170086\cdot T -0.0002037\cdot T^{2}[/tex]
Second Derivative
[tex]V'' = 0.0170086 - 0.0004074\cdot T[/tex]
Critical values from the first derivative are:
[tex]T_{1} \approx 79.531\,^{\textdegree}C[/tex] (absolute maximum) and [tex]T_{2} \approx 3.967\,^{\textdegree}C[/tex] (absolute minimum).
The temperature at which water has its maximum density is:
[tex]T \approx 3.967\,^{\textdegree}C[/tex]
Seventy-five percent of consumers prefer to purchase electronics online. You randomly select 88 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.
Answer:
Step-by-step explanation:
Find attached the solution
(a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.
(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.
Answer:
a. 0.71
b. 0.9863
Step-by-step explanation:
a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.
-To estimate the probability that a randomly selected house has a value less than $500,000:
[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]
Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71
b. -since 40 is larger than or equal to 30, we assume normal distribution.
-The probability can therefore be calculated as:
[tex]P(\bar X)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\=0.986336\\\\\approx 0.9863[/tex]
Hence, the probability that the mean value of the 40 houses is less than $500,000 is 0.9863
To estimate the probability that a house is valued less than $500,000, we count the bars below that value on the histogram. To estimate the probability that the mean value of 40 houses is less than $500,000, we use the Central Limit Theorem to calculate the z-score.
Explanation:(a) To estimate the probability that the selected house is valued at less than $500,000, we need to find the area under the histogram below the value of $500,000. Looking at the histogram, we see that there are 3 bars below $500,000. Each bar represents a count of houses, so we add up the counts of those 3 bars. The estimated probability is given by:
Estimated Probability = (Count of houses valued less than $500,000) / (Total count of houses)
(b) To estimate the probability that the mean value of the 40 houses is less than $500,000, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. We can then calculate the z-score for $500,000 using the formula:
z = (x - mean) / (standard deviation / sqrt(sample size))
Once we have the z-score, we can find the estimated probability using a standard normal distribution table or calculator.
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An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
A. No, the equation is not a good fit because the sum of the residuals is a large number.
B. No, the equation is not a good fit because the residuals are all far from zero.
C. Yes, the equation is a good fit because the residuals are not all far from zero.
D. Yes, the equation is a good fit because the sum of the residuals is a small number.
Answer:
B. No, the equation is not a good fit because the sum of the residuals is far from zero. Should be your answer
Step-by-step explanation:
Have a nice day :)
No, the equation is not a good fit because the sum of the residuals is far from zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation. An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.
We need to check whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is far from zero.
A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.
Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.
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A triangle has a perimeter of 10.2 kilometers. Two of the sides measure 3.4 kilometers and 3.4 kilometers. What is the length of the third side?
Answer:
3.4
Step-by-step explanation:
3.4+3.4= 6.8
10.2-6.8=3.4
Dali rolled up his painting and placed it in a cylinder 2 inches diameter. If the cylinder is 20 inches long find its volume. Round your answer to the nearest whole number
Answer:
The correct answer is 63 cubic inches.
Step-by-step explanation:
Dali rolled up his painting and placed it in a cylinder 2 inches diameter.
Diameter of the painting is 2 inches. This also implies diameter of the cylinder is 2 inches.
Radius of the cylinder is 1 inch.
Length of the cylinder is 20 inches.
Volume of the cylinder is given by π × [tex]r^{2}[/tex] × h = π × [tex]1^{2}[/tex] × 20 = 20π = 62.85 cubic inches ≈ 63 cubic inches.
Therefore the volume of the cylinder in which Dali placed his painting is given by 63 cubic inches.
-9-(-4) what is the answer to this equation.
Answer:
-5
Step-by-step explanation:
Answer:
The answer is -5
Step-by-step explanation:
Solve for Y
Just checking my answer to see if I’m right,
Thx! :D
What is the value of x in this equation? 4x + 2 – 23(92 + 92x) = 7
Answer:
-707/704
Step-by-step explanation:
4x + 2 - 2116 - 2116x = 7
-2112x = 2121
x = 2121/-2112 = -707/704
Answer:
x= 2121/-2112 = -707/704 = -1.00426136
Step-by-step explanation:
4x + 2 – 23(92 + 92x) = 7
Eliminate the 2 by substracting both side by -24x - 23(92+92x) = 5
2. Discriminate by multiplying -23 with 92 and -23 with 92x
4x - 2116 -2116x = 5
3. Add 2116 both sides to eliminate -2116
4x -2116x = 2121
4. combine 4x-2116x together
-2112x = 2121
5. Divide both sides with -2112
x= 2121/-2112 = -707/704 = -1.00426136
what is the perimeter of DEFG?
A, B, C or D
Given:
Given that the figure DEFG with vertices D(1,2), E(2,6), F(6,7) and G(5,3)
We need to determine the perimeter of DEFG.
The length of the sides can be determined using the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length of DE:
Substituting the coordinates D(1,2), E(2,6) in the formula, we get;
[tex]DE=\sqrt{(2-1)^2+(6-2)^2}[/tex]
[tex]DE=\sqrt{(1)^2+(4)^2}[/tex]
[tex]DE=\sqrt{17}[/tex]
Length of EF:
Substituting the coordinates E(2,6), F(6,7) in the formula, we get;
[tex]EF=\sqrt{(6-2)^2+(7-6)^2}[/tex]
[tex]EF=\sqrt{(4)^2+(1)^2}[/tex]
[tex]EF=\sqrt{17}[/tex]
Length of FG:
Substituting the coordinates F(6,7), G(5,3) in the formula, we get;
[tex]FG=\sqrt{(5-6)^2+(3-7)^2}[/tex]
[tex]FG=\sqrt{(-1)^2+(-4)^2}[/tex]
[tex]FG=\sqrt{17}[/tex]
Length of DG:
Substituting the coordinates D(1,2), G(5,3) in the formula, we get;
[tex]DG=\sqrt{(5-1)^2+(3-2)^2}[/tex]
[tex]DG=\sqrt{(4)^2+(1)^2}[/tex]
[tex]DG=\sqrt{17}[/tex]
Perimeter of DEFG:
The perimeter of DEFG can be determined by adding the side lengths DE, EF, FG and DG.
Thus, we have;
[tex]Perimeter=DE+EF+FG+DG[/tex]
Substituting the values, we have;
[tex]Perimeter=\sqrt{17}+\sqrt{17}+\sqrt{17}+\sqrt{17}[/tex]
[tex]Perimeter=4\sqrt{17}[/tex]
Thus, the perimeter of DEFG is 4√17
Hence, Option b is the correct answer.
If 2^2х = 2^3, what is the value of х?
Answer:
19
Step-by-step explanation:
if x=3
Answer:
x = 2
Evaluate the powers.Divide both sides by 4. Solution should be x = 2Find the value of 1/3 divided by 1/2
When dividing two fractions, it is important to know to multiply the first fraction by the reciprocal of the second fraction.
Reciprocal means basically a flipped fraction. 2/3 as a reciprocal is 3/2, etc.
1/3 / 1/2= 1/3 x 2/1=2/3