We have been given a function [tex]h(x)=\frac{1}{8}x^3-x^2[/tex]. We are asked to find the average rate of change of our given function over the interval [tex]-2\leq x\leq 2[/tex].
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]\text{Average rate of change}=\frac{h(2)-h(-2)}{2-(-2)}[/tex]
[tex]\text{Average rate of change}=\frac{\frac{1}{8}(2)^3-2^2-(\frac{1}{8}(-2)^3-(-2)^2)}{2+2}[/tex]
[tex]\text{Average rate of change}=\frac{\frac{1}{8}(8)-4-(\frac{1}{8}(-8)-(4))}{4}[/tex]
[tex]\text{Average rate of change}=\frac{1-4-(-1-4)}{4}[/tex]
[tex]\text{Average rate of change}=\frac{-3-(-5)}{4}[/tex]
[tex]\text{Average rate of change}=\frac{-3+5}{4}[/tex]
[tex]\text{Average rate of change}=\frac{2}{4}[/tex]
[tex]\text{Average rate of change}=\frac{1}{2}[/tex]
Therefore, the average rate of change over the interval [tex]-2\leq x\leq 2[/tex] is [tex]\frac{1}{2}[/tex].
The average rate of change of h over the interval -2 ≤ x ≤ 2 in the equation h(x)=1/8x³-x² is 3/8.
Explanation:To find the average rate of change of h over the interval -2 ≤ x ≤ 2, we need to calculate the difference in the values of h at the endpoints of the interval and divide it by the change in x.
First, let's find the value of h at x = -2: h(-2) = (1/8) * (-2)^3 - (-2)^2 = -(1/2).
Next, let's find the value of h at x = 2: h(2) = (1/8) * (2)^3 - (2)^2 = 1.
The change in x is 2 - (-2) = 4. So, the average rate of change of h over the interval -2 ≤ x ≤ 2 is (1 - (-1/2))/4 = 3/8.
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Halle drives 2.41 kilometers to the train station. Then she travels 15.8 kilometers on the train. Finally, she walks 0.45 kilometers to the building where she works.
How many kilometers does Halle travel in all?
Answer:
18.66
Step-by-step explanation:
2.41 + 15.8 + 0.45
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n=83, x=45, 98 percent
Could you please explain the steps and how to get to an answer? Thank you!
Answer:
The 98% confidence interval for the population proportion p is (0.4149, 0.6695).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 83, \pi = \frac{45}{83} = 0.5422[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 - 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.4149[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5422 + 2.327\sqrt{\frac{0.5422*0.4578}{83}} = 0.6695[/tex]
The 98% confidence interval for the population proportion p is (0.4149, 0.6695).
The GO transportation system of buses and commuter trains operates on the honor system. Train travelers are expected to buy their tickets before boarding the train. Only a small number of people will be checked on the train to see whether they bought a ticket. Suppose that a random sample of 200 train travelers was sampled and 24 of them had failed to buy a ticket. Estimate with 90% confidence the proportion of all train travelers who do not buy a ticket. Interpret the confidence interval you found.
Answer:
The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
n = 200
X = 24
Confidence level = 90%
Compute the value of sample proportion as follows:
[tex]\hat p=\frac{X}{n}=\frac{24}{200}=0.12[/tex]
Compute the critical value of z for 90% confidence level as follows:
[tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]
Compute the 90% confidence interval for the population proportion of all train travelers who do not buy a ticket as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.12\pm 1.645\times\sqrt{\frac{0.12(1-0.12)}{200}}\\\\=0.12\pm0.038\\=(0.082, 0.158)\\\approx (0.08, 0.16)[/tex]
The 90% confidence interval for the population proportion of all train travelers who do not buy a ticket is (0.08, 0.16).
The 90% confidence interval (0.08, 0.16) for the population proportion of all train travelers who do not buy a ticket implies that there is a 0.90 probability that the true proportion lies in this interval.
Or if 100 such intervals are computed then 90 of those intervals will consist of the true proportion.
Which of the following statements is true in a one-way ANOVA? a. The critical value of the test will be a value obtained from the F-distribution. b. If the null hypothesis is rejected, it may still be possible that two or more of the population means equal. c. The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations. d. All of these. e. None of these.
Answer:
d) All of the above
Step-by-step explanation:
A one way analysis of variance (ANOVA) test, is used to test whether there's a significant difference in the mean of 2 or more population or datasets (minimum of 3 in most cases).
In a one way ANOVA the critical value of the test will be a value obtained from the F-distribution.
In a one way ANOVA, if the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.
This one way test is an omnibus test, it only let us know 2 or more group means are statistically different without being specific. Since we mah have 3 or more groups, using post hoc analysis to check, it may still be possible it may still be possible that two or more of the population means are equal.
The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.
Let's say we are comparing the means of k population. The degree of freedom would be = k - 1
The correct option here is (d).
All of the above
The correct answer is all of the statements are true in a one-way ANOVA: the test uses the F-distribution, rejecting the null can mean two or more population means are equal, and degrees of freedom for treatment sum of squares is the number of groups minus one.
Explanation:The correct answer to which statement is true in a one-way ANOVA is d. All of these.
The critical value of the test comes from the F-distribution.If the null hypothesis is rejected, it is still possible that two or more of the population means equal, as rejecting the null suggests at least two means are different, not necessarily all.The degrees of freedom associated with the sum of squares for treatments equals one less than the number of populations (dfbetween = number of groups - 1).One-way ANOVA is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups. The F statistic in ANOVA is always right-tailed because larger F values fall in the right tail of the F-distribution curve, leading to the rejection of the null hypothesis.
What is the surface area
Sophia and her brother combined to read a total of 40 books over the summer. Sophia read four times as many books as her brother. How many books did each person read?
Answer:
Brother read 8 books
Sophia read 32
Step-by-step explanation:
Number of book Sophia and her brother read is 32 and 8.
Distribution of books:Given that;
Total number of books = 40 books
Number of book Sophia read = 4[Number of book Sophia's brother read]
Find:
Number of books each person read
Computation:
Assume;
Number of book Sophia's brother read = a
So,
Number of book Sophia read = 4a
So,
a + 4a = 40
5a = 40
a = 8
Number of book Sophia's brother read = 8 books
So,
Number of book Sophia read = 32 books
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Reginald read his novel three nights in a row. Each night, he read for
3/4 of an hour.
How many hours did Reginald read his novel altogether?
9 hours
2 1/2 hours
2 1/4 hours
4 hours
Answer:
2 1/4 hours
Step-by-step explanation:
Each night, he read for 3/4 hours = 3*60/4 = 45 minutes.
He read for 3 days.
So in total, he read for:
3*45 = 135 minutes.
135 minutes is 2 hours and 15 minutes. 15 minutes is 1/4 of an hour.
So the correct answer is:
2 1/4 hours
An SAT coaching company claims it's course can raise SAT scores of high school students (thus, when they take it a second time after being coached). Of course, students who retake the SAT without paying for coaching generally raise their scores also. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were not coached. For both the coached group and the uncoached group, the gain in score was recorded. The SAT coaching company wishes to test to see if their coaching provided better second attempts on average. What case is best
Answer:
Check the explanation
Step-by-step explanation:
(a) The appropriate test is the matched-pairs test because a student’s score on Try 1 is certainly correlated with his/her score on Try 2. Using the differences, we have xbar = 29 and s = 59.
(b) To test H0: mu=0 vs. H1 mu > 0, we compute
[tex]t = (29-0)/((59/sqrt(427))=10.16[/tex]
with df = 426. This is certainly significant, with P < 0.0005. Coached students do improve their scores on average
(a) H0: μ1 = μ2 vs. Ha: μ1 > μ2, where μ1 is the mean gain among all coached students and μ2 is the mean gain among uncoached students. H0 and Ha. Using the conservative approach, df = 426 is rounded down to df = 100 in (t table) and we obtain 0.0025 < P < 0.005. Using software, df = 534.45 and P = 0.004. There is evidence that coached students had a greater average increase.
(b) 8 ± t*(3.0235) where t* equals 2.626 (using df = 100 with (t table) ) or 2.585 (df = 534.45 with software). This gives either 0.06 to 15.94 points, or 0.184 to 15.816 points, respectively.
(c) Increasing one’s score by 0 to 16 points is not likely to make a difference in being granted admission or scholarships from any colleges.
This year’s school population in Waterloo is 135 percent of last year’s school population. This year’s student population is 756. How many students did the school have last year?
Answer:560
Step-by-step explanation:
Let a be the number of students the school have last year
135% of a=756
135/100 x a=756
135a/100=756
Cross multiplying we get
135a=756 x100
135a=75600
Divide both sides by 135
135a/135=75600/135
a=560
The probability that Lexie is on time for a given class is 98 percent. If there are 89 classes during the semester, what is the best estimate of the number of times out of 89 that Lexie is on time to class?
Answer:
87
Step-by-step explanation:
The expected value is the product of the probability and the outcome.
E = 0.98 (89)
E = 87.22
Rounded to the nearest integer, the expected number of classes is 87.
A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the 95% confidence interval (0.366 comma 0.506 )for the proportion of employees who prefer plan A. Identify the point estimate for estimating the true proportion of employees who prefer that plan.
Answer:
The point estimate for estimating the true proportion of employees who prefer that plan is 0.436
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 0.366
Upper bound: 0.506
Point estimate:
(0.366 + 0.506)/2 = 0.436
The point estimate for estimating the true proportion of employees who prefer that plan is 0.436
Answer:
[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]
And the point of estimate for the proportion of employees who prefer plan is on this case 0.436 or 43.6%.
Step-by-step explanation:
We define the parameter of interest as the proportion of employees who prefer plan p and we want to estimate this true parameter
The confidence interval for the this proportion is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
After calculate the 95% confidence interval we got (0.366, 0.506)
We can obtain the best estimate for the proportion of employees who prefer plan like this:
[tex]\hat p =\frac{Upper +Lower}{2}[/tex]
Where Upper and Lower represent the limits for the confidence interval and replacing we got:
[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]
And the point of estimate for the proportion of employees who prefer plan is on this case 0.436 or 43.6%.
The margin of error can be estimated using the fact that this confidence interval is symmetrical and we got:
[tex]ME=\frac{Upper-Lower}{2}= \frac{0.506-0.366}{2}=0.07[/tex]
Bonnie knits 3 centimeters of
scarf each night. After 12 nights
of knitting, how many
centimeters of scarf will Bonnie
have knit in total?
Answer:
3 x 12 = 36
Step-by-step explanation:
Compensation professionals in XYZ Company use regression analysis to determine the pay rates of its marketing professionals. There are 4 different marketing job titles in XYZ Company. Compensation professionals use job evaluation points assigned to each marketing job title and a salary survey data. In other words, they regress job evaluation points on the salary data. What does it mean when the R2 value of this regression turns out to be 0.85
Answer: This means that the salaries of their marketing professionals are not closely related to their job titles. In further explanation, this shows that a professional with a higher job title, may be paid a lower salary when compared to a professional with a lower job title.
A 0.85 R-Squared shows that the points are far from the trend lines. From this, we can assume that the marketing professionals are paid base on commission on sales, and not base on job position.
Step-by-step explanation: R-Squared is a measure used in statistics, to represent how much proportion of the dependent variables that is explained by the independent variables. A high value of R^2 shows a very low correlation between the dependent and independent variables, while a low value of R^2 shows that the dependent and independent variables are closely related. The R-Squared value are a measure of percentage value.
9/10 divided by (-6/5)
Answer:
-3/4
Step-by-step explanation:
9/10 ÷ (-6/5)
Copy dot flip
9/10 * -5/6
Rewriting
-5/10 * 9/6
-1/2 * 3/2
-3/4
Answer: -3/4
Step-by-step explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.
In other words we can rewrite 9/10 ÷ -6/5 as 9/10 · -5/6.
Before multiplying however, notice that we can cross-cancel
the 9 and 6 to 3 and 2 and the 5 and 10 to 1 and 2.
So we now have 3/2 · -1/2.
Now multiplying across the numerators
and denominators we get -3/4.
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.8 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 16 samples is 8.2 ppm with a standard deviation of 0.6. Assume the population is normally distributed. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is [tex]t = 2.67[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 7.8[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 7.8[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem, we have that:
[tex]X = 8.2, \mu = 7.8, \sigma = 0.6, n = 16[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{8.2 - 7.8}{\frac{0.6}{\sqrt{16}}}[/tex]
[tex]t = 2.67[/tex]
The value of the test statistic is [tex]t = 2.67[/tex]
Which formula is used to calculate the standard deviation of sample data?
cok
n-1
100. ()*(3*3)*==(x-)
0 /6 -> * (37)*(
n-1
Answer:
[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]
Step-by-step explanation:
In statistics, the standard deviation is a measure about the amount of variation of a dataset.
The variation is measured through comparison between each data and the mean of the dataset. This way, we could get a numerical information about how far are those values form the mean (which represents the central value).
The formula to find the standard deviation of a sample is
[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]
Where [tex]\mu[/tex] is the sample mean and [tex]N[/tex] is the total number of values there are.
In the formula you can notice the difference between each value ([tex]x_{i}[/tex]) and the mean ([tex]\mu[/tex]), That's why the standard deviation is commonly use to measure variation.
Therefore, the answer is
[tex]s=\sqrt{\frac{\sum (x_{i} -\mu)^{2} }{N-1} }[/tex]
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Find the residuals from the regression and verify that the residuals are approximately normally distributed. Height (inches), x 26.75 25.5 26.5 27 25 Head Circumference (inches), y 17.3 17.1 17.3 17.5 16.9
Answer:
[tex]y=0.259 x +10.447[/tex]
Now we can find the residulls like this:
[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]
[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]
[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]
[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]
[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]
So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally
Step-by-step explanation:
We have the following data given:
Height (inches), x 26.75 25.5 26.5 27 25
Head Circumference (inches), y 17.3 17.1 17.3 17.5 16.9
We need to find a linear model [tex] y = mx +b[/tex]
For this case we need to calculate the slope with the following formula:
[tex]m=\frac{S_{xy}}{S_{xx}}[/tex]
Where:
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}[/tex]
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}[/tex]
So we can find the sums like this:
[tex]\sum_{i=1}^n x_i =130.75[/tex]
[tex]\sum_{i=1}^n y_i =86.1[/tex]
[tex]\sum_{i=1}^n x^2_i =3422.06[/tex]
[tex]\sum_{i=1}^n y^2_i = 1482.85[/tex]
[tex]\sum_{i=1}^n x_i y_i =2252.28[/tex]
With these we can find the sums:
[tex]S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=3422.06-\frac{130.75^2}{5}=2.95[/tex]
[tex]S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=2252.28-\frac{130.75*86.1}{5}=0.765[/tex]
And the slope would be:
[tex]m=\frac{0.765}{2.95}=0.259[/tex]
Nowe we can find the means for x and y like this:
[tex]\bar x= \frac{\sum x_i}{n}=\frac{130.75}{5}=26.15[/tex]
[tex]\bar y= \frac{\sum y_i}{n}=\frac{86.1}{5}=17.22[/tex]
And we can find the intercept using this:
[tex]b=\bar y -m \bar x=17.22-(0.259*26.15)=10.447[/tex]
So the line would be given by:
[tex]y=0.259 x +10.447[/tex]
Now we can find the residulls like this:
[tex] e_1 = 17.3 - 17.375 = -0.075[/tex]
[tex] e_2 = 17.1 - 17.052 = 0.049[/tex]
[tex] e_3 = 17.3 - 17.311 = -0.011[/tex]
[tex] e_4 = 17.5 - 17.440 = 0.06[/tex]
[tex] e_5 = 16.9 - 16.922 = -0.022[/tex]
So then we can see that the residuals are not with an specified pattern (alternating sign) so then we can conclude that are distributed normally
Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5 superscript 33 1 over x d x space equals . State the definite integral and evaluate it:Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5 superscript 33 1 over x d x space equals . State the definite integral and evaluate it:
Answer:
[tex]\displaystyle A = \int\limits^{33}_{5} {\frac{1}{x}} \, dx[/tex]
[tex]\displaystyle A = \ln \frac{33}{5}[/tex]
General Formulas and Concepts:
Algebra II
Logarithmic PropertiesCalculus
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{x}[/tex]
Bounds: [5, 33]
Step 2: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^{33}_{5} {\frac{1}{x}} \, dx[/tex][Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle A = \ln |x| \bigg| \limits^{33}_5[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = \ln |33| - \ln |5|[/tex]Condense: [tex]\displaystyle A = \ln \frac{33}{5}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.2 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 180 engines and the mean pressure was 6.3 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.05 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.
Answer:
Given:
mean, u = 6.2
sample size, n = 180
Sample mean, X' = 6.3
s.d [tex] \sigma [/tex] = 0.9
Significance level = 0.05
The null and alternative hypothesis will be:
H0 : u = 6.2
H1 : u > 6.2
Degree of freedom = 180 - 1 = 179
Using t table, the t critical value,
t> t(0.05, 179) = 1.6534
The test statistic:
[tex] t = \frac{X' - u}{\frac{\sigma}{\sqrt{n}}} [/tex]
[tex] T = \frac{6.3 - 6.2}{\frac{0.9}{\sqrt{180}}} = 1.4907 [/tex]
Since the test statistic(t calculated value) 1.4907 < t critical value (1.6534), we fail to reject the null hypothesis H0.
Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins and 160 standard cabins, whereas a type-B vessel has 80 deluxe cabins and 120 standard cabins. Under a charter agreement with Odyssey Travel Agency, Deluxe River Cruises is to provide Odyssey with a minimum of 360 deluxe and 680 standard cabins for their 15-day cruise in May. It costs $42,000 to operate a type-A vessel and $51,000 to operate a type-B vessel for that period. How many of each type of vessel (x type-A and y type-B) should be used in order to keep the operating costs to a minimum
Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.
Step-by-step explanation: As it is stipulated, x relates to type-A and y to type-B.
Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:
60x + 80y ≤ 360
For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:
160x + 120y ≤ 680
To calculate how many of each type you need:
60x + 80y ≤ 360
160x + 120y ≤ 680
Isolating x from the first equation:
x = [tex]\frac{360 - 80y}{60}[/tex]
Substituing x into the second equation:
160([tex]\frac{360 - 80y}{60}[/tex]) + 120y = 680
-3200y+1800y = 10200 - 14400
1400y = 4200
y = 3
With y, find x:
x = [tex]\frac{360 - 80y}{60}[/tex]
x = [tex]\frac{360 - 80.3}{60}[/tex]
x = 2
To determine the cost:
cost = 42,000x + 51,000y
cost = 42000.2 + 51000.3
cost = 161400
To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400
Which dot plot shows a sample that is most representative of the number of pets in a household?
THE COMPLETE QUESTION IS:
Which dot plot shows a sample that is most representative of the number of pets in a household?
A. A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.
B. Adot plot going from 0 to 6. There are 2 dots above 1, 3 dots above 2, and 1 dot above 5.
C. A dot plot going from 0 to 6. There is 1 dot above 0, 2 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, 1 dot above 5, 2 dots above 6.
D. A dot plot going from 0 to 6. There is 1 dot above 1, 2 dots above 2, 3 dots above 3, 2 dots above 4, 1 dot above 5.
Answer:
A is the correct option
Step-by-step explanation:
A. A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.
A has 3+5+4+3+2+0+1 = 18 dots
The rest are not up to 18.
The best graphical representation of the number of pets in a household is: A dot plot going from 0 to 6. There are 3 dots above 0, 5 dots above 1, 4 dots above 2, 3 dots above 3, 2 dots above 4, 0 dots above 5, and 1 dot above 6.
What is a graph?A graph can be defined as the graphical representation of data (information) on both the horizontal and vertical lines, which are commonly called the x-axis and y-axis respectively.
The types of graph.In Mathematics, there are different types of graph and these include:
Scatter plotBar graphPie chartDot plot.A dot plot refers to a type of graph which comprises small data points that are plotted on a simple histogram-like graph. Thus, the number of pets in a household should be represented by using a dot plot with its value ranging from 0 to 6.
Read more on graphs here: https://brainly.com/question/25875680
what is the answer of this question?
Answer:
116
Step-by-step explanation:
8.2 / 2 = 4.1
a = [tex]\sqrt{7^{2}-4.1^{2} } = 5.6736[/tex]
0.5 x 8.2 x 5.6736 = 23.2618
23.2618 x 5 = 116.309 = 116
Use x for your variable.
The sum of four times a number and seven is ten more than the number.
Answer:
4x + 7 = x + 10: x = 1!
Step-by-step explanation:
Not sure if you wanted me to solve as well; but I figured I would do it just in case!
To solve this, use the following steps!:
[tex]4x+7=x+10\\-7\\4x=x+3\\-x\\3x=3\\x=1![/tex]
x = 1 Should be the correct answer!
The sum of four times a number and seven is ten more than the number can be express as follows:
4x - 3
let
the number = x
Therefore,
Four times the number = 4x
Seven is ten more than the number is as follows:
7 - x = 10x = 7 - 10x = -3Therefore, the sum of four times a number and seven is ten more than the number is as follows:
4x + (-3)4x - 3Algebraic expression4x - 3learn more on variable here: https://brainly.com/question/18681264
Patricia got a 5/25 balloon mortgage and her initial payments were $965. She
decided to refinance her balloon payment with a 30-year mortgage and her
new payments were $925. What is the total financed cost she paid for her
house?
Answer:
$390,900
Step-by-step explanation:
Given:
Initial payment = $965
New rapayment = $925 when she decided to refinance her ballon payment with a 30 year mortgage
In this case, a 5/25 ballon mortgage simply means loan repayment for the first 5 years is at a fixed rate.
Which means the total amount she paid in the first five years was=
12 * 5 * $965 = $57,900
When she refinanced the payment with a 30 year mortgage, her total payment = $925 * 12 * 30years = $333,000
Total financed cost Patricia paid =
$57,900 + $333,000 = $390,900
help me please it is math
Maria pulls colored marbles out of a bag one at a time. Her results are shown in the table below. Based on the outcomes, if 20 more marbles are pulled out of the bag and replaced, how many marbles can be expected to be white?
To find the expected number of white marbles in future pulls, calculate the probability of pulling a white marble from the current results, then multiply this probability by the number of new pulls.
Explanation:To solve this problem, we will first identify the probability of pulling a white marble out of the bag based on Maria's results. Then, we will multiply this probability by the number of new marbles being pulled out (20) to determine the expected number of white marbles.
Calculate the total number of marbles Maria pulled out and the number of those marbles that were white.Divide the number of white marbles by the total number of marbles to find the probability of pulling a white marble.Multiply this probability by 20 (the number of additional pulls) to find the expected number of white marbles.Note: Since the outcomes are being replaced, the probabilities don't change after each pull.
Learn more about Expected Value here:https://brainly.com/question/37190983
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Suppose that you found two different solutions for a system of two linear equations. How many solutions must the system have?
Answer:
One solution.
Step-by-step explanation:
A linear line only goes one way, and thus, two lines can only meet at one point.
That is unless, the linear equations are both the same, then they will have infinite solutions.
But what you're asking is if they're different so no, you cannot have two solutions for a system of two linear equations.
Answer:
0
Step-by-step explanation:
Two different solutions means the two equations aren't consistent - there's no unique solution that solves the whole system. Two lines can meet at at most one point, so in this case, no solution to the first equation will be a solution to the second. The system has 0 solutions.
Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long. Maria has 3 4 foot of trim left. What was the length of the trim when she started? Enter your answer in yards.
We have been given that Maria put trim around a banner that is the shape of a triangle. Each side is 21 inches long.
The amount of trim will be equal to perimeter of triangle. The perimeter of given triangle will be 3 times each side length that is [tex]3\times 21=63[/tex] inches.
Now we need to convert 63 inches into feet.
12 inches = 1 feet
63 inches = [tex]\frac{63}{12}[/tex] feet = 5.25 feet.
We are also told that Maria has [tex]\frac{3}{4}[/tex] foot of trim left, so total length of trim would be trim used plus trim left that is [tex]5.25+\frac{3}{4}=5.25+0.75=6[/tex] feet.
Since we need to find length of trim in yards, so we will convert 6 feet into yards.
3 feet = 1 yard
6 feet = [tex]\frac{6}{3}[/tex] yards = 2 yards
Therefore, the length of the trim was 2 yards.
Which of the following quadrilaterals are always parallelograms? Select all that apply. square rhombus trapezoid rectangle 2
Rectangle square rhombus
Step-by-step explanation:
For the data set 2.5, 6.5, 9, 19, 20, 2.5 what is the mean absolute deviation
Answer:
9
Step-by-step explanation:
it's 9 because you always look in the middle for the mean
will the product be greater or less then each factor? 56.9×2.01