Answer:
The correct answer is About 6.27.
TSS stands for total sum of squares. It is a measure of the variation in the data. It is calculated as follows:
TSS = Σ(y - y^)^2
Where:
y is the observed value
y^ is the predicted value
In this case, the observed values are the December snowfall data and the predicted values are the April flowrate data.
TSS = (22 - 20.81)^2 + (23 - 21.7)^2 + (21 - 20.09)^2 + (18 - 19.28)^2 + (26 - 23.36)^2 + (21 - 20.55)^2
TSS = 6.27
Step-by-step explanation:
The Total Sum of Squares (TSS) can be calculated by first finding the mean of the dataset, then subtracting this mean from each data point, squaring the result, and summing all these squared differences. The TSS for the provided dataset is approximately 34, not among the given choices, thus 'None of the above are close' is the correct answer.
Explanation:In this problem, we're asked to calculate the Total Sum of Squares (TSS), a statistical measure used to understand the variability in a dataset. For the given set of April Flowrate (Y) values, we first calculate the mean (average), which is (22+23+21+18+26+21) / 6 = 21.83 (rounded to 2 decimal places).
We then subtract this mean from each Y value, square the result, and add them together to get TSS. The calculation would proceed as follows:
(22-21.83)² = 0.0289(23-21.83)² = 1.3589(21-21.83)² = 0.6889(18-21.83)² = 14.7889(26-21.83)² = 17.4489(21-21.83)² = 0.6889The total sum of these squared differences gives us the TSS:
0.0289 + 1.3589 + 0.6889 + 14.7889 + 17.4489 + 0.6889 = 34.0034
So, the TSS for the described data set is roughly 34, which is not among the provided answer choices, so the correct answer is 'None of the above are close'.
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Find the probability​ P(E or​ F) if E and F are mutually​ exclusive, ​P(E)=0.34​, and ​P(F)=0.51.
The probability of either event E or event F occurring, when E and F are mutually exclusive, is 0.85.
If E and F are mutually exclusive events, it means that they cannot occur simultaneously. In such cases, the probability of either event E or event F occurring is the sum of their individual probabilities.
Given that P(E) = 0.34 and P(F) = 0.51, we can calculate the probability of E or F, denoted as P(E or F), as:
P(E or F) = P(E) + P(F)
Substituting the given values, we have:
P(E or F) = 0.34 + 0.51
Calculating the sum, we find:
P(E or F) = 0.85
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Casey buys a bracelet. she pays for the bracelet and pays $0.72 in sales tax. The sales tax is 6% what is the original price of the bracelet , before tax
The Original price of the bracelet, before tax, is $12.
Let's assume that the original price of the bracelet is x dollars.
The sales tax is 6%, which means that the tax paid is 6/100 * x = 0.06x dollars.
We know that Casey paid $0.72 in sales tax, so we can set up the equation:
0.06x = 0.72
Solving for x, we get:
x = 0.72/0.06
x = 12
Therefore, the original price of the bracelet, before tax, is $12.
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many elementary school students in a school district currently have ear infections. a random sample of children in two different schools found that 11 of 40 at one school and 12 of 30 at the other have ear infections. at the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools?
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.
To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.
The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.
Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:
z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.
The pooled proportion is given by:
p_hat = (x1 + x2) / (n1 + n2)
where x1 and x2 are the number of students with ear infections in each school.
Using the given data, we have:
n1 = 40, n2 = 30
x1 = 11, x2 = 12
p1 = x1/n1 = 11/40 = 0.275
p2 = x2/n2 = 12/30 = 0.4
p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355
The test statistic is:
z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197
Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.
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The spinner below is spun once. Find each probability as a percent rounded to the nearest whole number.
P(unshaded) = __%
P(even and less than 10) =__ %
The probabilities are given as follows:
P(unshaded) = 33%.P(even and less than 10) = 33%.How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Out of the 12 regions, 4 are unshaded, hence the probability is given as follows:
P(unshaded) = 4/12 = 1/3 = 0.33 = 33%.
Out of the 12 regions, 4 are even and less than 10, hence the probability is given as follows:
P(even and less than 10) = 4/12 = 1/3 = 0.33 = 33%.
Missing InformationThe spinner is given by the image presented at the end of the answer.
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which equation represents a line with a slope of -5/11 and a y-intercept 3/11
Answer:
y=-5/11x+3/11 (B)
Step-by-step explanation:
m= -5/11
b=3/11
substitute: y=-5/11x+3/11
In inferential statistics, the objective is to determine how probable it is that:
The alternative hypothesis is true.
The null hypothesis is true.
The alternative hypothesis is false.
The null hypothesis is false.
In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.
This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.
The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.
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Find an angle in each quadrant with a common reference angle with 53°, from 0°≤θ<360°
The angle of 53° is equals to,
53° in the first quadrant127° in the second quadrant 233° in the third quadrant307° in the fourth quadrant.The given angle = 53°
The given angle is present in the first quadrant only. To find the equivalent angle in the second quadrant, we have to subtract the given angle from 180°. So,the equivalent angle in the second quadrant = 180° - 53° = 127°.
To find the equivalent angle in the third quadrant, we have to add the given angle to 180°. So,equivalent angle in third quadrant = 180° + 53° = 233°.
To find the equivalent angle in the fourth quadrant, we have to subtract the given angle from 360°. So,equivalent angle in fouth quadrant = 360° - 53° = 307°.
From the above analysis, we have found the equivalent angles in all quadrants.
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An closed box with a square base is to have a volume of 7500 cm3. What should the dimensions of the box be if the amount of material used is to be minimum? (Use decimal notation. Give your answers to three decimal places. ) Recall: The surface area of a rectangular box is: =2⋅⋅+2⋅⋅ℎ+2⋅⋅ℎ , where = length, = width, and ℎ= height. Hint: Draw a sketch of the box and note that the base of the box is a square
To minimize the amount of material used for the box, we want to minimize its surface area. Since the base of the box is a square, let's denote its side length as s. Then, the height of the box can be expressed as 7500/s^2, using the given volume.
Using this information, we can express the surface area of the box as a function of s: A(s) = 2s^2 + 4sh, where h is the height of the box. Substituting 7500/s^2 for h, we get A(s) = 2s^2 + 4(7500/s^2)s.
To find the minimum amount of material used, we need to find the value of s that minimizes A(s). We can do this by finding the critical points of A(s) and then using the second derivative test to determine if they correspond to a minimum. Taking the derivative of A(s) and setting it equal to zero, we get:
A'(s) = 4s - 30000/s^3 = 0
Solving for s, we get s = 15∛125 ≈ 12.247.
To confirm that this value corresponds to a minimum, we take the second derivative of A(s) and evaluate it at s = 12.247:
A''(s) = 4 + 90000/s^4
A''(12.247) ≈ 0.143
Since A''(12.247) is positive, we can conclude that s = 12.247 corresponds to a minimum of A(s). Therefore, the of the box should be approximately 12.247 cm by 12.247 cm by 41.666 cm to minimize the amount of material used.
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A drug company claims that its new painkiller has exactly 5 mg. of codeine. You test the claim at a significance level (alpha) of 0.05. You randomly sample 100 pills made by the company and find the sample mean to be 4.7 milligrams of codeine with a sample standard deviation of 0.75 grams.
(a) What are the null and alternate hypotheses?
(b) Draw the picture of the distribution of the test statistics (under H0). Include critical value(s) and region(s) of rejection.
(c) What is the calculated (computed) value of the test statistic?
(d) What is your conclusion?
This means that there is evidence to suggest that the mean amount of codeine in the painkiller is not exactly 5 mg.
(a) The null hypothesis is that the mean amount of codeine in the painkiller is exactly 5 mg. The alternate hypothesis is that the mean amount of codeine in the painkiller is not exactly 5 mg.
(b) The picture of the distribution of the test statistics (under H0) would be a normal distribution with a mean of 5 mg and a standard deviation of 0.75 mg/sqrt(100) = 0.075 mg. The critical values for a two-tailed test at a significance level of 0.05 are -1.96 and +1.96. The region(s) of rejection are the values outside of this range. This can be represented in a graph as shaded areas on both sides of the distribution curve.
(c) The calculated value of the test statistic is (4.7 - 5) / (0.75 / sqrt(100)) = -2.67.
(d) Since the calculated value of the test statistic (-2.67) falls within the region of rejection, we reject the null hypothesis. This means that there is evidence to suggest that the mean amount of codeine in the painkiller is not exactly 5 mg.
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Fig. 15.20 shows a composite solid consisting of a cube of edge 28 cm and a square-based pyramid of height 16 cm. Calculate the volume of the solid.
The volume of the composite solid consisting of a cube and a square-based pyramid will be 26,099.2 cm³.
The volume of the cube is given by;
V_cube = s³ = 28³
V = 21,952 cm³.
The volume of the pyramid is given by V_pyramid = (1/3)Bh,
where; B = area of the base and h = height .
The base of the pyramid is a square with sides equal to the base of the cube therefore we have
B = s² = 28² = 784 cm².
Thus, V_pyramid = (1/3)(784)(16)
V = 4,147.2 cm³.
The total volume of the composite solid is the sum of the volumes of the cube and the pyramid then we get;
V_total = V_cube + V_pyramid = 21,952 + 4,147.2
V_total = 26,099.2 cm³.
Therefore, the volume of the solid is; 26,099.2 cm³.
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the price of a gallon of milk follows a normal distribution with a mean of $3.4 and a standard deviation of $0.2. find the price for which only 35% of milk vendors lower than?
Answer: $3.32
Step-by-step explanation:
-0.3853 = (x - 3.4) / 0.2
Solving for x, we get:
X = 3.32
Therefore, the price for which only 35% of milk vendors is lower than $3.32.
Christine went to mall at 11:30 am they shopped for 5 hours 35 minutes. What time did they finish shopping?
Answer:
5:05 PM
Step-by-step explanation:
Use a time calculator.
Answer:5:05pm
Step-by-step explanation:
It might be easier to split up the 5 hours and 35 min in minutes and hours
11:30 + 5 hours = 4:30pm
There is still 35 minutes left.
4:30 + 35 min = 5:05pm
∴, Christine finished shopping at 5:05pm
1) A savings account balance is compounded
annually. If the interest rate is 2.1% per
year and the current balance is $1,777.00,
what will the balance be 10 years from
now?
The total balance in the savings account after 10 years will be $2,187.48.
What is the accrued amount after 10 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $1,777Compounded annually n = 1Time t = 10 yearsInterest rate r = 12.1%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 2.1/100
r = 0.021
Now, plug the values into the above formula and simplify.
[tex]A = P(1 + \frac{r}{n} )^{(n*t)}\\\\A = 1,777(1 + \frac{0.021}{1} )^{(1*10)}\\\\A = 1,777(1 +0.021 )^{(10)}\\\\A = 1,777(1.021 )^{(10)}\\\\A = 2,187.48[/tex]
Therefore, the accrued amount is $2,187.48.
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Help me please! Will give brainliest if the option is available
answer
(1.2, 1) if its asking what i think it is
Step-by-step explanation:
the null hypothesis for the single factor anova states that all means are equal.
T/F
The null hypothesis for the single factor ANOVA states that all means are equally true.
The null hypothesis for a single-factor ANOVA (analysis of variance) states that all means are equal.
The alternative hypothesis, on the other hand, suggests that at least one of the means is different from the others.
The purpose of the ANOVA test is to determine whether there is sufficient evidence to reject the null hypothesis and conclude that there are significant differences between the means. A statistical formula used to compare variances across the means (or average) of different groups.
Hence, the statement is true .
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URGENT!! Will give brainliest :)
A line of best fit was drawn for 6 data points. What is the maximum number of these data points that may not actually be on the line?
• A. 6
О B. 3
O c. 5
O D. 4
The maximum number of points that may not be on the line is given as follows:
A. 6.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in a linear regression calculator.
When we insert the points on a calculator, we get a linear function that is obtained using the mean and sum of squares of the points. This means that the line has on average the least distance to the points, but it can happen that none of the points is exactly on the line.
Hence option A is the correct option in the context of this problem.
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Part A: Cassie hiked 4 tenths of a 4.7-mile trail. How many miles did Cassle have left to hike?
Part B: Dana was 1.6 miles ahead of Cassie. How many miles did Dana hike already?
The distance left to hike by Cassius is equal to 1.44 miles . Dana hiked 3.5986 miles
We are given that Cassie hiked 4 tenths of a 4.7-mile trail and Dana was 1.6 miles ahead of Cassie.
Since Cassius walked 6/10th of the trail of 3.6 miles.
Part of the trail remaining = 1 - 6/10 = 4/10 = 2/5
Distance remaining will be 2/5 of 3.6 miles
= 1.44 miles.
Hence distance left to hike by Cassius = 1.44 miles
b. Total distance by which Dana was ahead of Cassius = 1.6miles.
Distance left to hike by Dana= 1.44 miles - 1.6 miles = 0.0014 miles.
so, the distance hiked by Dana= 3.6 miles - 0.0014 miles = 3.5986 miles.
Dana hiked 3.5986 miles.
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Find the product using the Distributive Property. (2x+3)(x−4)
Answer:
2x² - 5x - 12------------------
Distributive Property is:
(a + b)(c + d) = ac + ad + bc + bdUse same rule to find the product:
(2x + 3)(x − 4) = 2x(x) - 2x(4) + 3x - 4(3) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12Look at picture below
Answer:
we cannot solve this as there is no picture shown, try linking in the picture please
A zorb is a large inflated ball within a ball. The formula for the radius r of a sphere with surface area A is given by r=\sqrt((A)/(4\pi )) . Calculate the radius of a zorb whose outside surface area is 49.29 sq m.
The radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.
We are given the surface area (A) of the zorb and asked to find its radius (r) using the formula r = √(A / 4π). Let's follow these steps to solve for the radius:
1. Write down the given information:
A (surface area) = 49.29 sq m
2. Write down the formula for the radius of a sphere:
r = (√A / 4π)
3. Plug in the given surface area (A) into the formula:
r = √(49.29 / 4π)
4. Calculate the value inside the square root:
49.29 / 4π ≈ 3.923
5. Take the square root of the calculated value:
r = √(3.923) ≈ 1.98
So, the radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.
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A triangle has two side lengths of 6.5 inches and 2.75 inches. Which of the following side lengths could be the third side?
A.) 2.5 inches
B.) 3.75 inches
C.) 5.5 inches
D.) 9.25 inches
Answer:
9.25 inches
Step-by-step explanation:
9.25 inches
Solve the equation. Enter your answer as an equation that shows the value of
the variable (like s = 2/3, or 4= w).
-3x+x-5= 25
-15 is the value of the variable x in the given equation -3x+x-5= 25
The given equation is -3x+x-5= 25
Minus three times of x plus x minus five equal to twenty five
x is the variable in the equation
Minus and plus are the operators
Combine the like terms in the equation
-2x-5=25
Add 5 on both sides
-2x=30
x=-15
Hence, the value of x in the equation is -15
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a) Complete
the table of values for y=x²-2x-3
b) i) Which of the three curves drawn
matches y = x² - 2x - 3?
ii) Estimate the value of y
when x = 2.5
iii) Find the values of x
when y = 1
b)i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward. b)ii) we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5. b)iii) the only value of x when y = 1 is x = 2.
Answers to the aforementioned questionsa)
| x | y
| -3 | 12
| -2 | 1
| -1 | -4
| 0 | -3
| 1 | -2
| 2 | -3
| 3 | 0
b) i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward.
ii) To estimate the value of y when x = 2.5, we can use the values of y when x = 2 and x = 3 to find the average rate of change, and then add or subtract that from the value of y when x = 2 or x = 3, respectively.
Using x = 2 and x = 3, we have:
Average rate of change = (y(3) - y(2)) / (3 - 2) = 3
So we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5.
iii) To find the values of x when y = 1, we can set y = 1 in the equation y = x² - 2x - 3 and solve for x:
x² - 2x - 3 = 1
x² - 2x - 4 = 0
(x - 2)² = 0
x - 2 = 0
x = 2
So the only value of x when y = 1 is x = 2.
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After heating up in a teapot, a cup of hot water is poured at a temperature of 20 3 ∘ 203 ∘ F. The cup sits to cool in a room at a temperature of 6 9 ∘ 69 ∘ F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: � = � � + ( � 0 − � � ) � − � � T=T a +(T 0 −T a )e −kt � � = T a = the temperature surrounding the object � 0 = T 0 = the initial temperature of the object � = t= the time in minutes � = T= the temperature of the object after � t minutes � = k= decay constant The cup of water reaches the temperature of 18 5 ∘ 185 ∘ F after 1.5 minutes. Using this information, find the value of � k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes. Enter only the final temperature into the input box.
The final temperature is 165 degree F.
Given that,
Ta = the temperature surrounding the object = 69ºF
T₀ = the initial temperature of the object = 203ºF
t = 1.5 min
T after 1.5 min = 185ºF
We know the temperature equation,
T = [tex]T_{\alpha}[/tex] + [tex](T_{0} - T_{\alpha })e^{-kt}[/tex]
Substitute the values,
185 = 69 + (203 - 69)[tex]e^{-1.5k}[/tex]
solving it we get
k = 0.077
To find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4. minutes.
Substitute into the formula and compute:
T = 69 + (203 - 69)[tex]e^{-(0.75)(4.5)}[/tex]
Hence,
T = 165 degree F.
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the national health and nutrition examination survey (nhanes) reported that in a recent year, the mean serum cholesterol level for u.s. adults was 202, with a standard deviation of 41 (the units are milligrams per deciliter). a random sample of 100 adults is chosen. what is the probability that the sample mean cholesterol level is less than 190?
Therefore, the probability that the sample mean cholesterol level is less than 190 is approximately 0.23%.
We can use the central limit theorem to approximate the distribution of the sample mean cholesterol level as normal with a mean of 202 and a standard deviation of 41/sqrt(100) = 4.1.
To find the probability that the sample mean cholesterol level is less than 190, we can standardize the sample mean using the formula:
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
Plugging in the values, we get:
z = (190 - 202) / (4.1) = -2.93
Now we can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.93. The probability is approximately 0.0023 or 0.23%.
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1.1-8. during a visit to a primary care physician's office, the probability of having neither lab work nor referral to a specialist is 0.21. of those coming to that office, the prob- ability of having lab work is 0.41 and the probability of having a referral is 0.53. what is the probability of having both lab work and a referral?
The probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%.
To find the probability of having both lab work and a referral, we can use the formula P(A and B) = P(A) + P(B) - P(A or B), where A and B are events and P is the probability of those events occurring.
Let A be the event of having lab work and B be the event of having a referral.
We know that P(A) = 0.41, P(B) = 0.53, and P(neither A nor B) = 0.21.
To find P(A or B), we can use the formula P(A or B) = P(A) + P(B) - P(A and B). We don't know P(A and B), but we can find it by using the fact that P(neither A nor B) = 0.21:
P(A or B) = P(A) + P(B) - P(A and B)
1 - P(neither A nor B) = P(A) + P(B) - P(A and B)
1 - 0.21 = 0.41 + 0.53 - P(A and B)
0.78 = 0.94 - P(A and B)
P(A and B) = 0.16
Therefore, the probability of having both lab work and a referral is 0.16.
The probability of having both lab work and a referral during a visit to a primary care physician's office can be found using the formula P(A and B) = P(A) + P(B) - P(A or B). Given that the probability of having lab work is 0.41, the probability of having a referral is 0.53, and the probability of having neither is 0.21, we can solve for P(A and B) and get a probability of 0.16. This means that there is a 16% chance of a patient having both lab work and a referral during their visit.
In conclusion, the probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%. This calculation was done using the formula P(A and B) = P(A) + P(B) - P(A or B), with the probabilities of having lab work, a referral, and neither being given.
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To indirectly measure the distance across a lake, Moussa makes use of a couple landmarks at points
�
P and
�
Q. He measures
�
�
OS,
�
�
SQ, and
�
�
RS as marked. Find the distance across the lake
(
�
�
)
(PQ), rounding your answer to the nearest hundredth of a meter.
The distance across the lake PQ will be 496.8 meters.
Given that:
Sides, OS = 210 m, SQ = 70 m, and RS = 124.2 m
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The distance across the lake PQ is calculated as,
PQ / RS = OQ / SQ
PQ / 124.2 = (210 + 70) / 70
PQ / 124.2 = 280 / 70
PQ = 496.8 m
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Need help asap please
Answer:
21x^2 + 7x
Step-by-step explanation:
The formula for the area of a rectangle is L x W. The length in this case is 3x+1 and the width is x. Multiply those together and you get 3x^2 + x.
The formula for the area of a triangle is 1/2BH. When you plug in the numbers, the area of the triangle is 24x^2 + 6x.
Now, you want to subtract the area of the triangle from the area of the rectangle. When you do this, you get your answer: 21x^2 + 7x.
Somebody help asap please.
You want to put up a fence that encloses a triangular region with an area greater than or equal to 60 square feet.The possible values of c are described by the inequality -------
(The base of the triangle is 12 and the height is c)
3. Is it possible to solve x (t ) for t, substitute it into y(t) to eliminate the parameter, t, and write it as a rectangular equation with x and y instead? x(t)=0. 5507t^2-1. 5393t-86. 1
Yes, it is possible to solve x(t) for t and substitute it into y(t) to eliminate the parameter t and write it as a rectangular equation with x and y instead.
Starting with the given equation:
x(t) = 0.5507t^2 - 1.5393t - 86.1
To solve for t, we can use the quadratic formula:
t = [-(-1.5393) ± sqrt((-1.5393)^2 - 4(0.5507)(-86.1))]/(2(0.5507))
Simplifying the equation:
t = [1.5393 ± sqrt(1.5393^2 + 190.2122)]/1.1014
t = [1.5393 ± 13.9769]/1.1014
t = -11.098 or 25.682
Since we're interested in the positive value of t, t = 25.682.
Now, substituting t = 25.682 into y(t):
y(t) = 0.5054t - 78.9
y(25.682) = 0.5054(25.682) - 78.9
y(25.682) = 1.504
Therefore, the rectangular equation for the given parametric equations is:
x = 0.5507t^2 - 1.5393t - 86.1
y = 0.5054t - 78.9
Substituting t = 25.682:
x = 358.6
y = 1.504
So the rectangular equation is:
(x, y) = (358.6, 1.504)
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