Answer:
The student GPA is 3.1875
Step-by-step explanation:
First we calculate the grade point by multiplying the grade with the weight;
= (3.9 * 5) + (2.1 * 3) + (2.9 * 4) + (3.4 * 4)
= 19.5 + 6.3 + 11.6 + 13.6
= 51
Total weight = 5+3+4+4=16
GPA = 51/16=3.1875
To calculate the student's GPA, we multiply each course grade by its credit hours, sum those totals to get the quality points, and then divide by the total number of credits. In this case, the student's GPA is 3.1875.
To calculate a student's Grade Point Average (GPA) for a term, each course grade is multiplied by the course's credit hours to get the total quality points for that course. Then, the sum of all quality points is divided by the total number of credit hours taken.
Step-by-Step GPA Calculation
For each course, multiply the grade by the number of credits:
(3.9 × 5) + (2.1 × 3) + (2.9 × 4) + (3.4 ×4).
Sum the results of these multiplications to get the total quality points.
Sum the total number of credits: 5 + 3 + 4 + 4.
Divide the total quality points by the total number of credits.
Let's do the math:
(3.9 × 5) = 19.5
(2.1 × 3) = 6.3
(2.9 × 4) = 11.6
(3.4 × 4) = 13.6
Total quality points = 19.5 + 6.3 + 11.6 + 13.6 = 51
Total credits = 5 + 3 + 4 + 4 = 16
The student's GPA for the term is the total quality points divided by the total credits:
GPA = 51 / 16 = 3.1875.
Select the correct answer.
Which type of discontinuity exists at x = 2 for f(x)=x^2-4/x-2?
A.
removable discontinuity
B.
jump discontinuity
C.
infinite discontinuity
D.
none of the above
Answer:
Answer A.
Step-by-step explanation:
Recall that [tex]f(x) = \frac{x^2-4}{x-2}[/tex]
we will calculate the lateral limits of f when x approches x=2. Note that
[tex] \lim_{x\to 2^{+}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{+}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]
[tex] \lim_{x\to 2^{-}} \frac{x^2-4}{x-2} = \lim_{x\to 2^{-}} \frac{(x-2)(x+2)}{x-2} = 2+2 = 4[/tex]
We can clasify the discontinuity as follows:
- Removable discontinuity if both lateral limits are equal and finite.
- Jump discontinuity if both lateral limits are finite but different.
- Essential discontinuity if one of the limits is not finite and the other one is finite.
Based on this classification, since both lateral limits are equal, the discontinuity is a removable discontinuity
An environmentalist would like to compare air pollution levels in cities A and B. From each city 10 measurements are taken. For city A, the average of all measurements (where measurements are percentage of pollutants in the air) is 5 percent with sample standard deviation 1.5 percent. For city B the average of all 10 measurements is 5.4 percent with sample standard deviation 2 percent. Assume that for each city air pollution level at a random time and location follows a normal distribution, and nd a 90% confidence interval for difference between the true average air pollution levels of city A and city B.
Answerhshxbx
Ste-by-step explanation:
Hwsjbb
Find the lateral area of the cylinder. Give answer in terms of pi. 6ft is the radius and 11ft is the height.
Answer:
[tex]132\pi[/tex]
Step-by-step explanation:
The lateral area is the area of a rectangle. Think of a soup can with the label removed and laid out flat on a table. The height of the rectangle is the same as the height of the can (cylinder). Where does the base of the rectangle come from? It's the circumference of the can "unrolled."
Area of a rectangle = base x height
Circumference of a circle [tex]C=2\pi r[/tex]
Lateral Area [tex]=2\pi r \times h[/tex] [tex]=2 \pi (6)(11) =132\pi[/tex]
today's local newspaper lists 20 stocks of local interest. of those stocks ten increased five decreased and five remained unchanged yesterday. if wwe decide to buy two of stocks what is the likelyhood that both increased yesterday?
Answer:
P(x=2) = 0.2368
Step-by-step explanation:
given data
stocks of local interest N = 20
stocks increased K = 10
stocks decreased = 5
remained unchanged = 5
solution
we take here no of stock that are increased randomly n = 2
so here Hypergeometric random variable can take integer value
{max(0, n+k - N ), min(n,K) } = {0,2}
so here
P(x=2)
so
P(x=k) = [tex]\frac{(^K_k)\times (^{N-K}_{n-k}) }{(^N_n)}[/tex] .......................1
P(x=2 ) = [tex]\frac{(^{10}_2)\times (^{20-10}_{2-2}) }{(^{20}_2)}[/tex]
solve it we get
P(x=2 ) = 0.236842
now we use excel function as
HYPGEOM.DIST (k,n,N.cumulative) .....................2
so it will be
HYPGEOM.DIST (2,2,10,,false)
we get
HYPGEOM.DIST (2,2,10,,false) = 0.236842
so
P(x=2) = 0.2368
Simplifying each side of the equation results in x2 − 3x − 4 = x2 − 5x + 6.
Find the solution:
x + 2
3x
−
1
x − 2
=
x − 3
3x
x =
Answer:
x = 5
Step-by-step explanation:
x² -3x -4 = x² - 5x + 6.
-x² - x²
-3x -4 = -5x + 6
+3x + 3x
-4 = -2x +6
-6 -6
-10 = -2x
÷-2 ÷-2
5 = x
Hope this Helps
Answer:
x = 5
Step-by-step explanation:
hope this helps!
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions. Online Content: Site 1 Online Content: Site 2 Describe how you would use the rules of exponents to simplify (7x2yz)3. You may indicate an exponent in your answer with ^. For example, 3x2 y2as 3x^2y^2. (Site 1)
Answer:
First, apply the power of a product rule by which you raise each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
Next, apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.
Therefore, the final result is:
[tex]343x^6y^3z^3[/tex]
Explanation:
The expression you have to simplify is:
[tex](7x^2yz)^3[/tex]
You have to apply two rules:
1. Power of a product2. Power of a power1. Power of a product
This rule states that the power of a product is equal to the product of each factor raised to the same exponent of the whole prduct:
For instance:
[tex](abc)^z=a^z\cdot b^z\cdot c^z[/tex]
Using this with the expression [tex](7x^2yz)^3[/tex] it is:
[tex](7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3[/tex]
In complete sentences that is: raise every factor, 7, x², x, and z to the exponent 3 and, then, multiply them.
2. Power of a power:
This rule states that to raise a power to a power, you must multiply the exponents.
For instance:
[tex](a^n)^m=a^{m\times n}[/tex]
You must apply that rule to the factor [tex](x^2)^3[/tex]
That is:
[tex](x^2)^3=x^{(3\times 2)}=x^6[/tex]
3. Final result and description using complete sentences:
The first step is to apply the power of a product rule by rasing each factor to the power 3, and then multiply all the factors, to obtain:
[tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]
The second step is to apply the power of a power rule, in virtue of which you raise the factor x² to the power 3, in this way:
[tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]
The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.
The final result is: [tex]343x^6y^3z^3[/tex]
What is the perimeter of the triangle if s=3 feet? Round your answer to the nearest hundredth
Answer:
9 feet = Perimeter of the triangle.
Step-by-step explanation:
Here, this question is incomplete and lacks essential data. So, still we will try to figure it out. What we can learn from this question.
So, first of all it talks about perimeter. So, let's understand first, what is perimeter and how it can be calculated for a triangle.
What is Perimeter?
So, Perimeter is actually the distance or path covered by a particular 2 dimensional shape. For example, square, triangle, rectangle.
Furthermore,
In this question, we have been given s = 3 feet. We can say that it is a length of one side of a triangle and triangle must be equilateral triangle having all sides equal to one another.
Equilateral Triangle have all sides equal to one another.
Here, we s1 = 3 so, other sides would be s2 = 3 and s3 = 3
Finally, here is the formula for the calculation of Perimeter of a triangle.
P = a + b + c
where, a, b, c represents sides of the triangle.
P = 3 + 3 + 3
P = 9
Hence, the perimeter of the triangle in this question is 9 feet.
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 6x − 6y subject to x 5 ≤ y y ≤ 2x 7 x + y ≥ 9 x + 2y ≤ 22 x ≥ 0, y ≥ 0.
Answer:
no optimal solution as feasible region is empty
Step-by-step explanation:
The complete question is:
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c = 6x − 6y subject to 5x ≤ y y ≤ 2x 7 x + y ≥ 9 x + 2y ≤ 22 x ≥ 0, y ≥ 0.
See the attachment to understand the following explanation.
The shaded regions shown in attachment obeys all constraints except for 5x ≤ y and y ≤ 2x. The shaded region 1 obeys all constraints except y ≤ 2x and shaded region 2 obeys all constraints except 5x ≤ y. So there is no feasbile region. Hence no optimal solution exists
To solve the linear programming problem, the constraints must be graphed to identify the bounded feasible region, if any exists. The objective function is then minimized by evaluating it at each vertex of this region. The solution is either one of these vertices or the problem may indicate no solution if the region is empty or the function is unbounded.
Explanation:The given linear programming (LP) problem requires us to minimize the objective function c = 6x - 6y subject to a set of given constraints. To solve this problem, we graph the constraints and identify the feasible region. The constraints are:
x + 5 ≤ yy ≤ 2x + 7x + y ≥ 9x + 2y ≤ 22x ≥ 0, y ≥ 0Given that the inequalities form a bounded region, we then inspect the vertices of this feasible region to find the point that minimizes the objective function. The solution is either one of these vertices or it is non-existent if the feasible region is empty or the objective function is unbounded. In this problem, given the constraints and the positive coefficients of the objective function, the feasible region is bounded, and thus we should be able to find a minimum point by evaluating the objective function at each vertex of the feasible region.
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Please help numbers 2-20 evens only
Answer: x=9,y=-1/3
Step-by-step explanation: This is for Q. 16
Rearrange terms to line up properly.
x-3y=10
x+3y=8
eliminate y terms
x=10
x=8 now add all like terms, remember it's a given that there's a one in
front of a variable.
2x=18 solve for x
x=9 now plug in the nine into one of the original eq.s and solve for y
9+3y=8
3y=-1
y=-1/3 always check solutions in both eq.s to vertify. they both work
Answer:
Q6: x= 10, y = -11
Q8: x= -3; y= 8
Q10: k= 7; j= -1
Step-by-step explanation:
Question6.
2x + y = 9..............1
-2x - 3y = 13...............2
Let's eliminate x by adding equation 1 and 2.
-2y = 22
y = 22/-2
y = -11
Substitute y = -11 in equation 1.
2x + y = 9
2x + (-11) = 9
2x - 11 = 9
2x = 9 + 11
2x = 20
x = 20/2
x = 10
x =10; y= -11
Question 8.
x + 2y = 13.............(I)
x + 6y = 45......…....(2)
By elimination method, let's take off x by subtracting equation 1 from 2.
6y - 2y = 45 - 13
4y = 32
y = 8.
Substitute y = 8 in equation 1.
x + 2y = 13
x + 2(8) = 13
x + 16 = 13
x = 13 - 16
x = -3
y= 8; x = -3
Question 10:
2j + 3k = 19 ..............1
2j + 7k = 47...............2
Let's eliminate j by subtracting equation 1 from equation 2.
4k = 28
k = 28/4
k= 7
Substitute k = 7 in equation 1.
2j + 3k = 19
2j + 3(7) = 19
2j + 21 = 19
2j = 19 - 21
2j = -2
j= -1
k= 7; j = -1
f(x) = (x + 5)(x + 6)
Answer:(-5,0) , (-6,0)
Y= (0,30)
Step-by-step explanation:
Let the Poisson random variable U (see p. 227) be the number of calls for technical assistance received by a computer company during the firm’s nine normal work- day hours. Suppose the average number of calls per hour is 7.0 and that each call costs the company $50. Let V be a Poisson random variable representing the number of calls for technical assistance received during a day’s remaining 3.10 Order Statistics 193 fifteen hours. Suppose the average number of calls per hour is 4.0 for that time period and that each such call costs the company $60. Find the expected cost and the vari- ance of the cost associated with the calls received during a twenty-four-hour day.
Answer:
Expected cost = $6,750
Variance of the cost = $373,500
Step-by-step explanation:
During normal 9 work hours: average number of calls = 7.0
Cost of each call = $50
During 15 off hours:
average number of calls = 4.0
Cost of each call = $60
Let's take U as the number of calls during the normal 9 hours.
I.e, [tex] U = U_1+U_2+U_3+U_4....+ U_9[/tex]
Therefore,
[tex] E(U) = E(U_1)+E(U_2)+E(U_3)+E(U_4)....+E(U_9)[/tex]
= 7+7+7+7+7+7+7+7+7
= 63
In Poisson random variable, Variance= mean, thus:
[tex] Var(U) =Var(U_1)+Var(U_2).....+Var(U_9) [/tex]
= 7+7+7+7+7+7+7+7+7
=63
Let's take V as the number of calls during the day's remaining 15 hours.
E(V) = Var(V)
= 15(4)
=60
The expected cost and the variance of cost associated with the calls received during a 24 hour day:
The expected cost =
$50U + $60V
= $50(63) + $60(60)
= $3150 + $3600
= $6750
The variance of the cost :
= Var(50U + 60V)
= 50²Var(U) + 60²Var(V)
= 2500*63 + 3600*60
= $373,500
Therefore, the expected cost is $6,750 and the variance of the cost is $373,500
On a coordinate plane, a rectangle has points (4, 1), (4, negative 3), (negative 2, negative 3), (negative 2, 1).
Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. How much soil will she need to cover the garden?
10 ft2
12 ft2
20 ft2
24 ft2
Answer:
24 feet
Step-by-step explanation:
sorry I'm so late
On the way to the Samuelsons’, Mr. Anderson filled his car with gas. He put in 9.7 gallons and paid $3.45 per gallon. Estimate the total charge. What was the actual charge for gas?
Answer:
Estimate = $34.50
Actual charge $33.47
Step-by-step explanation:
To estimate, we round the numbers
9.7 gallons rounds to 10 gallons
10 gallons * 3.45 per gallon =34.50
This is an overestimation
The actual charge
9.7* 3.45 =33.465
We round to the nearest cent
33.47
Answer:
Estimate: $34.5
Actual: $33.465
Step-by-step explanation:
9.7 is approximately 10
Estimate
10 × 3.45 = 34.5
Actual:
9.7 × 3.45 = 33.465
HELP ASAP PLEASE!!!
What is the range for the set of data?
a. 4
b. 6
c. 3.5
d. 0
Answer:
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
because i said so
Tiffany has a 30% chance of winning a game. She uses random numbers to simulate a series of 7 games. In her simulation, the numbers 0–2 represent a win, and the numbers 3–9 represent a loss. Select all the trials whose results show 3 wins in 7 games played. A. 8531905 B. 4963184 C. 7269108 D. 0689271 E. 7042351 F. 9094562
Answer:
C. 7269108
D. 0689271
E. 7042351
Step-by-step explanation:
If the number is 0,1 or 2, it is a win.
Otherwise, it is a loss.
Each number is a match.
A. 8531905
Two wins(0,1), 5 losses(8,5,3,9,5)
B. 4963184
One win(1), 6 losses(4,9,6,3,8,4)
C. 7269108
Three wins(2,1,0) and four losses (7,6,9,8)
D. 0689271
Three wins (0,2,1) and four losses (6,8,9,7)
E. 7042351
Three wins (0,2,1), four losses (7,4,3,5)
F. 9094562
Two wins (0,2) and five losses (9,9,4,5,6)
Answer:
C.
D.
E.
Step-by-step explanation:
The average maximum monthly temperature in Campinas, Brazil is 29.9 degrees Celsius. The standard deviation in maximum monthly temperature is 2.31 degrees. Assume that maximum monthly temperatures in Campinas are normally distributed. What percentage of months would have a maximum temperature of 34 degrees or higher?
We need to calculate a z-score to determine the probability of getting a month with a temperature of 34 degrees or higher, and then subtract that probability from 1 to get the final result.
Explanation:To solve this problem, we're dealing with a normal distribution. The average maximum monthly temperature in Campinas, Brazil is given as the mean (29.9 degrees). The standard deviation has been given as 2.31 degrees.
We're asked to find the percentage of months that would have a maximum temperature of 34 degrees or higher. This can be interpreted as finding the probability of a temperature being more than 34 degrees. We first need to find the number of standard deviations away from the mean 34 degrees is, which is known as Z-score.
The formula for Z-score is (X - mean) / standard deviation. So, our calculation would be (34 - 29.9) / 2.31. The resultant Z-score would have to be looked up in a standard normal distribution table, which will give us the probability up to that point. As we want the probability of the temperature being higher, we'll subtract the value we get from 1 (as total probability is 1), which would give us the percentage of months with a maximum temperature of 34 degrees or higher.
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Select the correct image.
Based on the albedo values given, identify the object that will reflect more than half of the solar radiation it receives.
Answer: The ice image, bottom left.
Step-by-step explanation:
The albedo values give information about the proportion of radiation that a given object surfaces, for example, if an object has an albedo value of 0.2, this means that the object reflects 0.2*100% = 20% of the radiation.
You usually can see that darker objects have a smaller albedo value, while clearer objects have a bigger albedo value, meaning that as clearer is the color, usually it reflects a bigger proportion of the radiation.
Here we have that the bigger albedo value is in the ice ( 0.55), so the correct image is the ice image, at the bottom left.
Lisandro is using this diagram to find the equation of a circle. He notices that the radius, the blue line, and the red line form a right triangle. Which shows his correct reasoning and equation
a) The length of the red line is |x + h|.
The length of the blue line is |y + k|.
The equation of a circle is (x + h)2 + (y + k)2 = r2.
b) The length of the radius is r.
The area of a circle is πr2.
The equation of the circle is y = πr2x.
c) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r2.
d) The length of the red line is |x – h|.
The length of the blue line is |y – k|.
The equation of a circle is (x – h)2 + (y – k)2 = r.
Answer:
The correct answer to the question is C.
Step-by-step explanation:
The length of the red line is |x – h|. The length of the blue line is |y – k|. The equation of the circle will be (x-h)²+(y-k)²=r².
What is the equation of a circle?The equation of a circle is given by the general equation,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where (h,k) are the coordinates of the centre of the circle, and r is the radius of the circle.
As it is given that the blue line and the red line are the radii of the circle, therefore, they will be joining any point on the circle to the centre of the circle.
Given that the blue line is represented by |y+k| while the red line is represented by |x+h|, therefore, the coordinate of the centre of the circle will be (h,k). And the radius of the circle will be r. Thus, the equation of the circle will be (x-h)²+(y-k)²=r².
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A survey of high school girls classified them by two attributes: whether or not they participated in sports and whether or not they had one or more older brothers. Use the following data to test the null hypothesis that these two attributes of classification are independent:
Answer:
From hypothesis, there is sufficient evidence to conclude that there is significant difference in two proportions.
Step-by-step explanation:
sample proportion for 1=12/20=0.6
sample proportion for 2=13/40=0.325
pooled proportion=25/60=0.4167
Test statistic:
z=(0.6-0.325)/sqrt(0.4167*(1-0.4167)*((1/20)+(1/40)))
z=2.037
p-value=2*P(z>2.037)=0.0417
As,p-value<0.05,we reject the null hypothesis.
There is sufficient evidence to conclude that there is significant difference in two proportions.
The normal curve with a mean of 0 and standard deviation of 1 is called ________________
Answer:
A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.
what is the ratio of 3 circles to 4 triangles
The ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.
To find the ratio of 3 circles to 4 triangles, we compare the number of circles to the number of triangles.
Given:
Circles = 3
Triangles = 4
The ratio of circles to triangles is expressed as 3:4. This means for every 3 circles, there are 4 triangles.
If we want to express it as a fraction, we can write it as 3/4. This implies that for every set of 3 circles, there are 4 triangles.
To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 1 in this case. Therefore, the simplified ratio is still 3:4.
In conclusion, the ratio of 3 circles to 4 triangles is 3:4, meaning there are 3 circles for every 4 triangles.
The complete question is here:
What is the ratio of 3 circles to 4 triangles?
what is the radius and diameter of the following circle
Answer:
Radius 6.5cm
Diameter 13cm
Step-by-step explanation:
Diameter ia a straight line passing from side to side through the center a circle or sphere.
Radius formula is simply derived by halving the diameter of the circle
13/2=6.5
Suppose you owe â$700 on your credit card and you decide to make no new purchases and to make the minimum monthly payment on the account. Assuming that the interest rate on your card is 2â% per month on the unpaid balance and that the minimum payment is 3â% of the totalâ (balance plusâ interest), your balance after t months is given by âB(t) = 700â(.9894tâ).
1. Find your balance at each of the given times in partsâ (a) throughâ (c) below.
(a) five months
(b) one year (remember that t is in months)
(c) is the balance paid off in two years?
The credit card balance at 5 months, 1 year, and 2 years to see the progression of debt repayment is $695, $669.67 and $669.70 respectively.
Calculate B(5) by substituting t = 5 into the formula B(t) = 700(.9894t), giving B(5) = 700(.9894*5) = $695.58.
Find B(12) by substituting t = 12 into the formula, giving B(12) = 700(.9894*12) = $669.67.
To check if the balance is paid off after 2 years, find B(24) = 700(.9894*24) = $632.70.
which indicates the balance is not paid off in 2 years.
During a chemical reaction, the function y=f(t) models the amount of a substance present, in grams, at time t seconds. At the start of the reaction (t=0) , there are 10 grams of the substance present. The function y=f(t) satisfies the differential equation dydt=−0.02y^2
The solution of the differential equation is:
[tex]y = \frac{1}{-0.1 + 0.02*t}[/tex]
How to solve the differential equation?
Here we need to solve:
[tex]\frac{dy}{dt} = -0.02*y^2[/tex]
This is a separable differential equation, we can rewrite this as:
[tex]\frac{dy}{y^2} = -0.02dt[/tex]
Now we integrate in both sides to get:
[tex]\int\limits\frac{dy}{y^2} = \int\limits-0.02dt\\\\-\frac{1}{y} = -0.02*t + C[/tex]
Where C is a constant of integration.
Solving for y, we get:
[tex]y = \frac{1}{-C + 0.02*t}[/tex]
And we know that for t = 0, there are 10 grams of substance, then:
[tex]10 = \frac{1}{-C + 0.02*0} = -\frac{1}{C} \\\\C = -1/10 = -0.1[/tex]
So the equation is:
[tex]y = \frac{1}{-0.1 + 0.02*t}[/tex]
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what is the value of h in the equation 8h = 60
Answer:
h= 7.5
Step-by-step explanation:
8h=60
One solution was found :
h = 15/2 = 7.500
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*h-(60)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
8h - 60 = 4 • (2h - 15)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
2.2 Solve : 2h-15 = 0
Add 15 to both sides of the equation :
2h = 15
Divide both sides of the equation by 2:
h = 15/2 = 7.500
One solution was found :
h = 15/2 = 7.500
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Answer: h = 7.5
Step-by-step explanation: To solve for h in this equation, we want to to get h by itself on the left side of the equation.
Since h is being multiplied by 8, to get h by itself, we need to divide by 8 on the left side of the equation.
If we divide by 8 on the left side,
we must also divide by 8 on the right side.
On the left, the 8's cancel out so we are simply left with h.
On the right we have 60/8 which is 7.5.
So we have h = 7.5.
who runs the fastest ? (ONLY ANSWER IF YOU KNOW IT BECAUSE CORRECT ONE GETS BRAINLIEST)
stephanie runs 14 feet per second
brooke runs 589 feet in 44 seconds
will runs 1 mile in 454 seconds
rob runs 548 feet in 1 minute
Answer:
Stephanie runs the fastest per second: 14 feet per second
Step-by-step explanation:
To find the fastest speed, you need to see which person runs the most per second:
Stephanie runs 14 feet per second
Brooke runs 589 feet in 44 seconds.
Find the amount of feet per second by dividing:
[tex]\frac{589}{44} =13.4[/tex]
Brooke runs about 13.4 feet per second
Will runs 1 mile in 454 seconds.
Convert the miles to feet:
There are 5,280 feet in a mile. If Will runs 5,280 feet in 454 seconds, divide to find how much he runs per second:
[tex]\frac{5280}{454}= 11.6[/tex]
Will runs about 11.6 feet per second.
Rob runs 548 feet in a minute.
Convert the minute into seconds. There are 60 seconds in a minute. Divide the feet by the seconds to find how fast he runs per second:
[tex]\frac{548}{60}= 9.1[/tex]
Rob runs about 9.1 feet per second.
Stephanie runs 14 feet per second, the fastest time:
| 14 |, 13.4, 11.6, 9.1
Finito.
GPA and study time. A survey was conducted on 218 undergraduates from Duke University who took an introductory statistics course in Spring 2012. Among many other questions, this survey asked them about their GPA and the number of hours they spent studying per week. The scatterplot below displays the relationship between these two variables. a) The explanatory variable is and the response variable is ? b) The relationship between the variables is and . c) Is this experiment or an observational study? A. Experiment B. Observational study d) Can we conclude that studying longer hours leads to higher GPAs? A. No. We cannot conclude that studying longer hours leads to higher GPA since this study is observational. B. Yes, we can conclude that studying longer hours leads to higher GPA since this study is an experiment. C. Yes, we can conclude that studying longer hours leads to higher GPA since this study this is an observational study. D. No. We cannot conclude that studying longer hours leads to higher GPA since this study is an experiment. E. We cannot draw any conclusion because the scatterplot has no distinct form.
Answer: a) The explanatory variable is hours of study per week and the response variable is GPA.
b) The relantioship between the variables seems to be positive.
c) B. Observational Study.
d) A. NO. We cannot conclude that studying loger hours leads to higher GPA since this study is observational.
Step-by-step explanation: a) Explanatory Variable is a type of independent variable, which means it is a variable that doesn't depend on the other variables. However, in explanatory variable, there is a subtle relation between variables. For that reason, Hours of Study per week is an explanatory variable. Response Variable is the dependent variable, it is the result when you change the other variable. For that reason, GPA is the response variable.
b) Observing the graphic, which is in the attachment, it can be observed that students who study more hours per week, tend to have higher GPA. For example, people who studied 60 hours per week have a GPA closer to 4.
c) Observational Studies are those experiment where the researches only observe their object of interest without changing or interfering in the outcome. Experimental Studies are the ones where the researchers introduce an interference and study their effect on the randomized groups.
Since this experiment is based on observation only, the study is an Observational Study.
d) Because it's an observational study, we can't correlate or associate the variables, since the researchers only obtain their results through observation of the behaviour of the students, without changing it.
Provided below are summary statistics for independent simple random samples from two populations. Use the nonpooled t-test and the nonpooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
X1 = 11, S1 = 5, n1 = 25, x2 = 10, S2 = 4, n2 = 20
A) What are the correct hypotheses for aright-tailed test? α = 0.05
i. Compute the test statistic.
ii. Determine the P-value.
B) The 90% confidence interval is from _______ to ________
Using the t-distribution, we have that:
a)
The null hypothesis is [tex]H_0: x_1 - x_2 \leq 0[/tex].The alternative hypothesis is [tex]H_1: x_1 - x_2 > 0[/tex]i) The test statistic is t = 0.746.
ii) The p-value is of 0.2299.
b) The 90% confidence interval is from -1.25 to 3.25.
Item a:
For a right-tailed test, we test if [tex]x_1[/tex] is greater than [tex]x_2[/tex], hence:
The null hypothesis is [tex]H_0: x_1 - x_2 \leq 0[/tex].The alternative hypothesis is [tex]H_1: x_1 - x_2 > 0[/tex]The standard errors are:
[tex]S_{e1} = \frac{5}{\sqrt{25}} = 1[/tex]
[tex]S_{e2} = \frac{4}{\sqrt{20}} = 0.8944[/tex]
The distribution of the difference has mean and standard error given by:
[tex]\overline{x} = x_1 - x_2 = 11 - 10 = 1[/tex]
[tex]s = \sqrt{S_{e1}^2 + S_{e2}^2} = \sqrt{1^2 + 0.8944^2} = 1.34[/tex]
We have the standard deviation for the samples, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{1 - 0}{1.34}[/tex]
[tex]t = 0.746[/tex]
The test statistic is t = 0.746.
The p-value is found using a t-distribution calculator, with t = 0.746, 25 + 20 - 2 = 43 df and 0.05 significance level.
Using the calculator, it is of 0.2299.Item b:
The critical value for a 90% confidence interval with 43 df is [tex]t = 1.6811[/tex].
The interval is:
[tex]\overline{x} \pm ts[/tex]
Hence:
[tex]\overline{x} - ts = 1 - 1.6811(1.34) = -1.25[/tex]
[tex]\overline{x} + ts = 1 + 1.6811(1.34) = 3.25[/tex]
The 90% confidence interval is from -1.25 to 3.25.
A similar problem is given at https://brainly.com/question/25840856
0.5 of what number is 15
Answer:
30
Step-by-step explanation:
0.5 * unknown number = 15
but
we see unknown number = 15 / 0.5 = 30
For a sample of 27 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,102,577 and SST = 7,622,089.
a. Calculate the standard error of the estimate.
Answer:
The standard error of the estimate is 413.4498
Step-by-step explanation:
According to the given data of ,in order to calculate the standard error of the estimate we would have to use the following formula:
Standard Error =sqrt(SSE/(n-p-1))
Standard Error =sqrt(4102577/(27-2-1))
Standard Error = 413.4498
The standard error of the estimate is 413.4498