MATHEMATICS COLLEGE

Please help me I’m so confused

Answers

Answer 1

Answer:

Given:

The given expression is $\sum_(1)^(10) 4\left((1)/(4)\right)^(n-1)$

We need to evaluate the given expression.

Solution:

The given expression is in the form of general form of geometric sequence $a_n=ar^(n-1)$

The common ratio is $r=(1)/(4)$ and the first term is a = 4.

The formula to find the sum of the series is given by

$S_n=a((1-r^(n))/(1-r))$

Substituting n= 10, a = 4 and $r=(1)/(4)$ , we get;

$S_(10)=4 \cdot (1-\left((1)/(4)\right)^(10))/(1-(1)/(4))$

$S_(10)=4 \cdot (1-(1)/(1048576))/(1-(1)/(4))$

$S_(10)=4 ( ((1048575)/(1048576))/((3)/(4)))$

$S_(10)=4 ( (1048575)/(1048576) * {(4)/(3))$

$S_(10)= (16777200)/(3145728)$

$S_(10)=5.33$

Thus, the sum of the 10 terms is 5.33

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If a car can travel 45 miles in 30min, how far will the car tavel in 2.5 hours?
Consider a random sample of ten children selected from a population of infants receiving antacids that contain aluminum, in order to treat peptic or digestive disorders. The distribution of plasma aluminum levels is known to be approximately normal; however its mean u and standard deviation o are not known. The mean aluminum level for the sample of n = 10 infants is found to be X = 37.20 ug/l and the sample standard deviation is s = 7.13 ug/1. Furthermore, the mean plasma aluminum level for the population of infants not receiving antacids is known to be only 4.13 ug/1.(a) Formulate the null hypothesis and complementary alternative hypothesis, for a two-sided test of whether the mean plasma aluminum level of the population of infants receiving antacids is equal to the mean plasma aluminum level of the population of infants not receiving antacids.(b) Construct a 95% confidence interval for the true mean plasma aluminum level of the population of infants receiving antacids.(c) Calculate the p-value of this sample (as best as possible), at the a=.05 significance level.(d) Based on your answers in parts (b) and (c), is the null hypothesis rejected in favor of the alternative hypothesis, at the a = .05 significance level? Interpret your conclusion: What exactly has been demonstrated, based on the empirical evidence?(e) With the knowledge that significantly elevated plasma aluminum levels are toxic to human beings, reformulate the null hypothesis and complementary alternative hypothesis, for the appropriate one-sided test of the mean plasma aluminum levels. With the same sample data as above, how does the new p-value compare with that found in part (c), and what is the resulting conclusion and interpretation?

I have no idea what I am doing. Here is one of my problems, A gas station sells 1500 gallons of gasoline per hour if it charges $ 2.10 per gallon but only 1300 gallons per hour if it charges $ 2.95 per gallon. Assuming a linear model

(a) How many gallons would be sold per hour of the price is $ 2.70 per gallon?
(b) What must the gasoline price be in order to sell 800 gallons per hour?
(c) Compute the revenue taken at the four prices mentioned in this problem -- $ 2.10, $ 2.70, $ 2.95 and your answer to part (b). Which price gives the most revenue?

Answers

You need to set up a linear graph. One side with gallons and the other with dollars. Point 1 will be at (1500, 2.10). Point 2 (1300, 2.95). Draw a straight line through these points in your graph and your graph will then give you the answers to your other questions.

Please Help !!!The line above goes through points (-5,5) and (0,3). What is the slope-intercept form of the equation of the line above?

A. y = (-5/2)x - 3

B. y = (-2/5)x + 3

C. y = (-2/5)x - 3

D. y = (2/5)x + 3

Answers

Answer:

Step-by-step explanation:

The equation we must find is in y = mx + b form. We are given that it intercepts (0,3), so the y-intercept it 3 and b = 3. We can find the slope with the two points we are given: m = (3-5)/(0(-5)) = -2/5. Substituting these values, we find: y = (-2/5)x + 3

Collect the data for our solar system

Answers

Answer:

AU:

Merc-0.39

Venus-0.72

Earth- 1

Mars- 1.52

Jupiter - 5.20

Uranus - 19.1

Neptune - 30

Years:

Merc-0.24

Venus-0.61

Earth- 1

Mars- 1.88

Uranus - 84?(maybe)

Neptune - 165

Step-by-step explanation:

edge

Answer:

Step-by-step explanation:

What is the slope intercept equation of the line below. Y-intercept=(0,2) slope=3/4

Answers

Answer:

y = 3/4x +2

Step-by-step explanation:

The slope intercept form of an equation is

y = mx+b

where m is the slope and b is the y intercept

Y-intercept=(0,2) slope=3/4

y = 3/4x +2

consider the quadratic form q(x,y,z)=11x^2-16xy-y^2+8xz-4yz-4z^2. Find an orthogonal change of variable that eliminates the cross product in q(x,y,z) and express q in the new variables.

Answers

Answer:

$q(x,y,z)=16x^(2)-5y^(2)-5z^(2)$

Step-by-step explanation:

The given quadratic form is of the form

$q(x,y,z)=ax^2+by^2+dxy+exz+fyz$ .

Where $a=11,b=-1,c=-4,d=-16,e=8,f=-4$ .Every quadratic form of this kind can be written as

$q(x,y,z)={\bf x}^(T)A{\bf x}=ax^2+by^2+cz^2+dxy+exz+fyz=\left(\begin{array}{ccc}x&y&z\end{array}\right) \left(\begin{array}{ccc}a&(1)/(2) d&(1)/(2) e\n(1)/(2) d&b&(1)/(2) f\n(1)/(2) e&(1)/(2) f&c\end{array}\right) \left(\begin{array}{c}x&y&z\end{array}\right)$

Observe that $A$ is a symmetric matrix. So $A$ is orthogonally diagonalizable, that is to say, $D=Q^(T)AQ$ where $Q$ is an orthogonal matrix and $D$ is a diagonal matrix.

In our case we have:

$A=\left(\begin{array}{ccc}11&((1)/(2))(-16) &((1)/(2)) (8)\n((1)/(2)) (-16)&(-1)&((1)/(2)) (-4)\n((1)/(2)) (8)&((1)/(2)) (-4)&(-4)\end{array}\right)=\left(\begin{array}{ccc}11&-8 &4\n-8&-1&-2\n4&-2&-4\end{array}\right)$

The eigenvalues of $A$ are $\lambda_(1)=16,\lambda_(2)=-5,\lambda_(3)=-5$ .

Every symmetric matriz is orthogonally diagonalizable. Applying the process of diagonalization by an orthogonal matrix we have that:

$Q=\left(\begin{array}{ccc}(4)/(√(21))&-(1)/(√(17))&(8)/(√(357))\n(-2)/(√(21))&0&\sqrt{(17)/(21)}\n(1)/(√(21))&(4)/(√(17))&(2)/(√(357))\end{array}\right)$

$D=\left(\begin{array}{ccc}16&0&0\n0&-5&0\n0&0&-5\end{array}\right)$

Now, we have to do the change of variables ${\bf x}=Q{\bf y}$ to obtain

$q({\bf x})={\bf x}^(T)A{\bf x}=(Q{\bf y})^(T)AQ{\bf y}={\bf y}^(T)Q^(T)AQ{\bf y}={\bf y}^(T)D{\bf y}=\lambda_(1)y_(1)^(2)+\lambda_(2)y_(2)^(2)+\lambda_(3)y_(3)^(2)=16y_(1)^(2)-5y_(2)^(2)-5y_(3)^2$

Which can be written as:

$q(x,y,z)=16x^(2)-5y^(2)-5z^(2)$

It takes a book editor 28 minutes to edit 6 pages. Find how long it takes her to edit 45 pages

Answers

Answer:

Around 9.57 minutes to edit

Step-by-step explanation:

Do 28 divided by 6 to get around 4.7. Then do 45 divided by 4.7 to get the answer.

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