Grinnell Glacier in Glacier National Park in the US covered about 142 acres in 2007 and was shrinking at a rate of about 4.4% per year.3 (a) Write a formula for the size, , of the Grinnell Glacier, in acres, as a function of years since 2007. (b) Use the model to predict the size of the glacier in the year 2020. (c) According to the model, how many acres of ice were lost from the glacier between 2007 and 2010

Answer:

Step-by-step explanation:

From the given information:

The number of children that were randomly allocated to each vaccination group; n₁ = 200,000

No of polio cases X₁ = 57

Now, in the vaccine group:

the proportion of polio cases is:

\(\hat p_1 = \dfrac{57}{200000}\)

=  0.000285

The number of children that were randomly allocated to the placebo group, n₂ = 200,000

No of polio cases X₂ = 142

In the placebo group

the proportion of polio cases is:

\(\hat p_2 = \dfrac{142}{200000}\)

Null and alternative hypothesis is computed as follows:

H₀: There is no difference in the proportions of polio cases between both groups.  

H₁: There is a difference in the proportions of polio cases between both groups.

Let assume that the level of significance ∝ = 0.05

The test statistic  can be computed as:

\(Z = \dfrac{\hat p_1-\hat p_2}{\sqrt{\dfrac{\hat p_1 \hat q_1}{n_1}+ \dfrac{\hat p_2 \hat q_2}{n_2}}}\)

\(Z = \dfrac{0.000285-0.000710}{\sqrt{\dfrac{0.000285(1-0.000285)}{200000}+ \dfrac{0.000710(1-0.000710)}{200000}}}\)

\(Z = \dfrac{-4.25\times 10^{-4}}{\sqrt{\dfrac{0.000285(0.999715)}{200000}+ \dfrac{0.000710(0.99929)}{200000}}}\)

Z = - 6.03

P-value =  2P(Z < -6.03)

From the Z - tables

P-value =  2 × 0.0000

= 0.000

We reject the H₀ provided that P-value is very less.

Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.

Answer:

x = 30°

y = 60°

z = 96°

Step-by-step explanation:

Well the angle from the center that intercepts 120° is equal to 120° since it is a central angle.

y = 60° because oof supplementary angles.

The measure of z is 48 * 2 because the 48° is an inscribed angle.

z = 96°

And, the arc that angle y intercepts is also the arc the x intercepts.

That arc is 60° because 180° - 120° = 60°

x is an inscribed angle, so x = 1/2 * 60°

x = 30°

Hope this helps.

One possible solution from the graph(attached at the end of the solution) is selling 9 bags of popcorn and 5 bags of candies.

As per the given data:

The number of popcorn bags is x

The number of candies is y

The cost of each popcorn bag is $7

The cost of each candy is $4

She has $80 to spend on them

Inequality is the nonequal comparison of two or more variables and numbers.

So the first inequality is

7 x + 4 y ≤ 80

Since she must buy no less than 16 bags of popcorn and candies

The second inequality is

x + y ≥ 16

The red area represents the 1st inequality

The blue area represents the 2nd inequality

The solutions lie in the common part of red and blue colors

One possible solution is ordered pair (9,5)

(Graph attached at the end of solution)

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

5.25 miles

Step-by-step explanation:

15 min=1/4 of hour

12/4=3

9/4=2.25

3+2.25=5.25

Answer:

d = 4.59 miles

Step-by-step explanation:

Distance Between Two Points in the Plane

Given two points A(x,y) and B(w,z), the distance between them is:

\(d=\sqrt{(z-y)^2+(w-x)^2}\)

The fishing boats leave the marina in perpendicular directions. The first boat travels north at v=12 mph for t=15 minutes. Converting to hours t=15/60=0.25 hours.

The distance covered by this boat is

d1 = 12*0.25 = 4 miles

The boat ends up at the point (0,4).

The second boat travels east at v=9  mph for the same time t=0.25 hours. The distance is:

d2= 9*0.25 = 2.25 miles

This boat ends up at the point (2.25,0)

The distance between them is

\(d=\sqrt{(4-0)^2+(0-2.25)^2}=\sqrt{16+5.0625}=\sqrt{21.0625}\)

Calculating the square root:

d = 4.59 miles

The four rectangles can be painted with 7 different paints in 840 ways.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order. For example, the permutation of set A={1,6} is 2, such as {1,6}, {6,1}, there are no other ways to arrange the elements of set A.

The formula for permutattion is;

\(P_r_n = \frac{n!}{(n-r)!} \\\)

where r = 4

n = 7

Substituting the values for n and r

\(P = \frac{7!}{(7-4)!}\)

\(P = \frac{7!}{3!}\)

P = 840 ways.

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10 pounds of barley should be used by the cook to mix in with the 35 quarts of the vegetable broth.

lets say we know that there is a mix of 2 pounds of barley into 7 quarts of vegetable broth, so we can say that,

2:7 is the ratio used for the mix

similarly we can say,

let the pounds of barley into 35 quarts of vegetable broth used be x

x:35 because its given that there are 35 quarts used in the vegetable soup so we need to find the value of 'x'

then, 2/7=x/35, that is pounds/quarts

then, x= 2/7 × 5

then, x = 2×5

therefore we know that x = 10

so we can say that there are 10 pounds of barley used in the mix by the cook along with the 35 quarts of vegetable broth.

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The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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You can withdraw an amount of $2063.91 periodically in order to make the account last the specified amount of time.

The principal amount can be found using the annuity formula.

A = P(r/12)/[1 - (1 +r/12)⁻¹²ⁿ]

Where A is the monthly payment, P is the principal amount, r is the annual interest rate, and n is the number of years.

We have been given data as:

Account balance: $400,000

Interest rate: 4.65%

Time: 30 years

Solving for A, we have

A = P(r/12)/[1 - (1 +r/12)⁻¹²ⁿ]

Substitute the values, and we get

A = P(0.0465/12)/[1 - (1 +0.0465/12)⁻¹²ˣ³°]

A = 1550/[1 - (1.003)⁻³⁶°]

A = 1550/[0.751]

A = 2063.91

Therefore, you can withdraw an amount of $2063.91 periodically in order to make the account last the specified amount of time.

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The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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Answer: 4000

Step-by-step explanation:

It is recommended that you visit your courses on D2L frequently, ideally at least once a day, to stay up-to-date with any new announcements or assignments posted by your instructor. This will help you stay on track with your coursework and prevent you from falling behind. Additionally, regular visits to your courses can help you participate in discussions with your peers and ask questions if you are unsure about any of the material. It's important to remember that online learning requires a high level of self-discipline and responsibility, so making a habit of checking in on your courses regularly can contribute to your overall success in the class.

The reasonable domain for the function f(x) = -2/3x + 4 in this situation is B. 0 ≤ x ≤ 6

In this question, we have:

Function, f(x) = -2/3x + 4

Where

x is the bottles of hand sanitizer per month

The function f(x) cannot be less than 0

So, we have

-2/3x + 4 = 0

This gives

-2/3x = -4

Solve for x

x = 6

This means that x cannot exceed 6

Hence, the domain is (b) . 0 ≤ x ≤ 6

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Answer:

The answer is down below

Step-by-step explanation:

v-u=◇velocity

\( = 9 - 5\)

◇velocity =4ms‐¹

acceleration =◇velocity/time

\(a = \frac{4}{5} \)

\(a = 0.8m {s}^{ - 2} \)

Change in velocity:

\( \sf \:final \: velocity - initial \: velocity = change \: in \: velocity\)

\( \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} \)

To find acceleration:

\( \rm \: a = \frac{ \triangle \: v}{\triangle \: t} \)

\( \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} \)

Answer:

19/3x+3 or 6 1/3x+3

Step-by-step explanation:

lets simplify:

1/3(4x+9)+5x.

distribute 1/3 :

4/3x+3+5x

add x together:

4/3x+5x=19/3=6 1/3.

final answer:

19/3+3

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.

Here we have

The inequality |2x + 2| > 6

To graph the solution to the inequality |2x + 2| > 6,

we can start by rewriting the inequality as two separate inequalities without the absolute value:

2x + 2 > 6 or 2x + 2 < -6

Simplifying these inequalities, we get:

2x > 4 or 2x < -8

x > 2 or x < -4

Therefore,

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

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Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

Answer:

84 sq meters

Step-by-step explanation:

First, divide the shape in 2 or more parts so that you can find it step by step

Divide this shape in three parts:

One part (blue): 2 m and 3 m rectangle

Second part (orange): 5 m and 12 m rectangle

Third part (red): 6 m and 3 m rectangle

(you can also see this below: in the pic there are three parts so you figure out that which is the correct value for the sides)

Now, find area of each shape by multiplying its values:

1st shape: 3 x 2 = 6

2nd shape: 5 x 12 = 60

3rd shape: 6 x 3 = 18

As you have the area of all the different shapes,

add all of them:

6 + 60 + 18 = 84 sq meters

I hope this helps :)

The correct solution to the system of linear equations is (2,1)

To Identify the correct solution to the system of linear equations, we have to solve for the vlaues of x and y.

Since y = 2x - 3 and y = x - 1. We can say:

2x-3 = x-1

2x -x = -1 + 3

x = 2

put x = 2 into y = x-1. That is:

y = x-1

y = 2-1

y = 1

Thus, the solution is x = 2, y = 1, which can be written as (2, 1)

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Answer:

30ft.

your welcome. ...................

The question is incomplete. The complete question is :

The fuel efficiency for a new helicopter engine is given by the continuous function r(c) where r is measured in gallons per mile and c is measured in miles. What are the units of \($\int_0^7 r(c) \ dc$\)   ?

Solution :

The given continuous function is :

r(c), here c is measured in miles and the unit of r is measured in gallons per mile.

So the unit of  \($\int_0^7 r(c) \ dc$\) is given by :

= gallons per mile x mile

= gallons

So, the final unit is gallons.

Answer:

A and C

Step-by-step explanation:

Answer:

A and C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3.5=3.500

that's the answer

Answer:

The answer is 24.1 unit²

Step-by-step explanation:

Volume of prisms=cross sectional area×h

cross sectional area=Volume of prisms/height

A=216.9/9

A=24.1 unit²

Answer:

179

Step-by-step explanation:

ones, (3+6)+(30+40)+(100+0)=179