5- For the regression equation 9 = 7 - 1.2x the predicted value y when x=4is? a) 0 b) 2.2√ c) 3.4 $1.6 6- If A and B make a partition of the sample space, (i. e AUB-S). Then the probability that at

The solution to the equation represented by One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x is (b) x = negative 4

The statement in the question is given as

One-fourth x minus one-eighth = Start Fraction 7 Over 8 End Fraction + one-half x

Mathematically, this statement can be represented as

1/4x - 1/8 = 7/8 + 1/2x

Multiply through the equation by 8

So, we have:

2x - 1 = 7 + 4x

Collect the like terms

4x - 2x = -1 - 7

Evaluate the like terms

2x = -8

Divide both sides by 2

x = -4

Hence, the solution is -4

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The equivalent system of first-order differential equations is:

To transform the given differential equation into an equivalent system of first-order differential equations, we can introduce new variables. Let's define:

x1 = x

x2 = x'

x3 = x''

x4 = x'''

Now, we can rewrite the original equation in terms of these new variables:

x4 - 5x'' - 3x' + 53sin(3t) = 0

Replacing the derivatives with the new variables, we have:

x4 = x4

x3 = x'''

x2 = x'

x1 = x

Now, we have a system of first-order differential equations:

x1' = x2

x2' = x3

x3' = x4 - 5x2 - 3x1 + 53sin(3t)

x4' = ?

We need to find an expression for x4' by differentiating one of the equations. Let's differentiate the equation x3' = x4 - 5x2 - 3x1 + 53sin(3t) with respect to t:

x4' = x3'' = (x4 - 5x2 - 3x1 + 53sin(3t))'

Differentiating each term, we get:

x4' = x4' - 5x2' - 3x1' + 159cos(3t)

Simplifying, we have:

x4' = -5x2 - 3x1 + 159cos(3t)

Therefore, the equivalent system of first-order differential equations is:

x1' = x2

x2' = x3

x3' = x4 - 5x2 - 3x1 + 53sin(3t)

x4' = -5x2 - 3x1 + 159cos(3t)

Note: The given differential equation is of the fourth order, so the resulting system has four first-order equations to represent it.

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Answer:

The answer you're looking for is D! I hope this helped :)

a. The probability that customers did not see dolphins on a randomly selected trip is 7/40.

b. The probability that customers did not see dolphins given that the trip was in the morning is 3/22.

c. The events of seeing dolphins and the time of the trip (morning or afternoon) are dependent events because the probability of seeing dolphins varies based on the time of the trip, as indicated by the different counts in the two-way table.

a. To find the probability that customers did not see dolphins on a randomly selected trip, we need to calculate the number of trips where dolphins were not seen and divide it by the total number of trips.

The number of trips where dolphins were not seen is the sum of the "no dolphins" counts in the morning and afternoon, which is 3 + 4 = 7.

Therefore, the probability of not seeing dolphins on a randomly selected trip is 7/40.

b. To find the probability that customers did not see dolphins under the condition that the trip was in the morning, we need to consider the number of trips in the morning where dolphins were not seen.

The number of morning trips where dolphins were not seen is given as 3.

Since we are conditioning on the trip being in the morning, the total number of trips we consider is limited to the morning trips, which is 19 + 3 = 22.

Therefore, the probability of not seeing dolphins given that the trip was in the morning is 3/22.

c. The events of seeing dolphins and the time of the trip (morning or afternoon) are dependent events.

This is because the probability of seeing dolphins is influenced by the time of the trip.

The probabilities of seeing dolphins differ between morning and afternoon trips, as indicated by the different counts in the two-way table.

If the events were independent, the probability of seeing dolphins would be the same regardless of the time of the trip.

However, since the probabilities vary based on the time of the trip, we can conclude that the events of seeing dolphins and the time of the trip are dependent.

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The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.

The confidence interval for a population proportion is calculated by the formula,

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

Where \(\bar{p}\) is the sample proportion and α is the level of significance.

It is given that,

The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are

The sample size n = 200;

The number of successes = 46

So, the sample proportion \(\bar{p}\) = 46/200 = 0.23

For a 95% confidence interval, the level of significance is

α = 1 - 95/100 = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Then, the z-score for the value 0.025 is

\(z_{\alpha/2}\) = 1.96 (from the table)

Thus, the confidence interval is

\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)

⇒ C.I = 0.23 ± (1.96) × \(\sqrt{\frac{0.23(1-0.23)}{200} }\)

⇒ C.I = 0.23 ± 1.96 × 0.0298

⇒ C.I = 0.23 ± 0.0584

So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.

Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.

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By farmers ....................

Answer:

64 degrees

Step-by-step explanation:

since x is corresponding to 64, they are congruent.

Answer:

x = 64

Step-by-step explanation:

x and 64° are corresponding angles and are congruent , then

x = 64

Hey there! I'm happy to help!

We see that if you add 5% to the original cost, we have $168 as our cost. This means that 105% of the original cost is 168. Let's set up an equation to find the original cost. Let's call our original cost c.

To turn a percent into a decimal, you divide by 100.

1.05c=168

We divide both sides by 1.05.

c=160

Therefore, the original cost was $160.

Have a wonderful day! :D

Hi!

(5+d)+(-8)=(5+d)-8

Hence, this is the required solution.

~SparklingFlower :)

Answer:

The present value of $225 received at the end of five years with an interest rate of 5% is $176.29.

Let x represent the number of winter olympics held in North America.

Let y represent the number of winter olympics held in Europe.

Let z represent the number of winter olympics held in North Asia.

The Winter Olympics have been held a total of 21 times on the continents of North America, Europe, and Asia.

This means that

x + y + z = 21

The number of European sites is 5 more than the total number of sites in North America and Asia.

This means that

y = x + z + 5

There are 4 more sites in North American than in Asia.

This means that

x = z + 4

These are the equations. We would solve simultaneously

The olympics was held 2 times in North America, 13 times in Europe and 6 times in Asia

what do you need answered the opp length?

Answer:

6^2-3^2=36-9=27

squareroot of 27= 3\(\sqrt{3}\)

Step-by-step explanation:

The month in which Sam will have read the same number of books as Janet is June.

To determine in which month Sam will have read the same number of books as Janet, let's analyze the table of Sam's book reading progress. Without the specific table provided, I will illustrate the steps to find the desired month.

Let's assume the table represents the number of books Sam has read each month:

Month Number of Books Read

Jan 0

Feb 2

Mar 4

Apr 6

May 8

Janet mentioned that she has read 10 books this year, with a consistent rate of 2 books per month. Given that information, we can see that Janet has read 2 books per month for every month of the year, including May.

To find the month where Sam will have read the same number of books as Janet, we need to determine when Sam's cumulative number of books matches or surpasses Janet's total.

By looking at the table, we can see that Sam will reach or surpass 10 books in the month of June. In June, Sam will have read a total of 10 books, the same number as Janet.

Therefore, the month in which Sam will have read the same number of books as Janet is June.

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what do u want me to do

I do not understand there is no question

The differentiation of the given equations is \(\frac{d}{dx}x^{2}=2x\).

Given that, \(\frac{d}{dx}x^{2}\).

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Differentiate using the Power Rule which states that \(\frac{d}{dx}x^{n}=nx^{n-1}\).

1) \(\frac{d}{dx}x^{2}=2x\)

2) \(\frac{d}{dx}(3x^{5})=15x^4\)

3) \(\frac{d}{dx}(9x^{2})=18x\)

4) \(\frac{d}{dx}(3x^{3})=9x^{2}\)

5) \(\frac{d}{dx}(2x^{7})=14x^6\)

6) \(\frac{d}{dx}(x^{7})=7x^6\)

Therefore, the differentiation of the given equations is \(\frac{d}{dx}x^{2}=2x\).

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Yes, a chi-square test can be used to test for a relationship between the number of citizen complaints and whether or not an officer commits serious misconduct.

A chi-square test of independence is appropriate when analyzing the relationship between two categorical variables. In this case, the number of complaints and the occurrence of serious misconduct are both categorical variables. The number of complaints can be grouped into categories (0-2, 3-5, 6), and the occurrence of serious misconduct can be categorized as either "yes" or "no".

By conducting a chi-square test of independence, the researcher can determine whether there is a significant association between the number of complaints and the occurrence of serious misconduct. The test will assess whether the observed frequencies in each category differ significantly from what would be expected if there were no relationship between the variables.

However, it's important to note that other assumptions of the chi-square test should be met, such as the independence of observations and expected cell frequencies greater than 5. Additionally, the appropriateness of the chi-square test depends on the specific research question and the nature of the data. Therefore, the researcher should carefully consider the context and characteristics of the study before deciding to use a chi-square test.

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The required simplified value of k is 8 for given conditions.

Given that,
f(x) = x³ + kx + 9, and x + 1 is a factor of f(x) , then what is the value of the of k is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,

f( x ) =  x³ + kx + 9  / x + 1
remainder = 9 - (k+1), it should be equal to zero for the proper factor. So,
9 - (k + 1 ) = 0
9 = k +1
k = 8

Thus, the required simplified value of k is 8.

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Side of the cube = 2 cm

Width of the rectangular prism = 9 cm

Length of the rectangular prism = 9cm

Height of the rectangular prism = 4 cm

Now,

The volume of total water (submerged cube)

= width of the rectangular prism x length of the rectangular prism x height of the cube

= 9 x 9 x 2 = 162 cm^3

As we know that 1 cm^3 = 1ml

So,

162 cm^3 = 162 ml

Hence the volume of water required to fill the prism such that the cube is submerged is 162 ml.

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Answer:

C.

Step-by-step explanation:

The mean at Belmont is 16.75, the median is 15.5, and the mode is 13.

The mean at Tyler is 10.9, the median is 10.5, and the mode is 13, 10, and 6.

9514 1404 393

Answer:

  24

Step-by-step explanation:

Let d represent Donald's age now. Then Natali's age now is d+38. The age relationship 5 years ago was ...

  (d+38) -5 = 3(d -5)

  d +33 = 3d -15 . . . . . eliminate parentheses

  48 = 2d . . . . . . . . . . . add 15-d

  24 = d . . . . . . . . . . . . . divide by 2

Donald is 24 years old now.

_____

Alternate solution

You can also work this by considering that 5 years ago, Natalie's age was more than Donald's age by twice Donald's age then. Hence Donald was 38/2 = 19 at that time. Now, Donald is 19+5 = 24.

El valor que satisface D es 188.

El modelo matemático será así:

D/d = 12(resto 8)

si escribimos 8 como resto de D, entonces:

(D-8) /d=12

D-8= 12d o se puede escribir D= 12d+8

luego sustituya D= 12d+8 por D+d= 203

D+d= 203

(12d +8) +d= 203

13d= 203-8

13d= 195

re=15

sustituir d=15 en D+d= 203

D+d= 203

D+15=203

D=203-15

D=188

El modelo matemático es una forma de interpretación humana al traducir o formular problemas existentes en forma matemática, de modo que el problema pueda resolverse utilizando las matemáticas.

El uso principal de los modelos matemáticos es ayudar a las personas a comprender los problemas y simplificarlos para que puedan resolverse.

, los siguientes son algunos de los usos que se obtienen al utilizar un modelo matemático, a saber:

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Answer:

The answer is "Option a".

Step-by-step explanation:

please find the attached file.

In the given question, the positive correlation shows the scatterplot and, by adding six now higher calories, low-fat pasta, is the positive value for the new correlation of the coefficient will be decreasing.

In this question, the points are more close to the line and increasing from left to right, which can be mostly like, that's why the choice "a" is correct.

To find the optimal consumption of goods X and Y, we need to use the marginal utility approach. The marginal utility of a good is the additional utility gained from consuming one more unit of that good.

Given the utility function U(x, y) = sqrt(x) + sqrt(y) and prices pX = 5 and pY = 1, we can write the marginal utility of good X as MUx = 1/(2*sqrt(x)) and the marginal utility of good Y as MUy = 1/(2*sqrt(y)).

To maximize utility, we need to allocate our income in such a way that the marginal utility per dollar spent is equal across goods. In other words, we want to spend more on the good that gives us more utility per dollar.

Let's set up the equation for the marginal utility per dollar spent:
MUx / pX = MUy / pY

Substituting in the marginal utility expressions and prices, we get:
1/(2*sqrt(x)) / 5 = 1/(2*sqrt(y)) / 1

Simplifying, we get:
sqrt(y) = 5sqrt(x)

Now we can use the budget constraint to solve for optimal consumption. The budget constraint is:
pX * x + pY * y = income

Substituting the prices and income values, we get:
5x + y = 60

We can use the earlier equation (sqrt(y) = 5sqrt(x)) to substitute for y in terms of x:
y = 25x

Substituting this into the budget constraint, we get:
5x + 25x = 60

Simplifying, we get:
x = 1.5

Substituting this value into y = 25x, we get:
y = 37.5

Therefore, the optimal consumption of goods X and Y is x = 1.5 and y = 37.5.

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Answer:

B=28

Step-by-step explanation:

Answer:

decimal form: 4.52

fraction: 4 13/25

Step-by-step explanation:

Answer:

Decimal 4.52

Fraction 4  13/25

Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the y-value is -2, the x-value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

\(\displaystyle y=a(x-h)^2+k\)

Where a is the leading coefficient and (h, k) is the vertex.

Since the vertex is (-2, -3), h = -2 and k = -3:

\(\displaystyle y=a(x-(-2))^2+(-3)\)

Simplify:

\(y=a(x+2)^2-3\)

We are also given that y = -2 when x = -5. Substitute:

\((-2)=a(-5+2)^2-3\)

Solve for a. Simplify:

\(\displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}\)

Therefore, our full vertex equation is:

\(\displaystyle y=\frac{1}{9}(x+2)^2-3\)

We can expand:

\(\displaystyle y=\frac{1}{9}(x^2+4x+4)-3\)

Simplify:

\(\displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}\)

The coefficient of the squared term of the equation is 1/9.

Answer:

\(A= 6x^2-11x-35\)

Step-by-step explanation:

Given data

Length=  2x-7

Width= 3x+5.

Area= L*W

substitute

\(A= (2x-7)* (3x+5)\)

Open bracket

\(A= 6x^2+10x-21x-35\)

collect like terms

\(A= 6x^2-11x-35\)

Hence the area is

\(A= 6x^2-11x-35\)

The shifted coordinates for each of the following are (20,-11) and (6,2).

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given, (x,y) → (x + 10, y - 6)

a)  when the input is (10,-5) -

10 + 10 = 20

- 5 - 6 = - 11

(20,-11)

b) when the input is (-4,8) -

-4 + 10 = 6

8 - 6 = 2

(6,2)

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Answer:

The function is a growth function so I guess A, B and D

suggest a growth curve

Step-by-step explanation:

the slope in this graph represents the relationship between the prey population and the number of predator offspring produced per unit of time.

the slope indicates how much the number of predator offspring changes for a given change in the prey population. A steeper slope indicates that a small change in the prey population leads to a large change in the number of predator offspring, while a flatter slope indicates that a large change in the prey population is needed to produce the same change in the number of predator offspring.

Overall, the slope provides important information about the dynamics of predator-prey interactions and can help researchers understand how changes in one population affect the other. This is a relatively long answer, but I hope it helps clarify the role of slope in this type of graph.


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