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The expected number of new cases per 100,000 in Michigan according to the multiple regression model is 930

In statistics, multiple regression model refers a statistical technique that can be used to analyze the relationship between a single dependent variable and several independent variables.

Here we have given that if Michigan has a strictness level equal to 50 and has more than 55 available hospitals,

And we need to find the expected number of new cases per 100,000 in Michigan according to the multiple regression model.

While we looking into the given question, we have identified the value of

Strictness level = 50

Available hospital = 55

New cases per day = 100,000

Then the expected number is calculated by using the multiple regression model is written as,

=> 50x + 55y ≤ 100,000

When we solve it graphically, then we get, the graph like the following,

As per the given graph, the expected number is 930.

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The value of SSE (sum squared error) is 40 in the given analysis of the variance problem if SST = 120 and SSR = 80. Option b is correct.

Here the words SSE means Sum Squared Error, SST means Sum of Squares Total and SSR means Sum of Square Regression.

In the SSE accuracy measure, errors are squared and then added. It is used when the data points are similar in magnitude.

The formula is SST = SSR + SSE ⇒ SSE = SST - SSR

The given values of the analysis of the variance problem are

SST = 120; SSR = 80

Then, the value of SSE = SST - SSR = 120 - 80 = 40

So, option b is correct.

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72 square units is the area of rectangle when coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3

The area of Rectangle is length times of width.

The coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)​

The distance from AB

Distance=√(x₂-x₁)²+(y₂-y₁)²

=√(5-5)²+(-9-3)²=√(-12)²=√144=12

The distance from BC

=√(-1-5)²+(-9+9)²=√36=6

Length is 12 units and width is 6 units

Area of rectangle=Length×Width

=12×6

=72 square units

Hence, 72 square units is the area of rectangle when coordinates of the vertices of a rectangle are A (5, 3), B (5,-9), C (-1,-9), and D (-1, 3)

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Answer:

B. [tex]\triangle UVZ \cong \triangle YVX[/tex] (SSS)

From the given image, we can say that the congruency postulate is that; Triangle UTZ ≅ Triangle YVX by SSS

There are 6 main triangle congruency postulates namely;

1. SSS which means the three corresponding sides of both triangles are congruent.

2. SAS which means that 2 corresponding sides and the included corresponding angle are congruent.

3. ASA which means that 2 corresponding angles and the included corresponding side are congruent.

4. AAS which means that 2 corresponding angles and the non-included corresponding angle are congruent.

5. Hypotenuse-Leg Congruence Theorem which states that If the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.

From the given image of both triangles, we can see that all three corresponding sides are congruent to each other which indicates SSS Congruency postulate.

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The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

[tex]\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}[/tex]

Now, differentiate P with respect to x, and we get,

[tex]\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}[/tex]

Solving the above equation to zero, we get,

[tex]\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}[/tex]

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

[tex]\begin{aligned}y&=108-36\\y&=72\end{aligned}[/tex]

Thus, the two positive numbers are 36 and 72.

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Answer: 7

Step-by-step explanation:

We substitute n for 14 to get the equation 14-7, which equals 7.

To solve for the distance covered in the first two hours, we need to calculate the velocity at time t = 0 and t = 2.The car will have covered 44 miles during the first 2 hours of driving.

The velocity of the car t hours after leaving Austin is given by the equation V = 12 + 5t - 32. To solve for the distance covered in the first two hours, we need to calculate the velocity at t = 0 and t = 2.

At t = 0, V = 12 - 32 = -20. This means that the car was travelling at -20 miles per hour when it left Austin. Since velocity and distance are inversely proportional, the car had covered 0 miles when it left Austin.

At t = 2, V = 12 + 10 - 32 = -10. This means that the car was travelling at -10 miles per hour after 2 hours. Since velocity and distance are inversely proportional, the car had covered 44 miles after 2 hours by time.

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The given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

We shall represent this as 1.5 pizzas in decimal form.

In this case, the dot stands in for the decimal point, the number before the dot, in this case, "1," represents one entire pizza, and the number after the decimal point, or the fractional component, represents the other half of the pizza.

So, we have the rational number:

1/4

Convert to decimal as follows:

1/4 = 0.25

Rounding off to the nearest thousandth: 0.2500 ⇒ 0.25

Therefore, the given rational number 1/4 in the decimal form is 0.25 which is to the nearest thousandths.

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Answer:

17 feet

Step-by-step explanation:

We can use the Pythagorean therom, since the triangle has a 90 degree angle:

         8^2 + 15^2 = x^2

         64  +  225 = x^2

          x^2 = 289

           x = 17 feet

See the attached worksheet.

Answer:

$215.50

Step-by-step explanation:

To calculate the amount of interest that Albert will earn on his account over the course of 4 years, we can use the formula for compound interest:

Interest = principal * (1 + rate/n)^(n*t) - principal

Where:

principal is the initial amount of money in the account ($1,000 in this case)

rate is the annual interest rate (5% in this case)

n is the number of times that interest is compounded per year (annually in this case, so n=1)

t is the number of years the money is invested (4 years in this case)

Plugging these values into the formula, we get:

Interest = $1,000 * (1 + 0.05/1)^(1*4) - $1,000

= $1,000 * (1.05)^4 - $1,000

= $1,000 * 1.2155 - $1,000

= $215.50

To the nearest cent, the interest Albert will earn in 4 years is $215.50.

The time that is needed to complete the pending work is 211.2 minutes.

To calculate the percentage, divide the value by the total value and then multiply the resultant by 100.

If the amount of work is 52%.

100% - 52% = 48%

The total minutes that are required is 440 minutes.

you have 48% of the 440 minutes left to work.

48% / 100 = .48 * 440 =211.2

Therefore, the time that is needed to complete the pending work is 211.2 minutes.

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Emma is asking an empirical question so that she she can test her hypothesis

What is a Empirical hypothesis?

Something empirical is something based on real evidence .

Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic

A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet

So, According to the question

Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis

Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.

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A triangle can be formed with side lengths 4, 8, 11. Yes, because 4 + 8 > 11

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

If the sum of any two sides is greater than the sum of the third, then the difference of any two sides is less than the sum of the third. The sum of any two sides must be greater than the sum of the third. The longest side in a triangle is the side opposite a larger angle.

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Answer:   You can buy a 9-pound bag for $8.37.

Step-by-step explanation:

[tex]\frac{5lbs}{4.65} =\frac{p}{8.37}[/tex]    

Then, we cross multiply, and we get:

5(8.37) = 4.65p

  41.85 = 4.65p   [We divided 4.65 by both sides]

         9 = p

The approximation for the function g(4.2) is 12.44

From the table, we know that g'(4) = 2.2

g (4) = 12

Using the line tangent to the graph of g at x=4 ,

g (4.2)  = g (4 ) + (4.2 -4 )2.2

           = 12 + 0.44

           = 12.44

The approximation for the function g(4.2) is 12.44. So ,option A is correct.

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The simplest polynomial with the given roots will be equal to x⁴ + 5x² - 36.

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and raising non-negative integers to power, together with uncertainty and coefficients. x² + 4x + 7 is an illustration of a single indeterminate x polynomial.

The total of terms with the pattern [tex]kx^n[/tex] forms a polynomial. Where n is indeed a positive number and k is any number. For instance, the polynomial 3x + 2x - 5 exists.

As per the given information in the question,

The given roots are 3i, -2, 2

As we know that if 3i is a root then -3i is also a root.

Then, the factored form of this polynomial will be:

p(x) = (x - 3i)(x + 3i)(x + 2)(x - 2)

= (x - (3i)²) (x² -2x + 2x - 4)

It will become: (x² + 9)(x² - 4)

It can be further expanded,

x⁴ - 4x² + 9x² - 36

x⁴ + 5x² - 36

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The rate of change of the volume when radius of sphere is 11 inch is 2904π inch³/minutes

According to the question,

The radius r of a sphere is increasing at a rate of 6 inches per minutes

Volume of sphere is 4/3 πr³

We have to find Rate of change of volume when r = 11 inch

Differentiating volume of sphere w.r.t time

V = 4/3 πr³

=> dV/dt = 4 πr² . dr/dt ---------(1)

As it is given that ,

dr/dt = 6

Substituting the value in equation (1)

=>  dV/dt = 4 πr² . 6

=> dV /dt = 24 πr²

r = 11

=> dV /dt = 24 π(11)²

=> 2904 π inch³/minutes is rate of change of volume

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Two triangles are said to be congruent if their sides (S) and angles (A) are the same. SAS, ASA, SSS, and RHS serve as the triangle's congruence criteria. A triangle's congruency is not determined by SSA.

What does a math congruent mean?

Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

                   Draw two circles with the same radius, for instance, then cut them out and stack them.

How are three congruent?

An equilateral triangle is one that has all three of its sides be in line with one another. We add a slash mark to the sides that are congruent. An equilateral triangle's angles are 60°.

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Hi how are you call 112 you will get nice

The distance falls by the object in 3 seconds is 88.2 meters

The distance that an object falls when it is dropped is directly proportional to the square of the amount of time

Consider the distance as d and the time as t

Then the relationship will be

d ∝ t^2

d = kt^2

The distance falls in 2 seconds = 39.2 meters

Substitute the values in the equation

39.2 = k × 2^2

39.2 = 4k

k = 39.2 /4

k = 9.8

When the time = 3 seconds

The distance = 9.8 × 3^2

= 9.8 × 9

= 88.2 meters

Therefore, the object fall 88.2 meters in 3 seconds

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The equation in standard form for the circle will be;

⇒ (x + 2)² + (y - 9)² = 1

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle that has a diameter with endpoints (-2,10) and (-2,8).

Now,

Since, The circle that has a diameter with endpoints (-2,10) and (-2,8).

Hence, The radius of circle is the half of the distance between two points of the diameter.

So, Radius = 1/2 (√ (8 - 10)² + (- 2 - (-2))²

                 = 1/2 √4

                = 1/2 × 2

                 = 1

Thus, Radius (r) of circle = 1

And, The center of circle is midpoint of the endpoints of the diameter.

Hence, Centre = (- 2 + (-2))/2, (10 + 8)/2

                       = - 4/2 , 18/2

                       = (- 2, 9)

Hence, The equation of circle with center (-2, 9) and radius 1 is;

⇒ (x - (-2))² + (y - 9) = 1²

⇒ (x + 2)² + (y - 9)² = 1

Thus, The equation in standard form for the circle will be;

⇒ (x + 2)² + (y - 9)² = 1

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Answer:

6300 ft

Step-by-step explanation:

Answer:

The volume of Raj's classroom would be 6,300 cubic feet which is the multiplication of the floor area and the height of the room.

What is the volume of the cuboid?

The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.

The volume of a cuboid is length × breadth× height

Raj's classroom floor area measures 525 square feet. The ceiling height of the room is 12 feet.

The volume of Raj's classroom is the multiplication of the floor area and the height of the room.

The volume of Raj's classroom = the floor area × the height of the room

The volume of Raj's classroom = 525 × 12

The volume of Raj's classroom = 6,300 cubic feets

Thus, the volume of Raj's classroom would be 6,300 cubic feet.

The center of the circle shifted 6 units to the right when it's center is on line x=6.

A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle. A circle can be compared to a hula hoop. The circle is only present at the border's points.

Here,

Centre of circle=(-4,3)

-4+6=2

New centre is (2,3).

When the circle's center is on line x=6, its center has moved 6 units to the right.

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Yes, a test of statistical significance be conducted before or after computing d and interpreting its value.

The p-value is an important phrase for hypothesis testing in the context of statistical significance of data.

The p-value is defined as a function of observed sample outcomes that is used to evaluate statistical hypotheses. Before running the test, a threshold value must be chosen.

The significance is a figure that represents the probability that the outcome of a study occurred entirely by chance. The statistical significance can be low or high. It does not always imply practical significance. When a researcher does not use language carefully in their experiment report, the significance may be misconstrued.

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Answer:

Step-by-step explanation:

Assuming that you mean x² + 5x + 6

the factors are (x + 2) and (x + 3).

The binomial series is used to expand a binomial expression of the form (a + b)^n, where 'a' and 'b' are constants and 'n' is a positive integer. In this case, we are expanding (1-x)^1/3.

Step 1: Rewrite the expression using the binomial theorem. We can rewrite (1-x)^1/3 as (1 + (-x))^1/3.

Step 2: Use the binomial theorem to expand the expression.

The binomial theorem states that (a + b)^n

= nC0*a^n + nC1*a^(n-1)*b + nC2*a^(n-2)*b^2 + ... + nCn*b^n.

Since 'n' is a 1/3 in this case, we can rewrite the expression as

(1 + (-x))^1/3

= 1C0*1^1/3 + 1C1*1^(1/3-1)*(-x) + 1C2*1^(1/3-2)*(-x)^2 + ...

Step 3: Substitute the values. We can substitute the values into the expression to get (1 + (-x))^1/3

= 1 + (-x) + (-x)^2 + ...

Step 4: Simplify the expression. The expression simplifies to

(1 - x + x^2 - x^3 + ...).

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p < 0.10, there is sufficient evidence to conclude that the machines' maker should perform a recalibration.

In this question we have,

The population mean μ = 1.00

The sample size n = 49

The sample mean X = 1.06

The standard deviation σ = 0.22cm

The significance level α = 0.10

So, the hypothesis is:

The null hypothesis: H0: μ = 1

The alternative hypothesis: Ha: μ ≠ 1

Thus, the test statistic value is,

z = (X - μ)/(σ/√n)

= (1.06 - 1)/(0.22/√49)

= 0.06 / 0.03142

= 1.91

So, for z = 1.91, the p-value is 0.028067.

The provided significance level of 0.10 is not met by the p-value of (0.028067).

Therefore, there is enough evidence to support the claim that the machines' manufacturer needs to recalibrate them.

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The critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom is a.) 2.492

It should be noted that in order yoo find the critical t-value for a 98% confidence interval with 24 degrees of freedom, you will need to use a t-table to look up the value in the t-distribution.

In this situation, the t-distribution is a probability distribution that is used to estimate population parameters when the sample size is small and the population standard deviation is unknown.

In a two-tailed test, the critical t-value is the value that is exceeded by the test statistic with a probability of 0.02 in each tail of the distribution. Here, the critical t-value is 2.492. The correct option is A.

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Using the t-table (located in the tutorial), what is the critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom? Answer choices are rounded to the thousandths place.

a.) 2.492

b.) 1.311

c.) 1.699

d.) 2.045

(a) The probability that there are no clients in the system is 0.3333

(b) The average number of customers waiting is 1.33

(c) The average number of customers in the system is 2

(d) The average time a customer spends waiting is 3.33 min

(e) The average time a customer spends in the system is 5 min

(f) The probability that arriving customers will have to wait for service is 0.6667.

Given that,

Customers of Willow Brook National Bank can conduct financial transactions at a drive-up teller window without getting out of their cars. On weekday mornings, the drive-up teller window receives 24 customers each hour, or 0.4 customers per minute, arriving at random.

Arrival rate λ = 24 customers per hour or 0.4 customers per minute

Service rate  μ​ = 36 customers per hour or 0.6 customers per minute

Utilizing the single-server drive-up bank teller operation previously mentioned, establish the following system operational characteristics:

(a) The probability that there are no clients in the system is

P₀ = 1 - λ /μ

= 1 - (24/36)

= 1/3

= 0.3333

(b) The average number of customers waiting

Lq = λ²/ [μ(μ - λ)]

= 242/[36×(36-24)]

= 1.33

(c) the average clientele using the system.

L = Lq + λ/μ  

= 1.33 + (24/36)

= 2

(d)the average length of time a consumer must wait.

Wq = λ/ [μ(μ - λ)]

= 24/[36×(36-24)]

= 0.0555 hr

= 3.33 min

(e) The average time a customer spends in the system

W = Wq + 1/μΧ

= 0.0555 + (1/36)

= 0.0833 hr

= 5 min

(f) the probability that clients who arrive will have to wait for service.

= 1 - P₀

= 1 - 0.3333

= 0.6667

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