suppose $5$ different integers are randomly chosen from between $20$ and $69$, inclusive. what is the probability that they each have a different tens digit?

The coordinates of the circumcenter of a triangle with vertices A(0,1),

B(2, 1) , and C(2, 5)  is (1,3).

What is circumcenter of triangle?

The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).

Given:  A triangle with vertices A(0,1), B(2, 1) , and C(2, 5).

Using distance formula:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

AB = 2 units

BC = 4 units

AC = √20 units

The midpoint of AC:

\(= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\\= (\frac{2+0}{2}, \frac{5+1}{2}) \\= (\frac{2}{2} , \frac{6}{2})\\ = (1, 3)\)

The midpoint of AC is (1, 3).

Hence, The coordinates of the circumcenter of a triangle with vertices A(0,1),  B(2, 1) , and C(2, 5)  is (1,3).

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(a) The revenue function for this product as a function of time is R(t) = 37t² + 76t + 1   (b) R'(3) = 298 which means that the revenue is increasing at a rate of $298 per month at this time.

(a) The revenue for this product is given by:

R(t) = x(t) × p(t)

Substituting x(t) and p(t) into this equation, we get:

R(t) = (t^2 + 4t - 1) × (45 - 2t)

R(t) = 45t^2 - 90t + 180t - 8t^2 - 4t + 1

R(t) = 37t^2 + 76t + 1

Therefore, the revenue function for this product is R(t) = 37t² + 76t + 1.

(b) To evaluate R'(3), we first find the derivative of R(t):

R'(t) = 74t + 76

Then, we substitute t = 3 into this equation:

R'(3) = 74(3) + 76

R'(3) = 298

This means that at t = 3 months, the rate of change of revenue with respect to time is $298 per month. In other words, the revenue is increasing at a rate of $298 per month at this time.

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Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.

To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.

The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.

Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.

The pooled proportion is given by:

p_hat = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of students with ear infections in each school.

Using the given data, we have:

n1 = 40, n2 = 30

x1 = 11, x2 = 12

p1 = x1/n1 = 11/40 = 0.275

p2 = x2/n2 = 12/30 = 0.4

p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355

The test statistic is:

z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197

Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.

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1) 3,500 rounded to the nearest ten thousand is 0.

2) 462,183.5062749 rounded to the nearest tenth is 462,183.5.

3) 6 + (-3) - 5 is equal to -2.

QUESTION 1:The given number is 3,500. To round it to the nearest ten thousand, we need to see which ten thousand is closest to the number. In this case, 3,500 is between 0 and 10,000. Since 0 is closer, we round down to 0. So, 3,500 rounded to the nearest ten thousand is 0.

QUESTION 2: To round the given number, 462,183.5062749, to the nearest tenth, we need to look at the digit in the hundredths place (the second digit after the decimal point), which is 0. Since 0 is less than 5, we round down the digit in the tenths place to 3.

Therefore, 462,183.5062749 rounded to the nearest tenth is 462,183.5.

QUESTION 3:We have to evaluate 8 to the 8th power. That means we have to multiply 8 by itself 8 times. Using a calculator, we can find that 8^8 is equal to 16,777,216.

QUESTION 4:When solving the expression 6 + (-3) - 5, we should follow the order of operations, which is: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Since there are no parentheses or exponents in this expression, we can simply perform addition and subtraction from left to right.

6 + (-3) = 3, then 3 - 5 = -2.

Therefore, 6 + (-3) - 5 is equal to -2.

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Answer:

10.7

Step-by-step explanation:

Hello There!

The image shown below shows the relationship between two chords formed inside of a circle

So the product of the lengths of the lines in the same chord is equal to the product of the other length of the chords lines if that makes sense

So basically 6 * 16 = 9 * x

we can now use this equation that was just made to solve for x

6 * 16 = 96

96 = 9x

*divide each side by 9*

96/9=10.66666667 *round to the nearest tenth* 10.7

9x/x

we're left with x = 10.7

There are 0 or no real solutions for the equation 4x²=-4x-4.

So,

Given the equation: 4x²=-4x-4

Then,

No factor for this equation.

Therefore, there are 0 or no real solutions for the equation 4x²=-4x-4.

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Answer:

c

Step-by-step explanation:

im smart

The graph that shows a polynomial function with an even degree is option D.

A function is a law that relates two variables, a dependent and an independent variable with each other.

The domain and range of a function is always defined, the domain is all the values that can be an input to the function and the range is all the valuess that a function can have.

A function that involves positive integer powers as exponents of a variable in an equation is called a polynomial function, like the quadratic equation,

An even degree polynomial function, represented by y = x², have graphs that either open upwards or downwards.

A function is even if, for each x in the domain of f, f (- x) = f (x).

In an even function, the graph is symetrically along y axis.

The only graph that is symmetrical along the y axis is graph D.

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Answer:

(6,0)

Step-by-step explanation:

reflect the graph on mirror line answer should be (6,0)

Answer:

Using translation concepts, it is found that the dotted graph is given by:

f(x - 1) - 4

------------------

For function f(x), the solid line, it has a zero at x = -1, while the dashed line has a zero at x = 0, which means that it was moved 1 unit to the right, thus f(x - 1).

The dashed line is also below the function f(x), so 4 was subtracted, thus f(x - 1) - 4.

Step-by-step explanation:

Answer:

\( {x}^{2} = {(13 - 6)}^{2} + {9}^{2} = {7 }^{2} + {9}^{2} \\ = 130 \\ x = \sqrt{130} = 11.4\)

Answer: I believe the answer is x = 38°

114° / 3

x = 38°

Hope this helps :)

Answer:

qjjsHope this helps you.

Answer:

x < 50

Step-by-step explanation:

No more means that it cannot equal 50. Therefore we can remove the 1st two options.

We now have the 3rd option and 4th option to choose from.

The 4th option is incorrect because the inequality is saying that a number is greater than 50.

∴ x < 50 is our answer.

The range of the data on the 4th of July parade is greater than the range of the data in the New Years's Day parade.

A dataset's range, which reflects the gap among its greatest and lowest values, is measured statistically.

By deducting lowest value from the greatest value, it is computed. If range of total data is wider in Fourth of July parade than it is in the New Year's Day parade, then highest and lowest figures in Fourth of July parade will be further apart than highest and lowest values in New Year's Day parade.

For example, if highest value in 4th of July parade is 100 and lowest value is 10, then total range is 100 - 20 = 80.

If the highest value in the New Year's Day parade is 60 and the lowest value is 20, then the range is 60 - 20 = 40.

Thus, here range of the data in 4th of July parade is greater than range of the data in the New Year's Day parade.

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Answer: 91/200

Step-by-step explanation: i got it right on the quiz.

Answer:

C

Step-by-step explanation:

Answer:

x=17

Step-by-step explanation:

we know the sum of angles in atriangle is 180°

x +17 + 4x -34 +6x +10 = 180

x+4x+6x +17 -34 +10 = 180

11x -7 =180

11x = 180 +7

x = 187/11 = 17

The problems realted to doubling growth rate is solved using an exponential model. If it takes 80 minutes to fill the container, then it will take 79 minutes to fill one half of the container. The dealing sequence is a,a²,a⁴, a¹⁶,...... where a is intial amount.

An exponential model, is used here. The reason for this is that the growth rate is very high which an exponential model can accurately replicate. We have a yeast population is doubling in the container every minute. That is if it's population in container is half at present then the container become full filled in next minute. This also means is that if we know the quantity after a certain number of minutes, the quantity a minute earlier must have been half of that. Let the intial amount be 'x'. Total time taken by yeast to fully fill up the container = 80 minutes

We have to determine the time it take to fill one half of the container. Now, the container gets full in 80 minutes. Half of this quantity must have been meant that the container was half full. Thus, the container was half full 79 minutes after the yeast was put in it. We are dealing with a sequence something like that a, a², a⁴,___.

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Answer:

y=3x+5

Step-by-step explanation:

first you find the slope by doing rise over run. then you would put the slope into point-slope formula which is y-y1=m(x-x1), then you simplify into y=mx+b  (slope intercept form). which gets you your final answer.

Answer:

\(3\frac{1}{3}\ ft^3\)

Step-by-step explanation:

A rectangular prism is a polyhedron with six rectangular faces. The volume of a prism is given by:

Volume = width * height * length

From the diagram, the rectangular prism is made up of cubes. Each cube is has a size of 1/3 ft by 1/3 ft.

The height of the prism is made up of 5 cubes. Height = 5 * 1/3 = 5/3 ft.

The length of the prism is made up of 3 cubes. length = 3 * 1/3 = 1 ft.

The width of the prism is made up of 2 cubes. Width = 2 * 1/3 = 2/3 ft.

The volume of the prism = width * height * length = 2/3 * 5/3 * 1 = 10/9 ft³ =  \(3\frac{1}{3}\ ft^3\)

Answer:

it is 3 1/3 good day

Step-by-step explanation:

Answer:

No, she is not correct. Because this is a proportional relationship.

Step-by-step explanation:

Proportional relationships are relationships having equal ratios.

here, Mandy's conclusion is incorrect because the relationship is proportional, and it has a uniform ratio of 5.

column 1               column 2           column 2/column1

   'x'                            'y'          

    1                             5                               5

    2                            10                              5

    5                            25                             5

    10                           50                             5

As we clearly see that ratio of column 2 and column 1 is same for every row, therefore we can conclude that the given relation in the relation is proportional.

Thus,  the given relation is proportional.

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Answer:

C

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

10(3x−4)=30−5x

Step 1: Simplify both sides of the equation.

10(3x−4)=30−5x

(10)(3x)+(10)(−4)=30+−5x(Distribute)

30x+−40=30+−5x

30x−40=−5x+30

Step 2: Add 5x to both sides.

30x−40+5x=−5x+30+5x

35x−40=30

Step 3: Add 40 to both sides.

35x−40+40=30+40

35x=70

Step 4: Divide both sides by 35.

 35x         70

____   = _____

 35            35  

x=2

Please mark as brainliest if answer right

Have a great day, be safe and healthy  

Thank u  

XD

Really sorry if it is complicated

Given vector field, F(x, y, z) = y cos (xy) i + x cos (xy) j – sin z k To calculate the curl of F, we need to take the curl of each component and subtract as follows,∇ × F = ( ∂Q/∂y - ∂P/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂R/∂x - ∂Q/∂y ) k...where P = y cos(xy), Q = x cos(xy), R = -sin(z)

Now we calculate the partial derivatives as follows,

∂P/∂z = 0, ∂Q/∂y = cos(xy) - xy sin(xy), ∂R/∂x = 0...

and,

∂P/∂y = cos(xy) - xy sin(xy), ∂Q/∂z = 0, ∂R/∂y = 0

Therefore,

∇ × F = (cos(xy) - xy sin(xy)) i - sin(z)j

The curl of F is given by:

(cos(xy) - xy sin(xy)) i - sin(z)j.

To state whether F is conservative, we need to determine if it is a conservative field or not. This means that the curl of F should be zero for it to be conservative. The curl of F is not equal to zero. Hence, the vector field F is not conservative. Let C be the curve joining the origin (0,1,-1) to the point with coordinates (1, 2V2,2) defined by the following parametric curve:

r(t) = n* i + t}j + tcos atk, 15t52.

The curve C is defined as follows,r(t) = ni + tj + tk cos(at), 0 ≤ t ≤ 1Given vector field, F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk Using the curve parameterization, we get the line integral as follows,∫CF.dr = ∫10 F(r(t)).r'(t)dt...where r'(t) is the derivative of r(t) with respect to t

= ∫10 [(t cos(at))(cos(n t)) i + (n cos(nt))(cos(nt)) j + (-sin(tk cos(at)))(a sin(at)) k] . [i + j + a tk sin(at)] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) + (-a t sin(at) cos(tk))(a sin(at))] dt

= ∫10 [(t cos(at))(cos(n t)) + (n cos(nt))(cos(nt)) - a^2 (t/2) (sin(2at))] dt

= [sin(at) sin(nt) - (a/2) t^2 cos(2at)]0^1

= sin(a) sin(n) - (a/2) cos(2a)

The vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is given. Firstly, we need to calculate the curl of F. This involves taking the curl of each component of F and subtracting. After calculating the partial derivatives of each component, we get the curl of F as (cos(xy) - xy sin(xy)) i - sin(z)j. Next, we need to determine whether F is conservative. A conservative field has a curl equal to zero. As the curl of F is not equal to zero, it is not a conservative field. In the second part of the problem, we have to calculate the scalar line integral of the vector field F. dr along the curve C joining the origin to the point with coordinates (1, 2V2, 2). We use the curve parameterization to calculate the line integral. After simplifying the expression, we get the answer as sin(a) sin(n) - (a/2) cos(2a).

The curl of the given vector field F(x, y, z) = y cos(xy) i + x cos(xy)j – sin zk is (cos(xy) - xy sin(xy)) i - sin(z)j. F is not conservative as its curl is not zero. The scalar line integral of the vector field F along the curve C joining the origin to the point with coordinates (1, 2V2,2) is sin(a) sin(n) - (a/2) cos(2a).

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Answer:

No

Step-by-step explanation:

Since x increases exponentially by the 2nd power, it is not linear, it is a quadratic equation.

Answer:

x=-9

Step-by-step explanation:

move the variable to the left hand side and change its sign

combine like terms

and then solve like a two step equation

Answer:

x = -9

Step-by-step explanation:

move the terms: you need to move the variable to the left-hand side and change its sign so the new equation would be 2x-3x=4+5

combine like terms: add the x values together and add the integers together the new equation would be -x=9

You need x to be positive so divide both sides by -x to make the x positive and that will you give the answer of -9

Answer:

15d² + 7d - 4

Step-by-step explanation:

Distribute

(5d + 4)(3d -1)

5d (3d - 1) + 4(3d - 1)

Distribute

15d² - 5d + 4(3d- 1)

Distribute

15d² - 5d + 12d- 4

Simplify

15d² + 7d - 4

Answer:

x=2.5

Step-by-step explanation:

5x<12          1. /5 on both sides

x= 2.5    

Answer:

x<2.4

Step-by-step explanation:

5x < 12

x < 12/5

x < 2.4

On the number line, draw an arrow going towards left from 2.4, with an open circle at 2.4

Answer:

2

Step-by-step explanation:

To find the slope given two points you do \(\frac{y2-y1}{x2-x1}\)

so we just plug in the y values and x values

\(\frac{-7-5}{-2-4}\)

\(-7-5=-12\)

\(-2-4=-6\)

\(\frac{-12}{-6} =2\)

Therefore the slope is 2

Answer:

a) -9

b)-9

Step-by-step explanation:

a) - 4 - 5

Subtract 5 from -4 to get -9.

-9

factor: ( - 1) × 32

b) - 2 - 7

Subtract 7 from -2 to get -9.

-9

( - 1) × 32