given the four digits 2, 4, 6, and 7, how many different positive two-digit integers can be formed using these digits if a digit can be repeated in an integer?

Answer:

bvcnfghnh

Step-by-step explanation:

gfhtfv

Answer:

Step-by-step explanation:

This problem is on ratios, the ratio of one quantity to another is a way to represent their relative size.

Moreso, the scale of a drawing tells us to what extent the drawing has been increased (maximized) or decresed (minimized)

now given that the actual dimention of the appartmentis 28ft wide

and on the drawing the apartment is 7 inches wide, we can see that the actual dimension has been reduced by a factor of 28/7= 4

hence the scale to represent this reduction is

1 inch to represent 4 feet

The value of the middle of the three is 25.

Let x be the first odd integer, then the next two consecutive odd integers are x+2 and x+4. The sum of these three consecutive odd integers is given as 75, so we can write the equation:

x + (x+2) + (x+4) = 75

Simplifying the left side of this equation gives:

3x + 6 = 75

Subtracting 6 from both sides gives:

3x = 69

Dividing by 3 gives:

x = 23

So the first odd integer is 23, and the next two consecutive odd integers are 25 and 27. The middle of these three is the second consecutive odd integer, which is 25. Therefore, the value of the middle of the three is 25.

Learn more about   value from

https://brainly.com/question/24078844

#SPJ11

To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.

Given:

f(x, y) = xy

Partial derivative with respect to x (keeping y constant):

∂f/∂x = y

Partial derivative with respect to y (keeping x constant):

∂f/∂y = x

So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):

∇f(4, 7) = (7, 4)

The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:

z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)

Substituting the values:

z - 28 = (7, 4) · (x - 4, y - 7)

Expanding the dot product:

z - 28 = 7(x - 4) + 4(y - 7)

z - 28 = 7x - 28 + 4y - 28

z = 7x + 4y - 56

Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.

To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.

learn more about vector here

https://brainly.com/question/24256726

#SPJ11

Answer:

79°

Step-by-step explanation:

Asking questions, formulating a hypothesis, testing the hypothesis, drawing conclusions, and reporting the results are steps in the: scientific method.

Scientific method refers to a process that has been the hallmark of natural science since the 17th century and entails systematic observation, measurement, and experiment as well as the creation, examination, and change of hypotheses.

Now,

Hence, Asking questions, formulating a hypothesis, testing the hypothesis, drawing conclusions, and reporting the results are steps in the: scientific method.

To learn more about scientific method, refer to the link: https://brainly.com/question/17216882

#SPJ4

The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Read more about the equation

brainly.com/question/14614141

#SPJ1

Answer:

That answer is correct

Step-by-step explanation:

all of the other ones have errors in them, the domain is every dot above below or on the x-axis.

The width of the river at that point can be estimated to be approximately 1,579 feet.

To estimate the width of the river, we can use the concept of similar triangles. Let's consider the situation from a side view perspective. The height of the Gateway Arch, which acts as the vertical leg of a triangle, is given as 630 feet. The angle of depression to the closer bank is 45°, and the angle of depression to the farther bank is 18°.

We can set up two similar triangles: one with the height of the arch as the vertical leg and the distance to the closer bank as the horizontal leg, and another with the height of the arch as the vertical leg and the distance to the farther bank as the horizontal leg.

Using trigonometry, we can find the lengths of the horizontal legs of both triangles. Let's denote the width of the river at the closer bank as x feet and the width of the river at the farther bank as y feet.

For the first triangle:

tan(45°) = 630 / x

Solving for x:

x = 630 / tan(45°) ≈ 630 feet

For the second triangle:

tan(18°) = 630 / y

Solving for y:

y = 630 / tan(18°) ≈ 1,579 feet

Therefore, the estimated width of the river at that point is approximately 1,579 feet.

To know more about similar triangles, refer here:

https://brainly.com/question/29191745#

#SPJ11

Answer:

Distance between points m and p = 12.53 unit (Approx.)

Step-by-step explanation:

Given:

Co-ordinate of points

m(-10, 3)

p(-4, -8)

Find:

Distance between points m and p

Computation:

Distance between two points = √(x1 - x2)² + (y1 - y2)²

Distance between points m and p = √(-10 + 4)² + (3 + 8)²

Distance between points m and p = √(-6)² + (11)²

Distance between points m and p = √36 + 121

Distance between points m and p = √157

Distance between points m and p = 12.53 unit (Approx.)

Answer:

x=9

Step-by-step explanation:

Use the intersecting chord theorem:

RE*ET = UE*ES

Substitute values

21 (2x+2) = 30 (x+5)

Expand:

42x+42 = 30x + 150

transpose and simplify

42x-30x = 150 - 42

12x = 108

x = 9

Answer:

6

Step-by-step explanation:

The answer is 6. You're looking for the rate of change in the number of DVD's. from 9,15,21,27, each time you add 6, so +6 is your constant variation.

Answer:

Your first step is to distribute the 2 in 2(x+3)

Step-by-step explanation:

The after you complete this step you will make the equation look like

- x - 2x = 6 - 15.

Work it out like you would normally do!

Answer: Distributive Property, follow PEMDAS (the first is parenthesis)

x = 3

Step-by-step explanation:

The area of the square wall will be 576 square feet.

A quadrilateral with four equal sides is called a square. There are numerous items in our environment that have a square shape. Equal sides and interior angles that are both 90 degrees distinguish each square shape.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.

Given that the side of the square wall is 24 ft. The area of the square will be calculated as:-

Area = Side²

Area = ( 24 )²

Area = 576 Square feet

Therefore, the area of the square will be 576 square feets

To know more about the area of the square follow

https://brainly.com/question/25092270

#SPJ1

Answer:

401.92

Step-by-step explanation:

Bases: 2(4^2 π)=32π

Curved Surface: 12*(2*4π)=96π

96π+32π=128π=128(3.14)≈401.92

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

The calculated length of the segment EF is (c) 5

from the question, we have the following parameters that can be used in our computation:

The trapezoid

The length of segment EF can be calculated using

EF = 1/2 * Sum of BC and AD

using the above as a guide, we have the following:

EF = 1/2 * (3.3 + 6.7)

Evaluate

EF = 5

Hence, the length of segment EF is (c) 5

Read more about midsegments at

https://brainly.com/question/7423948

#SPJ1

Answer:

Correct option: C) 90 degrees

Step-by-step explanation:

When we have a tangent segment to a circle, the angle made with the radius of the circle and the tangent segment is always a right angle, that is, 90 degrees. In other words, the radius and the tangent segment are always perpendicular.

If QR is tangent to the circle P, and PQ is the radius of the circle, the segment PQ is perpendicular to the segment QR, so the angle PQR is equal 90 degrees.

Correct option: C)

Answer:

Angle PQR is 90 so answer would be C

Step-by-step explanation:

Answer:

301.76

Step-by-step explanation:

I'll add a diagram for better understanding.  

Look at the diagram

The angle with a question mark in purple is the the bearing from the phone to the transmitter.

To figure out that angle we will have to figure out the angle inside the triangle on that side and we will subtract that from 360 to find the answer.

Since this is a right angled triangle, we can use SOH CAH TOA to figure out the angle inside.

For the angle we have to figure out, 21 is the opposite and 13 is adjacent.

so we will use TOA

tan\(x\\\) = O/A

tan\(x\) = 21/13

tan inverse(21/13) = \(x\)

\(x\) = 58.2405

This is the phone's angle inside the triangle
subtract this from 360 to find the bearing

360 - 58.2405 = 301.76

At the end of year 10, if you deposit $100 now and $200 two years from now in a savings account that pays 10% interest, you would have approximately $725.89. The correct option is D.

To calculate the total amount at the end of year 10, we need to consider the initial deposit of $100 and the deposit of $200 two years from now. The interest rate is 10%.

First, let's calculate the future value of the initial deposit of $100 over 10 years using the compound interest formula:

FV = PV * (1 + r)^n

where FV is the future value, PV is the present value, r is the interest rate, and n is the number of periods.

Substituting the values, we have:

FV1 = $100 * (1 + 0.10)^10 = $100 * 1.10^10 ≈ $259.37

Next, let's calculate the future value of the $200 deposit made two years from now. We have eight years for this deposit to accumulate interest. Using the same formula:

FV2 = $200 * (1 + 0.10)^8 = $200 * 1.10^8 ≈ $466.52

Finally, we sum up the future values of both deposits:

Total amount = FV1 + FV2 ≈ $259.37 + $466.52 ≈ $725.89

Therefore, at the end of year 10, you would have approximately $725.89. Since none of the given answer choices match this amount, the correct answer would be D. none.

To know more about interest rate refer here:https://brainly.com/question/28236069#

#SPJ11

The function can be expressed as a piecewise function as,

f(x) = -1, x < 3 and x > 3

f(x) = -4, x = 3

A piecewise function is a function which has different definitions of values for different intervals.

Given is a graph of a function.

A line is drawn through y = -1 for all the points of x, except at the point x = 3.

At x = 3, the value of y = -4

So we can define the function as,

f(x) = -1 for all x other than 3 and f(x) = -4 for x = 3.

Or in other words,

f(x) = -1, for x < 3 and x > 3

f(x) = -4 for x = 3

Hence the piecewise function defined is f(x) = -1, for x < 3 and x > 3

f(x) = -4 for x = 3.

Learn more about Piecewise Functions here :

https://brainly.com/question/12561612

#SPJ1

Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

To learn more about : positive root

https://brainly.com/question/31512158

#SPJ8

Answer:

n = 1/5

Step-by-step explanation:

Let's solve your equation step-by-step.

5(n− 1 /10 )= 1/ 2

Step 1: Simplify both sides of the equation.

5(n− 1 /10 )= 1 /2

(5)(n)+(5)( −1 /10 )= 1/2

(Distribute)

5n +  −1 /2 = 1 /2

Step 2: Add 1/2 to both sides.

5n +  −1 /2  +  1 /2  =  1 /2  +  1 /2

5n=1  

Step 3: Divide both sides by 5.

5n /5  =  1 /5

n=  1 /5

Answer:

Q = (4, - 1)

Step-by-step explanation:

DF is the diameter of the circle with center Q.

So, Q is the midpoint of DF.

By mid point formula.

\(Q = \bigg( \frac{1 + 7}{2}, \: \: \frac{3 - 5}{2} \bigg) \\ \\ Q = \bigg( \frac{8}{2}, \: \: \frac{ - 2}{2} \bigg) \\ \\ Q = (4, \: \: - 1)\)

The planet that has the larger mass is the planet B and the measurements in standard forms are

From the question, we have the following parameters that can be used in our computation:

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

Read more about standard forms at

https://brainly.com/question/1708649

#SPJ1

Answer:

Step-by-step explanation:

if it's talking about between the numbers 75 to 97, then it's 22.

The product that is the factored form of the polynomial 3x⁴ - 2x² + 15x² - 10 is (x² + 5)(3x² - 2).

In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

The polynomial is first correctly stated as follows

This is rearranged, grouped and solved as follows:

\(\sf 3x^4+15x^2-2x^2-10\)

\(\sf (3x^4+15x^2)-(2x^2+10)\)

\(\sf 3x^2(x^2+5)-2(x^2+5)\)

Factorizing the common factors, we have the product of the factored form of the polynomial as follows:

\(\boxed{\rightarrow\bold{(x^2 + 5)(3x^2 - 2)}}\)

Thus, the product that is the factored form of the polynomial 3x⁴ - 2x² + 15x² - 10 is (x² + 5)(3x² - 2).

Learn more about the polynomial at:

https://brainly.com/question/30520457

The average rate of return is 6.332%.

The given problem is that $100,000 from a retirement account is invested in a large cap stock fund.

After 25 yr, the value is $172,810.68.

Part 1 of the problem asks us to use the model 4-Pe to determine the average rate.

So, let's solve it.4-Pe Model

The 4-Pe model of investing explains the relationship between investment return, dividend payout, growth rate, and the initial price-to-earnings ratio.

The four variables that make up the formula are P0, P1, E1, and D1.

The formula is:

P0 = (D1 / R) - (g - R)(P1 / R)

Where:

P0 = Current price

P1 = Future price

D1 = Dividend payout in the next period

R = Expected rate of return

g = Expected growth rate

So, we have:

P0 = $100,000

P1 = $172,810.68

D1 = $172,810.68 - $100,000 = $72,810.68

R = ?

g = ?

Now, we will solve for R using the formula:

P0 = (D1 / R) - (g - R)(P1 / R)$100,000

= ($72,810.68 / R) - (g - R)($172,810.68 / R)

Multiplying throughout by R, we get:

$100,000R = $72,810.68 - (g - R)($172,810.68)

Expanding and simplifying: $100,000R

= $72,810.68 - $172,810.68g + $172,810.68R$72,810.68 - $100,000R

= $172,810.68g - $72,810.68R$172,810.68g

= $172,810.68R + $100,000R - $72,810.68$172,810.68g

= $272,810.68R - $72,810.68$172,810.68g + $72,810.68

= $272,810.68R$100,000

= $272,810.68R - $172,810.68g

R = ($100,000 + $172,810.68g) / $272,810.68

Substituting the value of P0, P1, and D1 in the above formula, we get:

R = ($100,000 + $72,810.68) / $272,810.68R

= $172,810.68 / $272,810.68R

= 0.6332 or 6.332%

Therefore, the average rate of return is 6.332%.

To know more about average rate visit:

https://brainly.com/question/32208982

#SPJ11

Answer:

k- 1

Step-by-step explanation: