michael has $85 in his bank account. He deposits $10 each week. write an equation representing the number of weeks, it will take him to save $400.

The sum of the geometric series is 513.

To find the sum of a geometric series, we use the formula:

S_n = a[tex](1-r^{n})[/tex] / (1 - r)

where S is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, we know that the first term is 3, and the common ratio is -2. To find the number of terms, we need to determine what value of n satisfies the equation:

768 = 3 x [tex](-2^{n-1} )[/tex]

We can simplify this equation by dividing both sides by 3:

256 = [tex](-2^{n-1} )[/tex]

Taking the logarithm of both sides (to base 2), we get:

n - 1 = [tex]log_{2}[/tex](256)

n - 1 = 8

n = 9

Therefore, there are 9 terms in the series for this question.

Using the formula for the sum of a geometric series, we have:

S = 3(1 - [tex](-2^{9} )[/tex] / (1 - (-2))

S = 3(1 - (-512)) / 3

S = 3(513) / 3

S = 513

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Answer:

I guess the value be 26x

hope it helps u

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The cost price that was used to get the book is: R.S 172

The parameters given are:

Marked Price: M.P = RS. 250

Discount allowed = 10%

The formula to find the selling price here will be:

S.P = M.P * (100 - Discount)/100

Thus:

S.P = 250 * (100 - 14)/100

S.P = 250 * 0.86

S.P = R.S 215

Since the profit is 25%, then we have:

Cost Price = (S.P * 100)/(100 + Gain%)

Cost price = (215 * 100)/(100 + 25)

Cost Price = 21500/125

Cost price = R.S 172

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After answering the provided question, we can conclude that C. The expression interquartile range (IQR) of team B's scores exceeds that of team A's scores.

An expression in mathematics is a collection of representations, digits, and huge corporations that represent a statistical correlation or fitness regime. A square root, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, basic arithmetic, rapid spread, polarisation, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

We can see from the box plots in the image that the box plot for team B is wider than the box plot for team A, indicating that team B has a wider range of scores. As a result, the correct statement comparing the distribution spreads is:

C. The interquartile range (IQR) of team B's scores exceeds that of team A's scores.

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The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. This statement is not correct.

When a pyramid and a prism have the same base and height, the volume of the pyramid is one-third ([tex]\frac{1}{3}[/tex]) the volume of the prism.

This can be seen from the formula for the volume of a rectangular prism, which is:

[tex]The volume of the prism = base area x height[/tex]

And the formula for the volume of a rectangular pyramid is:

The volume of the pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Since the base area and height of the pyramid and prism are the same, we can compare their volumes by dividing the volume of the pyramid by the volume of the prism:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex] x base area x height/base area x height

Simplifying this expression, we get:

[tex]\frac{The volume of pyramid}{Volume of prism}[/tex] = [tex]\frac{1}{3}[/tex]

Therefore, the volume of a pyramid with the same base and height as a prism is one-third [tex](\frac{1}{3})[/tex] the volume of the prism.

The complete question is:-

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is the volume of the prism. True/False.

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Answer:

A bicycle with 26 inch diameter wheels travels a distance of 200 feet. Find the number of revolutions. I am not sure

Step-by-step explanation:

The volume of the coffee can rounded to the nearest 10th of a decimal place is 226. 08 cubic inches

It is important to note that the coffee can takes the shape of a cylinder.

The formula for calculating the volume of a cylinder is expressed with the equation;

V = πr²h

This is so as the parameters are enumerated thus;

Also, r = diameter/2 = 6/2 = 3 inches

From the information given, we have that;

Volume = 3.14 × (3)² × 8

Multiply the values

Volume = 226. 08 cubic inches

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We may infer that the constant of proportionality (unit rate) between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone because the unit rate is the same for both weeks.

The unit rate, or constant of proportionality, between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone.

We divide the total sum by the quantity of cones purchased to determine the unit rate.

The unit rate for last week is: $22 x 4 cones = $5.50 per cone.

The unit price for this week is: $33 divided by six cones, or $5.50 each cone.

We may infer that the constant of proportionality (unit rate) between the amount spent and the quantity of ice cream cones purchased is $5.50 per cone because the unit rate is the same for both weeks.

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Answer:

B linear

Step-by-step explanation:

If the rate of change stayed the same then it has to be a straight line so no C or D, and it cant be A be cause there is a rate of change.

The ramp will rise 20.79 inches from the ground at its highest end.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's assume that the ramp will be in the shape of a right triangle, where the length of the base (the horizontal distance from the ground to the highest end of the ramp) is 36 inches and the angle between the base and the hypotenuse (the ramp itself) is 30 degrees.

We can use trigonometry to find the height of the ramp (the vertical distance from the ground to the highest end of the ramp).

First, we need to find the length of the hypotenuse. We can use the formula:

hypotenuse = base / cosine(angle)

In this case, the base is 36 inches and the angle is 30 degrees, so:

hypotenuse = 36 / cosine(30) = 41.57 inches (rounded to the nearest hundredth)

Next, we can use the formula for the sine of an angle:

sine(angle) = opposite / hypotenuse

In this case, the opposite side (the height of the ramp) is what we want to find. So we can rearrange the formula to solve for the height:

height = sine(angle) x hypotenuse

Plugging in the values we know, we get:

height = sine(30) x 41.57 = 20.79 inches (rounded to the nearest hundredth)

Therefore, the ramp will rise 20.79 inches from the ground at its highest end.

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Answer:

n is greater than negative 12

Step-by-step explanation:

I put the answer on the attached please see it

The correct options are:

x² + (y-6)² = 36

x² + (y+8)² = 36

How does diameter work?

the distance that a straight line must travel in order to connect two points on opposite edges of a circular object or shape The diameter is twice as large as the radius. The pond's circumference is six feet.

Since the circle's centre is on the y-axis, its x-coordinate is zero. Moreover, the circle's radius is 6 units because its diameter is 12 units.

As a result, the equations that depict circles with a centre on the y-axis and a diameter of 12 units are as follows:

(x-0)² + (y-h)² = r², where h is the y-coordinate of the center and r is the radius of the circle.

(x-0)² + (y-k)² = r², where k is the y-coordinate of the center and r is the radius of the circle.

2 = r2, where k is the circle's center's y-coordinate and r is its radius.

We can see from these equations that circles with a diameter of 12 units and a centre on the y-axis are represented by the following equations:

x² + (y-6)² = 36 (center at (0,6))

x² + (y+6)² = 36 (center at (0,-6))

As a result, the following choices depict circles that satisfy these requirements:

x² + (y-6)² = 36

x² + (y+8)² = 36

The appropriate choices are thus:

x² + (y-6)² = 36

x² + (y+8)² = 36

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Answer:

8.09017

calculations

The value of the ratio t:m:w in its simplest form is 3:8:28.

To simplify the ratio t:m:w, we need to find the common factor between t, m, and w.

Using the given ratios, we can write t:m:w as (3x):(8x):(28y), where x is the common factor between t and m and y is the common factor between m and w.

From the given ratio t : m = 3:8, we can say that t is equal to 3 and m is equal to 8.

Similarly, from the given ratio m:w = 4:7, we can say that m is equal to 4 and w is equal to 7.

So, we have

t : m = 3:8 and m:w = 4:7

Multuiply second by 2

t : m = 3:8 and m:w = 8:14

So, we have

t : m : w = 3 : 8 : 14

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Answer:

To eliminate x, add the two equations together:

5x + 4y = -7

(-5x - 2y = 1)

2y = -6

Solve for y:

2y = -6

y = -3

Substitute y = -3 into one of the original equations, say -5x - 2y = 1, and solve for x:

-5x - 2y = 1

-5x - 2(-3) = 1

-5x + 6 = 1

-5x = -5

x = 1

Therefore, the solution is (x, y) = (1, -3).

Step-by-step explanation:

Answer: There is not enough information to answer the question accurately.

The length of the minor arc in a tree ring depends on the circumference of the tree ring and the angle that the arc subtends at the center of the ring. Without additional information about the sizes and shapes of the two tree rings, we cannot determine the length of the minor arc in the large tree ring based solely on the length of the minor arc in the small tree ring.

Step-by-step explanation:

Therefore , the solution of the given problem of triangle comes out to be  x = 15 .

A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward rectangular form. A, B, and C are the only three sides that set a triangle apart from a simple triangle. When the boundaries are not exactly collinear, Euclidean geometry results in a singular area instead of a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

Triangle ABC ,

=> x /5 = x-6/3

=> 3x = 5x - 30

=> 2x = 30

=> x = 30/2

=> x = 15

Therefore , the solution of the given problem of triangle comes out to be   x = 15 .

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Answer:

The digit 6 in 46.12 is in the tenths place. Therefore, 1/10 the value of 6 in 46.12 is simply 6/10 or 0.6.

Answer: The distance from the ball to the goal is 11.86 ft.

Step-by-step explanation:

Answer:

≈ 11.9 feet

Step-by-step explanation:

Answer: 22

Step-by-step explanation:

perimeter = a+b+c+d

84 = 4x+4x+(4x+2)+(4x+2)

84 = 16x + 4

80 = 16x

5 = x

length:

=4x+2

=4(5)+2

=22

Alex does not have enough strawberries to make fruit salad and jam.

A mixed fraction is a fraction that is created by fusing a fraction with a whole number.

An improper fraction is a fraction that cannot be further simplified and has a numerator higher than or equal to the denominator. For instance, 13/5 is a bad fraction. Let's find the mixed fraction equivalent of this incorrect fraction. Divide the denominator by the numerator in step 1. Step 2: Track down the rest. In step 3, arrange the numbers as follows: quotient, followed by a portion of the remainder or divisor.

Given that, Alex wants to use 1 3/4 and 3 1/2 cups of strawberries.

Thus the total strawberries are:

1 3/4 + 3 1/2

= 7/4 + 7/2

Taking LCM we have:

= 21/4 = 5.2 cups

Hence, Alex does not have enough strawberries to make fruit salad and jam.

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The type of sampling used to conduct a study on depression among the elderly is convenience sampling, which is a type of non-probability sampling technique where samples are selected because they are conveniently available and accessible, and the sample size for this study was calculated to be 30.

The type of sampling used to conduct a study on depression among the elderly is convenience sampling. Convenience sampling is a type of non-probability non-probability  where samples are selected because they are conveniently available and accessible .

In this study, a sample of 30 patients in one nursing home was used for the convenience sampling. The formula for calculating the sample size for convenience sampling is [tex]N = (N1*N2)/(N1+N2[/tex]), where N is the sample size, N1 is the population size, and N2 is the desired sample size. In this case, N1 is the total number of elderly patients in the nursing home, and N2 is 30. Therefore, the sample size for this study is calculated as follows: [tex]N = (N1*30)/(N1+30) = 30[/tex].

Convenience sampling is a quick and easy way of obtaining a sample, but it can be biased due to the presence of sampling errors and selection bias. Sampling errors occur when the sample is not representative of the overall population, while selection bias occurs when certain groups of people are more likely to be included in the sample than others. Therefore, it is important to consider the potential sources of bias when conducting a study using convenience sampling.

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We can use the Pythagorean theorem to find the diagonal distance across the rug. According to the theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (the hypotenuse).

In this case, the length and width of the rug form the two shorter sides of a right triangle, and the diagonal distance is the hypotenuse. So we can use the formula:

diagonal^2 = length^2 + width^2

Plugging in the values given in the problem, we get:

diagonal^2 = 8^2 + 5^2

diagonal^2 = 64 + 25

diagonal^2 = 89

To solve for the diagonal, we take the square root of both sides:

diagonal = sqrt(89)

Using a calculator, we get:

diagonal ≈ 9.43 feet

Therefore, the diagonal distance across the rug is approximately 9.43 feet.

Answer:73

Step-by-step explanation:

add 75 + 60 + 85 = 220

then divide  to divide you need to find how much times you added then divide by 220 so 75 + 60 + 85 which is 3 times so you divide 220 by 3 and you get 73.33333333333333 or 73

Therefore, the expression that represents the value of the stock after the two years have passed in terms of x is:

A = 1.7673x

By dividing the number of shares they possess by the total number of outstanding shares and multiplying the result by 100, stockholders can calculate their ownership stake in a corporation.

After the first year, the value of the stock increased to:

x + 0.37x = 1.37x

After the second year, the value of the stock increased to:

1.37x + 0.29(1.37x) = 1.37x + 0.3973x = 1.7673x

Therefore, the expression that represents the value of the stock after the two years have passed in terms of x is:

A = 1.7673x

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Answer:

I hope this explains it!

Step-by-step explanation:

1. Select which conversion approach you wish to use:

a. Convert from actual (real) size to scale.

b. Convert from scale to actual (real) size.

2. Enter the scale factor; for example, if you wish to work with a 1/6th scale, input 6.

3. Enter the dimensions of the actual object (or measurements of the scaled object if you are planning on converting a scale to an actual size)

4. Select the unit of measurement from the drop-down list

5. Click on the "Convert" button to generate the results.

Using synthetic division, you can solve the following equation: (x^(4)+x^(3)-8x^(2)-13x-7)-:(x+2).

Step 1: Write down the coefficients of the polynomial in the top row of the synthetic division table.


x^(4)  x^(3)  -8x^(2)  -13x  -7

Step 2: Write the divisor in the left-most column.


   x+2


Step 3: Bring down the first coefficient of the dividend and write it in the second row of the table.


x^(4)  x^(3)  -8x^(2)  -13x  -7 | x+2

        x^(3)  -8x^(2)  -13x  -7


Step 4: Multiply the divisor by the number in the second row and write it in the third row.


x^(4)  x^(3)  -8x^(2)  -13x  -7 | x+2

        x^(3)  -8x^(2)  -13x  -7 | x+2

            x^(2)  -15x  -19


Step 5: Subtract the third row from the second row and write it in the fourth row.


x^(4)  x^(3)  -8x^(2)  -13x  -7 | x+2

        x^(3)  -8x^(2)  -13x  -7 | x+2

            x^(2)  -15x  -19  | x+2

                -7x  -26


Step 6: Bring down the next coefficient in the first row and repeat steps 4 and 5.


x^(4)  x^(3)  -8x^(2)  -13x  -7 | x+2

        x^(3)  -8x^(2)  -13x  -7 | x+2

            x^(2)  -15x  -19  | x+2

                -7x  -26  | -7

                   -22


Step 7: Multiply the divisor by the number in the fourth row and write it in the fifth row.


x^(4)  x^(3)  -8x^(2)  -13x  -7 | x+2

        x^(3)  -8x^(2)  -13x  -7 | x+2

            x^(2)  -15x  -19  | x+2

                -7x  -26  | -7

                   -22  | -14


Step 8: Subtract the fifth row from the fourth row and write it in the sixth row.


x^(4)  x^(3)  -8x^(2)  -13x  -7 | x+2

        x^(3)  -8x^(2)  -13x  -7 | x+2

            x^(2)  -15x  -19  | x+2

                -7x  -26  | -7

                   -22  | -14

                       8


Step 9: The final answer is: (x^(4)+x^(3)-8x^(2)-13x-7)/(x+2) = x^3-7x^2-15x-26 + 8/(x+2).

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The solution to the differential equation is:

$$v(t)=\frac{V_0+kCe^{-Ct}}{1+kCe^{-Ct}}$$
Where $V_0$ is the initial velocity and $C$ is the proportionality constant. The limiting velocity of the falling body as $t \to \infty$ is: $$v_{\infty}=\frac{V_0}{1+kC}$$

The instantaneous velocity of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t: v ( t ) = d d t x ( t ) . v ( t ) = d d t x ( t ) . Like average velocity, instantaneous velocity is a vector with dimension of length per time.

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Answer:

2.5 cm

Step-by-step explanation:

In any right triangle, the formula [tex]a^2+b^2=c^2[/tex] can be used to find its side lengths.

Given the side lengths,

[tex]a = 2 \\b = 1.5\\\\2^2+1.5^2=c^2\\4+2.25=c^2\\6.25=c^2\\c=\sqrt{6.25}\\c=2.5[/tex]

Answer:

Therefore, ackrabbits can reach speeds of approximately 59 feet per second.

Step-by-step explanation:

First, we need to convert miles to feet:

40 miles/hour * 5,280 feet/mile = 211,200 feet/hour

Then, we need to convert hours to seconds:

1 hour = 60 minutes/hour * 60 seconds/minute = 3,600 seconds/hour

211,200 feet/hour / 3,600 seconds/hour = 58.67 feet/second

Rounding to the nearest whole number, we get:

59 feet/second

Therefore, ackrabbits can reach speeds of approximately 59 feet per second.