find the approximate surface area of a bowling ball with a raius of 5 inches

Answer:  B

Step-by-step explanation:

To solve the equation, it was first required to get rid of the fraction by multiplying both sides by 7 and then to isolate r, the running miles, you subtract 105 from both sides resulting in Gisele running 35 miles per week.

The question is asking to find the number of miles Gisele runs each week, which is represented by the variable r in the equation. We start with the equation: 1/7(105 + r) = 20. This equation is derived from the fact that Gisele covers a total of 20 miles each day, for 7 days, and that total comprises both her cycling and running mileages. If she cycles 105 miles each week, then the distance she runs is the remaining part of those total 20 miles she covers each day. We multiply both sides of the equation by 7 to get rid of the fraction: 105 + r = 140. Now, if we subtract 105 from both sides of the equation, we get the solution for r as; r = 140 - 105 = 35 miles. Hence, Gisele runs 35 miles each week.

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Answer: 10

Step-by-step explanation:

Solution :

Given that, Celia earned $5.00.

She saved $1.00 and spent the rest.

To find the ratio of the amount saved to the amount spent , we must first calculate the amount spent.

To calculate the amount spent, subtract the amount saved from the total money earned.

Amount spent by Celia = amount earned - amount saved [tex] = 5-1 = 4 [/tex]

[tex] ratio= \frac{amount\:saved}{ amount\:spent} =\frac{1}{4} \\
\\
ratio= 1:4 [/tex]

Hence, 1:4 is the ratio of the amount saved to the amount spent.

Answer: 60 cents

Step-by-step explanation:

Answer:

Table 1

Step-by-step explanation:

We have the function [tex]f(x)=8(\frac{1}{4})^{x}[/tex].

Now, the function g(x) is obtained by reflecting f(x) across y-axis.

i.e. g(x) = f(-x)

i.e. [tex]g(x)=8(\frac{1}{4})^{-x}[/tex]

So, substituting the values of x in f(x) or g(x), we will discard some options.

2. For x=0, the value of [tex]f(0)=8(\frac{1}{4})^{0}[/tex] i.e. f(0) = 8.

As in table 2, f(0) = 0 is given, this is not correct.

3. For x=0, the value of [tex]g(0)=8(\frac{1}{4})^{-0}[/tex] i.e. g(0) = 8.

As in table 3, g(0) = -8 is given, this is not correct.

4. For x=0, the value of [tex]g(0)=8(\frac{1}{4})^{-0}[/tex] i.e. g(0) = 8.

As in table 3, g(0) = 0 is given, this is not correct.

Thus, all the tables 2, 3 and 4 do not represent these functions.

Hence, table 1 represents f(x) and g(x) as the values are satisfied in this table.

The fraction of the word 'Supercalifragilisticexpialidocious' that has the letter 'i' is 7/34, which is already in its simplest form.

The word 'Supercalifragilisticexpialidocious' contains 34 letters. To find what fraction of this word has the letter 'i' in it, we first need to count how many times the letter 'i' appears. The letter 'i' appears 7 times in the word. Therefore, the fraction of the word that has the letter 'i' in it is 7/34.

It is important to note that this fraction can be simplified. However, since both 7 and 34 are prime numbers with respect to each other (they have no common factors other than 1), the fraction 7/34 is already in its simplest form.

Answer:

perfect competition

Step-by-step explanation:

because i did the test.

The range is 24 and the interquartile range is the difference between the median of the second-half to the first-half is 8.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The data set below represents the total number of touchdowns a quarterback threw each season for 10 seasons of play.

29, 5, 26, 20, 23, 18, 17, 21, 28, 20

Arrange in ascending order, we have

5, 17, 18, 20, 20, 21, 23, 26, 28, 29

The range will be given as

→ Range = 29 - 5 = 24

The interquartile range will be given as

→ Interquartile range = median of second-half - median of first-half

→ Interquartile range = 26 - 18

→ Interquartile range = 8

The range is 24 and the interquartile range is 8.

More about the median link is given below.

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The solution to the system of equations involving line A (y = 7x + 12) and a perpendicular line B passing through a given point involves finding the negative reciprocal of the slope of line A for line B, using the point-slope formula to get line B's equation, and solving the system to find their point of intersection.

The question revolves around finding the equation of line B, which is perpendicular to line A (y = 7x + 12) and passing through a given point, then solving the system of equations formed by lines A and B. First, we identify that the slope of line A is 7. Since line B is perpendicular to line A, its slope will be the negative reciprocal of 7, which is -1/7. Assuming the point it passes through is provided in the question, we can use the point-slope formula y - y1 = m(x - x1) to find the equation of line B. After determining the equation of line B, we solve the system of equations represented by lines A and B to find the point of intersection, which will be the solution to the system.

To solve the system of equations, we would set the equations equal to each other and solve for one variable, then substitute back to find the other variable. This process involves algebraic manipulation such as substitution or elimination method. The final solution will be the coordinates (x,y) where both lines intersect.

The answer to question 13 is (B). [tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]

The answer to question 14 is (A). [tex]\(x - 9\) and \(x + 3\)[/tex]

The answer to question 15 is (A). [tex]\((x - 6)\) and \((x - 5)\).[/tex]

The answer to question 16 is (A). [tex]\((x + 6y)(x + 4y)\).[/tex]

The answer to question 17 is (A).[tex]\(2x - 5\) and \(3x + 4\).[/tex]

The answer to question 18 is (B). [tex]\((5x + 7)\) and \((x - 2)\).[/tex]

To find a simpler form of the product [tex]\((4x - 6y^3)^2\)[/tex], we apply the formula for squaring a binomial, which is [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]. Here, [tex]\(a = 4x\)[/tex] and [tex]\(b = 6y^3\).[/tex]

So, [tex]\((4x - 6y^3)^2 = (4x)^2 - 2(4x)(6y^3) + (6y^3)^2\).[/tex]

Calculating each term, we get:

[tex]\((4x)^2 = 16x^2\),[/tex]

[tex]\(-2(4x)(6y^3) = -48xy^3\),[/tex]

[tex]\((6y^3)^2 = 36y^6\).[/tex]

Putting it all together, we have:

[tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]

To find the possible dimensions of the rectangle, we need to factor the trinomial [tex]\(x^2 + 6x - 27\).[/tex] We look for two numbers that multiply to -27 and add up to 6. These numbers are 9 and -3.

So, [tex]\(x^2 + 6x - 27 = (x + 9)(x - 3)\).[/tex]

We factor the trinomial [tex]\(x^2 + x - 30\)[/tex] by finding two numbers that multiply to -30 and add up to 1. These numbers are 6 and -5.

So, [tex]\(x^2 + x - 30 = (x - 6)(x + 5)\).[/tex]

To factor [tex]\(x^2 - 10xy + 24y^2\)[/tex], we look for two numbers that multiply to \[tex](24y^2\)[/tex] and add up to -10y. These numbers are -6y and -4y.

So, [tex]\(x^2 - 10xy + 24y^2 = (x - 6y)(x - 4y)\)[/tex].

To find the possible dimensions of the barnyard, we factor the trinomial [tex]\(6x^2 + 7x - 20\).[/tex] We need two numbers that multiply to [tex]\(6 \times -20 = -120\)[/tex] and add up to 7. These numbers are 15 and -8. We then split the middle term accordingly and factor by grouping:

[tex]\(6x^2 + 15x - 8x - 20 = 0\),[/tex]

[tex]\(3x(2x + 5) - 4(2x + 5) = 0\),[/tex]

[tex]\((3x - 4)(2x + 5)\).[/tex]

We factor the trinomial [tex]\(5x^2 - 3x - 14\)[/tex] by finding two numbers that multiply to [tex]\(5 \times -14 = -70\)[/tex] and add up to -3. These numbers are -10 and 7. We then split the middle term accordingly and factor by grouping:

[tex]\(5x^2 - 10x + 7x - 14 = 0\),[/tex]

[tex]\(5x(x - 2) + 7(x - 2) = 0\),[/tex]

[tex]\((5x + 7)(x - 2)\).[/tex]

Answer:

  P(z < 1.45) ≈ 0.92647

Step-by-step explanation:

Several forms of technology are available for finding the area under the standard normal curve. There are probability apps, web sites, spreadsheets, and calculator functions.

The area under the standard normal curve between two values of z is given on many spreadsheets and by many calculators using the normalcdf(a,b) function. In this form, 'a' is the lower bound, and 'b' is the upper bound of the z-values for which the area is wanted.

For the problem at hand, the value of 'a' is intended to be negative infinity. A calculator allows input of no such value, so some "equivalent" value must be used. (At least one calculator manual suggests -1e99.)

The area of the normal curve below z=-8 is less than 10^-11, so -8 is a suitable stand-in for -∞ on a calculator that displays a 10-decimal-digit result. All the decimal digits shown are accurate, not affected by our choice of lower bound.

The attachment shows the value of the expression is about ...

  P(z < 1.45) ≈ 0.92647

Answer with explanation:

We have to find , P (z< 1.45).

 Breaking ,z value into two parts, that is , In the column,the value at, 1.40 and in the row ,value at , 0.05,the point where these two value coincide,gives value of Z<1.45.

The value lies in the right of mean.

So, P(z<1.45)=0.9265

In the,Normal curve, at the mid point of the curve

Mean =Median =Mode

Z value at Mean = 0.5000

→So, if you consider , the whole curve,

P(Z<1.45)= 0.9265 × 100=92.65%=92%(approx) because we don't have to consider ,z=1.45.

→But, if you consider, the curve from mean ,that is from mid of the normal curve

P (z<1.45)=92.65% - 50 %

           =42.65% =42 %(approx) because we don't have to consider ,z=1.45.

Answer:

Option a. [tex]\$6,455[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have      

[tex]t=4\ years\\ A=\$7,160.06\\ r=0.026\\n=4[/tex]  

substitute in the formula above  and solve for P

[tex]7,160.06=P(1+\frac{0.026}{4})^{4*4}[/tex]  

[tex]7,160.06=P(1+\frac{0.026}{4})^{4*4}[/tex]  

[tex]P=7,160.06/1.109227=\$6,455[/tex]  

Answer:

Option A.

Step-by-step explanation:

The vertices of Polygon ABCD are A(0, 2), B(0, 8), C(7, 8), and D(7, 2).

Plot all vertices on the coordinate place.

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

First we need find the slope of each sides, using the above formula.

[tex]m_{AB}=\frac{8-2}{0-0}=\infty[/tex]

[tex]m_{BC}=\frac{8-8}{7-0}=0[/tex]

[tex]m_{CD}=\frac{8-2}{7-7}=\infty[/tex]

[tex]m_{AD}=\frac{2-2}{7-0}=0[/tex]

The slope of vertical lines is ∞ and slope of horizontal line is 0. It means sides AB and CD are vertical lines and sides BC and AD are horizontal lines.

Vertical and horizontal lines are perpendicular to each other. It means all interior angles of the polygon are right angles.

From the below figure it is clear that

[tex]AB=6[/tex]

[tex]BC=7[/tex]

[tex]CD=6[/tex]

[tex]AD=7[/tex]

Opposite sides are equal and interior angles are right angles, so the polygon is a rectangle.

Perimeter of the polygon is

[tex]Perimeter=AB+BC+CD+AD[/tex]

[tex]Perimeter=6+7+6+7=26[/tex]

Perimeter of polygon ABCD is 26 linear units.

Therefore, the correct option is A.

Answer:

2/9

Step-by-step explanation: