A basketball player scored 12, 25, 16, and 13 points in her last four games. What is the mean number of points per game she scored during this period

To generate the image we need to perform a rotation. To perform a rotation every point on the function or figure must mantain the same distance of the center of rotation and move in a circle around it. We can see that the operation used was a rotation, because we can trace a circle between each point from the function to the image around the origin. The angle of rotation was 180 degrees.

One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.

The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.

To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.

To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.

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The equivalenet expression is 54\(n^{-11}\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

(\(6n^-5\))(\(3n^-3\))²

We can simplify as follows:

(\(6n^-5\))(\(9n^-6\))

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

\(n^-5 * n^-6 = n^-11\)

So the simplified expression is:

\(54n^-11\)

Therefore, the expression \((6n^-5)(3n^-3)^2\) is equivalent to \(54n^-11.\)

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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2 numbers are possible, 64 and 96.

Therefore, option (c) is correct.

We can solve this question using trial and error method.

Given, an integer n's length is the number of prime factors whose product is equal to n.

Since we have to find a two-digit positive integer whose length is 6:

Let us take 2 as our first prime factor (as 2 is a prime number)

2*2*2*2*2*2 = 64.

Here, we have got 1 number with length 6.

Let us take 3 as our 2nd prime factor (as 3 is a prime number).

3*3*3*3*3*3 = 96.

Here, we have got 2 numbers with length 6.

Now, let us try:

2*2*2*2*2*3 = 144

Since we need only 2 digit numbers, this is not possible.

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Answer: 0.628

Step-by-step explanation:

Probability of U.S. smartphone owners have made an effort to limit their phone use in the past : p = 0.4702

Sample size : n= 54

Mean : \(\mu =(54)(0.4702)=25.39\)

Standard deviation:

\(\sigma=\sqrt{(54)(0.4702)}=\sqrt{25.39}\\\\\approx5.039\)

The probability that between 22 and 29 (inclusively) will have attempted to limit their cell phone use in the past will be :

\(P(22\leq x\leq29)=P(21<x<30)=P(\dfrac{21-25.39}{5.039}<\dfrac{X-\mu}{\sigma}<\dfrac{30-25.39}{5.039})\\\\=P(-0.8712<z<0.914864)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(z<0.914864)-P(z<-0.8712)\\\\=P(z<0.914864)-(1-P(z<0.8712))\\\\=0.8198685-(1-0.8081775)\ \ \ [\text{ By p-value table}]\\\\=0.628046\)

Hence, the required probability = 0.628

The sum of the terms is x^7+10x^4+4x^3-5x^11-10x^6

To determine the value, we need to know that algebraic expressions are described as expressions that are composed of factors, constants, variables, terms and coefficients.

These algebraic expressions are also identified with the presence of arithmetic operations,

These operations are;

From the information given, we have that;

7x^7+10x^4+4x^3-5x^11-10x^6-6x^7

collect the like terms

7x^7 - 6x^7+10x^4+4x^3-5x^11-10x^6

add the like terms

x^7+10x^4+4x^3-5x^11-10x^6

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Answer:

60

Step-by-step explanation:

50 - 7×6 / 3 + (4×6)

50 - 14 + 24 = 60

Answer:

650,000,000

Step-by-step explanation:

6.5x10^8

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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To find the slope between two coordinates, you use the formula:

m = y2 - y1/x2 - x1

If coordinate A is (-2, 5) and coordinate B is (3, -4), then:

y2 = -4

y1 = 5

x2 = 3

x1 = -2

So, just substitute the points into the formula.

m = -4 - 5/3 - (-2)

m = -9/5

The slope of the line is -9/5.

Answer:

C = 20 + 0.001x

C = $20 + $0.001x

Step-by-step explanation:

Let x represent the number of minutes spent talking on the phone.

Given;

Fixed monthly charge F = $20

Charge per 10 minutes V = $0.01

Charge per minute = V/10 = $0.01/10 = $0.001

The equation to model the cost of a monthly cell phone bill;

Total cost = fixed cost + variable cost

C = F + (V/10)x

Substituting the values;

C = 20 + 0.001x

Answer: 8000

Step-by-step explanation:

The 8 in the number 348,000 is in the thousands place.

So it represents the value of 8,000 .

Answer:

\(x = -10 + 4 \sqrt7 \ , \ x = -10 - 4 \sqrt7\)

Step-by-step explanation:

x²+20x-12=0

a = 1, b = 20, c = -12

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2x}\)

\(x = \frac{-20 \pm \sqrt{448}}{2}\\\\x = \frac{-20 \pm \sqrt{8 \times 8 \times 7}}{2}\\\\x = \frac{-20 + 8\sqrt{7}}{2} \ , \ x = \frac{-20 - 8 \sqrt7}{2}\\\\x = \frac{-10 + 4\sqrt{7}}{1} \ , \ x = \frac{-10 - 4 \sqrt7}{1}\\\\x = -10 + 4 \sqrt7 \ , \ x = -10 - 4 \sqrt7\)

The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.

To determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.

Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):

Number of half-lives = (Total time elapsed) / (Half-life)

Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545

Since we can't have a fraction of a half-life, we take the integer part, which is 5.

Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:

Remaining amount = Initial amount * (1/2)^(Number of half-lives)

Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:

Remaining amount = 1000 grams * \((1/2)^5\)

Remaining amount ≈ 1000 grams * 0.03125

Remaining amount ≈ 31.25 grams

Therefore, after 2 hours, approximately 31.25 grams of francium will be left.

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We have the following arithmetic sequence:

Now, the general n-term of this sequence can be written in the following way:

where n takes the following values:

We see that this general term reproduces the sequence about:

We can find the 13th term of sequence simply replacing n by 13 in the general formula above, we get:

Answer

The 13th term of the sequence is:

Answer:

2*2h4g15

Step-by-step explanation:

count how many "g"s there are and same with "h"

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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Based on the plot, the number of practice puzzles per week that members solve if they finish the contest puzzle

in one hour is c 4

The line of best fit for the scatter plot shows that there is a positive correlation between the number of practice puzzles solved per week and the time it takes to solve a contest puzzle. This means that as the number of practice puzzles solved per week increases, the time it takes to solve a contest puzzle decreases.

If a member finishes a contest puzzle in one hour, they are on the line of best fit. This means that they solve approximately 4 practice puzzles per week.

The other options are incorrect. Option a is too high, option b is too low, and option d is not on the line of best fit.

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Answer: 26 pounds

Step-by-step explanation:

Let +a+ = pounds of coffee A used

Let +b+ = pounds of coffee B used

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

(1) +4.1a+%2B+5.8b+=+709.8+

(2) +b+=+4a+

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

(1) +41a+%2B+58b+=+7098+

Substitute (2) into (1)

(1) +41a+%2B+58%2A4a+=+7098+

(1) +41a+%2B+232a+=+7098+

(1) +273a+=+7098+

(1) +a+=+26+

26 pounds of coffee A were used

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

check:

(2) +b+=+4a+

(2) +b+=+4%2A26+

(2) +b+=+104+

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

(1) +41a+%2B+58b+=+7098+

(1) +41%2A26+%2B+58%2A104+=+7098+

(1) +1066+%2B+6032+=+7098+

(1) +7098+=+7098+

Answer:

the answer is 2

Step-by-step explanation:

Answer: length = 4.5 m, width = 3 m

Step-by-step explanation:

When a shape is enlarged using a scale factor, you simply multiply each of the sides by the scale factor.

length = 3 * 1.5 = 4.5 m

width = 2 * 1.5 = 3 m

Answer:

12180

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

Is the 3 to 2 part to part?  Out of every 5 people, 3 prefer pizza and 2 do not.  We can us this to set up a proportion.

3/5 = 120/x  The 3 represent the part that like pizza over the whole of 5.  The second ratio is showing the actual number of people that liked pizza over the total number of people.

What would be multiply 3 by to get 120? 40.  So, we will multiply 5 times 40 to get the total number of people.  5 x 40 = 200

The 95% confidence interval for the true percent of car owners in this city who received a speeding ticket this year is 44.63% to 49.37%

The formula for calculating the confidence interval is expressed as:

CI = p±z√p(1-p)/n

Given the following parameters

n = 1700

p = 799/1700

p = 0.47

z-score at 95% interval = 1.96

Substitute the given values

CI = 0.47 ±1.96√0.47(1-0.47)/1700

CI =0.47 ±1.96(0.0121)

CI = 0.47±0.0237

CI = 0.47+0.0237, 0.47-0.0237

CI = (0.4463, 0.4937)

Hence the 95% confidence interval for the true percent of car owners in this city who received a speeding ticket this year is 44.63% to 49.37%

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Answer:

1 ticket =$36

Step-by-step explanation:

216÷6= $36

Answer:

36

Step-by-step explanation:

Divide 216 by 6 to get the total amount per ticket

The length in each circle is:

(a) CD = 19.5 units

(b) UZ = 12.8 units

(a) The Intersecting Secant-Tangent Theorem states that "if two secant lines intersect outside a circle, and a tangent line is drawn from the point of intersection to the circle, then the product of the lengths of the two secant segments is equal to the square of the length of the tangent segment".

Using the theorem, we have:

EC * ED = EG²

6.5 * ED = 13²

6.5ED = 169

ED = 169/6.5

ED = 26 units

ED = EC + CD

26 = 6.5 + CD

CD = 26 - 6.5

CD = 19.5 units

(b) The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

UZ * UW = UX * UY

UZ * 40 = 8 * 64

40UZ = 512

UZ = 512/40

UZ = 12.8 units

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Since the ratio is given by:

The error that Katerina made awas that she did x/y, then to complete the table: