The Eagles basketball team played a game against their rivals last night. The team made 28 baskets and scored 65 points. Some baskets were 2-point baskets, and some baskets were 3-point baskets. Let
represent the number of 2-point baskets, and let
represent the number of 3-point baskets.

How many of each type of basket were made in the game?

The area of the given circle is  1.76625 square feet.

Remember that the area of a circle of radius R is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know the diameter (2 times the radius) of the circle, which is 1.5ft, then the radius is:

R = 1.5ft/2 = 0.75ft

Then the area of the circle is:

A = 3.14*(0.75ft)²

A = 1.76625 ft²

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Answer:

Abiola stayed at work for 8 hours and 40 minutes.

Step-by-step explanation:

Abiola wasted 20 minutes waiting for her friend, so she actually left for work at 7:50 am (7:30 am + 20 minutes).

She arrived at work at 8:20 am, so she spent 30 minutes (8:20 am - 7:50 am) traveling to work.

Abiola worked from 8:20 am to 4:00 pm, which is a total of 7 hours and 40 minutes (4:00 pm - 8:20 am).

She then stayed at work for an additional 1 hour to watch African Magic, so in total, she was at work for 8 hours and 40 minutes (7 hours and 40 minutes of work + 1 hour of watching African Magic).

Therefore, Abiola stayed at work for 8 hours and 40 minutes.

The Wigwam Motel in Holbrook, Arizona is famous for its large tepees shaped like cones. the floor space inside each tepee is approximately 153.94 square feet.

(a) To find the slant height of the tepee, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with the height and the radius of the base as the legs.

The radius of the base is half of the diameter, so r = 14/2 = 7 feet. The height of the tepee is 32 feet. Let's call the slant height "s".

Using the Pythagorean theorem, we have:

s² = r² + h²

s² = 7² + 32²

s² = 49 + 1024

s² = 1073

s = sqrt(1073)

s ≈ 32.77 feet

Therefore, the slant height of the tepee is approximately 32.77 feet.

(b) To find the floor space inside the tepee, we need to calculate the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(7)²

A = 49π

A ≈ 153.94 square feet

Therefore, the floor space inside each tepee is approximately 153.94 square feet.

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The values of a, h, and k are 5, -6 and -2, respectively

In the given function:

y = 5/(x+6) - 2

The function is in the form of a rational function, f(x) = a/(x-h) + k, where a = 5, h = -6, and k = -2.

Therefore, the values of a, h, and k are:

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The measure of the angles formed by the lines are 30°, 30°,  150° and  150° by definition of vertically opposite angles.

When two straight lines intersect each other at some angle, say line AB intersect line CD, then the opposite angles formed by the two lines are called vertically opposite angles. A pair of vertically opposite angles are equal to each other.

There are two pairs of opposite angles formed by intersection of two straight lines.

The total sum of all the angles formed by intersection of two straight lines is 360°.

Let angle X = x° and angle Y= y° be a pair of opposite angles.

Let the other pair of opposite angles be of angle M = m° and angle N = n°.

Thus, by definition of opposite angles and sum of all angles on intersection of two lines we get,

angle X + angle Y + angle M + angle N = 360°

⇒ x° + y° + m° + n° = 360°

⇒ x° + x° + m° + m° = 360°

⇒ 2( x° + m°) = 360°

⇒ x° + m° = 180° ___ (1)

Also, the measure of one of the angles is five times the measure of another of the angles formed by the lines.

This relation can be written as,

angle X = 5 times of angle M

⇒ x° = 5m° ___(2)

Since angle X and angle M are not a pair of opposite angles but are supplementary angles as observed in equation (1).

Putting equation (2) in equation (1) we get,

5m° + m° = 180°

⇒ 6m° = 180°

⇒ m° = 30°

Thus, x° = 5(30°) = 150°

Hence the angles are 30°, 30°,  150° and  150°.

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Does this table represent a function: C. No, because one x-value corresponds to two different y-values.

In Mathematics and Geometry, a function can be defined as a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).

Based on the table shown above, we can reasonably infer and logically deduce that it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values);

3  → 4

4 → 4

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Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.

The formulas 2x + 3 and 7, for instance, are identical when written as 2x + 3 = 7, where x has been the variable. The x-value that fulfils the equality can be found by solving this equation. In this instance, we can take 3 out of both sides to get 2x = 4, and thereafter divide each sides by 2 to get x = 2. To describe relationships amongst quantities and to solve issues, equations are used widely in mathematics as well as in chemistry, chemistry, economics, and other sciences. They are also utilised in daily life, such as in financial computations and the solution of time, distance, and speed-related issues.

given

Assume that x biology textbooks were sold in total.

The issue states that there were 72 more physics textbooks sold than there were biology textbooks. Hence, x + 72 is the total number of physics textbooks sold.

It states that 300 textbooks were sold in total. Thus, we can create the following equation:

[tex]x + (x + 72) = 300[/tex]

When we simplify and find x, we obtain:

[tex]2x + 72 = 300\\2x = 300 - 72[/tex]

2x = 228

x = 114

Hence, 114 biology textbooks were sold.

The quantity of sold physics textbooks is given by x + 72, or 114 + 72 = 186.

Hence, 186 physics textbooks and 114 biology textbooks were sold as it states that 300 textbooks were sold in total.

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There are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music

To determine the number of ways the Grandview high school band can manage the order of their performance of six pieces of music, we need to find the number of permutations of six objects taken six at a time.

The following is the formula for the number of permutations of n objects taken r at a time:

P(n, r) = n! / (n - r)!

In this case, we need to find P(6, 6), which is:

P(6, 6) = 6! / (6 - 6)!

= 6! / 0!

= 6 x 5 x 4 x 3 x 2 x 1

= 720

Therefore, there are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music.

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Results from the Simple Interest:

1. The amount Tucker will receive in interest after 5 years = $1,165.50.

2 The simple interest rate Wilson would need to make his $9,000 grow to $85,000 in 16 years =  53%.

3. The number of years it will take for $7,000 to double in an account with 2.8% simple interest = ≈36 years.

4. The ending balance after 6 years = $25,472.

Using Simple interest formula: S.I. = P × R × T

Simple interest (SI) formular = Interest (I) = Principal (P) * Rate (R) * Time(T)

Given:

P= $7,400

R = 3.15% or 0.0315

T = 5 years

Plugging in the values:

Interest = ($7,400 * 0.0315 * 5)

Interest = $1,165.50

2) Using SI  formular: I = P* R * T

Given:

P = $9,000

I = $85,000 - $9,000 = $76,000 (as the total cost is the principal plus interest)

T = 16 years

Plugging in the values:

$76,000 = $9,000 * Rate * 16

R = $76,000 / ($9,000 * 16)

To convert  to percentage, we multiply by 100:

Rate = 0.531 * 100

Rate = 53.1%.

3) Using SI  formular: I = P* R * T

Given:

P = $7,000

R = 2.8%

I = P

T = ?

Plugging in the values and solving for Time (T):

$7,000 = $7,000 * 0.028 * T

T = $7,000 / ($7,000 * 0.028) = 35.7

T  ≈36 years

4. Using SI  formular: I = P* R * T

Given:

P = $20,000

R = 4.56%

T = 6 years

Plugging in the values:

P = $20,000

R = 4.56% or 0.0456

T = 6 years

Ending Balance (EB) = P + (Pl *  R * T)

EB = $20,000 + ($20,000 * 0.0456 * 6)

EB = $20,000 + $5,472

EB = $25,472

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The volume of the sphere with a diameter of 28 millimeters is 4398.23 cubic millimeters.

To find the volume of a sphere with a diameter of 28 millimeters, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.

Step 1: Calculate the radius.

Since the diameter is 28 millimeters, the radius is half of that, which is 14 millimeters (28/2).

Step 2: Use the volume formula.

V = (4/3)πr³

V = (4/3)π(14³)

Step 3: Calculate the volume.

V = (4/3)π(2744)

V ≈ 4398.23 cubic millimeters

So, the volume of the sphere with a diameter of 28 millimeters is approximately 4398.23 cubic millimeters.

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As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.

A function in mathematics is a rule or association that gives each input value a distinct output value. A function, then, is a collection of ordered pairs, each pair consisting of an input value (also known as an argument or predictor variable) and the control signal value (also known as the value or dependent variable). The output value for each given input value can be found using the formula or graph of a function.

Option B provides the justification for why a graph that fails the vertical line test cannot be used to represent a function: One x-value is coupled with numerous y-values on a vertical line.

A vertical line is not a function since a function cannot have one x-value associated with multiple separate y-values.

To ascertain whether a graph accurately depicts a function, use the vertical line test.

Each vertical line that crosses the graph more than once has an x value and several y values, which is against the definition of a function.

As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.

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Answer: True

9/4 = 2 1/4

Step-by-step explanation:

:) See the images below to know more.

Answer:

3.6

Step-by-step explanation:

a^3+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

square root to get c alone

3.6055512754639=c

rounded= 3.6

Answer: 3.6

Step-by-step explanation: pythagorean theorem

A^2 + B^2 = C^2

3^2=9

2^2=4

13

Square root of 13 rounded to nearest 10th

3.6

Raw answer: 3.60555127546

Answer:

The words "per" and "each" are associated with quantity and division. They are used to express the ratio or rate of one thing in relation to another. For example, "The cost is $10 per pound" or "Each student receives one book."

Answer:

The words per and each are associated with Division.

Step-by-step explanation:

Think of the words "percent". We can divide the word into two easier terms, "per" and "cent". Per means for each. Dividing also means for each.

I'm trying my best without an answer key to help me see what you want to be answered, let me know if there is something specific you would like to know. :)

-a friendly 8th grader :D

A greater standard deviation for scores on the first quiz than on the second quiz would state that the results were less consistent on the first quiz than on the second quiz.

The standard deviation of a data-set measures the consistency of the data-set, and the higher the standard deviation, the less consistent the data-set is.

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The total number of ways to climb n stairs is the sum of the number of ways to climb n-1 stairs and the number of ways to climb n-2 stairs.

An equation that represents a sequence based on a rule is called a recurrence relation. Finding the following term (next term) based on the prior term (previous term) is made easier.

The recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time is:

an = an-1 + an-2

This is because to climb n stairs, the person can either take one stair from n-1 stairs and climb the remaining n-1 stairs, or take two stairs from n-2 stairs and climb the remaining n-2 stairs.

Therefore, the total number of ways to climb n stairs is the sum of the number of ways to climb n-1 stairs and the number of ways to climb n-2 stairs.

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The value of cotθ given that cscθ = 8/7 using trigonometric identities is √(15)/7.

To find the value of cotθ given cscθ = 8/7, we can use the relationship between trigonometric functions:

cscθ = 1/sinθ and cotθ = cosθ/sinθ

First, we can find the value of sinθ by using the definition of cscθ:

cscθ = 1/sinθ

8/7 = 1/sinθ

sinθ = 7/8

Next, we can use the value of sinθ to find the value of cosθ using the Pythagorean identity:

sin²θ + cos²θ = 1

cos²θ = 1 - sin²θ

cos²θ = 1 - (7/8)²

cos²θ = 1 - 49/64

cos²θ = 15/64

Taking the square root of both sides, we get:

cosθ = ±√(15)/8

Since cscθ is positive and cotθ is positive, we need to take the positive square root:

cosθ = √(15)/8

Finally, we can use the definition of cotθ to find the value of cotθ:

cotθ = cosθ/sinθ

cotθ = (√(15)/8) / (7/8)

cotθ = √(15)/7

In conclusion, to find the value of cotθ given cscθ, we can use the relationship between trigonometric functions and the Pythagorean identity to find the values of sinθ and cosθ, and then use the definition of cotθ to find its value.

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Yes, since the new additive is more efficient and a proportional difference of 0.4 or more occurred 7 times out of 200, making the difference statistically significant. The correct answer is A) .

The dotplot can be used to determine whether the 0.4 observed proportional difference is statistically significant. Few dots are at or above 0.4 in any direction, as can be seen by looking at the dotplot. In particular, it appears that there are no dots to the left of the observed difference and only roughly 7 dots that are at or beyond 0.4. Therefore, at the 5% level of significance, the observed proportional difference of 0.4 is statistically significant. Hence the correct answer is option: A.

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The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.

Here is a detailed explanation:

a = 1 (coefficient of x²),

b = -7 (co - efficient of x), and

c = 12 are the trinomial's coefficients and constant (constant term).

Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).

The two numbers are -3 and -4.

Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers

Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).

Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).

Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).

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There are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.

When flipping a coin 4 times, there are 2 possible outcomes (heads or tails) for each flip.

Therefore, there are a total of 2^4 = 16 possible outcomes for 4 coin flips.

To find the number of favorable outcomes for getting two heads and two tails (in any order), we can use combinations.

We need to choose 2 coin flips out of 4 to be heads, which can be done in C(4,2) = 6 ways.

Once we have chosen the positions for the heads, the remaining positions must be tails.

So there are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.

These outcomes are:

HH-TT

HT-HT

TH-HT

TT-HH

HT-TH

TH-HT

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The total amount of money she would have at the end of her shift would be 0.75x + 10

If the barista makes an average of $0.75 from each customer and she has $10 in her tip jar at noon, we can use this information to estimate how much money she will have at the end of her shift if she serves more customers.

Let's assume that the barista serves "x" more customers during her shift, and that each customer gives her an average of $0.75 in tips. The total amount of money she would make from the tips of these "x" customers would be 0.75x.

Adding the $10 she already has in her tip jar, the total amount of money she would have at the end of her shift would be:

Total = 0.75x + 10

The amount of money the barista would have at the end of her shift would depend on the number of customers she serves after noon. For instance, if she serves 20 more customers after noon, then the total amount of money she would have at the end of her shift would be:

Total = 0.75(20) + 10 = $25

Therefore, the amount of money the barista would have in her tip jar at the end of her shift depends on the number of customers she serves and the amount of money each customer gives her in tips.

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To calculate a derivative using implicit differentiation, follow these steps:
1. Write down the equation:

2. Differentiate both sides with respect to x:

3. Solve for dy/dx or y':

4. Simplify the result:

Write down the equation:

Start by writing down the equation involving both variables x and y, where y is an implicit function of x.
Differentiate both sides with respect to x: Apply the chain rule, product rule, or quotient rule, as needed, while differentiating both sides of the equation with respect to x.

Remember that when differentiating any term involving y, you'll also need to multiply by the derivative of y with respect to x, denoted as dy/dx or y'.
Solve for dy/dx or y': After differentiating both sides, you will have an equation involving dy/dx or y'.

Solve for this term to find the derivative.
Simplify the result: Simplify your answer as much as possible, if needed.
Remember to use implicit differentiation when the equation is not easily solved for y in terms of x.

It's a powerful technique that helps find derivatives in situations where explicit differentiation isn't feasible.

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Answer:

Set your calculator to degree mode.

[tex] \tan( \beta ) = \frac{7}{12} [/tex]

[tex] \beta = {tan}^{ - 1} \frac{7}{12} = 30.26 \: degrees[/tex]

Answer:

Step-by-step explanation:

$10,008.61

Answer:

We can use the following formula for the cosine of the sum of two angles:

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

To use this formula, we need to find the values of cos(α), sin(α), cos(β), and sin(β).

Since tan(α) = 4/3 and α is in the first quadrant, we can use the Pythagorean identity to find sin(α) and cos(α):

tan^2(α) + 1 = sec^2(α)

(4/3)^2 + 1 = sec^2(α)

16/9 + 1 = sec^2(α)

25/9 = sec^2(α)

sec(α) = 3/5

cos(α) = 1/sec(α) = 5/3

sin(α) = tan(α) * cos(α) = (4/3) * (5/3) = 20/9

Since cos(β) = -4/5 and β is in the third quadrant, we can use the Pythagorean identity again to find sin(β):

sin^2(β) + cos^2(β) = 1

sin^2(β) = 1 - cos^2(β)

sin(β) = -√(1 - cos^2(β)) (since sin(β) is negative in Q3)

sin(β) = -√(1 - (-4/5)^2) = -√(1 - 16/25) = -√(9/25) = -3/5

Now we can substitute these values into the formula for cos(α+β):

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

cos(α + β) = (5/3) * (-4/5) - (20/9) * (-3/5)

cos(α + β) = -4/3 + 4/3

cos(α + β) = 0

Therefore, cos(α+β) = 0.

If "cow" means that number is correct in value but in the wrong position, then the three-digit secret number is 714.

A "cow" means a digit is "correct in value" but in the "wrong position".

A "bull" means a digit is both "correct in value" and in the "correct position".

⇒ For the first guess (751),

There is 1 cow and 1 bull, which means that one digit is "correct in value" and in the "correct position" (1 bull), and another digit is "correct in value" but in the "wrong position" (1 cow).

⇒ For the second-guess (574),

There is 1 cow and 1 bull, which indicates that "one-digit" is "correct in value" and in the "correct position", and "another-digit" is "correct in value" but in the "wrong-position".

⇒ For the third guess (317),

There is 1 cow and 1 bull, which means that "one digit" is "correct in value" and in the "correct position", and "another digit" is "correct in value" but in the "wrong position".

So, Based on these clues, we can say that the correct secret number has 1 cow and 1 bull.

This means that two digits in the secret number are correct in value, with one digit in the correct position (1 bull), and another digit in the wrong position (1 cow). So, the secret number is likely 714, because it satisfies these conditions.

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The given question is incomplete, the complete question is

Deduce the 3-digit secret number.

[A cow means a number is correct in value but in the wrong position. A bull indicates that a number is both correct in value and in the correct position. i.e. 2 cows and 1 bull would indicate that all three numbers were correct but two were in the wrong positions. ]

Guess     Secret Number   Cows    Bulls

 1st                   751                  1            1

 2nd                 574                 1            1

 3rd                  317                  1            1

The value of ZC is 16 units for the given circle and its identities.

A straight line that touches the circle at a single point—the point of tangency—is the tangent of a circle. The digression is opposite to the span of the circle at the place of juncture, and it broadens outward from the circle in the two bearings.

In the circle two external secant segments are LE and ZE, according to the external secant theorem;

⇒ LE × DE =  ZE × CE               (Here, ZE = ZC + 2)

⇒ 9 × 4      =  (ZC + 2) × 2

⇒ ZC + 2 = 18

⇒ ZC = 18 - 2

⇒ ZC = 16

Therefore, the value of ZC is 16 units.

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The requreid Miriam's test does not provide significant evidence that the true population mean is less than 18.

Since the sample size is small (n = 7) and the population standard deviation is unknown, we should use a t-test for this hypothesis test.

The test statistic is calculated as follows:

t = (x - μ) / (s / √n)

Given that Miriam's test statistic is t = -1.9, we can estimate the p-value associated with this test statistic. This denotes the probability of observing a test statistic as extreme as -1.9 or more extreme, assuming the null hypothesis is true.

Using a t-distribution table with 6 degrees of freedom (n-1), we find that the p-value for a one-tailed test at the 5% significance level is approximately 0.051.

Since the p-value (0.051) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have sufficient evidence to conclude that the population mean is less than 18 at a 5% level of significance.

Thus, Miriam's test does not provide significant evidence that the true population mean is less than 18.

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In normal distribution the area above 66 for a n(60, 10) is 0.726

What is normal distribution?

In probability theory and statistics, the Normal Distribution, which is also called the Gaussian Distribution, is the most significant continuous probability distribution.  It is also called a bell curve. In this distribution a large number of random variables are either nearly or exactly represented. Moreover, it can be used to approximate other probability distributions,

From the given data n(60, 10) so mean = 60 and standard deviation= 10

Now x≥ 66

so the z-score will be (66-60)/10

                                   = 6/10

                                   = 0.6

Now P(z>0.6)= 1- P(z< 0.6)

                     = 0.726

So, in normal distribution the area above 66 for a n(60, 10) is 0.726.

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