Triangle ABC is given where m(angle)A=33 degrees, a=15 in., and the height, h, is 9 in. How many distinct triangles can be made with the given measurements? Explain your answer.

Please do give the correct answer by showing your work, other ways I will report you!

Sally uses 3 1/2 cups of flour for each batch, therefore, the total amount of flour needed to make four batches of cookies is 28 cups.

To multiply a mixed number by a whole number, we first need to convert the mixed number to an improper fraction. In this case, the mixed number is 3 1/2, which can be written as the improper fraction 7/2. To do this, we multiply the whole number (3) by the denominator (2) and add the numerator (1) to get 7. Then, we write the result (7) over the denominator (2) to get 7/2.

Next, we multiply the improper fraction (7/2) by the whole number (4) to get the total amount of flour needed for four batches of cookies. To do this, we multiply the numerator (7) by 4 to get 28, and leave the denominator (2) unchanged. Therefore, the total amount of flour needed to make four batches of cookies is 28 cups.

To make four batches of cookies, Sally needs 28 cups of flour. To calculate this, we converted the mixed number of 3 1/2 cups of flour to an improper fraction of 7/2 and then multiplied it by four.

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The problem of multicollinearity. Multicollinearity refers to a situation in which two or more independent variables in a multiple linear regression model are highly correlated with each other.

This can lead to problems in estimating the regression coefficients accurately and can also result in unstable and inconsistent estimates of the coefficients. Multicollinearity can also make it difficult to determine the individual effects of the independent variables on the dependent variable, as well as to detect which variables are significant predictors.

Multicollinearity can also have a negative impact on the validity of hypothesis tests and can lead to over-fitting of the model. When the independent variables are highly correlated with each other, the regression coefficients are less precise and can have large standard errors, making it difficult to determine their significance.

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Multicollinearity occurs when two or more independent variables are highly correlated, meaning that one can be easily predicted from the other. This can lead to an unreliable model as it can produce inaccurate results.

Multicollinearity occurs when two or more independent variables in a multiple linear regression model are highly correlated, meaning that one can be easily predicted from the other.

If an independent variable is an exact linear combination of other independent variables, then the model is suffering from multicollinearity, which can cause the coefficients to be unstable and have large standard errors.

To address this issue, researchers can use techniques such as principal component analysis or ridge regression to reduce the correlation between the independent variables. These techniques can help improve the accuracy and reliability of the model.

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Answer:

per teacher = 20 students

per tutor = 12 students

72 students = 18 tutors

Step-by-step explanation:

Divide 60 by 3 to get 20

Divide 48 by 4 to get 12

Divide 72 by 4 to get 18

To find the direction cosines and direction angles of the vector (7, 2, -3), we need to first calculate the magnitude of the vector. The direction cosines of the vector (7, 2, -3) are (7/√(62), 2/√(62), -3/√(62)) and the direction angles, correct to the nearest degree, are α ≈ 26°, β ≈ 15°, and γ ≈ 109°.

Next, we need to find the direction cosines of the vector. Direction cosines are the cosines of the angles between the vector and the x, y, and z axes. The direction cosines are given by the components of the vector divided by its magnitude.

The direction cosine of the x-axis is given by 7/√(62), the direction cosine of the y-axis is 2/√(62), and the direction cosine of the z-axis is -3/√(62). The magnitude of the vector is given by the square root of the sum of squares of its components. In this case, the magnitude is √(7² + 2² + (-3)²) = √(62).

Thus, cos(α) = 7/√(62), cos(β) = 2/√(62), and cos(γ) = -3/√(62). To find the direction angles, we need to take the inverse cosine of each direction cosine. This will give us the angle between the vector and each axis.

\(α = cos⁻¹(7/√(62)) ≈ 26°, β = cos⁻¹(2/√(62)) ≈ 15°,\) and\(γ = cos⁻¹(-3/√(62)) ≈ 109°.\) Therefore, the direction cosines of the vector (7, 2, -3) are (7/√(62), 2/√(62), -3/√(62)) and the direction angles, correct to the nearest degree, are α ≈ 26°, β ≈ 15°, and γ ≈ 109°.

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To determine the coordinate of point P after the described rotations, let's go step by step.

First, the point P(3, 5) is rotated 180 degrees clockwise about the point A(3, 2). To perform this rotation, we need to find the vector between the center of rotation (A) and the point being rotated (P). We can then apply the rotation matrix to obtain the new position.

Let \(\vec{AP}\) be the vector from A to P. We can calculate it as follows:

\(\vec{AP} = \begin{bmatrix} 3 \\ 5 \end{bmatrix} - \begin{bmatrix} 3 \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 3 \end{bmatrix}\).

Now, we can apply the rotation matrix for a 180-degree clockwise rotation:

\(\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}\),

where \(\theta\) is the angle of rotation in radians. Since we want to rotate 180 degrees, we have \(\theta = \pi\).

Applying the rotation matrix, we get:

\(\begin{bmatrix} x' \\ y' \end{bmatrix} = \begin{bmatrix} \cos(\pi) & -\sin(\pi) \\ \sin(\pi) & \cos(\pi) \end{bmatrix} \begin{bmatrix} 0 \\ 3 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} 0 \\ 3 \end{bmatrix} = \begin{bmatrix} 0 \\ -3 \end{bmatrix}\).

The new position of P after the first rotation is P'(0, -3).

Next, we need to rotate P' (0, -3) 90 degrees counterclockwise about the point B(1, 1).

Again, we calculate the vector from B to P', denoted as \(\vec{BP'}\):

\(\vec{BP'} = \begin{bmatrix} 0 \\ -3 \end{bmatrix} - \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} -1 \\ -4 \end{bmatrix}\).

Using the rotation matrix, we rotate \(\vec{BP'}\) by 90 degrees counterclockwise:

\(\begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix} \begin{bmatrix} x' \\ y' \end{bmatrix}\),

where \(\theta\) is the angle of rotation in radians. Since we want to rotate 90 degrees counterclockwise, we have \(\theta = \frac{\pi}{2}\).

Using the rotation matrix, we get:

\(\begin{bmatrix} x'' \\ y'' \end{bmatrix} = \begin{bmatrix} \cos \left(\frac{\pi}{2}\right) & -\sin\left(\frac{\pi}{2}\right) \\ \sin\left(\frac{\pi}{2}\right) & \cos\left(\frac{\pi}{2}\right) \end{bmatrix} \begin{bmatrix} -1 \\ -4 \end{bmatrix} = \begin{bmatrix} 0 & -1 \\ 1 & 0\end{bmatrix} \begin{bmatrix} -1 \\ -4 \end{bmatrix} = \begin{bmatrix} 4 \\ -1 \end{bmatrix}\).

The final position of P after both rotations is P''(4, -1).

Therefore, the coordinate of point P after the rotations is (4, -1).

Answer:

d

Step-by-step explanation:

1 = 1 cup

1/2 can be 2/4

2/4+1/4=3/4

1+3/4 = 1 3/4

Answer:

2 millimeters.

Step-by-step explanation:

1 millimeter : 6 meters

x millimeters : 12 meters

x = (12÷6) × 1

x = 2×1

x = 2 millimeters

Answer:

30

Step-by-step explanation:

Hi I am so not helpful do not use this answer

The best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Mrs. Brown's yard has three ant hills, each with a different number of ants. To estimate the total number of ants in the yard, we simply add up the number of ants in each hill.

The first hill has 4,867,190 ants, the second has 6,256,304, and the third has 3,993,102. When we add these numbers together, we get a total of 15,116,596 ants in Mrs. Brown's yard. Of course, this is just an estimate, as there may be other ant hills or individual ants scattered around the yard.

However, this calculation gives us a good approximation of the number of ants in the yard based on the information given.

To estimate the total number of ants in Mrs. Brown's yard, we can add up the number of ants in each of the three ant hills:4,867,190 + 6,256,304 + 3,993,102 = 15,116,596.

Therefore, the best estimate of the number of ants in Mrs. Brown's yard is 15,116,596.

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Step-by-step explanation:

remember, i = sqrt(-1)

let's go left to right :

(3i)(5i) = 3×sqrt(-1)×5×sqrt(-1) = 3×5×sqrt²(-1) = 15×-1 = -15

-15×(6+5i) = -90 - 75i

Answer:

x = 40

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc , then

x = \(\frac{1}{2}\) × 80 = 40

Answer:

1. NP

2. P

3. P

4. NP

Step-by-step explanation:

if this helped, Mark as brainliest, thank you

Answer:

Not polynomial for the first one.

second is polynomial.

third is polynomial.

and fourth is not polynomial.

Step-by-step explanation:

oh wait- yeah the other person is right too LOL

The simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

The square root of any number is equal to a number, which when squared gives the original number. Let us say n is a positive integer, such that  \(\sqrt{n.n}=\sqrt{(n)}^2=n\)

Given that, the two numbers,

3 square root of 5= \(3\sqrt{5 }\)

2 square root of 2 = \(2\sqrt{2}\)

Sum of these two numbers = \(3\sqrt{5}+2\sqrt{2}\)

We cannot simplify this term further.

The simplest form by adding two numbers is \(3\sqrt{5}+2\sqrt{2}\)

As it is clear, it is a irrational number.

Because, \(\sqrt{2}\) and \(\sqrt{5}\) is a irrational number.

Hence, the simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

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\(\large\text{Hey there!}\)

\(\mathsf{5x - 2y}\\\mathsf{= 5(2) - 2(-1)}\\\mathsf{= 5(2) - (-2)}\\\mathsf{= 5(2) + 2}\\\mathsf{= 10 + 2}\\\mathsf{= 12}\\\\\\\large\text{Therefore, your answer is: \huge\boxed{\mathsf{12}}}\huge\checkmark\)

\(\large\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answers:

664/83 = 8

640/80 = 8

510/30 = 17

600/30 = 20

7,704/24 = 321

8,000/20 = 400

Hope this helps!

Answer:

C) 0.179

Step-by-step explanation:

Since the trials are independent, this is a binomial distribution:

Recall:

Given:

Calculate:

Therefore, the probability that the archer will get exactly 4 bull's-eyes with 10 arrows in any order is 0.179

Thomas' annual rate of return after fees was 7.87%. Thomas' annual rate of return after fees can be calculated using the below-given formula.

Annual Rate of Return = (1 + Average Annual Rate of Return) x (1 - Expense Ratio) - 1
Plugging in the values given in the question, we get:
Annual Rate of Return = (1 + 0.084) x (1 - 0.005) - 1
Annual Rate of Return = 0.0787 or 7.87%

Therefore, Thomas' annual rate of return after fees was 7.87%. It is important to consider expenses like the expense ratio when calculating investment returns as they can significantly affect the overall performance of the investment. In this case, the 0.5% expense ratio reduced Thomas' annual rate of return from the fund's average of 8.4% to 7.87%. It is important to keep in mind the impact of fees and expenses when choosing an investment as they can eat into returns over time and affect the overall success of the investment.

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Answer:

45

Step-by-step explanation:

Total mini chocolates in a bowl= 85

ration of kit kats to hersheys bars = 8:7

ration of kit = 8

Total ratio= 15

Number of kit kats= ratio of kit Kat/ total ratio × total number of mini chocolates

Number of kit Kat = 8/15 × 85= 45

Hence, there are 45 kit kats present there.

Answer:

There were about 45 kit kats.

Step-by-step explanation:

With the information provided, you know that the the ratio of kit kats to hersheys bars is 8:7 and that there are 85 mini chocolates in a bowl, so to be  able to find the number of kit kats there first you can say that you have 15 units because if you add the numbers on the ratio 8+7=15. Then, you divide the total amount of mini chocolates by the units to find the number of chocolates in each unit:

85/15=5.66

Now, you can multiply the ratio of hersheys bars which is 7 for the number of chocolates per unit to find the amount of hersheys bars:

7*5.66=40

Finally, you can multiply the ratio of kit kats which is 8 for the number of chocolates per unit to find the amount of kit kats:

8*5.66=45

According to this, the answer is that there were about 45 kit kats.

Answer:

Centre is (4,2) and radius is 10

Step-by-step explanation:

The circle equation is of form,

=> (x - a)² + (y - b)² = r²

where the centre is (a,b) and radius is 'r'.

In the given problem, we are asked to use implicit differentiation to find the value of dy/dx at the point (2,-3), where y is defined implicitly by the equation 5x³ + 4y³ = -68.

To find dy/dx using implicit differentiation, we differentiate both sides of the equation with respect to x, treating y as a function of x. We apply the chain rule to differentiate the terms involving y, and the derivative of y with respect to x is denoted as dy/dx.

Differentiating the equation 5x³ + 4y³ = -68 with respect to x, we get:

15x² + 12y²(dy/dx) = 0

Now, we can substitute the given point (2,-3) into the equation to evaluate dy/dx. Plugging in x = 2 and y = -3, we have:

15(2)² + 12(-3)²(dy/dx) = 0

Simplifying the equation, we can solve for dy/dx, which gives us the exact value of the derivative at the point (2,-3).

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Assuming an annual appreciation rate of 5.4 percent, collection of 47 1952 silver dollars, purchased at face value, will be worth approximately $148.51 when you retire in 2057.

To calculate the future value of your collection, we can use the formula for compound interest: FV = PV * (1 + r)ⁿ, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. In this case, the present value is the face value of the silver dollars, which is equal to 47 * $1 = $47.

To find the future value in 2057, we need to calculate the number of years from the present to 2057, which is 2057 - current year. Assuming the current year is 2023, the number of years is 2057 - 2023 = 34.

Plugging in the values, we have

FV = $\(47 * (1 + 0.054)^{34\) = $\(47 * (1.054)^{34\) ≈ $148.51.

Therefore, your collection of 47 1952 silver dollars will be worth approximately $148.51 when you retire in 2057, assuming they appreciate at an annual rate of 5.4 percent.

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Answer:

-11°F

Step-by-step explanation:

The temperature was -4° in the morning. The temperature dropped 7° later.

Subtract 7 from -4.

\(-4-7=\boxed{-11}\)

The temperature should be -11°F.

Hope this helps.

The temperature was -4°F this morning. If the temperature dropped 7°F then the temperature now should be -11° fahrenheit.

We have got an equation that can relate these three units of measurement of temperature, as given below:

\(\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}\)

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in Fahrenheit, and also K represents the measurement of equally intense temperature in kelvin.

Given that the temperature was -4° in the morning. And the temperature dropped 7° later.

We have to Subtract 7 from -4.

-4 - 7 = 11

Thus, The temperature now should be -11°F.

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Answer:

64

Step-by-step explanation:

She drinks 4 ounces every 30 minutes.

4*2= 8 She drinks 8 ounces in an hour.

8*8=64 She drinks 64 ounces in 8 hours

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

2-5f ≤ 52, so -5f ≤ 50

f≥-10, because we flip the sign when multiplying or dividing by a neg number for inequalities.

Draw a closed circle on -10 and in the direction all the way towards the right arrow.

The number is 11 and the equation is 4M - 23 = 21 where M is the number.

It is a mathematical statement that shows that two mathematical expressions are equal.

Example:

3x – 5 = 16

We have,

Let the number be M.

Twenty-three less than 4 times a number is 21.

Times = multiplication

less than = subtraction

We can write this as:

4M - 23 = 21

4M = 21 + 23

4M = 44

M = 44/4 = 11

Thus the number is 11 and the equation is 4M - 23 = 21 where M is the number.

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Answer:

A and C.

Step-by-step explanation:

A. 4/18 = 6/27     2/9 = 2/9 (Correct)

B. 4/6 = 16/36     2/3 = 4/9 (Unequal)

C. 3/4 = 9/12     3/4 = 3/4 (Correct)

D. 5/9 = 8/12     5/9 = 2/3 (Unequal)

The solution to the given system is (3,8).

Step-by-step explanation:

To draw a graph system for a linear equation,

Step 1: Consider two x values and draw a line joining the new points.

y = x + 5  ⇒1

y = 2x + 2  ⇒2

For both equations substitute two random values for x.

Let us Consider x=0 and x=10.

For equation 1,

y=x+5.                           y=x+5

y=0+5.                           y=10+5

y=5                                y=15

The new points for equation 1 are (0,5) and (10,15).

Draw a big straight line passing through these two points.

For equation 2,

y=2x+2.                         y=2x+2

y=0+2.                           y=20+2

y=2                                y=22.

The new points for equation 1 are (0,2) and (10,22).

Again, draw a big straight line passing through these two points.

Step 2: Mark the intercepting point and that will be the solution for the given system.

For this system, the solution is (3,8).

To check this answer equates both equations,

x+5=2x+2.

2x-x=5-2.

x=3.

Substitute the x value in any of the equations,

y=3+5.

y=8.

The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

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