What is the slope of the line that contains the points (-3,-5/2), and (3, -8)?

Answer:

angle-side-angle. that's my answer

The graphs of y = 2cos(x) - 1 and y = 2sin(x + π/2) - 1 are both sinusoidal curves, which means they oscillate up and down periodically.

A sinusoidal curve is a type of curve that represents the behavior of a sinusoidal function. The sine function is periodic and oscillates between a maximum value and a minimum value as the input variable (usually x) changes.

The graphs of y = 2cos(x) - 1 and y = 2sin(x + π/2) - 1 are both sinusoidal curves, which means they oscillate up and down periodically.

Similarities:

1) Both curves have the same amplitude of 2, which means they oscillate between y = 1 and y = -3.

2) Both curves have the same vertical shift of -1, which means the lowest point of each curve is at y = -3 and the highest point is at y = 1.

3) Both curves have the same period of 2π, which means they repeat themselves every 2π units along the x-axis.

4) Both curves have the same frequency of one cycle per 2π units along the x-axis.

Differences:

1) The curve y = 2cos(x) - 1 is a cosine curve, which means it starts at its highest point and moves downwards. The curve y = 2sin(x + π/2) - 1 is a sine curve, which means it starts at its middle point and moves upwards.

2) The curve y = 2cos(x) - 1 reaches its highest point at x = 0 and its lowest point at x = π, while the curve y = 2sin(x + π/2) - 1 reaches its middle point at x = 0 and its highest and lowest points at x = π/2 and x = 3π/2, respectively.

3) The curve y = 2cos(x) - 1 is an even function, which means it is symmetric about the y-axis, while the curve y = 2sin(x + π/2) - 1 is an odd function, which means it is symmetric about the origin.

In summary, both curves have the same amplitude, vertical shift, period, and frequency, but they have different shapes and symmetry properties due to the use of cosine and sine functions.

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a.The radius of the hot tub is 4 feet. b. The amount of water that the hot tub can hold is 176.96 cubic feet c. The amount of water that Rita should put in the hot tub in order to follow the recommendation is 141.57 cubic feet.

a. Find the radius of the hot tub.

Given: Circumference = 25.12 feet

Formula: Circumference = 2 * pi * radius

1: Plug in the given circumference and the value of pi.

25.12 = 2 * 3.14 * radius

2: Solve for the radius.

radius = 25.12 / (2 * 3.14)

radius ≈ 4 feet

So, the hot tub's radius is 4 feet.

b. How much water can the hot tub hold?

Given: Radius = 4 feet, Depth = 3.5 feet

Formula: Volume = pi * radius^2 * depth

1: Plug in the radius, depth, and the value of pi.

Volume = 3.14 * (4^2) * 3.5

2: Calculate the volume.

Volume ≈ 176.96 cubic feet

So, the hot tub can approximately hold 176.96 cubic feet.

c. How much water should Rita put in the hot tub to follow the recommendation?

Given: Recommended capacity = 80% of full capacity

Formula: Recommended water = 0.8 * full capacity

1: Plug in the full capacity (volume) calculated in part b.

Recommended water = 0.8 * 176.96

2: Calculate the recommended water amount.

Recommended water ≈ 141.57 cubic feet

So, Rita should put approximately 141.57 cubic feet of water in the hot tub to follow the recommendation.

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Answer:

m= r-n/2

Step-by-step explanation:

2m+n=r

2m=r-n

m=r-n/2

Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

The mean of the data set is   427.5

We know that the mean of the data set as computed is obtained from; 345+340+400+625/ 4=  427.5

To obtain the variance of the data.

We now have to take the difference of the values and square it.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Thus;

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

The variance is 13556.2

For  the Standard deviation (S.D) of the data;

σ = √13556.25

σ =116.43

The Standard deviation of the data is 116.4

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Answer:

Super Fast Food typically has less wait time, because it has a smaller median. The median wait time for Super Fast Food is 12 minutes, which is smaller than the median wait time for Fast Chicken, which is 12.5 minutes. The median is the value that separates the top 50% and the bottom 50% of the data, so a smaller median suggests that the wait times are generally shorter. The mean is not given for either drive-thru, so it cannot be used to make a comparison.

You've completed the Gram-Schmidt process for QR factorization and filled in the third column of matrices Q and R: R(1,3) = a3 · q1, R(2,3) = a3 · q2, R(3,3) = a3 · q3

Given that you already have the first two orthonormal vectors q1 and q2, let's proceed with determining q3 and completing the third column of matrices Q and R.

Step 1: Calculate the projection of the original third column vector, a3, onto q1 and q2.
proj_q1(a3) = (a3 · q1) * q1
proj_q2(a3) = (a3 · q2) * q2

Step 2: Subtract the projections from the original vector a3 to obtain an orthogonal vector, v3.
\(v3 = a3 - proj_q1(a3) - proj_q2(a3)\)

Step 3: Normalize the orthogonal vector v3 to obtain the orthonormal vector q3.
q3 = v3 / ||v3||

Now, let's fill in the third column of the Q and R matrices:

Step 4: The third column of Q is q3.

Step 5: Calculate the third column of R by taking the dot product of a3 with each of the orthonormal vectors q1, q2, and q3.
R(1,3) = a3 · q1
R(2,3) = a3 · q2
R(3,3) = a3 · q3

By following these steps, you've completed the Gram-Schmidt process for QR factorization and filled in the third column of matrices Q and R.

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Answer:

2/7<4/5<5/6<7/9

Step-by-step explanation:

The fractions in ascending order will be 2/7<7/9<4/5<5/6.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The given number is,

7/9,2/7,4/5,5/6

The fraction with the smallest numerator is the smallest for fractions with the same denominator. Put the numbers 2/7,4/5,5/6,7/9. In ascending order, for instance. The fraction with the highest denominator is the smallest when all the fractions have the same numerator.

The LCM of the denominator 9,7,5 and 6 is 630.

The term equivalence for the denominator is,

490/630,180/630,504/630,525/630

The fractions in ascending order are,

180/630<490/630<504/630<525/630

2/7<7/9<4/5<5/6

Thus, the fractions in ascending order will be 2/7<7/9<4/5<5/6.

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Based on the information in the circle graph,  Brandi's total monthly allowance is equal to $50.

A circle graph is used to represent information in a circle. The circle is divided into different section to represent the magnitude of each grouping.

Total allowance = amount allocated to clothes / percentage of circle graph that is allocated to clothes

$20 / 0.40  = $50

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The absolute minimum value of f(x, y) is -16, occurring at the points (7, 0) and (7, 10). Therefore, the minimum value is -16.

To find the absolute minimum and absolute maximum of the function f(x, y) = 6 - 4x + 7y on the closed triangular region with vertices (0, 0), (7, 0), and (7, 10), we need to evaluate the function at the critical points and the boundary of the region.

Critical points: To find critical points, we need to take the partial derivatives of f(x, y) with respect to x and y and set them equal to zero.

∂f/∂x = -4 = 0

∂f/∂y = 7 = 0

Since there are no solutions to these equations, there are no critical points within the region.

Boundary of the region: We need to evaluate the function at the vertices and on the sides of the triangle.

Vertices:

f(0, 0) = 6 - 4(0) + 7(0) = 6

f(7, 0) = 6 - 4(7) + 7(0) = -16

f(7, 10) = 6 - 4(7) + 7(10) = 60

Sides:

Side 1: From (0, 0) to (7, 0)

y = 0

f(x, 0) = 6 - 4x + 7(0) = 6 - 4x

The minimum occurs at x = 7 with a value of -16.

Side 2: From (0, 0) to (7, 10)

y = (10/7)x

f(x, (10/7)x) = 6 - 4x + 7((10/7)x) = 6 - 4x + 10x = 6 + 6x

The minimum occurs at x = 0 with a value of 6.

Side 3: From (7, 0) to (7, 10)

x = 7

f(7, y) = 6 - 4(7) + 7y = -22 + 7y

The minimum occurs at y = 0 with a value of -22.

From the above evaluations, we can conclude:

The absolute minimum value of f(x, y) is -16, occurring at the points (7, 0) and (7, 10).

The absolute maximum value of f(x, y) is 60, occurring at the point (7, 10).

Therefore, the minimum value is -16.

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Answer:

y=3.5

x=13.5

Step-by-step explanation:

5y+38=17y-4

42=12

y=3.5

7x+30=11x-24

54=4x

x=13.5

The scale factor of the drawing of the neighborhood park would be = 2000.

The scale factor is defined as the ratio between the scale of the original object and the new object, which represents it but in a different size (larger or smaller).

The width of the neighborhood park. in real life = 8 meters

To convert 8 meters to millimetres is to multiply by 1000

= 8 × 1000 = 8000 mm

The scale factor = 4 × X = 8000

make X the subject of formula;

X = 8000/4

X = 2000.

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Answer:

c

Step-by-step explanation:

took the test

Answer:

Option C is the correct answer

\( x = 34 \\y=17\sqrt3\)

Step-by-step explanation:

\( \sin \: 30 \degree = \frac{17}{x} \\ \\ \frac{1}{2} = \frac{17}{x} \\ \\ x = 17 \times 2 \\ \\ x = 34 \\ \\ \tan \: 30 \degree = \frac{17}{y} \\ \\ \frac{1}{ \sqrt{3} } = \frac{17}{y} \\ \\ y = 17 \sqrt{3} \)

Many children develop the ability to do simple arithmetic problems during their early childhood years, typically between the ages of 4 and 6. Correct option is a).

During this time, children start to understand basic mathematical concepts such as counting, addition, and subtraction. They may also begin to recognize and name numbers and use basic math vocabulary. However, it's important to note that every child develops at their own pace and some may show these skills earlier or later than others. It's also important for parents and caregivers to provide opportunities for children to practice and reinforce these skills through activities such as counting objects, playing number games, and solving simple math problems.

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Hey there!☺

\(Answer:\boxed{y=60.36}\)

\(Explanation:\)

To write 60.36 as expanded form, you will have to make it an equation. And this is how it would be written:

\(y=60.36\)

Hope this helps!☺

Answer: 19/21>8/9

Step-by-step explanation:

common denominator is 63

19*3=57 so thats 57/63

8*7=56 so thats 56/63

87/14 or 6 3/4. That's an improper fraction and then a mixed fraction. Same answer though

Answer:

Multiply the probabilities of the outcomes. 4/10*6/10 = 24/100 = 12/50 = 6/25.

The answer is 6/25.

Step-by-step explanation:

How I got my answer all you have to do is multiply the probabilities and you get 6/25.

The volume of Sam's model is 136.5 cubic inches.

The volume of the prism is 6.5 * 7 * 9 = 409.5 cubic inches.

The volume of the rectangular pyramid is given by 1/3*Base area*height.

In this case, the base area of the pyramid is the same as the base of the prism which is 6.5*7 = 45.5 square inches.

The height of the pyramid is the same as the height of the prism which is 9 inches.

Substituting these values in the formula above we get:

1/3*45.5*9 = 136.5 cubic inches.

Therefore, the volume of Sam's model is 136.5 cubic inches.

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approximately 3.6 milliliters of medication would be needed for this prescription.

To calculate the total milliliters of medication needed for this prescription, we will use the formula dosage × frequency × day supply.

In this case, the dosage is 2 drops per ear, the frequency is twice a day, and the day supply is 9 days.

First, let's find out how many drops are needed per day:
2 drops/ear × 2 ears = 4 drops
Since the frequency is twice a day, multiply this number by 2:
4 drops × 2 = 8 drops per day

Now, multiply the number of drops per day by the day supply (9 days):
8 drops/day × 9 days = 72 drops

Typically, 1 drop is approximately 0.05 millilitres. To find out how many millilitres of medication are needed, multiply the total number of drops by the volume of one drop:

72 drops × 0.05 mL/drop = 3.6 mL

So, approximately 3.6 millilitres of medication would be needed for this prescription.

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Approximately 1.8 milliliters of medication would be needed for this prescription.

To calculate how many milliliters of medication would be needed for this prescription, we need to use the following formula:

dosage × frequency × day supply.
The dosage is 2 drops, the frequency is twice a day, and the day supply is 9 days.
First, we need to convert drops to milliliters.

One drop is equal to approximately 0.05 milliliters.

2 drops would be equal to 0.1 milliliters.
Next, we can plug in the values into the formula:
\(0.1 milliliters/drop \times 2 drops/twice a day \times 9 days = 1.8 milliliters. \)

The patient will be using exactly 2 drops in each ear for each dose, and that there will be no waste or spillage of the medication.

To determine how many milliliters of medicine would be required for this prescription:

dose frequency day supply.

The recommended dosage is 2 drops, twice day, with a 9-day supply.

We must first convert droplets to milliliters.

A drop is around 0.05 milliliters in volume. As a result, 2 drops are equivalent to 0.1 milliliters.

The values may then be entered into the formula as follows:

0.1 milliliters each drop times twice daily for nine days equals 1.8 milliliters.

As a result, this prescription would require about 1.8 milliliters of medicine.

It's crucial to note that this estimate is predicated on the patient applying precisely 2 drops to each ear for each dose.

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When Andrew goes bowling, his scores are normally distributed with a mean of 115 and a standard deviation of 11 . Then the probability of his score being between 86 and 115 is 0.2047

Mean = μ = 115

SD = σ = 11

Let x1 be the first data point and x2 the second data point

We have to find the z-scores for both data points

x1 = 86

x2 = 106

So,

Z1 = ( x1- mean)/ SD

   = 86- 115 / 11

   = -29/11

   = -2.6363

Z2 =  ( x2-mean)/SD

    = 106 -115 /11

     = -0.8181

And We have to find area to the left of both points then their difference to find the probability.

So, Area to the left of z1 = 0.00427

Area to the left of z2 = 0.20897

Probability to score between 135 and 167 = z2-z1 =  0.20897-0.004270

                                                                                 = 0.2047

Hence,

The probability of his score being between 86 and 115is 0.2047

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Answer:

a₁₃ = - 27x - 41

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 3x + 7

d = a₂ - a₁ = - 5x + 3 - (- 3x + 7)

                 = - 5x + 3 + 3x - 7

                 = - 2x - 4

Then

a₁₃ = - 3x + 7 + 12(- 2x - 4)

     = - 3x + 7 - 24x - 48

     = - 27x - 41

The true statement is the range of Mrs Plum's class is 14 greater than the range of Mr Scarlet's class.

A box plot is a graph that is used to describe a dataset. A box plot is made up of two lines and a box. The two lines are known as whiskers.

The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the whiskers is the range.

Range is used to measure the variation of a dataset. It is the difference between the maximum number and the minimum number.

Range = maximum number - minimum number

Range of Miss Scarlet's class = 98 - 65 = 33

Range of Miss Plum's class = 98 - 51 = 47

Difference in range = 47 - 33 = 14

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Answer:

lemme guess algebra test?

Step-by-step explanation:

The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.

The new value of the stock in Company A is:

\(4500 + (5 \times 4500) = $4725\)

The new value of the stock in Company B is:

\(3900 + (11 \times 3900) = 4339\)

The total value of the investor's stock account after the increase is:

$4725 + $4339 = $9064

To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:

($9064 - $8400) / $8400 = 0.0795

We then multiply this decimal by 100 to get the percentage increase:

0.0795 x 100 = 7.95%

Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

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Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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