If the first number in the dividend is less then the divisor do you put 0 first and then keep dividing or don't put it at all.

The cosine function has period 2π. This means that if we add or subtract 2π to any value of θ, the cosine of the new value will be the same as the cosine of the original value.

For example, if θ = π/3, then cosθ = −1/2. If we add 2π to π/3, we get 5π/3. The cosine of 5π/3 is also −1/2. This is because the cosine function has a period of 2π.

We can use this property to find all the values of θ, 0≤θ≤2π, for which cosθ=−1/2. We start by finding the smallest positive value of θ for which cosθ=−1/2. This value is π/3.

We can then find all the other values of θ by adding 2π to π/3. These values are 5π/3, 7π/3, 9π/3, and so on.

Therefore, the values of θ, 0≤θ≤2π, for which cosθ=−1/2 are π/3, 5π/3, 7π/3, 9π/3, and so on.

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Answer:

C

Step-by-step explanation:

First we need to figure  out what it means when we say a function is increasing.

Here is a small tip:

As x goes up, the y will go up as well.

In this case, we say the function is increasing.

From the graph we see that the function is increasing from -3 to 3.

so the interval will be [-3, 3]

In this part, when x goes up, y goes up as well.

Answer:

41%

Step-by-step explanation:

35/85=0.411

0.411x100=

41%

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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10.59 is the value of the given side b.

In our case, we know that side A has a length of 15 units and is opposite angle A, which measures 27 degrees.

Using the sine rule, we can write:

b/sin(27°) = 15/sin(40°)

To find the value of b, we can rearrange the equation:

b = (15 * sin(27°)) / sin(40°)

evaluate the trigonometric functions and calculate b:

b ≈ 10.59

Therefore, using the sine rule of the triangle, we find that the value of side b is approximately 10.59 units.

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Answer:

(18 is wrong, the slope is 1/3)

Step-by-step explanation:

Using the equation in the top right

11.) (-10-(-4))/(-12-(-20))= -(3/4)

12.) (-8+5)/(0+12)= -(1/4)

13.) (16-(-6))/(15-(-19))=  (11/17)

14.) (-9-9)/(7+6)= -(18/13)

15.) (-15+20)/(-18+18)= No solution

16.) (12+18)/(11-12) = -30

Answer:

Step-by-step explanation:

answer: owen can afford to keep and drive the car for 4 days.

The total owing on the car rental is R(d) = ($77.25/day)d + ($0.12/mile)m ≤ $330.  Substitute 1 for d (that is, the rental is for 1 day) and 175 for m:

R(d) = ($77.25/day)(d days) + ($0.12/mile)(175 miles) ≤ $330

    =   $77.25d                   + $21     ≤ $330

This simplifies to   $77.25d + $21 ≤ $330, or

                                $77.25d ≤ $309

Solving this by dividing both sides of the above equation by $77.25, we get                          

d = ($309)/($77.25) = 4

The general solution to the differential equation. If initial conditions are given, we can solve for the constants C1 and C2.

The given differential equation is:

y ln x * (dx/dy) = [(y+1)/x]^2

We can solve this equation by separation of variables, which means we can rearrange the equation so that all the x terms are on one side and all the y terms are on the other side. Then, we can integrate both sides with respect to their respective variables.

First, we rewrite the equation in a form suitable for separation of variables:

y ln x dx = [(y+1)/x]^2 dy

Next, we separate the variables and integrate both sides:

∫y ln x dx = ∫[(y+1)/x]^2 dy

Integrating the left-hand side by parts, we have:

u = ln x dv = y dx

du/dx = 1/x v = (1/2) y^2

∫y ln x dx = (1/2) y^2 ln x - ∫(1/2) y dx

= (1/2) y^2 ln x - (1/4) y^2 + C1

where C1 is the constant of integration.

Integrating the right-hand side, we use the substitution u = y+1:

u = y+1 du = dy

∫[(y+1)/x]^2 dy = ∫(u/x)^2 du

= (1/x^2) ∫u^2 du

= (1/3x^2) u^3 + C2

where C2 is the constant of integration.

Substituting this back into the original equation, we have:

(1/2) y^2 ln x - (1/4) y^2 + C1 = (1/3x^2) (y+1)^3 + C2

This is the general solution to the differential equation. If initial conditions are given, we can solve for the constants C1 and C2.

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Answer:

The answer is 39

Step-by-step explanation:

75 + 3 = 78

78/2 = 39

The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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If there exists a solution, then the vector (1, 6, 2) is a linear combination of the given vectors. We can solve this system of equations to determine the values of a, b, and c.

To determine whether the vector (1, 6, 2) is a linear combination of the vectors (1, 2, -1), (3, 1, 1), and (-4, 0, 6), we need to check if there exist scalars (constants) such that when we multiply each vector by its respective scalar and sum them up, we obtain the vector (1, 6, 2). Let's assume the scalars are a, b, and c for the three vectors respectively.

We can set up the following system of equations:

a(1, 2, -1) + b(3, 1, 1) + c(-4, 0, 6) = (1, 6, 2)

This can be written as:

(1a + 3b - 4c, 2a + b, -a + b + 6c) = (1, 6, 2)

By comparing the corresponding components, we obtain the following system of equations:

1a + 3b - 4c = 1

2a + b = 6

-a + b + 6c = 2

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The correct statement regarding R-squared is: "Its value is always between -1.0 and 1.0. A value of 1.0 indicates the line is a perfect fit for the data."

R-squared (²) is a statistical measure that represents the proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model. The value of R-squared ranges from -1.0 to 1.0.

A value of 1.0 indicates that the regression line perfectly fits the data, while a value of 0 indicates that the model cannot explain any variance in the dependent variable. A negative value indicates that the model is worse than just using the mean of the dependent variable.

Therefore, the best fit line for the data is the one that has an R-squared value closest to 1.0, indicating that it explains a high percentage of the variance in the dependent variable based on the independent variable(s). It is important to note that an R-squared value above 1.0 is not possible and may indicate a mistake in the calculations.

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Answer:

Frequency

Step-by-step explanation:

Hope this helps.

Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

(33*3+1 )/3 = 100/3%

Then you need to convert that to decimal by dividing 100

100/300 = 0.3333

which is 1/3 in decimal form

The ratios involved in the ROI formula are the net profit and the investment cost.

The ROI (Return on Investment) formula includes the following ratios:

Net Profit: The net profit represents the profit gained from an investment after deducting expenses, costs, and taxes.

Investment Cost: The investment cost refers to the total amount of money invested in a project, including initial capital, expenses, and any additional costs incurred.

The ROI formula is calculated by dividing the net profit by the investment cost and expressing it as a percentage.

ROI = (Net Profit / Investment Cost) * 100%

Therefore, the ratios involved in the ROI formula are the net profit and the investment cost.

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The closest estimate to the actual value of √0.65 is option B: 0.086, which gives an estimate of √0.65 ≈ 0.293.

Therefore, B is the best estimate of √0.65 among the given options.

We can estimate the value of √0.65 using the given options and comparing them to the actual value of √0.65, which is approximately 0.806.

0.065 -> √0.065 ≈ 0.255

0.086 -> √0.086 ≈ 0.293

0.81 -> √0.81 = 0.9

0.86 -> √0.86 ≈ 0.927

It's important to note that while estimation is a useful tool, it is not as accurate as precise calculations, so it's always best to verify the estimate using more accurate methods when necessary.

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Answer:

1. 49

2. 35

3. 4

4.  140

5. 189

Step-by-step explanation:

1. Face A is a square with a height of 7 cm, so the length and width have to be 7 too. 7*7=49.

2. area=base*height/2. The base is 7, the height is 10, their product is 70. 70/2=35.

3. In the net, 4 traingles labeled B are present

4. area of b triangles*number of b triangles: 35*4=140

5. square+b triangles=surface area. 49+140=189.

Answer:

below

Step-by-step explanation:

1. Area for Face A (the square)

Formula: A=a^2

A = Area, a = side

Fill in:

A = 7^2

Solve:

7 ^2, aka 7 x 7 = 49

2. Area for Face B (the flat triangles)

Formula: A = 1/2 × b × h

b = base, h = height

Fill in:

A = 1/2 × 7 × 10

Solve:

(Multiplying by 1/2 is the same as dividing by 2)

A = 1/2 x 7 x 10
7 × 10 = 70

divide by 2

70/2 = 35

Now we count how many Face B triangles there are, and add the area of each one together:

# of Face B Triangles: 4

multiply it by 35, or just add 35 4 times: 140

3. Total Surface Area for Pyramid:

Base Surface Area = 7^2 = 49

Lateral Surface Area = 2 × 7 × √(7/2)^2 + 10^2 =148.32734070292

Total Surface Area = 197.32734070292

Answer:

\( \frac{189}{64} \)

Step-by-step explanation:

\( \frac{7}{4} \times \frac{9}{4} \times \frac{3}{4} \)

9*7*3

63*3

189

4*4*4

16*4

64

\( \frac{189}{64} \)

Answer:

(14, - 3 )

Step-by-step explanation:

Under the translation < 6, 0 >

Add 6 to the x- coordinate and 0 to the y- coordinate, that is

B(8, - 3 ) → B'(8 + 6, - 3 + 0 ) → B'(14, - 3 )

The answer is 55 possible selections of 4 books from this shelf that include at least one paperback. Option D (55) is the correct answer.

To answer your question regarding the possible selections of 4 books from a shelf with 8 books (2 paperbacks and 6 hardbacks) that include at least one paperback, we'll use combinatorics.
Calculate the total possible combinations of selecting 4 books out of 8 without any conditions:
This can be calculated using the combination formula, C(n, r) = n! / (r! * (n-r)!), where n is the total number of books (8) and r is the number of books to be selected (4).
C(8, 4) = 8! / (4! * (8-4)!) = 70
Calculate the total possible combinations of selecting 4 hardback books only:
Here, n is the total number of hardbacks (6) and r is the number of books to be selected (4).
C(6, 4) = 6! / (4! * (6-4)!) = 15
Calculate the number of combinations that include at least one paperback:
Since we know the total combinations and the combinations with hardbacks only, we can subtract the latter from the former to get the number of combinations with at least one paperback.
Number of combinations with at least one paperback = Total combinations - Combinations with hardbacks only = 70 - 15 = 55
So, there are 55 possible selections of 4 books from this shelf that include at least one paperback.

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Answer:

3 hours.

Step-by-step explanation:

Let's say that they both start at a point A. If Bill travels south 45 miles in hour and Landin drives 30 miles north in one hour, after one hour, Bill is going to be 45 miles lower than point A and Landin will be 30 miles above point A, so they will be 45 + 30 = 75 miles apart. After two hours, they will be another 75 miles apart, so they will be a total of 75 + 75 = 150 miles apart. After 3 hours, they will be another 75 miles apart, so they will be a total of 150 + 75 = 225 miles apart.

The maximum value of f(x, y)=x2-x-y on the region where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1.

To find the maximum value, we can set up a system of inequalities and solve it:

0 ≤ x ≤ 1
0 ≤ y ≤ 1
f(x, y)=x2-x-y

Since both x and y are greater than or equal to 0, their product will also be greater than or equal to 0. Therefore, the maximum value of the equation is when x = 1 and y = 0, since it maximizes the positive value of x2 while minimizing the negative value of -x-y. This means that the maximum value of f(x, y) is 1.

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The maximum value of f(x,y)=x^{2}-x-yf(x,y)=x 2 −x−y on the region where \{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} is 0.

To find the maximum value, we need to find the critical points of the function and test them within the given region. The critical points are where the partial derivatives of the function are equal to 0.

The partial derivative with respect to x is:
f_x(x,y)=2x-1

The partial derivative with respect to y is:
f_y(x,y)=-1

Setting these partial derivatives equal to 0, we get:
2x-1=0 --> x=1/2
-1=0 --> no solution for y

So the only critical point within the given region is (1/2, y) for any value of y. However, since the partial derivative with respect to y is always -1, the function is decreasing with respect to y. Therefore, the maximum value will occur when y is at its smallest value, which is 0.

Plugging in x=1/2 and y=0 into the original function, we get:
f(1/2,0)=(1/2)^{2}-(1/2)-0=0

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Answer:

Dyscalculia is a learning disorder that affects a person's ability to understand number-based information and math

Answer:

4Hz

Step-by-step explanation:

Standard form of a sine or cosine function,

y = acos(b(x+c))

where a is the amplitude, b is the value to find the period. and c is the phase shift.

Period = \frac{2\pi}{b}

From the equation given in the question,

\(y = 3cos(8\pi \: t + \frac{\pi}{2} ) \\ y = 3cos(8\pi(t + \frac{1}{16} )) \: \: (factorising \: 8\pi \: out)\)

We can see:

Amplitude = 3,

Period = \frac{2\pi}{8\pi} = 1 / 4

Phase Shift = 1 / 16

Now we want to find the frequency.

Frequency = 1 / Period

= 1 / (1/4)

= 4Hz

Answer:

\(\displaystyle 4\)

Step-by-step explanation:

\(\displaystyle y = Acos(Bx - C) + D\)

When working with a trigonometric equation like this, always remember the information below:

\(\displaystyle Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A|\)

So, the first procedure is to find the period of this graph, and when calculated, you should arrive at this:

\(\displaystyle \boxed{\frac{1}{4}} = \frac{2}{8\pi}\pi\)

You will then plug this into the frequency formula, \(\displaystyle T^{-1} = F.\) Look below:

\(\displaystyle \frac{1}{4}^{-1} = F \\ \\ \boxed{4 = F}\)

Therefore, the frequency of motion is four hertz.

I am delighted to assist you at any time.

Answer:

16 sundaes

Step-by-step explanation:

since one gallon is 8 pints, multiple it by 2 and you get 16.

in most counties, there were fewer than 75 bear kills in 2014.

The given data shows the number of bears killed in 2014 for 52 counties in Pennsylvania. The frequency table provided indicates the frequency with which the number of bear kills falls into different class limits. For instance, there were 15 counties where the bear kills were between 1-25, 10 counties where the kills were between 26-50, and so on.
The data can be represented visually using a histogram, which will show the distribution of the data and help us understand the most common range of bear kills. Looking at the frequency table and the histogram, we can see that the majority of counties had a lower number of bear kills, with the peak occurring in the 51-75 class limit.
It's important to note that this data only represents one year in one state, and does not necessarily provide a complete picture of bear populations or hunting practices. However, it does give us an idea of the frequency of bear kills across different counties in Pennsylvania in 2014.

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Answer:

p(x) = 5x + 20

Step-by-step explanation:

11x - 6x + 20

5x + 20

The graph {D} represents the correct domain.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given are the function graphs as shown in the image.

Therefore, the graph {D} represents the correct domain.

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