angle 1 and angle 3 are ___ angles.

The family of curves with polar equations r = 1 c cos() can be rewritten as x = c cos() and y = c sin(), using the conversion formulas r cos() = x and r sin() = y. This means that each curve in the family is a circle centered at the origin with radius c, rotated by an angle of 90 degrees.

As c changes, the radius of each circle changes, and therefore the size of each circle changes. If c is positive, the circle will be in the first and third quadrants of the Cartesian plane, and if c is negative, the circle will be in the second and fourth quadrants.

When c = 0, we get a circle of radius 0, which is just the single point at the origin. This makes sense, since cos(0) = 1 and all other values of cos() are between -1 and 1, so the equation r = 1 c cos() can only be satisfied when c = 0 if cos() = 0, which occurs only at = 0 and = pi.

In summary, as c changes, the family of curves with polar equations r = 1 c cos() changes in size and position, but remains circular in shape. When c = 0, the curve is just a single point at the origin.

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The numerator degree of freedom for the F test statistic to determine if the factor bread was significant would be 3.

This is because there are 4 different kinds of bread, but when conducting a two-way ANOVA test, one of the groups is always used as the reference group. Therefore, there are only 3 groups of bread that are being compared to each other. The denominator degree of freedom would be 56 (60 total samples minus 4 groups of bread and 5 groups of meat).

The F test statistic would determine if there is a significant difference in revenues between the different kinds of bread, while also controlling for the effect of the different kinds of meat.

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Answer:

C

Step-by-step explanation:

Let's just look at the point G(3) = 3

this point only occurs through one equation which is

g(x) = (1/3)x^2

Answer:

The answer is 1/3x^2 or in your case C.

Step-by-step explanation:

Well I just add the points on Desmos graphing.  The 3rd one was able to hit the points (3,3) and (-3,3). The others did not.

Answer:

5/6 or 0.83

Step-by-step explanation:

Reduce the fraction:

3/6 + 1/3

Transform the expression:

3+2

 6

Calculate:

5/6

Answer/Solution:

5/6 or 0.83

Answer:

y=3/2x+13

Step-by-step explanation:

To find the slope of a perpendicular line, you have to find the negative inverse of the slope. The negative inverse of -2/3 is 3/2.

This means that the equation of the perpendicular line is y=3/2x+a.

To find a, you have to input the given points into the new equation. If you input the given points into the equation you get 4 = 3/2(-6)+a. When you solve that equation, you get a=13.

When you input the a value into the new equation, you get a final equation of y=3/2x+13.

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The solution to the rational expression 2/9 + 3/8 = 6/x is x = 16. To solve the equation, we need to find a common denominator for the fractions. The least common multiple of 9 and 8 is 72.

Multiplying the numerator and denominator of the first fraction by 8, and the numerator and denominator of the second fraction by 9, we get (16/72) + (27/72) = 6/x.

Combining the fractions on the left side, we have (16 + 27)/72 = 6/x. Simplifying further, we get 43/72 = 6/x. To solve for x, we can cross-multiply: 43x = 72 * 6. Dividing both sides of the equation by 43, we find x = 72 * 6 / 43, which simplifies to x ≈ 10.605. Rounded to the nearest whole number, x is approximately equal to 11.

To verify our solution, we can substitute x = 11 back into the original equation: 2/9 + 3/8 = 6/11. Evaluating both sides, we find that 2/9 + 3/8 is approximately 0.77778, while 6/11 is also approximately 0.77778. Since both sides are equal, our solution of x = 11 is correct and satisfies the original equation.

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Using the slope-intercept form, the equation that represents the amount of battery charge y, in miles, after traveling for x hours is: y = -23x + 410

Equation of straight line can be defined as y = mx+b where m is slope of a line.

To create the equation in slope-intercept form, we need to find the slope and y-intercept.

The slope represents the rate at which the battery charge decreases, which is 46 miles every 2 hours. This can be expressed as:

slope = -23 miles/hour

The negative sign indicates that the battery charge decreases over time.

The y-intercept represents the initial battery charge when the car is fully charged, which is 410 miles.

Using the slope-intercept form, the equation that represents the amount of battery charge y, in miles, after traveling for x hours is: y = -23x + 410

where x is the number of hours the car has been traveling and y is the remaining battery charge in miles.

Therefore, Using the slope-intercept form, the equation that represents the amount of battery charge y, in miles, after traveling for x hours is:

y = -23x + 410

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The answer is 15.To determine the number of different homes that can be built, we need to consider the different combinations of interior plans and home exteriors.

Given that there are three different interior plans and five different home exteriors, we can use the multiplication principle to find the total number of combinations. Multiplying 3 by 5 gives us 15 unique combinations.Let's break it down: For each of the three interior plans, we have five options for the home exterior. This means that for the first interior plan, we can pair it with any of the five home exteriors. Similarly, for the second interior plan, we can also pair it with any of the five home exteriors, and the same applies to the third interior plan.

Using the multiplication principle, we multiply the number of options for each choice together to find the total number of combinations. In this case, it is 3 (interior plans) multiplied by 5 (home exteriors), which equals 15. Therefore, the developer can build 15 different homes by combining the three interior plans with the five home exteriors. In conclusion, the answer is 15.

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Answer:

\(area = \pi {r}^{2} \\ = \frac{22}{7} \times {( \frac{8}{2} )}^{2} \\ = 50.3 \: {km}^{2} \)

Answer:

m=24

Step-by-step explanation:

12=0.5m

Divide 12 by 0.5

m=24

Answer:

Step-by-step explanation:

12% of .5metre is 0.5x12/100=6/100=0.06 metre

Answer:

12=b

Step-by-step explanation:

2b+7=3b-4 is what your gonna do ti solve the problem because both segments have the same length. Then you solve for b by -2b from each side. Then it will become 7=b-4. Add 4 to the seven to get 12=b

Answer:

This Is CORRECT

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/2 slope

just took the test

General form y= ax^2+bx+c

standard form y = a(x-h)^2+k

where

(h,k)= vertex = (7,2)

Since the zero are at -1 and 15 we have the points

(-1,0) and (15,0)

We will use one of the points (-1,0) and the vertex in the general form:

0= a(-1-7)^2+2

0= a(-8)^2+2

0= a64+2

-2 =a64

-2/64 =a

-1/32 =a

y= -1/32 (x-7)^2+2

y =-1/32 (x-7)(x-7)+2

y= -1/32 (x^2-14x+49)+2

y= -1/32 x^2+7/16x-49/32+2

y= -1/32x^2+7/16x-113/32

Answer: I believe it’s f(x)=4(3)^x-1

Step-by-step explanation:

In this scenario, the shape of the sampling distribution of X-bar is approximately normal.

The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.

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Answer:

the value of c​ 4,-3

Step-by-step explanation:

We find that the surface integral evaluates to 54π. the surface integral ∫∫S (x^2 + y^2 + z^2) dS,

where S is the part of the cylinder x^2 + y^2 = 9 that lies between the planes z = 0 and z = 3, together with its top and bottom disks, evaluates to 54π.

To evaluate the surface integral, we can use the formula ∫∫S f(x, y, z) dS, where f(x, y, z) is the integrand and dS represents the surface element.

In this case, the integrand is (x^2 + y^2 + z^2) and the surface S is defined by the equation x^2 + y^2 = 9 and bounded by the planes z = 0 and z = 3, including the top and bottom disks.

We can express the surface integral as the sum of three parts: the lateral surface of the cylinder and the two disk surfaces. The lateral surface can be parameterized as x = 3cosθ, y = 3sinθ, and z ranges from 0 to 3. The two disk surfaces have their own parameterizations.

By performing the calculations, integrating over each surface element, and summing the results, we find that the surface integral evaluates to 54π.

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The expected value of winnings is 4.17.

We are given that;

A dice is rolled 3times

Now,

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

If you roll a die up to three times and each time you roll, you can either take the number showing as dollars or roll again.

The expected value of the game rolling twice is 4.25 and if we have three dice your optimal strategy will be to take the first roll if it is 5 or greater otherwise you continue and your expected payoff 4.17.

Therefore, by probability the answer will be 4.17.

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Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

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Answer:

the inverse is option B.............

The expanded form of the logarithm log₃(x³y²) can be expressed as log₃(x³) + log₃(y²).

To understand why we expand this logarithm, let's first recall the properties of logarithms. One property states that the logarithm of a product is equal to the sum of the logarithms of its factors. Using this property, we can split the logarithm of the product x³y² into separate logarithms for x³ and y².

Now, let's expand the logarithm further. Applying another property of logarithms, which states that the logarithm of a power is equal to the exponent multiplied by the logarithm of the base, we can simplify log₃(x³) as 3log₃(x). Similarly, log₃(y²) can be simplified as 2log₃(y).

Therefore, the expanded form of log₃(x³y²) is 3log₃(x) + 2log₃(y). This expansion allows us to separate the variables x and y, making it easier to work with and manipulate the logarithm expression.

In summary, by using the properties of logarithms, we can expand log₃(x³y²) into 3log₃(x) + 2log₃(y). This expansion allows us to simplify and separate the logarithm into individual terms for each variable.

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Complete question :

In one year, the population of Douglas, the former copper mining town on the U.S.-Mexico border, shrunk by 200. Over the last ten years, the town’s population is going down at an average rate of 1.16% per year. Douglas’ current population in November 2020 is 15,140. a. Write an equation to model the population decay of Douglas using the data given. b. If the town’s population loss continues to occur at this rate, what will the population of Douglas in 6 months from now? Round your answer to the nearest integer. c. If the town’s population loss continues to occur at this rate, what will the population of Douglas in one year? Round your answer to the nearest integer. d. If the town’s population loss continues to occur at this rate, what will the population of Douglas in November 2027? Round your answer to the nearest integer.

Answer:

15052 ; 14,964 ; 13953

Step-by-step explanation:

Given that:

Rate of population decline = 1.16% annually

Population in November 2020 = 15140

A = I(1 - r)^t

Where ;

A = final population

I = initial population

r = rate of decline

t = number of years

Population in 6 months

t = 6 months = 0.5 year, r = 1.16% = 0.0116

A = 15140(1 - 0.0116)^0.5

A = 15140(0.9884)^0.5

A = 15051.931

A = 15052 ( nearest integer)

Population after 1 year :

A = 15140(1 - 0.0116)^1

A = 15140(0.9884)^1

A = 14964.376

A = 14964 ( nearest integer)

Population in 2027:

t = 2027 - 2020

A = 15140(1 - 0.0116)^7

A = 15140(0.9884)^7

A = 13952.596

A = 13953 ( nearest integer)

The critical value for a 98% confidence interval with a sample size of n=30 and known standard deviation  is 2.756.

When constructing a confidence interval, the critical value represents the number of standard errors above and below the sample mean that encompasses the specified confidence level. A larger confidence level requires a larger critical value, and a larger sample size will generally result in a smaller critical value, assuming that the population standard deviation is known. In this case, with a sample size of 30 and a 98% confidence level, the critical value is calculated to be 2.756, rounded to 3 decimal places.

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Kay deposited (c)$93.44  in cash and coins.

Money or coins that are legal tender can be used to pay for goods, debts, or services. Additionally, as stated by a corporation, it occasionally includes the worth of assets that can be quickly converted into cash. In its physical form, cash is another name for money. Bank accounts and marketable securities, such as government bonds and banker's acceptances, are typically included in the definition of "cash" in a business context.

We proceed from the whole backward. The amount deducted for cash received is first added back,

498.01+213.51 = 711.52

Each cheque that was deposited is then subtracted:

711.52-40.25 = 671.27

671.27-57.68 = 613.59

613.59-520.15 = 93.44

She started with (c) $93.44 in cash and coins.

Correct Question :

How much did kay deposit in cash and coins? a. $404.57 b. $213.51 c. $93.44 d. $284.50

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Answer:

a. (5, 10).

Step-by-step explanation:

When the equation is (x - 5)^2 + (y - 10)^2, you can find the center from that. The x-coordinate of the center will be x - 5 = 0, so x = 5. The y-coordinate for the center will be y - 10 = 0, so y = 10.

Your center of the circle will be a. (5, 10).

Also, if you want to know the radius, you find the number to the right of the equation (in this case, (10)^2), and find the square root of the number. So, the radius of this circle is 10 units.

Hope this helps!

Answer:

Equation: 100 = 2x + 4y

There are 9 4 points problems

Step-by-step explanation:

In this case, we know that we have a test that in total, we must sum 100 points. This could be with question of 2 points or questions of 4 points.

We do not know exactly how many questions of 2 or 4 point are, but we can write an equation that could give us an idea.

Let's call "x" the number of questions worth 2 points.

Let's call "y" the number of questions worth 4 points.

All together must give 100 points, therefore, the logic equation to do this is:

Now, for the second part of this problem, we want to know how many 4 points problems would be in the test if we have 32 questions of 2 points. For that, we use the above equation, and solve for y:

100 = 2(32) + 4y

100 = 64 + 4y

100 - 64 = 4y

36 = 4y

Hope this helps

The given 2.0 seconds period, T, of the small angle oscillation gives the radius of the hoop as approximately 0.5 meters.

The small angle oscillation approximation for the period is presented as follows;

\( T_{0} = 2 \cdot \pi \cdot \sqrt{ \frac{l}{g} } \)

Where;

T0 = The period of oscillation = 2.0 s

l = The length of the oscillating object = The diameter of the hoop

g = Acceleration due to gravity

Therefore;

l = The diameter of the hoop = 2 × The radius of the hoop, r.

Which gives;

\( T_{0} = 2 \cdot \pi \cdot \sqrt{ \frac{2 \cdot r}{g} } \)

Solving gives;

\( 2 \approx 2 \times \pi \cdot \sqrt{ \frac{2 \cdot r}{9.81} } \)

\( r \approx \frac{9.81}{2}\times \left(\frac{1}{π} \right)^2 \approx 0.5 \)

The radius of the hoop, r ≈ 0.5 m

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Answer:

c = 730 cm

Step-by-step explanation:

To solve this question we just need to use the law of sines:

The ratio between a side in the triangle and its opposite angle is always the same.

So we have that:

\(a / sin(A) = c / sin(C)\)

\(714 / sin(78) = c / sin(90)\)

sin(78) is equal 0.9781 and sin(90) is equal 1, so we have:

\(714 / 0.9781 = c / 1\)

\(c = 714 / 0.9781 = 730\ cm\)

There is no relationship between the variables shown by the scatterplot.

A scatter plot is a form of graph that demonstrates the relationships between two variables. On the graph, each data point is displayed as a point, and the two variables are shown as lines on the x- and y-axes.

When there is no association between the two variables, the data points are scattered randomly around the graph.  The fact that there is a random scatter of the points shows that there is no relationship between them.

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