Suppose that the function g is defined, for all real numbers, as follows.

Using trigonometric identities when  cosθ = √2/2 and 3π/2 < θ < 2π

Trigonometric identities are mathematical equations that contain tigonometric ratios

Since cosθ = √2/2 and 3π/2 < θ < 2π, we desire to find sinθ and tanθ. We proceed as follows

a. To find sinθ, using the trigonometric identity

sin²θ = 1 - cos²θ

⇒ sinθ = ±√(1 - cos²θ)

So, substituting the value of cosθ into the equation, we have that

sinθ = ±√(1 - cos²θ)

sinθ = ±√(1 - (√2/2)²)

= ±√(1 - 2/4)

= ±√[(4 - 2)/4]

= ±√[2/4]

= ±√2/2

Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.

So, sinθ = -√2/2

b. To find tannθ, using the trigonometric identity

tan²θ = sec²θ - 1

⇒ tanθ = ±√(sec²θ - 1)

= ±√(1/cos²θ - 1)

So, substituting the value of cosθ into the equation, we have that

tanθ = ±√(1/cos²θ - 1)

tannθ = ±√(1/(√2/2)² - 1)

= ±√(1/2/4 - 1)

= ±√(4/2 - 1)

= ±√[2 - 1]

= ±√1

Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.

So, tanθ = -1

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There are 12 animals that are neither dogs nor cats.

If 5/8 of the animals are dogs, then the remaining 3/8 of the animals are not dogs.

3/8 x 96 = 36

if 1/4 of the animals are cats, then the remaining 3/4 of the animals are not cats.

3/4 x 96 = 72

The number of animals that are neither dogs nor cats is calculated as;

96 - 36 - 72 = 12

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Answer: b is correct

Step-by-step explanation:

Answer:

78/97

Step-by-step explanation:

First, add up all the balls to find the total amount of balls in the bag (19+28+21+29). Then determine how many balls are not blue (you could either take the total and subtract 19 or add up all the colors that are not blue). There are 97 balls total and 78 of them are not blue which is shown as 78/97. 78/97 cannot simplify further.

In order to do a comparison for percents, you must convert them to decimal form and then juxtapose the decimal values side by side to see which is greater or less.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent sign is commonly used, however the acronyms pct., pct, and sometimes pc are also used. A % is a number with no dimensions; it has no unit of measurement.

To calculate the percentage, divide the amount by the total value and multiply the result by 100.

Divide a percentage by 100 to get a decimal. So 25% is equal to 25/100, or 0.25. Multiply a decimal by 100 (simply shift the decimal point two places to the right) to convert it to a percentage. For example, 0.065 equals 6.5% and 3.75 equals 375%.

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The incorrect statement is b. When an aeroplane takes off, the work done by its weight is negative.

The inaccurate assertion is:

b) When a plane removes, the work done by its weight is positive.

The right assertion is:

b) When a plane removes, the work done by its weight is negative.

Clarification:

At the point when a plane removes, the work done by the heaviness of the plane is negative in light of the fact that the weight acts the other way to the dislodging of the plane. As indicated by the work-energy hypothesis, work done by the heaviness of the plane will diminish its motor energy, and that implies that the work done is negative. Hence, articulation (b) is inaccurate.

a) Work and energy have various units.

This assertion is right. Work has units of Joules (J) and energy additionally has units of Joules (J), however they are not exactly the same thing.

c) The possible energy of spring increments when it is broadened and diminishes when it is packed.

This assertion is right. The potential energy put away in a spring is straightforwardly corresponding to its expansion or pressure. While a spring is broadened, its potential energy increments, and when it is packed, its potential energy diminishes.

d) On the off chance that the work done by outside powers on a framework is negative, the energy of the framework diminishes.

This assertion is right. On the off chance that the work done by outside powers on a framework is negative, the energy of the framework diminishes.

The work-energy hypothesis expresses that the net work done on a framework is equivalent to the adjustment of its motor energy, and in the event that the net work is negative, the dynamic energy diminishes, and that implies that the energy of the framework diminishes.

e) When a body is falling unreservedly from a level, its dynamic energy stays consistent.

This assertion is erroneous. At the point when a body is falling unreservedly from a level, its potential energy is changed over into dynamic energy as it falls. Hence, its motor energy increments as it falls, and its potential energy diminishes.

f) The unit of force is watt.

This assertion is right. The unit of force is watt (W), which is characterized as the pace of taking care of business or the pace of move of energy.

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The complete question is:

Identify the wrong statement among the following. Rewrite them by making necessary corrections.

a) Work and energy have different units.

b) When an aeroplane takes off, the work done by its weight is positive.

c) The potential energy of spring increases when it is extended and decreases when it is compressed.

d) If the work done by external forces on a system is negative then the energy of the system decreases.

e) When a body is falling freely from a height, its kinetic energy remains constant.

f) The unit of power is watt.

The first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

= n(E) / n+S)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Thus, the first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

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Drag tiles to fill in the blanks to complete the expression that could be used to predict the number of winners of a game. Tiles may be used once or not at all. A)Total Number of Possible Outcomes B)Number of Winners C)Number of Unfavorable Outcomes D)Number of Games P(event) = Number of Favorable Outcomes _________________________ ????????????????????????????? = ????????????????????????????? _________________________ 11 Total Number of Contestants

The matrix row operation on the matrix A gives us: 0x + 10y - 25z = 4

There are 3 primary basic operations that are utilized on the rows of a matrix when we utilize the matrix to solve a particular system of linear equations . The aim is usually to get the left region of the matrix to resemble the identity matrix .

The three primary operations are:

Switching Rows

Multiplying a Row by a Number

Adding Rows

Now, from the given matrix, the equations are:

x - y + 5z = -1

x - y - 4z = 5

5x + y + 0z = -1

We are told to add -5 times row 1 to row 3 and this gives:

-5x + 5x + 5y + 5y - 25z + 0z = 5 - 1

0x + 10y - 25z = 4

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The True statements about the correlation are: (1), (2), (3), (5), (6) and (7)

1) We know that the adding, subtracting, multiplying or dividing a constant to all of the data points in one or both variables does not change the correlation coefficient.

So, the first statement is True.

2) We know that the correlation measures the strength of the pattern around a line of regression as well as the direction of the line. So, interchanging the variables would not change the correlation. The correlation between x and y is the same as the correlation between y and x.

Thus the second statement is True.

3) We know that the correlation coefficient does not have any units.

It is just a number between -1 to +1.

Thus the third statement is True.

4) We know that the outlier may weaken the correlation. It makes the data more scattered. So the correlation coefficient r gets closer to 0.

Thus the fourth statement is False.

5) We know that if the correlation coefficient r is close to 1 then it is a strong positive correlation and if r is close to -1 then it is a strong negative correlation.

Thus the fifth statement is True.

6) We know that the corrletaion coefficient values can range from -1 to 1.

Thus the sixth statement is True.

7) We know that the y-intercept is nothing but the point at which the regression line intercepts the y-axis. The y-intercept of the regression line and the correlation coefficient have the same sign.

Thus the seventh statement is True.

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When a cylinder is cut parallel to its base, the plane section that results is a circle. This circle will have the same radius as the cylinder's base. The center of the circle will be located at the center of the cylinder's base. This type of cut will create a circular cross-section that is parallel to the base of the cylinder.

The simplified expression based on tej values given is 3a⁴b + 4a³b³.

An expression is a combination of variables, constants, and operators that can be evaluated to produce a single value. In programming languages, expressions are used to represent computations and are often used to assign values to variables, compare values, or perform mathematical operations. Expressions can be simple, such as a single variable or constant, or complex, involving multiple operations and variables.

It should be noted that to simplify the expression a²b(3a² +4ab²), we can distribute the a²b term to the terms inside the parentheses using the distributive property of multiplication:

a²b(3a² +4ab²) = 3a⁴b + 4a³b³

Therefore, the simplified expression is 3a⁴b + 4a³b³.

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Answer:

Step-by-step explanation:

To predict the number of bacteria after 10 hours using the formula P = Aekt, where P is the final population, A is the initial population, k is the growth rate, and t is the time elapsed, we need to first find the value of k.

dw

We know that after 4 hours, the population grew from 3,000 bacteria to 3,600 bacteria. So we can set up an equation:

3,600 = 3,000e^(4k)

Dividing both sides by 3,000 gives:

1.2 = e^(4k)

Taking the natural logarithm of both sides gives:

ln(1.2) = 4k

Solving for k, we get:

k = ln(1.2)/4

k ≈ 0.051

Now that we have the value of k, we can use the formula to predict the number of bacteria after 10 hours:

P = 3,000e^(0.051*10)

P ≈ 5,426

Therefore, we predict that after 10 hours, there will be approximately 5,426 bacteria present in the culture.

Answer:

It's not clear what figure is being referred to. The provided numbers could be dimensions of a shape, but without additional information or context, it's impossible to determine the area of the figure. Can you please provide more details or a diagram?

Step-by-step explanation:

The value of null and alternative hypothesis are change beliefs and certainty test statics, p-value, and inference are the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.

Climate Change Beliefs:

Null Hypothesis (H0): There is no significant relationship between climate change beliefs and certainty.

Alternative Hypothesis (Ha): There is a significant relationship between climate change beliefs and certainty.

Test Statistic: Pearson's correlation coefficient (r)

The Pearson correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, we will use it to determine the relationship between climate change beliefs and certainty.

P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.

Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between climate change beliefs and certainty. If the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that there is insufficient evidence to suggest a significant relationship.

Class Time Use:

Null Hypothesis (H0): There is no significant relationship between class time use, income class, and sleeping.

Alternative Hypothesis (Ha): There is a significant relationship between class time use, income class, and sleeping.

Test Statistic: Multiple regression analysis

Multiple regression analysis is used to determine the relationship between a dependent variable and two or more independent variables. In this case, class time use, income class, and sleeping will be the independent variables, and we will use it to determine the relationship with the dependent variable.

P-Value: The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming that the null hypothesis is true.

Inference: If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant relationship between class time use, income class, and sleeping.

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Step-by-step explanation:

How do you have two equal to signs omg?

Anyway,

x+6+2x=2x+6+4x+6+2x=2x+6+4

3x+6=8x+12=2x+10

0=5x+6=2x+10

0=3x-4=0

3x-4=0

3x=4

x = 4/3 = 1 ⅓

The experimental probability of spinning a 2 on Olivia's spinner is 0.1667.

The experimental probability of spinning a 2 on Jackie's spinner is 0.02 or 2%.

Olivia and Jackie are playing a game with a spinner. Olivia's spinner has 12 equal sections, two of which are marked as "funny 2". Jackie's spinner has 100 equal sections, and two of them are marked as "fun 2".

To find the experimental probability of spinning a 2 in Olivia's spinner, we first need to determine the total number of possible outcomes, which is the number of sections on the spinner. In this case, the spinner has 12 sections. Out of these, two sections are marked as "funny 2". Therefore, the number of favorable outcomes is 2.

Experimental probability of spinning a 2 in Olivia's spinner can be calculated as Experimental probability = Number of favorable outcomes / Total number of possible outcomes

= 2 / 12

= 1 / 6

= 0.1667

Therefore, the experimental probability of spinning a 2 on Olivia's spinner is 0.1667.

To find the experimental probability of spinning a 2 in Jackie's spinner, the total number of possible outcomes is the number of sections on the spinner, which is 100. Out of these, two sections are marked as "fun 2". Therefore, the number of favorable outcomes is 2.

Experimental probability of spinning a 2 in Jackie's spinner can be calculated as Experimental probability = Number of favorable outcomes / Total number of possible outcomes

= 2 / 100

= 0.02

Therefore, the experimental probability of spinning a 2 on Jackie's spinner is 0.02 or 2%.

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Answer: X = 25

Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25

Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.

Answer:

The Babylonian numeral <|| <<|||| represents the number 51 in the Babylonian numeral system.

To convert it to the Hindu-Arabic numeral system, we first need to determine the place values of the symbols. The symbol <|| represents 50 and <<|||| represents 1.

So, we can write the number as:

50 + 1 = 51

Therefore, the Hindu-Arabic numeral equivalent of the Babylonian numeral <|| <<|||| is 51.

We can start by finding the rate at which the printer is printing photos. Since it takes 3 minutes to print 6 photos, we can calculate the rate as 6 photos / 3 minutes = 2 photos/minute. This means that for every minute that passes, the printer prints 2 photos.

Now that we know the rate, we can use it to find out how long it will take to print 16 photos. Since the rate is 2 photos/minute, we can set up an equation to solve for y (time) when x (photos) is 16: 2 = 16/y. Solving for y, we get y = 16/2 = 8.

Therefore, when x (photos) is 16, y (time) is 8 minutes. This means that it will take the printer 8 minutes to print 16 photos.

If y (time) is 5 minutes, we can use the rate we calculated earlier to find out how many photos the printer will print in that time. Since the rate is 2 photos/minute, we can multiply it by the time to find out how many photos will be printed: 2 photos/minute * 5 minutes = 10 photos.

Therefore, if y (time) is 5 minutes, the printer will print 10 photos.

If y (time) is 7 minutes, we can use the rate we calculated earlier to find out how many photos the printer will print in that time. Since the rate is 2 photos/minute, we can multiply it by the time to find out how many photos will be printed: 2 photos/minute * 7 minutes = 14 photos.

Therefore, if y (time) is 7 minutes, the printer will print 14 photos.

Answer: A

Step-by-step explanation:

A dilation is not a rigid transformation, which means it has to scale the object into a different measure. So, enlarging or reducing the size of an object is a dilation.

The given angles are:

M arc CB=64°,M<AOC= 116° ,M arc AD=26°,M arc DFB=154°,M<CDB=32°.

First, we use the property that the measure of a central angle is equal to the measure of the intercepted arc.

Given that <COB = 64°, we know that the measure of arc CB is also 64°.

Next, we use the fact that the measure of an angle made on the circumference is half the measure of the angle made at the center.

We know that the measure of intercepted arc AD is 26°, and since the angle made at the center, <ABD, is 13°, we can calculate that the measure of arc AD is 2 x 13° = 26°.

Using the fact that a semicircle has a measure of 180°, we know that the measure of arc DFB is 180° - 26° = 154°.

Finally, we can use the angle CDB to find the missing angle.

We know that <CDB is an angle made on the circumference and that the measure of arc CB is 64°.

Thus, we can calculate that <CDB = 64°/2 = 32°.

Therefore, the missing angle is 32°.

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A formula for y in terms of x and c is y = c⁵√x

In inverse variation, as the value of one of the variables increases, the value of the other decreases and as the value of one of the variable decreases, the other increases.

From the information given, we have that;

y ∝1/√x

Now, let's find the constant value, k, we have;

y√x = k

We have that their values are;

y = c⁴, x = c²

Substitute the values, we have;

c⁴√c² = k

k = c⁵

Now, substitute the values

y = k√x

y = c⁵√x

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Answer:

The answer for <M is 28°

Step-by-step Explanation:

<P=180-48

<P=132°

base angles in an isosceles are equal

<M+<N+<P=180

3y+1+2y+2+132=180

3y+2y+3+132=180

5y+135=180

5y=180-135

5y=45

divide both sides by 5

5y/5=45/5

y=9

<M=3(9)+1=27+1=28°

Answer:

  (a)  (-5,20) and (4,11)

Step-by-step explanation:

You want the solutions to the system of equations ...

Using the second equation to substitute for y in the firs equation, we have ...

  x +x² -5 = 15

  x² +x -20 = 0 . . . . . subtract 15, put in standard form

  (x +5)(x -4) = 0 . . . . . factor

A product is zero only when one or more factors is zero. The values of x that make the factors zero are ...

  x = -5  and  x = 4

The corresponding values of y are ...

  y = 15 -x

  y = 15 -{-5, 4} = {20, 11}

The solutions are (x, y) = (-5, 20) and (4, 11).

By making the financially irresponsible decision of maxing out your credit card limit, you might not have money for an emergency situation.

As, There is no foolproof technique to determine how much you can spend in excess of your credit limit, but you can go over it.

When determining the risk of accepting an over-the-limit transaction, card issuers may take into account a number of criteria, including your prior payment history.

Now, maxing out credit card leads to negative results.

So, either not have money for an emergency situation or not be able to buy the things you need.

But we can still spend after maxing out the limit.

Thus, not have money for an emergency situation is correct option.

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Answer:

Step-by-step explanation:To solve this problem, we need to work backwards from the final price that Gina paid and determine the discounted price before tax was added.

Let x be the original price of the laptop. After a 25% discount, the discounted price is:

Discounted price = x - 0.25x = 0.75x

Next, we add 7% tax to the discounted price:

Final price = (0.75x) + 0.07(0.75x) = 0.8025x

We know that the final price that Gina paid was $963, so we can set up an equation:

0.8025x = 963

Solving for x, we get:

x = 1200

Therefore, the original price of the laptop was $1200, and the discounted price before tax was:

Discounted price = 0.75x = 0.75(1200) = $900

To check, we can add the 7% tax to the discounted price:

Final price = $900 + 0.07($900) = $963

This matches the price that Gina paid, so we can be confident in our answer.

The volume of the triangular prism is 36 in³.

A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.

To calculate the volume of the triangular prism, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

The anser is letter C)

Step-by-step explanation:

because it multiplies x3

0,5×3=1,5

1,5×10=15

10×3=30

Answer:

1cm=30m