What is the explicit formula for this arithmetic sequence?
-12,-17, -22, -27, ...

The mode is the category with the highest frequency in the distribution.

In a dataset or distribution, the mode refers to the value or category that appears most frequently. It represents the peak or most common observation in the dataset. Unlike the mean and median, which are measures of central tendency, the mode focuses on the frequency or occurrence of specific values or categories.

For example, if we have a dataset of test scores: 85, 92, 78, 92, 77, 85, 90. In this case, the mode would be 92 since it appears twice, which is more frequently than any other value.

In categorical data, the mode refers to the category or group with the highest frequency or count. For example, if we have a dataset of favorite colors: red, blue, green, blue, blue, yellow, green. In this case, the mode would be blue since it appears more frequently than any other color.

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Answer: $119.00

Step-by-step explanation:

To calculate the pay for the day, we need to determine the number of hours worked in the morning and the number of hours worked in the afternoon.

The morning shift starts at 8:00 AM and ends at 12:15 PM, which is a total of 12:15 - 8:00 = 4 hours and 15 minutes. The afternoon shift starts at 1:00 PM and ends at 5:15 PM, which is a total of 5:15 - 1:00 = 4 hours and 15 minutes.

Since there are 60 minutes in an hour, the total number of hours worked in the morning is 4 hours + 15 minutes / 60 minutes = 4.25 hours. The total number of hours worked in the afternoon is also 4.25 hours.

The total number of hours worked on the day is 4.25 + 4.25 = 8.5 hours.

To find the pay for the day, we need to multiply the number of hours worked by the wage rate:

Pay = 8.5 hours * $14/hour = $119

Rounding this number to the nearest hundredth gives us $119.00.

Answer:

9.2oz

Step-by-step explanation:

The probability of winning by picking the number 30 in roulette is 1/38.

In the game of roulette, the wheel consists of 38 spaces, with numbers 0 through 36 and an additional space marked 00. When you pick a specific number, such as 30, the probability of that number coming up on the wheel can be determined by calculating the ratio of favorable outcomes to the total number of possible outcomes.

In this case, there is only one favorable outcome, which is the ball landing on the number 30. The total number of possible outcomes is 38 since there are 37 numbered spaces (0 through 36) and one additional space for 00. Therefore, the probability of winning by picking the number 30 is 1 out of 38.

To put it simply, if you were to play roulette many times, you would expect the number 30 to come up approximately once every 38 spins on average. This probability remains the same for each individual spin, as each spin of the roulette wheel is an independent event.

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Answer:

The growth rate is 1.07%

Step-by-step explanation:

y=ab(to the power of x)

b is the growth/decay rate

b is 1.07% here

Answer:

7%

Step-by-step explanation:

The population of ants in the colony can be represented by the function f(t) = 1400(1.07)

Function = 1400( 1 + 7%)

= 1400(1 + 0.07)

= 1400(1.07)

Growth rate = 7%

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

\(\Huge \fbox{72 mph}\)

Step-by-step explanation:

Step 1:

Convert \(\bold{32 m/s}\) to \(\bold{km/h}\) by multiplying by 3.6 (since \(\bold{1 m/s}\) = \(\bold{3.6 km/h}\))

\(\large \text{32 m/s $\times$ 3.6 = 115.2 km/h}\)

Step 2:

Convert \(\bold{115.2 km/h}\) to \(\bold{mph}\) using the given conversion factor of \(\bold{8 km/h = 5 mph}\)

\(\large \text{115.2 km/h $\div$ 8 km/h = 14.4}\\\text{14.4 $\times$ 5 mph = 72 mph}\)

Therefore, \(\bold{32 m/s}\) is equivalent to \(\bold{72 mph}\).

----------------------------------------------------------------------------------------------------------

In the standard conversion unit, 32 m/s equals 72 mph in mph

The conversion equation is given as

\(\sf 8 \ km/h = 5 \ mph\)

Convert 8 km to meters

So, we have the following equation

\(\sf 8 \times 1000 \ m/h = 5 \ mph\)

Evaluate the products

So, we have the following equation

\(\sf 8000 \ m/h = 5 \ mph\)

Convert 1 hour to seconds

So, we have the following equation

\(\sf 8000 \ m/3600 s = 5\ mph\)

Evaluate the quotient

So, we have the following equation

\(\sf \dfrac{20}{9} \ m/s = 5 \ mph\)

Multiply both sides by 9/20

\(\sf 1 \ m/s = \dfrac{9}{20} \times 5 \ mph\)

Multiply both sides by 32

\(\sf 32 \times 1 \ m/s = 32 \times \dfrac{9}{20} \times 5 \ mph\)

Evaluate the products

\(\sf 32 \ m/s = 72 \ mph\)

Hence, the equivalent of 32 m/s in mph is 72 mph

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Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

Answer:

Let s be the speed of the plane. Then s - 100 is the speed of the car.

640/s = 240/(s - 100)

640(s - 100) = 240s

8(s - 100) = 3s

8s - 800 = 3s

5s = 800, so s = 160 mph

The speed of the plane is 160 mph, and the speed of the car is 60 mph.

Answer:

T-shirt is x

pants is y -> 2y=45

total is : 4x+2y=119

as we know 2y=45

4x+45=119

4x = 119-45

x= 74/4

each T-shirt is 18.5

The marginal revenue function is R'(z) = -0.092 dollars, the marginal cost function is C'(z) = 75 - 0.16z dollars, and the marginal profit function is P'(z) = 0.16z - 75.092 dollars.

The given revenue function is R(z) = 1052 - 0.092z dollars.

Differentiating R(z) with respect to z, we get the marginal revenue function:

R'(z) = -0.092

The given cost function is C(z) = 1000 + 75z - 0.08z² dollars.

Differentiating C(z) with respect to z, we get the marginal cost function:

C'(z) = 75 - 0.16z

The profit function is given by P(z) = R(z) - C(z).

Differentiating P(z) with respect to z, we get the marginal profit function:

P'(z) = R'(z) - C'(z)

      = -0.092 - (75 - 0.16z)

      = -0.092 - 75 + 0.16z

      = 0.16z - 75.092

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Answer:

-6

Step-by-step explanation:

16x-21x-16=21x-21x+14

Than -5x-16+16=14+16

-5x/5=30/5

=-6

12. 5x² - 180 = 0

5x² = 0 + 180

5x² = 180

x² = 180/5

x² = 36

x = √36

x = 6

13. 3x² - 100 = 332

3x² = 332 + 100

3x² = 432

x² = 432/3

x² = 144

x = √144

x = 12

14. ⅔x² - 8 = 16

⅔x² = 16 + 8

⅔x² = 24

2x² = 24 × 3

2x² = 72

x² = 72/2

x² = 36

x = √36

x = 6

15. ½x² - 5 = 5

½x² = 5 + 5

½x² = 10

x² = 10 × 2

x² = 20

x = √20

16. x² + 1 = 3x² - 13

1 + 13 = 3x² - x²

14 = 2x²

14/2 = x²

7 = x²

√7 = x

17. 2(x² + 4) = 10

2x² + 8 = 10

2x² = 10 - 8

2x² = 2

x² = 2/2

x² = 1

x = √1

x = 1

18. 3(x² - 1) = 9

3x² - 3 = 9

3x² = 9 + 3

3x² = 12

x² = 12/3

x² = 4

x = √4

x = 2

19. 2(x + 3)² = 8

2(x² + 3² + 2×x×3) = 8

2(x² + 9 + 6x) = 8

2x² + 18 + 12x = 8

2x² + 12x = 8 - 18

2x² + 12x = -10

2(x² + 6x) = -10

x² + 6x = -10/2

x(x + 6) = -5

x + 6 = -5/x

6 = -5/x - x

6 = -5/x - x²/x

6 = (-5 -x²)/x

6x = -5 - x²

The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

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Answer:

Step-by-step explanation:

Hhahahahahahahahhahahahahahaha

In theory, Option D. All of these stages occurs at prisoner classification.

Prisoner classification occurs during transfer, in preparation for release, and after problems occur. All of these stages are important for assessing an inmate's risk and providing appropriate security.

Prisoner classification involves assessing an inmate's risk level and providing an appropriate security level based on the results. This assessment is conducted during various stages, such as during transfer to another institution, in preparation for release, and after the inmate encounters problems. The classification process may involve evaluating an:

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The vertex is at (2, 1),

The focus is at (14, 1).

The directrix is the vertical line x = -10.

The distance between the vertex and the focus is 12 units, which is equal to the distance between the vertex and the directrix.

The vertices are located at (2 + 1/12, 1) and (2 - 1/12, 1), while the co-vertices are located at (2, 1 + 1/12) and (2, 1 - 1/12).

We have,

To classify the conic and find the standard form of the equation, we can first complete the square for y terms:

3y^2 - x - 6y + 5 = 0

3(y^2 - 2y) = x - 5

3(y^2 - 2y + 1) = x - 5 + 3

3(y - 1)^2 = x - 2

Now we have the equation in standard form, which is that of a parabola opening right.

Thus, the conic is a parabola.

The standard form of the equation is:

3(y - 1)^2 = x - 2

The vertex of the parabola is (2, 1). Since the parabola opens right, the focus and directrix are to the right of the vertex.

To find the focus and directrix, we need to use the formulae:

p = 1 / (4a)

focus: (h + p, k)

directrix: x = h - p

where (h, k) is the vertex and a is the distance from the vertex to the focus or directrix.

From the standard form, we can see that a = 1 / (4*3) = 1 / 12.

Thus, p = 12.

The focus is located at (2 + 12, 1) = (14, 1).

The directrix is a vertical line located at x = 2 - 12 = -10.

To find the vertices, we need to add or subtract a from the x-coordinate of the vertex.

The vertices are located at (2 + a, 1) and (2 - a, 1), so:

(2 + a, 1) = (2 + 1/12, 1) and (2 - a, 1) = (2 - 1/12, 1).

To find the co-vertices, we need to add or subtract a from the y-coordinate of the vertex.

The co-vertices are located at (2, 1 + a) and (2, 1 - a),

so:

(2, 1 + a) = (2, 1 + 1/12) and (2, 1 - a) = (2, 1 - 1/12).

Thus,

The vertex is at (2, 1),

The focus is at (14, 1).

The directrix is the vertical line x = -10.

The distance between the vertex and the focus is 12 units, which is equal to the distance between the vertex and the directrix.

The vertices are located at (2 + 1/12, 1) and (2 - 1/12, 1), while the co-vertices are located at (2, 1 + 1/12) and (2, 1 - 1/12).

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Answer:

2 1/4 is the answer

Step-by-step explanation:

4 2/4÷2= 2 1/4

Answer:

2 1/4

Step-by-step explanation:

Set up a table with the labels flour and cookies on the flour side have 4 1/2 on the cookies side have 48 then in another row 24. Divide 24 by 48 to find out what to multiply 4 1/2 by to get the answer.48 divided by 24 is .5 so you would multiply 4 1/2 by .5 to get 2 1/4

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

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Answer:

you must be so stiupid that you have to use answers ff a website to cheat for school

Step-by-step explanation:

The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

-3

Step-by-step explanation:

Answer: -3

Step-by-step explanation: The additive inverse tells us that if we

add a number and the opposite of that number, the result will be 0.

So in this problem, 3 + (-3) = 0.

Step-by-step explanation:

C. represent the number line for x

where x ix

Answer:

6/12 but to simplify it would be 1/2

Answer:

\(\frac{2}{3} *\frac{3}{4}\)       = 1/2

Step-by-step explanation:

2/3 * 3/4

6/12=1/2

Given statement solution is :- The value of the number is -1/9.

Let's solve the problem step by step.

Let's assume the number we're looking for is represented by the variable "x".

The problem states that the sum of 9 times the number (9x) and 7 is equal to 6. We can write this as an equation:

9x + 7 = 6

To isolate the variable "x," we need to move the constant term (7) to the other side of the equation. We can do this by subtracting 7 from both sides:

9x + 7 - 7 = 6 - 7

This simplifies to:

9x = -1

Finally, to solve for "x," we divide both sides of the equation by 9:

9x/9 = -1/9

This simplifies to:

x = -1/9

So, the value of the number is -1/9.

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The sampling method described in which the population is first divided into groups and then random samples are drawn from each group is called stratified sampling. In this sampling method, the population is divided into homogeneous subgroups called strata, based on some characteristic of interest such as age, gender, income level, or geographic location. Random samples are then drawn from each stratum, and the data collected from each sample are combined to form the final sample.

Stratified sampling is often used when the population is heterogeneous, meaning that it has distinct subgroups with different characteristics that may affect the outcome of the study. By dividing the population into homogeneous subgroups, stratified sampling increases the precision of the estimates and reduces the sampling error, compared to simple random sampling. Stratified sampling also ensures that each subgroup of the population is represented in the sample, which may be important for making inferences about the entire population. However, stratified sampling can be more complex and time-consuming than simple random sampling, especially if the population has many subgroups.

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The area between the curves y = 8/(1 + x⁴) and y = 4x² is approximately 6.193 square units.

To find the area between the curves, we need to determine the points of intersection and integrate the difference between the two functions over that interval.

To find the area between the curves y = 8/(1 + x^4) and y = 4x^2, we can plot the curves and calculate the definite integral of the positive difference between the two functions over the interval where they intersect. Here's how you can use a graphing calculator to visualize and calculate the area:

Turn on the graphing calculator and enter the equations of the curves:

For the first curve y = 8/(1 + x^4)

For the second curve, y = 4x^2

Adjust the appropriate window settings on the calculator to ensure that the region of interest is visible. You can set the x-axis range to span the intersection of two curves.

Graph the equations to see the area between the curves.

Determine the values ​​of x where the curves intersect. These are the x values ​​where the two equations have the same y values. You can use the intersection function of the calculator to find these points.

Once you have the intersections, calculate the definite integral of the positive difference between the two curves in the interval where they intersect. This integral will give you the area between the curves.

Alternatively, if you cannot use a graphing calculator or prefer to calculate the area by hand, you can proceed as follows:

Construct an equation to find the points of intersection:

8/(1 + x^4) = 4x^2

Solve the equation to find the values ​​of x where the curves intersect.

Once you have the intersections, set up an integral to find the area between the curves:

A = ∫[a, b] (8/(1 + x^4) - 4x^2) dx

Here [a, b] represents the interval where the curves intersect.

Calculate the definite integral using appropriate integration techniques or software.

The result of the integral will give you the area between the curves.

The area between the curves y = 8/(1 + x⁴) and y = 4x² is approximately 6.193 square units.

Please note that the above steps provide a general guideline for finding the area between two curves. The actual calculations and values ​​will depend on the specific intercepts and integration limits you get from solving graphs or equations.

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The equation describing Linda's Age and Liam's age will be: Liam's Age(Baby Brother) + 3 = Linda Age.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.

Here, let us denote Linda's age as L and Liam's age as B. We are given that Linda is 3 years older than Liam, so we can write the equation as L = B + 3

This equation states that Linda's age (L) is equal to Liam's age (B) plus 3 years. Therefore, Linda's age can be determined by adding 3 years to Liam's age.

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