Must a function that is decreasing over a given interval always be negative over that same interval? Explain.

The length AC will be 5.83 and the angle ACD will be 34.45°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The length AC will be calculated as,

AC² = 5² + 3²

AC = √ ( 25 + 9 )

AC = √34

AC = 5.83

The angle ACD will be,

tanθ = P / B

θ = tan⁻¹ = ( 4 / 5.83)

θ = 34.45°

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Answer:

y=5

Step-by-step explanation:

RS  +    ST   =    RT

9y+2     +     2y+3       =   60

11y         +      5         = 60

11y   =     55

Y = 5

Answer:

16 minutes

Step-by-step explanation:

80% of 20 =

10% ×8= 2×8=16

16 mins

Answer:

120 divided by 10 is 12. 120 divided by 12 is 10.

Answer:

Step-by-step explanation:

As no identity applies on this, we use distributive property, the property is:

(

a

+

b

)

(

c

+

d

)

=

a

(

c

+

d

)

+

b

(

c

+

d

)

Using that

2

(

5

+

6

b

)

+

5

b

(

5

+

6

b

)

Expand the brackets

10

+

12

b

+

25

b

+

30

b

2

Solve

10

+

37

b

+

30

b

2

Answer:

Step-by-step explanation:

58÷24

Answer: D - 58÷24

It is because division is also written in fraction form. The first number (58) is the numerator and the second number which divides the first (24) is the denominator.

hope it helps, I'd appreciate a brainliest.

Step-by-step explanation:

i used elimination method

Answer:

1/3(n)+11

Step-by-step explanation:

n represents a number

Grouped Frequency Distribution

Class Interval: Frequency:

0 – 10         2

10 – 20         3

20 – 30         4

30 – 40         2

Grouped Frequency Distribution is a method of organizing and displaying data in a tabular form, where the data is divided into intervals or groups. It is also known as a Frequency Table or a Grouped Frequency Table.

In this example, Ms. Thompson's test scores were distributed into classes of 0–10, 10–20, 20–30, and 30–40. The frequency of a class is the number of test scores in that class. The frequency of the 0–10 class was 2, meaning two students scored between 0 and 10 on the test. The frequency of the 10–20 class was 3, meaning three students scored between 10 and 20 on the test. The frequency of the 20–30 class was 4, meaning four students scored between 20 and 30 on the test. Finally, the frequency of the 30–40 class was 2, meaning two students scored between 30 and 40 on the test.

This grouped frequency distribution makes it easier to analyze the data and identify any patterns or trends in the test scores. It is also useful for summarizing data into a more manageable and easily understandable form.

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The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m.

The logical expression that represents the statement "Despite the fact that it is sunny today, I will bring my umbrella" is (B) s∧m. This is because the conjunction "and" (∧) is used to connect two statements that must both be true in order for the overall statement to be true. In this case, both s (It is sunny today) and m (I will bring my umbrella) must be true in order for the statement to be true.

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(B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."


The logical operator ∧ (conjunction) connects two propositions and represents the idea of "and." Therefore, s∧m means "It is sunny today and I will bring my umbrella." This is the logical expression that represents the statement given in the question.


To summarize, the correct answer is (B) s∧m, which represents the logical expression for "Despite the fact that it is sunny today, I will bring my umbrella."
Main Answer: The correct logical expression is (B) s∧m.

In the given statement, "Despite the fact that it is sunny today, I will bring my umbrella," both propositions s (It is sunny today) and m (I will bring my umbrella) are true at the same time. The logical expression that represents this is s∧m, which means "s AND m" are both true.

The statement "Despite the fact that it is sunny today, I will bring my umbrella" is best represented by the logical expression (B) s∧m, as it shows that both s and m are true.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Using permutation, there are a total of 24 different orders possible.

If there are a total of 4 floats in a parade then the number of possible orders = 4!

If we further calculate it we will get,

               4 x 3 x 2 x 1 = 24

So there are a total of 24 possible orders in which the floats should appear.

The concept used here is the number of arrangements and the technical term used for it in mathematics is a permutation. A permutation is a mathematical calculation that involves finding the number of ways a particular set can be arranged.

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Answer:

An upward trend

Step-by-step explanation:

When data points on a graph show a steady upward trend, it is typically referred to as a "positive correlation" or "positive trend."

We have,

A positive correlation means that as one variable increases, the other variable tends to increase as well.

In other words, there is a positive relationship between the two variables being plotted on the graph.

Positive correlation is often represented by a line that slopes upward from left to right on a scatter plot or graph.

Thus,

When data points on a graph show a steady upward trend, it is typically referred to as a "positive correlation" or "positive trend."

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Answer:

A right triangle

Step-by-step explanation:

A right triangle would meet these characteristics. A triangle's inner angles always add up to be 180 degrees. A right triangle has one angle at 90 degrees meaning the other two angles need to be less than 90 degrees and sum up to be 90 degrees. This would indicate that both of these angles' exterior angles would be obtuse because they would be wider than 90 degrees.

From the above evaluations, we can see that the absolute maximum value occurs at t = 3^(3/2) with f(3^(3/2)) = 1.4495, and the absolute minimum value occurs at t = -1 with f(-1) = 0.

To find the absolute maximum and absolute minimum values of the function f(t) = t - t^(1/3) on the interval [-1, 5], we need to evaluate the function at its critical points and endpoints within that interval.

Critical Points:

We find the critical points by taking the derivative of f(t) and setting it equal to zero:

f'(t) = 1 - (1/3)t^(-2/3)

Setting f'(t) = 0 and solving for t:

1 - (1/3)t^(-2/3) = 0

1 = (1/3)t^(-2/3)

3 = t^(-2/3)

3^(3/2) = t

t = 3^(3/2)

Endpoints:

We evaluate the function at the endpoints of the interval, t = -1 and t = 5.

Now, we compare the function values at these critical points and endpoints to determine the absolute maximum and minimum values.

Evaluate f(t) at t = -1:

f(-1) = -1 - (-1)^(1/3) = -1 - (-1) = -1 + 1 = 0

Evaluate f(t) at t = 3^(3/2):

f(3^(3/2)) = 3^(3/2) - (3^(3/2))^(1/3) = 3^(3/2) - 3 = 1.4495

Evaluate f(t) at t = 5:

f(5) = 5 - 5^(1/3)

Now, we compare the function values:

f(-1) = 0

f(3^(3/2)) = 1.4495

f(5) = 5 - 5^(1/3)

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Given:

Total number of students at Colfax Middle School = 270

Ratio of boys to girls is 5:4.

Total number of students at Winthrop Middle School = 180

Ratio of boys to girls is 4:5.

The two schools hold a dance and all students from both schools attend.

To find:

The fraction of the students at the dance are girls

Solution:

There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.

\(5+4=9\)

Number of boys \(=270\times \dfrac{5}{9}=150\)

Number of girls \(=270\times \dfrac{4}{9}=120\)

There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.

\(4+5=9\)

Number of boys \(=180\times \dfrac{4}{9}=80\)

Number of girls \(=180\times \dfrac{5}{9}=100\)

Now,

Total number of students in both schools \(= 270+180\)

                                                                \(= 450\)

Total number of girls in both schools \(= 120+100\)

                                                         \(= 220\)

The fraction of the students at the dance are girls is

\(\text{Required fraction}=\dfrac{\text{Total number of girls in both schools}}{\text{Total number of students in both schools}}\)

\(\text{Required fraction}=\dfrac{220}{450}\)

\(\text{Required fraction}=\dfrac{22}{45}\)

Therefore, the required fraction is \(\dfrac{22}{45}\).                                

The rectangle will form a cylinder when it rotates about the dashed line.

We have to given that;

To find plane figure which generates a cylinder when it rotates about the dashed line.

Hence, By figure we get;

When we rotate all the figure about the dashed line, we get;

The circle will form a sphere.

The rhombus (it can also be a square) will form a 2 cones attached at the bottom.

The rectangle will form a cylinder.

The triangle will form a cone.

Hence, The rectangle will form a cylinder when it rotates about the dashed line.

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Answer:B

Step-by-step explanation:

Answer:

B-  \(x\leq 1\)

Step-by-step explanation:

On an inequality graph when the dot is filled in that means it is \(\leq\) or \(\geq\).

So, on this graph, the dot is filled in and pointing to the right.

Therefore, x is less than or equal to 1

or,  \(x\leq 1\)

Answer:

48.25 mm^2

Step-by-step explanation:

Well you really need to find 4 sides.

There are 2 different sides, one is the bottom and the rest are the sides.

All sides are the same except for the bottom.

The bottom has the two measures of base and height, base being 5 and height being 4.3

Following the formula of an area for a triangle a=bh/2, you’d hey 10.75.

Now for the rest you have a base of 5 and a height of 5, same process, different numbers. You’d get 12.5. Since there are only 3 faces remaining and all of them are the same we can triple 12.5 to 37.5 (by multiply by 3) and then add up the two numbers.

37.5+10.75= 48.25mm

Answer:

a. \(3^4\)

b. \(7^5\)

c. \(10^2\)

d. \(5^7\)

Step-by-step explanation:

When multiplying or dividing numbers with exponents, the rule is that you add the exponents together if multiplying, or subtract them if dividing. This is only possible with numbers of the same base (the number before the exponent).

\(3^2\) multiplied by \(3^2\) is \(3^4\) because the exponents, 2 and 2, are added together. The bases remain unchanged.

\(7\) times \(7^4\) is \(7^5\) because another way to write \(7\) is \(7^1\), and the exponents can be added together from there.

The same logic can be applied to the division questions, but with subtraction instead of addition.

Answer:

See below

Step-by-step explanation:

There probably are multiple ways to say this ....here is one

five times the quantity of twenty five minus w  then added to the quantity 3 divided by w

(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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Answer:

6.28cm

Step-by-step explanation:

I think for me the easiest would be to find the circumference and divide by 4, since the arc is 1/4 of the circumference of the circle.

C=2πr

C=2(3.14)(4)

C = 25.12cm

25.12cm/4 = 6.28

The correct option is the: b The treatments are the organic and traditional fertilizer

Treatments are defined as what we want to compare in the experiment. It can consist of the levels of a single factor, a combination of levels of more than one factor, or of different quantities of an explanatory variable.

Treatments are usually administered to experimental units by 'level', where level implies amount or magnitude. For example, if the experimental units were given 5mg, 10mg, 15mg of a medication, those amounts would be three levels of the treatment.

Therefore, we can conclude that in this question, the treatments are the organic and traditional fertilizer.

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Answer:

$200

Step-by-step explanation:

30 * 5=150 +50=200

The value of the a_5 is -405 if the a_1 =5 and a_n=-3a_{n-1} which is a geometric sequence with common ratio -3.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

\(\rm a_1 = 5\\\\\rm a_n = -3a_{n-1}\)

Plug n = 2

\(\rm a_2 = -3a_{2-1}\\\\\rm a_2 =- 3a_{1}\\\\a_2 = -15\)(as,  \(\rm a_1 = 5\))

Plug n = 3 we get:

\(a_3 = -45\)

Plug n = 4, we get:

\(\rm a_4 =- 135\)

Now plug n = 5, we get:

\(\rm a_5 = -405\)

Thus, the value of the a_5 is -405 if the a_1 =5 and a_n=-3a_{n-1} which is a geometric sequence with common ratio -3.

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Answer:

There are 13 years 6 months and 12 days.

Step-by-step explanation:

Let's convert the scientific notation to standard form of minutes

7.01568x10^6 =7015680 minutes

Now, let's convert this to number of days because each day has 24*60=1440 minutes.

So, number of days in 7015680 minutes is \(\frac{7015680}{1440}\)=4872 days

Now, change this 4872 days to years, months and days.

We know 1 year has 12 months and one month has 30 days.

So,

Number of years =\(\frac{4872} {12*30}\)=13.53333333 years

Now, convert 0.53333333 years to months.

0.53333333*12=6.4 months.

Now, convert 0.4 months to days.

0.4* 30 =12 days.

So, there are 13 years 6 months and 12 days.