what is the symbol of an inverse function​

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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4{8.2+3.7(4.4×8.8 -18.86)}=

4(8.2+3.7(38.72-18.86))=

4(8.2+(3.7)(19.86))=

4(8.2+73.482)=

(4)(81.682)=

326.728

Answer:

X can be any of those numbers depending on which equation it is in

Step-by-step explanation:

Answer:

5(5v+4)=17v+8v+9+9

25v+20=25v+18

25v-25v=18-20

0v=-2

i think soooo

this question is very very irrelevant

Step-by-step explanation:

The number 3.01 is a statistic, the symbol for the number 3.01 is μ_hat; and To conduct a simulation-based test of significance, we need to compare the observed mean (3.01 hours) with the hypothesized mean (2.75 hours).

The number 3.01 is a statistic.

The symbol for the mean number of hours per day spent watching TV for the sample of 100 Cal Poly students is μ_hat.

To conduct a simulation-based test of significance, we need to compare the observed mean (3.01 hours) with the hypothesized mean (2.75 hours). The null hypothesis is that the population mean (μ) is equal to 2.75 hours, and the alternative hypothesis is that the population mean is not equal to 2.75 hours.

Steps to find p-value:

1. Calculate the difference between the observed mean and the hypothesized mean: d = μ_hat - 2.75 hours

2. Generate a large number of random samples with the same sample size as the original sample, and calculate the mean of each sample.

3. Calculate the difference between the mean of each sample and the hypothesized mean and store the values in a list.

4. Count the number of differences that are equal to or greater than the difference between the observed mean and the hypothesized mean (d).

5. Divide the count by the total number of simulations to get the p-value. This gives us the probability of getting a sample mean equal to or greater than the observed mean if the null hypothesis is true.

6. Compare the p-value with the significance level (α) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than α, we reject the null hypothesis and conclude that the data provide evidence that the average number of hours per day Cal Poly students spending the time watching TV is different from 2.75 hours.

If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the average number of hours per day Cal Poly students spending the time watching TV is different from 2.75 hours.

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--The given question is incomplete; the complete question is

"Reconsider Dr Sameer's research question about how much time Cal Poly students spend watching television. Suppose that Dr Sameer surveys a random sample of 100 Cal Poly students, and for this sample, the mean number of hours per day spent watching TV turns out to be 3.01 hours.

1. Is the number 3.01 a parameter or a statistic?

2. Assign an appropriate symbol to the number 3.01.

3. Describe how you can conduct a simulation‐based test of significance to investigate whether the data provide evidence that the average number of hours per day Cal Poly students spend watching TV is different from 2.75 hours. Be sure to provide details on how one would find a p‐value."--

Answer:

A Between 1.43 in. and 1.47 in.

Step-by-step explanation:

If the circumference is between 9 and 9.25 inches, and we know that circumference equals 2 * pi * radius, we can solve to find that the radius equals the circumference divided by 2pi. So we get between 1.43 in and 1.47in

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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Answer:

I answer to the problem is x = 7

Step-by-step explanation:

\(2(x - 3) = 8(x - 6)\)

\(2x - 6 = 8x - 48\)

\( - 6 = 6x - 48\)

\(42 = 6x\)

\(x = \frac{42}{6} \)

\(x = 7\)

The research explores the various factors that may influence the learning choices of first-year undergraduates, such as the family and educational background of the student, their socioeconomic status and the availability of resources, among others.

Factor is a mathematical quantity which is multiplied with another quantity to give a product. Factors can also be defined as the numbers that divide a given number exactly. Factors are used in everyday life to calculate many different types of problems, such as compound interest, speed, distance and time, and more. Factors are also used in statistics and probability to determine the likelihood of certain events occurring.

The paper will also examine the various types of postgraduate courses that are available to undergraduates, including those offered by universities and other institutions, such as professional courses or distance learning programmes.

The research adopts a qualitative approach, and will use semi-structured interviews with first-year undergraduates to gain an understanding of their learning choices, and the factors that influence them. Interviews will be conducted with students in different disciplines, in order to gain an insight into how the different disciplines shape students' learning preferences. The research will also use questionnaires to obtain data on the socioeconomic background, family background and educational background of students.

In addition, the research will use documentary analysis of university prospectuses and websites, and information from other sources, such as employers and professional bodies, to gain an understanding of the various postgraduate courses that are available to undergraduates. This data will be used to compare and contrast the learning choices of undergraduates from different disciplines and economic backgrounds.

Finally, the research will use an interpretive approach to analyse the data collected and develop a theory of the factors that influence the learning choices of first-year undergraduates. The theory will be used to inform the design of initiatives to help undergraduates make informed decisions about their learning choices.

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Answer:

Step-by-step explanation:

From the information given:

Consider X to be the random variable denoting the bad debt ratios for Ohio Bank.

Then, \(X \sim N ( \mu, \sigma ^2)\)

Thus the null hypothesis and the alternative can be computed as:

Null hypothesis:

\(H_o : \mu \leq3.5\%\)

Alternative hypothesis

\(H_1 : \mu > 3.5\%\)

The type I and type II error is as follows:

Type I:

The mean bad debt ratio is > 3.5% when it is not

Type II:

The mean bad debt ratio is ≤ 3.5% when it is not.

The test statistics can be calculated by using the formula:

\(t = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}\)

where;

sample size n = 7

mean = 6+8+5+9+7+5+8 = 48

sample mean \(\overline x =\dfrac{48}{7}\)

\(\overline x\) = 6.86

sample standard deviation is :

\(s = \sqrt{\dfrac{\sum( x -\overline x)^2}{n-1}}\)

\(s = \sqrt{\dfrac{( 6 -6.86)^2+( 8-6.86)^2+ ( 5 -6.86)^2 + ...+( 7 -6.86)^2+ ( 5 -6.86)^2+( 8 -6.86)^2 }{7-1}}\)

s = 1.573

population  mean \(\mu = 3.5\)

Therefore, the test statistics is :

\(t = \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}}\)

\(t = \dfrac{6.86- 3.5}{\dfrac{1.573}{\sqrt{7}}}\)

\(t = \dfrac{3.36}{\dfrac{1.573}{2.65}}\)

\(t = \dfrac{3.36\times {2.65}}{{1.573}}\)

t = 5.660

At significance level of 0.01

\(t_{0.01} = 3.707\)  

P - value = P(T > 5.66)

P - value = 1 - (T < 5.66)

P - value = 1 - 0.9993

P-value = 0.0007

Therefore, since \(t_{0.01} < t\) , we reject the null hypothesis and conclude that the claim that the mean bad debt ratio for Ohio banks is higher than the mean for all financial institutions is true.

The z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

The sample scores are given as:

2, 3, 5, 5, 6.

Calculate the mean and the standard deviation using a statistical calculator.

From the statistical calculator, we have:

\(\bar x = 4.2\) --- mean

\(\sigma_x = 1.64\) --- standard deviation

The z-score is then calculated using

\(z= \frac{x - \bar x}{\sigma}\)

Where:

x = 2, 3, 5, 5, 6.

So, we have:

\(z_1= \frac{2 - 4.2}{1.64} = -1.34\)

\(z_2= \frac{3 - 4.2}{1.64} = -0.73\)

\(z_3= \frac{5 - 4.2}{1.64} = 0.48\)

\(z_4= \frac{5 - 4.2}{1.64} = 0.48\)

\(z_5= \frac{6 - 4.2}{1.64} = 1.10\)

Hence, the z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

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The condition that must be true about the probabilities is P(A and B) = xy

The probabilities of the events A and B are given as:

P(A) = x

P(B) = y

Given that events A and B are independent events, then we have the following equation

P(A and B) = P(A) * P(B)

The equation becomes

P(A and B) = x * y

P(A and B) = xy

Hence, the condition that must be true is P(A and B) = xy

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solve for x

\(\frac{x-5}{3} -\frac{x-2}{4} =7\)

Multiply both sides of the equation by 12, the least common multiple of 3,4.

4(x−2)−3(x−2)=84

Use the distributive property to multiply 4 by x−2.

4x−8−3(x−2)=84

Use the distributive property to multiply −3 by x−2

4x−8−3x+6=84

Combine 4x and −3x to get x

x−8+6=84

Add −8 and 6 to get −2.

x−2=84

Add 2 to both sides.

x=84+2

Add 84 and 2 to get 86

x=86

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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Answer:

Step-by-step explanation:

Consider the initial given value problem

\(y'=-x-y,y(1)=1\)

Use Euler's Method

\(\Delta =0.1\)

Then, we have

\(y(t_1=1.1)=y(t_0+\Delta)\\\\=y_0+\Delta y'(t_0)\\=1+(0.1)(-1-1)\\=1-0.2\\=0.8\\=y_1\)

\(y(1.2)=y_1+\Delta y'(t_1,y_1)\\=0.8+0.1(-1.1-0.80\\=0.61\\=y_2\\\\y(1.3)=y_2+\Delta y'(t_2,y_2)\\=(0.61)+(0.1)(-1.2-0.61)\\=0.429\\=y_3\\\\y(1.4)=(0.429)+0.1(-1.3-0.429)\\=0.2561\)

Now estimate y when x =2.4 for the solution curve satisfy y(1) = 0

Then,

\(y(1.1)=y_0+ \Delta y'(t_0)=0+(0.1)(-1-0)=-0.1\)

\(y(1.2)=-0.1+0.1(-1.1+0.1)=-0.2\\y(1.3)=-0.2+0.1(-1.2+0.2)=-0.3\\y(1.4)=-0.3+0.1(-1.3+0.3)=-0.4\\y(1.5)=-0.4+0.1(-1.4+0.4)=-0.5\\y(1.6)=-0.5+0.1(-1.5+0.5)=-0.6\\y(1.7)=-0.6+0.1(-1.6+0.6)=-0.7\\y(1.8)=-0.7+0.1(-1.7+0.7)=-0.8\\y(1.9)=-0.8+0.1(-1.8+0.8)=-0.9\\y(2.0)=-0.9+0.1(-1.9+0.9)=-1.0\\y(2.1)=-1.0+0.1(-2.0+1)=-1.1\\y(2.2)=-1.1+0.1(-2.1+1.1)=-1.2\\y(2.3)=-1.2+0.1(-2.2+1.2)=-1.3\\y(2.4)=-1.3+0.1(-2.3+1.3)=-1.4\)

Hence,Euler's approximation y(2.4) = -1.4

Respuesta:

el descuento fue de 20%

Answer:

go to math papa dot com. he will give you the answers . trust me . algebra is not fun...

Answer:

11/4     0.75    60%    1/2     0.2

Step-by-step explanation:

Given

11/4  0.2   60%   0.75   1/2

Required

Order from largest to smallest

Convert all numbers to decimal

\(11/4 = 2.75\) ; \(60\% = 0.60\) and \(1/2 = 0.50\)

So, the numbers are:

2.75    0.2     0.60     0.75     0.50

From largest to least, we have:

2.75    0.75     0.60   0.50   0.2

Convert all numbers back to their original form

11/4     0.75    60%    1/2     0.2

Answer:

1433 m^2

Step-by-step explanation:

Area of the triangle

16 x 16 x 1/2 = 128

Area of the hexagon

A = \(\frac{3\sqrt{3} }{2} *a^2\)

a is a side of the hexagon

A =  \(\frac{3\sqrt{3} }{2} * 16^{2}\) = 665.1075101...

There are 6 triangles so...

128 x 6 = 768

Therefore the surface area is

665.1075101... + 768 = 1433.10751 m^2

The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".

When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.

In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.

a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.

b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.

c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.

d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.

Therefore, "time(length)" is the most suitable and appropriate name for the function.

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Answer:

Opposite angles

Step-by-step explanation:

Where two lines intersect each other, the angles opposite to each other are opposite angles. Opposite angles have the same measure.

I hope this helps!

Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer....

Hope it helps!

Brainliest pls!

Follow me!

Surface area of the room:

area of ceiling + floor + the four walls

ceiling area = floor area

Total surface = 15 + 15 +32 = 62 m²

Answer:

Step-by-step explanation:

Since the above figure is a right angled triangle we can use trigonometric ratios to find y

To find y we use tan

tan∅ = opposite/ adjacent

From the question

the opposite is y

the adjacent is 350 ft

Substitute the values into the above formula

That's

\( \tan(27) = \frac{y}{350} \)

y = 350 tan 27

y = 178.3339

We have the final answer as

Hope this helps you

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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The amount of gas that mom's truck can hold would be 24 gallons.

In order to calculate the gas capacity of the truck, we must first compare how much more the truck is able to hold compared to dad's car. As the truck can accommodate 50% additional fuel, this amount can be calculated by multiplying the car's capacity by 0.5:

Additional gas = 16 gallons × 0. 5 = 8 gallons

The amount of gas that mom's truck can hold is therefore:

= Truck's tank capacity = 16 gallons + 8 gallons = 24 gallons

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Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

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Answer:

1) D: -8 < x ≤ 2, R: -4 ≤ y ≤ 11.

2) D: -8 ≤ x ≤ -3 U 2 ≤ x < ♾️,

R: -6 ≤ y ≤ -5 U -3 ≤ y < ♾️.

Answer:

Theta=1.57rad, 4.71rad, 0rad, 2π rad, π rad and –π rad

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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