Given the equation, proof it.

Answer:

[-4,2] is the range

Step-by-step explanation:

A parent function of sine is known to have range of -A ≤ y ≤ A where A stands for amplitude.

Therefore, we would have the range:

[tex] \displaystyle{ - 3 \leqslant g(x) \leqslant 3}[/tex]

But since there's a vertical shift of -1, we have to subtract -1 from both -3 and 3.

[tex] \displaystyle{ - 4 \leqslant g(x) \leqslant 2}[/tex]

Therefore, the range of function is [-4,2]

Given that ABCD is a rhombus, the value of x is 29. Option A

A rhombus is a parallelogram having four equal sides and, occasionally, one without any right angles.

A rhombus's diagonals are perpendicular to each other.

sum the equation to 180

x + 3x -26 + 90 = 180

4x = 180 - 90 + 26

4x = 116

We have to divide through the equation by 4 in order to get the value of x

4x / 4  = 116 / 4

x = 29

Hence the value of x in the given rhombus is 29

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Answer:29 is the answer

Step-by-step explanation:

On solving the given question, by the equation, A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer .A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

J can ride his bike 8 mph faster than A can ride. It takes A 3 hours longer than J to ride 48 miles. How fast can J ride?

Let r = rate that J rides, in miles per hour.

Then rate that A rides is (r – 8).

distance = rate * time

time = distance/rate

Time taken by J to ride 48 miles = 48/r.

Time taken by A to ride 48 miles = 48/(r – 8).

But A's time is 3 hours more than J's time.

48/(r – 8) = 3 + 48/r

Solve that for r.

48/(r – 8) = 3r/r + 48/r

48/(r – 8) = (3r + 48)/r

Multiply both sides by (r – 8)r.

[tex]48(r) = (3r + 48)(r - 8)\\ 48r = 3r2 -24r + 48r -384\\ 0 = 3r2 - 24r -384\\ 0 = r2 -8r - 128\\ 0 = (r -16)(r + 8)[/tex]

So r = 16 mph or r = –8 mph.

J riding 48 mi at 16 mph takes 3 hours.

A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer.

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Answer: a=9 b=11

Step-by-step explanation:

This is a parallelogram; we know by the definition of the shape that the opposites sides are congruent.

That means a, the opposite of the 9, is 9.

That means b, the opposite of the 11, is 11.

The probability that hugo will solve rubik's cube in less than 8 minutes is 0.4375.

We have given that,

the amount of time it takes hugo to solve a rubik's cube is continuous and uniformly distributed between 4.5 minutes and 12.5 minutes.

i.e. a = 4.5 and b = 12.5

The probability that we find a value of X lower than x is given by the f

P(X < x) = [tex]\frac{x-a}{b-a}[/tex]

We have to find probability that it takes hugo less than 8 minutes to solve rubik's cube.

Therefore

P(X < 8) =  [tex]\frac{8-4.5}{12.5-4.5}[/tex]

             = [tex]\frac{3.5}{8}[/tex]

P(X < 8) = 0.4375

Hence the probability that it takes hugo less than 8 minutes to solve a rubik's cube is 0.4375%.

The uniform continuous distribution is one of the simplest probability distributions in statistics. Is is a continuous distribution, this means that it takes values within a specified range. A continuous uniform distribution takes values in a range [a,b].

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The value of test statistics  as calculated from the given data is 0.092.

p = 1 - P(Z < Z')

Z' = (8200-8000)/ (1500/√100)

Z'= 1.3

p = 1 - P(Z < Z')

= 1 - P(Z < 1.3)

= 1 - 0.908

= 0.092

The Z-score, also known as the standard score, indicates how far a data point deviates from the mean. It represents the number of standard deviations an element has from the mean. As a result, the Z-Score is expressed in terms of standard deviation from the mean.

A z score is a statistical measurement that indicates how far a raw score deviates from the mean of a distribution. A z score is used in a z test to test hypotheses. It is also used in prediction intervals to calculate the likelihood of a random variable falling between two values.

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Answer:

chronological

or +1 each number up

Step-by-step explanation:

The middle number on the 50th row is 891.5.

The nth row is 18n - 17.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

We see that there are 18 numbers in each row.

The numbers are consecutive natural numbers.

Now,

We can see that,

The first number of each row is 1.

The first number of the second row is 19.

The first number of the third row is 37.

The first number in each row can form a series.

1, 19, 37,....

This series is an arithmetic sequence.

First term = 1

Common difference = 18

The nth term is a + (n - 1)d.

50th term.

= 1 + (50 - 1)18

= 1 + 49 x 18

= 1 + 882

= 883

This means,

The 50th row will have the following series.

883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900.

The middle number is the midpoint of 891 and 892.

= 891.5

The nth row.

= 1 + (n - 1)18

= 1 + 18n - 18

= 18n - 17

Thus,

The middle number on the 50th row is 891.5.

The nth row is 18n - 17.

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the area between first two curves is 10.67-unit, 2nd two curves is 8-unit, 3rd two curves is 7.5 unit, and the last two curves is

area bounded by two curves means the curves have intersected each other and we can determine the point of intersection of them. In the next we apply the integration with limit formula for the equation of curves in where the point of intersection acts as the upper and lower limit.

while determining area we get either negative value or positive value depending on the position of curve in the xy  coordinate but in real life the value of area is written as a positive number.

1. the curve y=x² and y=4x

let the two curves intersects each other so x²- 4x= 0

                                                    x=0, 4

                                   for this value of x, we determine the values of y

                                  y= 0, 16

  now we determine the area between two curves by using the formula, ∫x²dx-∫4xdx

            ∫₀⁴(x²-4x) dx

               [1/3×x³-³4/2×x²]₀⁴

   area = -10.67

2. the curves y=x+1 and y=5 is intersected as we need to calculate the area bounded by them, 5=x+1 and x=4

for x=4, we get y= 5

now the area will be ∫₀⁴(x+1-5)dx

                                     [1/2x²- 4x] ⁴

                                 area= -8 unit

3. in case of 3rd two curves, x=y² and x-y=2

                                   y²-y=2, hence y= -1, 2

   the x values are x= 1, 4

the area bunded by them is ∫₋²₁{y²-(y-2)}dy

                                [1/3y³-1/2y²+2y]₋²₁

                                area =7.5 unit

4. from the last two curves y=4+x, y²= 2-x

  hence, the area calculated are 10.67-unit, 8 unit and 7.5 unit respectively.

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Answer:

650 connections

Step-by-step explanation:

Each classroom has 25 connections including the office, therefore 26classrooms(including the office) are connected to 25 places: 26*25=650 connections

Answer:

1/2 & 0.5

Step-by-step explanation:

Answer:

To solve this problem, we can set up a system of two equations to represent the given information:Let A be the cost of an apple and B be the cost of a banana.Then the first equation is: 4A + 3B = 4.48

The second equation is: 3A + 4B = 4.76To find the values of A and B, we can solve this system of equations using substitution or elimination.Using substitution, we can solve for A in the first equation and substitute that expression into the second equation:4A + 3B = 4.48

A = (4.48 - 3B)/4Substituting this expression for A into the second equation gives:3((4.48 - 3B)/4) + 4B = 4.76

3(4.48 - 3B) + 4B = 4.76

13.44 - 9B + 4B = 4.76

4.44 - 5B = 4.76

-5B = -0.32

B = 0.064Now that we have found the value of B, we can substitute it back into the first equation to find the value of A:4A + 3(0.064) = 4.48

4A + 0.192 = 4.48

4A = 4.288

A = 1.072Therefore, the cost of an apple is £1.072 and the cost of a banana is £0.064.

Step-by-step explanation:

Answer:

The answer is below

Answer:

3 hours and 45 minutes

Step-by-step explanation:

ggggggggggggg

The slope of each pair point is listed below:

Case A: m = - 4

Case B: m = 6 / 7

Case C: m = - 3

Case D: m = 4

Case E: m = - 5 / 2

In this problem we find five cases of two points that are part of a line, whose slope (m) can be calculated by means of secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Now we determine the slope for each case:

Case A:

m = (10 - 2) / (7 - 9)

m = 8 / (- 2)

m = - 4

Case B:

m = [- 5 - (- 11)] / [- 1 - (- 8)]

m = 6 / 7

Case C:

m = [3 - (- 6)] / (2 - 5)

m = 9 / (- 3)

m = - 3

Case D:

m = (- 1 - 3) / (5 - 6)

m = - 4 / (- 1)

m = 4

Case E:

m = (2 - 7) / (6 - 4)

m = - 5 / 2

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Answer:

[tex]\boxed{0.49}[/tex]

Step-by-step explanation:

To find the price of one orange, we need to determine how much Gaya and Esteban paid for their oranges in total and then divide that amount by the number of oranges they bought.Gaya paid £1.25 for 1 orange and 1 cauliflower, so she paid £1.25 for her orange.Esteban paid £1.95 for 3 oranges and 1 cauliflower, so he paid £1.95 - £1.25 = £0.70 for his 3 oranges.In total, Gaya and Esteban paid £1.25 + £0.70 = £1.95 for 4 oranges.So, the price of one orange is £1.95 / 4 = £<<1.95/4=0.49>>0.49. Answer: \boxed{0.49}.

The probability that Alice and Bob form a match is [tex]^{24} C_{5}[/tex] * (([tex]^{24} C_{4}[/tex])*20*19) / [tex]^{24} C_{5}[/tex] * [tex]^{24} C_{5}[/tex].

To answer the question, we use the probability by its complement.

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event.

In this case, probability space is ([tex]^{24} C_{5}[/tex])^2 where there is match for 4 or 5.

For number of ways for 5 adjectives match is ([tex]^{24} C_{5}[/tex]).

For number of ways for 4 adjectives match is ([tex]^{24} C_{4}[/tex])*20*19.

We first choose 4 adjectives which are match and then there are 20*19 ways for both of them to choose an adjective each from remaining 20 adjectives.

Then, the desired probability is:

[tex]^{24} C_{5}[/tex] * (([tex]^{24} C_{4}[/tex])*20*19) / [tex]^{24} C_{5}[/tex] * [tex]^{24} C_{5}[/tex]

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system  so it is false.

A multicore processors is an electronic component that has two or more processor cores attached for higher performance and lower power consumption. These processors also enable more efficient execution of numerous activities, such as with parallelization and multithreading.

Here,

It is because of the following disadvantages:

Although Peterson's technique is effective for two processes, it is the best plan for the important part in user mode.

Additionally, this solution involves busy waiting, wasting CPU time. So that “SPIN LOCK” problem can emerge. And any busy waiting solution may encounter this issue.

Therefore, Peterson's solution is not a valid solution to the critical section problem on modern multi-core system  so it is false.

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5 Trumpets

10 Trumpets

8 Trombones

6 Trombones for 15 Trumpets

The most appropriate test to use the given situation is option (B) two sample z test

Total number of alumni were surveyed = 1046

Number of alumni attempted at least one class reunion = 653

Similarly, in public university, 791 out of 1327 sampled alumni claimed they have attended at least one class reunion.

The two sample z test is used to compare the means of two samples to see if it is feasible that they come from the same population.

The difference in the sample proportion is statistically significant

Therefore, the correct test for the situation is option (B) two sample z test

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According to the test 0 is not plausible value for the difference between the population means.

What is population mean?

There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.

We have

n1 = 504,  x f = 3.13

n2 = 400,  x m = 2.87

(a) Hypothesis: H0: μf = μm   V/s  H1: μf ≠ μm

Yes, because according to the test 0 is not plausible value for the difference between the population means.

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Complete question:

Complete question is attached below.

The possible value of 3rd side is x ≤  35.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the length of two sides of a triangle are 20 and 15.

Triangle inequality theorem:

The sum of two sides of a triangle is always greater than the third side.

The of two sides of the triangle is (20 + 15) = 35.

According to triangle inequality theorem,

The third side of the triangle must be less than 35.

Assume that the length of the third side is x.

Therefore, x ≤  35.

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Answer:

commission. This is a common industry practice, and it is reasonable to assume that Harlan earned this percentage from his sales.

Step-by-step explanation:

On solving the provided question we can say that  the equation of the line will be  y+11 = 0.

The slope of a line is how steeply it slopes from left to right. The slope of a line is determined by dividing its rise (vertical change) by its slope, which is its horizontal change. Regardless of whatever two locations on the line you pick, the slope of the line is always constant (it never changes).

To find the coordinates of two points on the line, choose two. Find the difference between these two locations' y-coordinates (gradients). Find the difference between these two places' x coordinates (runs). Divide the change in the y coordinate by the difference in the x coordinate (slope/history or slope).

Here,

slope, m= 0 as these are parallel line.

so the equation of the line will be

y-y1 = m(x-x1)

y+11 = 0

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Step-by-step explanation:

so, for (4, 8) × 1/4, what is 4×1/4 ? and what is 8×1/4 ?

(1, 2)

similar for (4, -8) it is (1, -2).

similar for (-8, 0) it is (-2, 0).

similar for (8, 0) it is (2, 0).

that's it. that's really all there is to it. you multiply all the coordinates by the scale factor.

Answer:

20o

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180o.

so 25 + 135 + ? = 180

? = 180 - 25 - 135

? = 20

Answer:

2.4 would be the answer i took this before

Step-by-step explanation:

a) The mean number of website searches differs between the day and evening advertisements based on this hypothesis:

[tex]H_{0} :[/tex] μ[tex]_{x}[/tex]-μ[tex]_{y}[/tex] = 0

[tex]H_{a} :[/tex] μ[tex]_{x}[/tex]-μ[tex]_{y}[/tex] ≠ 0

The null hypothesis in the question states that the mean number of website searches does not differ between the day and evening advertisements and the alternative hypothesis states that the mean number of website searches differs between the day and evening advertisements. It can be written as:

[tex]H_{0} :[/tex] μ[tex]_{x}[/tex]-μ[tex]_{y}[/tex] = 0

[tex]H_{a} :[/tex] μ[tex]_{x}[/tex]-μ[tex]_{y}[/tex] ≠ 0

b-1) From the below excel output screenshot the t-test statistical value is I -0.3476.

b-2) From the below excel output the critical t value comes as 2.0017. So, the rejection region includes all the values greater than 2.0017 and less than -2.0017.

c) The calculated t-statistic value is not falling in the rejection region. So we do not reject the null hypothesis.

Do not reject [tex]H_{0}[/tex]. At the 5% significance level, we conclude the mean number of website searches not differ between the day and evening advertisements.

(The below excel screenshot shows the customized formula and the output which is required to find the values required to test the hypothesis.)

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The claim that a drug is effective at 1% is not sufficiently supported by the available data.

Participant 1 2 3 4 5 6

Before 185 220 190 158 227 211

After 175 215 195 155 230 207

Difference = Before - After = 10 5 -5 3  -3 4

Participant 7 8 9 10 11 12

Before 260 156 201 300 180 270

After 258 159 201 290 172 272

Difference = Before - After = 2 -3 0 10  8 -2

Participant 13 14 15 16 17 18

Before 293 183 205 151 291 166

After 290 185 200 146 287 166

Difference = Before - After = -7 -2 5 5  4 0

Hypothesis :

H0 : μd = 0

H0 : μd ≠ 0

10+5-5+3-3+4+2-3+10+8-2+3-2+5+5+4+0 = 44

The mean of d, [tex]d`[/tex] = Σd / n = 44 / 18 = 2.44

The standard deviation, S.d = 4.45 (using calculator)

The test statistic, T : [tex]d`[/tex] / (S.d/√n)

T = 2.44 / (4.45/√18)

T = 2.44 / 1.0488750

T = 2.326

Degree of freedom, df = n - 1 ; 18 - 1 = 17

P value = 0.0326

α = 0.01

Since P value < α ; we fail to reject H0

So the claim that a drug is effective at 1% is not sufficiently supported by the available data.

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