112 1/2 as a decimal

It is important to note that statistical hypothesis testing is only one tool that can be used to evaluate the significance of a particular parameter in a regression model.

What is Hypothesis?

A hypothesis is an educated guess while using reasonable thinking, about the answer to a scientific question. Although it is not proof in an experiment, it is the predicted outcome of the experimentation. It can either be supported or not supported at all, but it depends on the data gathered.

It is not accurate to simply compare the sums of squared deviations from the unrestricted and restricted regressions to test the hypothesis that a particular parameter (in this case, b1) is equal to zero. This approach does not take into account the fact that the restricted model is a special case of the unrestricted model, and as such, will always have a larger sum of squared deviations.

A more appropriate approach for testing the hypothesis that a particular parameter is equal to zero is to use statistical hypothesis testing. This involves formulating a null hypothesis (e.g. "b1 is equal to zero") and an alternative hypothesis ("b1 is not equal to zero"), and then using a test statistic and a critical value to determine whether or not to reject the null hypothesis. For example, you could use a t-test to compare the estimated value of b1 from the unrestricted model to zero, and based on the resulting p-value, you can decide whether or not to reject the null hypothesis.

It is important to note that statistical hypothesis testing is only one tool that can be used to evaluate the significance of a particular parameter in a regression model. Other approaches, such as using confidence intervals or information criteria, may also be used.

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\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

Answer:

C (The one before the last one)

Step-by-step explanation:

2000 = 180 + 50d

She already has 180

Plus the $50 she saves each day (d)

2000 is the goal, or what we want it to equal.

Answer:

0.675

Step-by-step explanation:

A dilation is a type of transformation that changes the size of a figure by multiplying the coordinates of each vertex of the figure by a determined scale factor "k"

If the scale factor is greater than 1, then the dilation is an enlargement, i.e. the new figure is bigger.

If the scale factor is less than 1, then the dilation is a reduction, i.e. the new figure is smaller.

The general rule for dilation is:

Original → Dilation

(x,y) → (kx,ky)

As mentioned before you have to multiply each coordinate by the scale factor k=1/2

1/2 is less than 1, so we expect the figure to be smaller than the original.

The resulting image will have the coordinates A'(0,2); B'(-2,4); C'(1.5,1.5); D'(2,-1) and it is a reduction.

The correct option is the third one.

Answer:

P(X is less than 348) = 0.2148

Step-by-step explanation:

Given that:

Sample proportion (p) = 0.3

Sample size = 1200

Let X be the random variable that obeys a binomial distribution. Then;

\(X \sim Bin(n = 1200,p =0.3)\)

The Binomial can be approximated to normal with:

\(\mu = np = 1200 \times 0.3 \\ \\ \mu= 360\)

\(\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{1200 \times (0.3)(1-0.3) } \\ \\ \sigma = 15.875\)

To find:

P(X< 348)

So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 348 lies between 347.5 and 348.5

Normal distribution:

x = 347.5, \(\mu\) = 360, \(\sigma\) = 15.875

Using the z test statistics;

\(z = \dfrac{x - \mu}{\sigma}\)

\(z = \dfrac{347.5 - 360}{15.875}\)

\(z = \dfrac{-12.50}{15.875}\)

z = -0.7874

z ≅ - 0.79

The p-value for P(X<347.5) = P(Z < -0.79)

From the z tables;

P(X<347.5) = 0.2148

Thus;

P(X is less than 348) = 0.2148

we know that

A parallelogram has two pair of congruent and parallel sides

so

AD=BC

AB=CD

and

AD is parallel to BC

AB is parallel to CD

so

the slope of AD is equal to the slope of BC

therefore

Answer:

Step-by-step explanation:

The high and low points are

The difference in elevation is:

Step-by-step explanation:

Answer:

32229 feet

Step-by-step explanation:

The high and low points are

31098 feet - 1131 feet

The difference in elevation is:

31098 - (-1131) = 32229 feet

Hope it will help you in your need

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

Step-by-step explanation:

D and E are complementary angles

the measures of angle D and E add to 90 degrees therefore angle D and E are Complimentary angles.

Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.

It is given that sin D = cos E

It is known that

\(\rm sin\theta = cos(90-\theta)\)

therefore

sin D = cos(90-D)= cos E

90-D = E

D+E = 90

As the measures add to 90 degrees therefore angle D and E are Complimentary angles.

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The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

An equation for a transformed cosine wave with the following properties can be written in the form:

y = A× cos(B(x - C)) + D

Where:

A = amplitude (positive value)

C = phase shift (horizontal shift of the wave)

D = vertical shift (shift of the wave up or down)

Here we have

Amplitude = 3

Period = π

Horizontal shift = None

Vertical shift  = 4 units  up  

As we know Period P = 2π/B

From the data => 2π/B = π

=> B = 2  

Hence,

Equation for a transformed cosine wave, y = 3 × cos(2(x - 0)) + 4

=> y = 3 × cos(2(x )) + 4

=> y = 3cos2x + 4  

Therefore,

The equation for a transformed cosine wave with the following properties is  y = 3cos2x + 4

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Solution :-

Here, we have been given that lines f and g are parallel. Thus, the angle measuring 135° and ∠2 are vertically opposite angles.

And we know that vertically opposite angles measure same. Thus,

∠2 = 135°

And,

∠2 + ∠6 = 180° ( Co - interior angles sum up to 180° )

135° + ∠6 = 180°

∠6 = 180° - 135°

∠6 = 45°

Hope that helps :)

When the height of the taller building is 500 metres above the ground and the angles of depression is at 12° and 25° , the  height of the smaller building is approximately 125.84 meters.

Find the height h of the smaller building using trigonometry

Let x and y be the distance between the two buildings and height of the observer in the taller building above the ground, respectively.

Then we have

\(tan(12^0) = h / (x + 500 - y)\)

\(tan(25^o) = h / (x + 500 + y)\)

Solve for h.

\(tan(12^o) * (x + 500 + y) = tan(25^o) * (x + 500 - y)\)

By expanding and rearranging, we have

\(x = (h/tan(25^o) - h/tan(12^o)) / 2\)

Substitute x into either of the original equations, we can solve for h:

\(h = (x + 500 - y) * tan(12^o)\)

Plug in the value of x

\(h = ((h/tan(25^o) - h/tan(12^o)) / 2 + 500 - y) * tan(12^o)\)

Multiply both sides by the common denominator of 2 * tan(12°)

\(2 * h * tan(12^o) = h * (1/tan(25^o) - 1/tan(12^o)) + (1000 - 2y) * tan(12^o)\\h = (1000 - 2y) * tan(12^o) / (2 * tan(12^o) - 1/tan(25^o) + 1/tan(12^o))\)

Plug in the given values of y = 500

h = 125.84 meters

Therefore, the height of the smaller building is approximately 125.84 meters.

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The amount of fewer euros he would receive as a result of the delay is 20 E.

The percentage loss that was caused by the delay is -4%.

Exchange rate is the rate at which one unit of a currency can buy another currency. In this question, the value of Euros appreciated by Monday. This is because $1 buys less Euros on Mondays. On the hand, dollars depreciates in value.

Amount of fewer Euros received = value of euros if it were exchanged on Friday - value of euros if it was exchanged on Monday

Value of euros if it were exchanged on Friday = 1.25 x 400 = 500 E

Value of euros if it was exchanged on Monday = 1.20 x 400 = 480 E

Difference = 500 E - 480 E = 20 E

Percentage loss = (Euros received on Monday / Euros that would have been received on Friday) - 1

Percentage loss = (480 / 500) - 1 = -0.04 = -4%

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Explanation/answer

Explanation: Because the mound builders built cities and traded far and wide throughout the midwestern region. Which Native American groups built cities? Answer Expert Verified The varying cultures collectively called Mound Builders were inhabitants of North America who, during a 5,000-year period, constructed various styles of earthen mounds for religious and ceremonial, burial, and elite residential purposes. DONT FORGET TO GIVE BRAINILEST

Answer:

mound builders

Step-by-step explanation:

Because the mound builders built cities and traded far and wide throughout the Midwestern region

To solve this problem, we need to know how much red paint Priya has. This information is not on the data card, so we need to know the amount of red paint Priya has in order to solve the problem.

Amount is a numerical value that can refer to the quantity of a particular item or resource. It can also refer to the sum of money due or owed for a product or service. In the context of mathematics, amount is often used to refer to a quantity, a measure, or a total. Amount can also be used to refer to the total value of a particular asset, such as a bank account or the total number of shares of a particular stock.

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Answer:

It is equal to 29..........

Answer:

29

Step-by-step explanation:

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.\(\)

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

The solutions of the given equations are x = 0 and x = -36.

We have,

To solve these equations:

9x - 7 = -7

We can add 7 to both sides to isolate the variable:

9x - 7 + 7 = -7 + 7

Simplifying the left-hand side and the right-hand side, we get:

9x = 0

Finally, dividing both sides by 9, we get:

x = 0

Next, to solve:

-1 = 5 + x/6

We can begin by subtracting 5 from both sides:

-1 - 5 = 5 + x/6 - 5

Simplifying the left-hand side and the right-hand side, we get:

-6 = x/6

Finally, multiplying both sides by 6, we get:

-36 = x

Thus,

The solutions of the given equations are x = 0 and x = -36.

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The complete question.

9x - 7 = -7

-1 = 5  + x/6

The ratio of losing to the total number of possible outcomes is 99.992:100, or 12499:12500.

In the game of Lucky Lauto, the probability of winning is 0.008%, which means that the probability of losing is 100% - 0.008% = 99.992%. This is the complement of the probability of winning, as the two probabilities must add up to 100%.

The ratio of the number of ways to succeed to the total number of ways that an experiment can happen is given by the probability of success. In this case, the probability of winning is 0.008%, so the ratio of winning to the total number of possible outcomes is 0.008:100, or 1:12500.

Similarly, the ratio of losing to the total number of possible outcomes is 99.992:100, or 12499:12500.

In conclusion, the probability of losing in Lucky Lauto is 99.992%, and the ratio of losing to the total number of possible outcomes is 12499:12500.

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The approximate 90% confidence interval for this situation is given as follows:

(70244, 70632).

The bounds of the confidence interval are given by the rule presented as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

From the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.645.

The parameters are given as follows:

\(\overline{x} = 70438, \sigma = 645.3, n = 30\)

The lower bound of the interval is given as follows:

\(70438 - 1.645 \times \frac{645.3}{\sqrt{30}} = 70244\)

The upper bound of the interval is given as follows:

\(70438 + 1.645 \times \frac{645.3}{\sqrt{30}} = 70632\)

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As per the given situation, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are often represented using function notation.

To find k, we need to know the value of g(x) for a specific value of x. Let's say we want to find k when x = 3. Then:

g(3) = k · f(3)

g(3) = k · 2(3)

g(3) = k · 6

If we know the value of g(3), we can solve for k:

g(3) = 15

15 = k · 6

k = 15/6

k = 2.5

Therefore, when g(x) = k · f(x), and f(x) = 2x, the value of k is 2.5.

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The counting principle says that we multiply the number of ways for each of these events together to get the total number of ways to get a license plate. Hence, there are \(158184000\) ways to create a license plate.

What is the counting principle?

The fundamental counting principle states that if there are \(p\) ways to do one thing and \(q\) ways to do another thing, then there are \(p\)×\(q\) ways to do both things.

So,

The number of ways to count the first number are \(9\) ways.

The number of ways to count the first letter are \(26\) ways

The number of ways to count the next letter are \(26\) ways

The number of ways to count the third letter are \(26\) ways

The number of ways to count the next number are \(10\) ways

The number of ways to count the next number are \(10\) ways

The number of ways to count the next number are \(10\) ways

So, the total number of ways to get a license plate is:-

\((9).(26).(26).(26).(10).(10).(10)=158184000\).

Hence, there are \(158184000\) ways to create a license plate.

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Answer:

ok sure

Step-by-step explanation:

So 'mean' basically just means average, and to get the average you must first add together all of the measurements. Then you have to divide that number by how many measurements you have, and in this case that would be 4.

       13 + 7 + 9 + 6 = 35

           35 ÷ 4 = 8.75

So  the answer to this question is 8.75

Answer: 0.35

Step-by-step explanation:

Times 7 = 2. 45kg

The range, in centimetres (cm), of the following lengths is 20.5 cm

What is the range?

The difference between the lowest and highest numbers is referred to as the range. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

Given, 15 cm, 0.5 cm, 10.3 cm, 16.7 cm, 21 cm, 8.6 cm

So, the highest value of length = 21 cm

the lowest value of length = 0.5 cm

Then, range = the highest value - the lowest value

                    = 21 - 0.5 = 20.5 cm

Hence, the range, in centimetres (cm), of the following lengths is 20.5 cm

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