Show that the series {x t
​
} given by x t
​
= 2
3
​
x t−1
​
− 2
1
​
x t−2
​
+w t
​
is nonstationary.

Answer:

1. -564

2. 11 1/2

3. 45/472

5. 3(2x - 1) = 3(2x) - 3(1)

6. 1/5(x) + 2y

= x/5 + 2y

7) 77.1km

8. 211.8 pizzas

Step-by-step explanation:

1. 4 (6) -2 (8) + 4-576

= 24 - 16 + 4 - 576

= 24 + 4 - 16 - 576

= 28 - 16 - 576

= 28 - 592

= -564

2. 2 3/4 + 8 3/4

Mínimo común múltiplo de los denominadores = 4

2 3/4 + 8 3/4

= (2 + 8) + (3 + 3/4)

= 10 + (6/4)

= 10 + 1 2/4

= 10 +1 1/2

= 11 1/2

3. (9/4) (6/59 (1/2) 2/6 ÷ 6/5

BODMAS

= 9/4 × 6/59 × 1/2 × 2/6 ÷ 6/5

= 9/4 × 6/59 × 1/2 × 2/6 × 5/6

= 45/472

5. Expresar el lenguaje común 6x -3

Factoriza la expresión algebraica

6x - 3 = 3 (2x - 1)

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

6. Expresar en lenguaje algebraico. "La quinta parte de un número más el doble de un número diferente.

Sea un número representado por x

Sea un número diferente representado por y

Por lo tanto:

1/5 (x) + 2 años

= x / 5 + 2y

7. Si con 7 L de gasolina recorrí 30 km, con 18 L, ¿cuántos kilómetros?

7 L = 30 km

18 L = x km

Cruz y

7L × x km = 18L × 30km

xkm = 18L × 30km / 7

= 77.142857143km

≈ 77.1 kilometros

8. Si con 17 pizzas gigantes comen 90 personas, con 40 pizzas ¿cuántas personas comen?

17 pizzas gigantes = 90 personas

40 pizzas =

Cruz multiplicar

40 pizzas × 90 personas / 17

= 211.76470588 pizzas

≈ 211.8 pizzas

Researchers developed a blood test which is quite fair. It gives a positive reaction of 97% people who have that disease and 5% who don't have that disease.

Therefore, the Probability of Type I error if the new blood test is used is 0.025.

H₀ : "the individual does not have the disease"

(a) Probability of Type I error of rejecting  when  is true =

Probability of concluding the individual has the disease when in fact the individual does not have the disease = 0.025 because the blood test erroneously gives a positive reaction in 2.5% of the people who do not have the disease.

(b) Probability of Type II error = Probability of fail to reject  when  is true= Probability of concluding the individual does not have the disease when in fact he has the disease = 0.05 because the blood test gives a positive reaction in 97% of the people who have the disease, this implies that the test gives a negative reaction in 5% of the people who have the disease.

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A. The power of the two-tailed hypothesis test with α = .05 is 0.53.

B. The power of the one-tailed hypothesis test with α = .05 is 0.95.

A hypothesis test is used to make decisions about a population based on sample data. It involves specifying a null hypothesis, collecting data, and then assessing the data to either reject or accept the null hypothesis.

A. The power of the two-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- (1-α)\(^{1/2}\)

=1- (1-0.05)\(^{1/2}\)

=0.525

=0.53

This means that the researcher has an 53% chance of correctly rejecting the null hypothesis that there has been no change in the IQ over the past 10 years.

B. The power of the one-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- α

=1- 0.05

= 0.95

This means that the researcher has a 95% chance of correctly rejecting the null hypothesis that there has been no increase in the IQ over the past 10 years.

This is a higher power than the two-tailed test because the one-tailed test focuses on detecting an increase in the IQ, while the two-tailed test can detect both an increase or decrease in the IQ.

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Answer:

You'll never know the answer.

Step-by-step explanation:

You'll never know the answer because there are so many brands of dog food out there.

Answer:

The symbol should be equal to.

They are the same when the first expression is multiplied.

Answer:

=

Step-by-step explanation:

6.738 × 10^-11 = 0.00000000006.738

0.00000000006738 = 0.00000000006738

In the standard curve for nitrophenol generated for use in this experiment, the nitrophenol concentration is reported on the x - axis.

What is standard curve?

A calibration curve, sometimes referred to as a standard curve, is a common technique used in analytical chemistry to compare an unknown sample to a group of standard samples with known chemical concentrations.

In order to calculate the nitrophenol concentration in mole/ml based on absorbance readings, the standard curve is drawn.

Based on the optical density, or OD410, or absorbance at 410 nm, this standard curve of absorbance is used to calculate the quantity of nitrophenol.

Therefore, the nitrophenol concentration is displayed on the x axis of the standard curve.

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Answer:

green because it sounds like garbage

Step-by-step explanation:

Answer:

the one u want to put em in?

Step-by-step explanation:

The time is needed between injections is 3.6 hours, i.e., the drug is to be injected again when the number of milligrams reaches 6 mg.

We have the exponential function of number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is

\(D(h)=25 {e}^{ - 0.4 h}\)

We have to solve for h (the numbers of hours) that would have passed when the D(h) (the amount of medication in the patient's bloodstream) equals 6 mg in order to know when the patient needs to be injected again.

\(6 = 25 {e}^{ - 0.4h} \)

\( \frac{6}{25} = \frac{25}{25} {e}^{ - 0.4h} \)

\(0.24= {e}^{ - 0.4h} \)

Taking logarithm both sides of above equation , we get,

\( \ln(0.24) = \ln( {e}^{ - 0.4h)} \)

Using the properties of natural logarithm,

\( \ln(0.24) = - 0.4h\)

\( - 1.427116356 = - 0.4h\)

\(h = \frac{1.42711635}{0.4} = 3.56779089\)

=> h = 3. 6

So, after 3.6 hours, the patient needs to be injected again.

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All five answers are (1) 285.7 ft2 (2) 1056 cm2 (3) 105 mm3 (4) 108 cm3 (5) 628 mm3 in accordance with the provided assertion.

In mathematics, volume refers to the amount of space present within a specific 3D object. As an example, the dimensions of a fish aquarium are three feet long, one foot broad, and two feet height.

By increasing the length, width, and height, or 3x1x2, which also equals six, the volume is determined. Consequently, the fish tank has a 6 cubic foot size.

(1) The lateral area of a cone can be calculated using the formula L = πrℓ, where r is the radius and ℓ is the slant height. Using the given values, we have:

L = π(7)(13) ≈ 285.7 ft²

Rounding to the nearest tenth, the answer is 285.7 ft².

(2) A = B + (1/2)Pl, where B is the base area, P is the base circumference, l is the slope height, and A is the surface area, can be used to determine the surface area of a square pyramid. Since the pyramid's foundation is square, we have:

B = (24)² = 576 cm²

The perimeter of the base is 4 times the base length, so we have:

P = 4(24) = 96 cm

Now we can use the formula to find the surface area:

A = 576 + (1/2)(96)(16) = 1056 cm²

Therefore, the surface area of the square pyramid is 1056 cm².

(3) The volume of a rectangular prism can be calculated using the formula V = lwh,

where

l is the length

w is the base

h is the height

V is the volume.

Substituting the given values, we have:

V = (5)(7)(3) = 105 mm³

Therefore, the volume of the rectangular prism is 105 mm³.

(4) The formula V = (1/3)Bh, where B is the base area, h is the height, and V is the volume, can be used to determine the volume of a square pyramid. Since the pyramid's foundation is square, we have:

B = (9)² = 81 cm²

Now we can use the formula to find the volume:

V = (1/3)(81)(4) = 108 cm³

Therefore, the volume of the square pyramid is 108 cm³.

(5) The volume of a cone can be calculated using the formula V = (1/3)πr2h, where r is the radius, h is the height, and V is the volume. Substituting the given values, we have:

V = (1/3)π(10)²(6) ≈ 628.3 mm³

Rounding to the nearest whole number, the answer is 628 mm³.

Therefore, the volume of the cone is 628 mm³.

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Using the two tangent exterior angle theorem:

x = 6

m(NK) = 153°

According to the two tangent exterior angle theorem, when you draw two tangent lines from a point outside a circle, the angle formed between them is equal to half the difference between the measures of the arcs they intercept inside the circle.

Therefore, using the above theorem, we have:

7x + 6 = 1/2[(25x + 3) - (9x + 3)]

Solve for x:

2(7x + 6) = 25x + 3 - 9x - 3

14x + 12 = 16x

14x - 16x = -12

-2x = -12

x = -12/-2

x = 6

m(NK) = 25x + 3 = 25(6) + 3

m(NK) = 153°

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Answer:

A

Step-by-step explanation:

70-271=20

Answer: it's 7/10

Step-by-step explanation:

the 49 simplifies to 7, and the 100 simplifies to 10

This standardized test, the low value for the 95% data range is 70.4 and the high value is 95.6.

The empirical rule states that for a normally distributed data set, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

In this case, the mean score is 83 and the standard deviation is 6.3.

To find the low and high values for the 95% data range, we need to calculate two standard deviations and subtract/add them to the mean.

Two standard deviations would be 2 * 6.3 = 12.6.

Subtracting 12.6 from the mean gives us

83 - 12.6 = 70.4,

which is the low value for the 95% data range. Adding 12.6 to the mean gives us

83 + 12.6 = 95.6,

which is the high value for the 95% data range.

In conclusion, for this standardized test, the low value for the 95% data range is 70.4 and the high value is 95.6.

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Answer:

D

Step-by-step explanation:

Given the 2 equations

y = 3x - 5 → (1)

6x - 2y = 10 → (2)

Substitute y = 3x - 5 into (2)

6x - 2(3x - 5) = 10

6x - 6x + 10 = 10 ( subtract 10 from both sides )

6x - 6x = 0 , that is

0 = 0 ← True

This indicates the system has infinitely many solutions → D

Answer:

t = 10

Step-by-step explanation:

z^t ⋅ z^5 = z^15

We know that a^b*a^c = a^(b+c)

z^(t+5) = z^15

Since the bases are the same, the exponents are the same

t+5 = 15

t = 15-5

t = 10

Answer:

Level 2:

45 x 45 = 2025

28 x 28 = 784

2025 + 784 = 2809

(sqrt)2809 = 53

53 units

Level 3:

(Start by graphing the coordinates)

Your shape should have one leg of 14 units, and one leg of 8 units.

14 x 14 = 196

8 x 8 = 64

196 + 64 = 260

(sqrt)260 = 16.1245155

(rounded to nearest tenth)

16.1 units

I`m not sure about the other two though, sorry :/

3. Using the Pythagorean theorem, x = 53 in.

4. 6, 9, and 11 does not form a right triangle because they are not a Pythagorean triple. i.e. 11² ≠ 9² + 6².

5. Using the distance formula, AB = 16.1 units

7. Height of the Pyramid using the Pythagorean theorem is: h = 5.2 units.

8. Length of diagonal = 10.2 units.

If c is the hypotenuse of a right triangle with a and b as its legs, the Pythagorean theorem states that c² = a² + b².

Diagonal (d) = √(l² + h² + w²)

l = length

w = width

h = height

3. Find x using the Pythagorean theorem:

x = √(45² + 28²)

x = 53 in.

4. 6, 9, and 11 does not form a right triangle because they are not a Pythagorean triple. i.e. 11² ≠ 9² + 6².

5. Using the distance formula, find AB:

AB = √(5−(−3))² + (6−(−8))²

AB = √260

AB = 16.1 units

7. Height of the Pyramid using the Pythagorean theorem:

h = √(6² - 3²)

h = 5.2 units.

8. Diagonal of the Rectangular Prism:

Length of diagonal = √(l² + h² + w²) = √(8² + 5² + 4²)

Length of diagonal = 10.2 units.

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The percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

The expression \(25(0.93)^x\)represents the height of the ball after x bounces. To find the percent change in height after each bounce, we need to calculate the ratio of the change in height to the original height and express it as a percentage.

Let's denote the height after the first bounce as h_1, the height after the second bounce as h_2, and so on.

The percent change in height after the first bounce is given by:

Percent change = [(h_1 - original height) / original height] * 100%

Using the given expression, we can substitute x = 1 to find h_1:

h_1 = \(25(0.93)^1\) = 23.25

Therefore, the percent change in height after the first bounce is:

Percent change = [(23.25 - original height) / original height] * 100%

To find the percent change after subsequent bounces, we can continue this process. For example, after the second bounce:

h_2 = \(25(0.93)^2\)

And the percent change in height after the second bounce would be:

Percent change = [(h_2 - h_1) / h_1] * 100%

You can repeat this process for each subsequent bounce to find the percent change in height after each bounce using the given expression.

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The linear function rule that describes the points in the table is \(y = 4x\).

To find the linear function rule that describes the points in the table, we need to observe the relationship between the x and y values. Looking at the given table, we can see that the y values are always 4 times the corresponding x values. This suggests that the linear function rule can be written as:

\(\[y = 4x\]\)

where \(x\) represents the input values and \(y\) represents the output values.

By substituting the given x values (1, 2, and 3) into the function rule, we can verify that the corresponding y values (4, 8, and 12) are obtained. This confirms that the linear function rule \(\(y = 4x\)\) accurately describes the relationship between the x and y values in the table.

Therefore, the linear function rule that describes the points in the table is \(\(y = 4x\)\).

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Answer:

44

Step-by-step explanation:

x-6=38

or, x= 38+6

hence, x=44

Answer:

44

Step-by-step explanation:

38 + 6 = 44

x = 44

6 less than 44 (x) is 38

Answer:

2x6x8

2x6=12

12x8=96

Step-by-step explanation:

Answer:

0.4 is the answer

Step-by-step explanation:

4/10 = 0.4

hope it's helpful

490

472 <490<500

it fits the criteria

Answer:

The polygon has 13 sides.

Step-by-step explanation:

The sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides. This formula can be set equal to the sum of the interior angles to determine how many sides it has.

(n - 2) * 180 = 1980

180n - 360 = 1980

180n = 2340

n = 13

A. Let x be the amount more you must spend to get free shipping. Then, the equation is:

$69.95 + x = $75

B. To solve the inequality that represents how much more you must spend to get free shipping, we can use:

$69.95 + x ≥ $75

Subtracting $69.95 from both sides, we get:

x ≥ $5.05

Therefore, you must spend at least $5.05 more to get free shipping.

C. It depends on whether the cost of the additional item plus the $69.95 exceeds $75. If the cost of the additional item is less than $5.05, then it may be worth purchasing in order to get free shipping. However, if the cost of the additional item plus the $69.95 is more than $75, then it may not be worth it as the shipping cost would still be less than the cost of the additional item.

The method that is invoked when an object is created is known as a constructor method.

Constructor in C++ is a special method that is invoked automatically at the time of object creation. It is used to initialize the data members of new objects generally.

The constructor in C++ has the same name as the class or structure. Constructor is invoked at the time of object creation. It constructs the values i.e. provides data for the object which is why it is known as constructors.

Constructor does not have a return value, hence they do not have a return type.

The prototype of Constructors is as follows:

<class-name> (list-of-parameters);

Constructors can be defined inside or outside the class declaration:-

The syntax for defining the constructor within the class:

<class-name> (list-of-parameters) { // constructor definition }

The syntax for defining the constructor outside the class:

<class-name>: :<class-name> (list-of-parameters){ // constructor definition}

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Answer:

3 3/5 + 1 1/4 = 4 17/20

7/8 + 1/12 = 23/24

8/9 - 2/5 = 22/45

5 1/4 - 2 2/3 = 2 7/12

Step-by-step explanation:

3 3/5 + 1 1/4

First convert into improper fractions

= 18/5 + 5/4

Now find the common denominator

72/20 + 25/20 =

97/20

Now simplify

4 17/20

Next problem:

7/8 + 1/12

find the common denominator

21/24 + 2/24 =

23/24

Next problem:

8/9 - 2/5

find the common denominator

40/45 - 18/45 =

22/45

Next problem:

5 1/4 - 2 2/3

First convert into improper fractions

21/4 - 8/3

find the common denominator

63/12 - 32/12 =

31/12

Now simplify

2 7/12

Answer:

30ft

Step-by-step explanation:

Given data

Volume= 360 ft^3

Area= 12 ft^2

We know that the expression for volume is

Volume= Area*Height

Substitute

360= 12*h

h= 360/12

h= 30 ft

Hence the height of the prism is 30ft