21. Simplify: (-3)? *(-2)?​

Answer:

59049.

Step-by-step explanation:

It is given that, 2 years later, two years ago, the population of this same city was 81,000 and today it is 65,610.

So, graph passing through (2,81000) and (-2,65610).

The general exponential function is

\(y=ab^x\)

where, a is initial value or present year population and b is growth factor.

Since graph passing through (2,81000) and (-2,65610), therefore the above equation must be satisfied by these points.

\(81000=ab^2\)    ...(1)

\(65610=ab^{(-2)}\)    ...(2)

Multiplying (1) and (2), we get

\(81000\times 65610=ab^2\times ab^{-2}\)

\(5314410000=a^2\)

Taking square root on both sides.

\(72900=a\)

Substitute a=72900 in (1).

\(81000=72900b^2\)

\(\dfrac{81000}{72900}=b^2\)

\(\dfrac{10}{9}=b^2\)

Taking square root on both sides.

\(\dfrac{\sqrt{10}}{3}=a\)

So, the population function is

\(y=72900\left(\dfrac{\sqrt{10}}{3}\right)^x\)

Substitute x=-4 in the above equation, to find the population of four years ago.

\(y=72900\left(\dfrac{\sqrt{10}}{3}\right)^{-4}\)

\(y=72900(0.81)\)

\(y=59049\)

Therefore, the population of four years ago is 59049.

Answer: $50.99

Step-by-step explanation:

Given

The computer game is Priced at \(\$59.99\)

It is marked down by \(15\%\)

Final price is

\(\Rightarrow 59.99-15\%\ \text{of}\ 59.99\\\Rightarrow 59.99(1-0.15)=59.99\times 0.85\\\Rightarrow \$50.99\)

The function that is defined as the inner product of the given vector space is given by;∫10fgdx

The given orthogonal basis for Span{1,x,x²} is computed below;The functions f,g and h in the equation below are elements of the span{1,x,x²}

f(x) = 1,g(x) = x,h(x) = x²

Therefore, we have;f(x) = 1,g(x) = x,h(x) = x².The first element of the orthogonal basis is computed as follows:

⟨f, f⟩ = ∫10(1 * 1) dx = 1

⟨g, g⟩ = ∫10(x * x) dx = 1/3

⟨h, h⟩ = ∫10(x² * x²) dx = 1/5

Hence, we have;||f|| = sqrt(⟨f, f⟩) = 1||g|| = sqrt(⟨g, g⟩) = 1/√3||h|| = sqrt(⟨h, h⟩) = 1/√5

The second element of the orthogonal basis is computed as follows;

g'(x) = g(x) - f(g(x))

⟨g, f⟩ = ∫10(x * 1) dx = 1/f(g(x)) = 1/2 * f(x) = 1/2

⟨g, g⟩ = 1/3⟨f, f⟩ = 1g'(x) = g(x) - f(g(x))= x - 1/2

Similarly, the third element of the orthogonal basis is computed as follows;

h'(x) = h(x) -f(h(x)) - g(h(x))

⟨h, f⟩ = ∫10(x² * 1) dx = 1/3f(h(x)) = 1/3 * f(x) = 1/3⟨h, g⟩ = ∫10(x² * x) dx = 1/4g(h(x)) = 1/4 * g(x) = x/4

⟨h, h⟩ = 1/5⟨f, f⟩ = 1h'(x) = h(x) -f(h(x)) - g(h(x)) = x² - 1/3 - x/4

Inner products are similar to dot products but they allow for more general vectors and spaces. They are positive-definite, which means that they return a positive number for any non-zero vector. Inner products must also satisfy four additional properties, which are linearity, conjugate symmetry, and positive-definiteness. The given vector space is defined as C[0,1], and the inner product is defined as the integral from 0 to 1 of the product of f(x) and g(x) with respect to dx. To find an orthogonal basis for Span{1,x,x²}, we need to first find the norm of each element of the basis. The norm of an element v is defined as the square root of the inner product of v with itself. After finding the norm of each element, we can use the Gram-Schmidt process to compute the orthogonal basis. This involves finding the projection of each element onto the span of the previous elements and then subtracting this projection from the original element to get the orthogonal component.

The resulting vectors will form an orthogonal basis for the given span.the orthogonal basis forSpan{1,x,x²} is {1, x - 1/2, x² - 1/3 - x/4}.

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The solution of the matrix in vector form is [-13 3 -3 4]

The given matrix equation is Ax = b, where A is a matrix with 1 row and 4 columns, and b is a matrix with 1 row and 3 columns

In this case, the augmented matrix is a 5x4 matrix, with the first 4 columns being A and the last column being b. The augmented matrix for this system is then:

=> \(\left[\begin{array}{ccc}1&2& 3\\3& 5 &2 \\-4 &2 &5 \\-13 &11 &8\end{array}\right]\)

To solve the system, we can use Gaussian elimination, which is a method of solving a system of linear equations by transforming the augmented matrix into a row-echelon form.

After applying Gaussian elimination to the augmented matrix, we get the following row-echelon form:

=> \(\left[\begin{array}{ccc}1& 0& 0 \\-1& 0 &-3 \\-3& 0& 4 \end{array}\right]\)

We can then find the solution of the system by back-substitution:

=> x₁ = -13, x₂ = 3, x₃ = -3, and x₄ = 4.

Therefore, the solution of the linear system is x = [-13 3 -3 4]

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The factorization  of the polynomial is:

(x - 4)*(x + i)*(x - i)

If (x - x₁) is a factor of a polynomial, then x₁ is a zero of the polynomial.

Now we can evaluate the polynomial in the values of the options and see which ones are zeros.

if x = 4

p(4) = 4³ - 4*4² + 4 - 4 = 0

So (x-  4) is a factor.

if x  = i

p(i)= i³ - 4*i² + i - 4

     = -i + 4 + i - 4  = 0

(x - i) is not a factor.

if x = -i

p(-i) = (-i)³ - 4*(-i)² - i - 4

        = i + 4 - i - 4 = 0

Then the factorization is:

(x - 4)*(x + i)*(x - i)

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Answer:

4th option is coreect

Step-by-step explanation:

Answer:

4th answer is correct.!

Step-by-step explanation:

The velocity function is s'(t) = 6t - 2, and the units are feet per minute. The acceleration function is s''(t) = 6, and the units are feet per minute squared.

a) To find the velocity, which is the derivative of the position function with respect to time, we need to use the limit definition of the derivative:

s'(t) = lim(h→0) [s(t+h) - s(t)] / h

= lim(h→0) [(3(t+h)2 - 2(t+h) + 1) - (3t2 - 2t + 1)] / h

= lim(h→0) [3t2 + 6th + 3h2 - 2t - 2h + 1 - 3t2 + 2t - 1] / h

= lim(h→0) [6th + 3h2 - 2h] / h

= lim(h→0) [6t + 3h - 2]

= 6t - 2

b) To find the acceleration, which is the derivative of the velocity function with respect to time, we need to take the derivative of the velocity function:

s''(t) = d/dt [6t - 2]

= 6

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The probability of meeting the manager's objectives is 0.0118.

The probability of meeting the manager's objectives if members for the team and the captain were randomly selected is very low, at 0.0118.

This is due to the fact that there are 50 basketball players in total, and the manager wants to select 5 of them, with 2 of them being seniors, 3 of them being juniors, and one of the seniors to be the captain.

This narrows the number of possibilities greatly and makes it a difficult task for the manager to fulfill.

Furthermore, the fact that the selection process is random does not help either.

This means that the manager has no control over who is chosen, and thus has to hope that the randomly selected group fulfills the desired criteria.

This makes the probability of meeting the manager's objectives even lower, as the chances of a completely random selection meeting the criteria is very low.

In conclusion,

The probability of meeting the manager's objectives if members for the team and the captain were randomly selected is very low, at 0.0118.

This shows that it is a difficult task for the manager to fulfill, and that the selection process should be carefully considered if they want to ensure that they meet their objectives.

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The proportion used to find the value of a is a/18 = 16/a

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given are three similar triangles, (refer to attached figure to separately see the similar triangles)

We know that, similar triangle have corresponding sides in equal ratio,

Therefore,

a/18 = 16/a

Hence, the proportion used to find the value of a is a/18 = 16/a

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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Answer:

they F (5) g (5)

Step-by-step explanation:

(fg)=(f.g)

and then this is the first doing (fg)(X)= f(x) [g(x)]

x=5

f(5).g(X)

and they final result is

they top of answer

happy answering

The the composition of f and g denoted by the expression (fg)(5) is equivalent to f(g(5))

The composition of two functions f and g is an operation where two functions f and g generates a new function h such that h(x)=f(g(x)).

First we find the value of g(x). If g(x)=y then f(g(x))=f(y).

The value of composition  (fg)(x) is equal to f(g(x)).

Thus the value of (fg)(5) is f(g(5)) .

If g(5)=c , some c.

Then (fg)(5)=f(g(5))=f(c)

Hence the value of the composition of f and g of 5 is f(g(5)).

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The probability that a block picked at random is red is 40%.

Using this formula

Probability=Red block/Red block+Orange block+Purple block

Where:

Red block=6%

Orange block=5%

Purple block=4%

Let plug in the formula

Probability=6/(6+5+4)

Probability=6/15

Probability=0.4×100

Probability=40%

Therefore the probability that a block picked at random is red is 40%.

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Answer:

t = 81

Step-by-step explanation:

81/-9 = -9

Answer:

81 = t

Step-by-step explanation:

-9 = t/-9

To isolate x, multiply -9 on both sides.

-9 = t/-9

*-9    *-9

81 = t

Hope this helped you...have a great day! C:

a) The Equation is  7.65x + 50 = 149.45.

b) The customer used the car for 13 hours.

c)  If the car used for 2 days i.e., 48 hours then the amount will be $471.12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given that;

Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.

And, a members bill was $149.45 last month.

a) Let number of hours for the customer use a car last month = x

So, 7.65x + 50 = 149.45

7.65x = 149.45 - 50

7.65x = 99.45

x = 13

b) The customer used the car for 13 hours.

c) If the car used for 2 days i.e., 48 hours

= 7.65x + 50

= 7.65(48)+ 50

= 471.2

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Here is your answer :

Answer 1 :

Volume of the Cylinder = πr²h

Therefore, The Volume of the Cylinder is 50.27 Feet

By Rounding, 50 Units/Feet

Answer 2 :

So, volume is always cubed since you have l x w x h.

A cubic ft is 12 in x 12 in x 12 in = 1728 in3.

35328.78/1728 = 20.44  

20.44 x 7.48 = 152.89

About 153 gallons

HOPE IT HELPS

Answer:1.08x10, ^56

Step-by-step explanation:

The final answer is Q / T + C.It's important to note that in both cases, the final answer represents (A) as the subject and is simplified to the best possible extent based on the given expressions.

Let's solve for (A) in both cases step-by-step:

Making (A) the subject: (xy - z) / X

To make (A) the subject, we want to isolate (A) on one side of the equation. Here's the step-by-step process:

Step 1: Distribute the division by X to both terms inside the parentheses:

(A * X) / X - z / X

Step 2: Simplify the expression:

A - z / X

Therefore, the final answer is A - z / X.Making (A) the subject:

(Q + TC) / T

To make (A) the subject, we follow a similar process:

Step 1: Distribute the division by T to both terms inside the parentheses:

Q / T + TC / T

Step 2: Simplify the expression:

Q / T + C.

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A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side²

The formula to find the side length.

s = √A

The length of the side is 11.8 feet.

A Square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side²

We have,

The total area of the square landing path:

A = 140 square feet.

The formula to use is given,

s = √A

Now,

s = √140

s = √4 x 35

s = 2√35

[ √35 = 5.92 ]

s = 2 x 5.92

s = 11.8 feet

Thus,

The length of the side is 11.8 feet.

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The solution is 84 boats

The total number of boats in the marina is 84 boats

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of boats in the marina be A

Now , the value of A is

And , the number of boats in the marina that are white = ( 3/4 ) A

So , the remaining boats = A - ( 3/4 ) A

The remaining boats = ( 1/4 ) A

And , 4/7 of the remaining boats are blue

So , substituting the values in the equation , we get

The number of boats in the marina that are blue = 4/7 ( ( 1/4 ) A )

The number of boats in the marina that are blue = ( 1/7 ) A

And ,

The remaining number of boats are red

So , the remaining number of boats = A - ( number of boats in the marina that are white + number of boats in the marina that are blue )

Substituting the values in the equation , we get

Number of boats in the marina that are red = A - ( 3/4 A + 1/7 A )

Number of boats in the marina that are red = A - ( 25/28 ) A

Number of boats in the marina that are red = ( 3/28 ) A

Now , There are 9 red boats , so substituting the value in the equation ,

Number of boats in the marina that are red = 9 = ( 3/28 ) A

On simplifying the equation , we get

( 3/28 ) A = 9

Multiply by 28 on both sides of the equation , we get

3A = 9 x 28

Divide by 3 on both sides of the equation , we get

A = 3 x 28

A = 84 boats

Therefore , the value of A is 84 boats

Number of red boats = 9 boats

Number of white boats = ( 3/4 ) A = 3/4 x 84 = 63 boats

Number of blue boats = ( 1/7 ) A = 1/7 x 84 = 12 boats

Total number of boats = 9 + 12 + 63 = 84 boats

Hence , The total number of boats is 84 boats

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The Kelvin temperature at 25°C is 298.15 K. The Kelvin scale is an absolute temperature scale and is widely used in scientific and industrial applications.

To convert Celsius to Kelvin,

you can use the formula: K = °C + 273.15. So,

25°C= 25 + 273.15 = 298.15 K.

This means that the Kelvin temperature at 25°C is 298.15 K.

The Kelvin scale is an absolute temperature scale and is widely used in scientific and industrial applications. Unlike the Celsius and Fahrenheit scales, which are based on human-defined reference points, the Kelvin scale starts at absolute zero, which is the theoretical temperature at which all matter has no thermal energy.

When working with temperature, it's important to choose the appropriate scale and to convert accurately, as the unit of measurement can affect temperature comparisons and calculations. Additionally, knowing the relationship between the different temperature scales can be useful in a variety of fields, such as thermodynamics, thermochemistry, and cryogenics.

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Answer:

The value of x = 7

Step-by-step explanation:

x²-14x + 49

=> x² - 7x - 7x + 49

=> x ( x - 7) - 7 ( x - 7 )

=> (x - 7) (x - 7)

=> x = 7

Answer:

3x - y - 2 =0

Step-by-step explanation:

Equation of line in point slope form is given as:

\( y-y_1 =m(x-x_1)\)

Plug \( _1 =4\:y_1= 10\: \& \: m = 3\) in the above equation, we find:

\( y-10 =3(x-4)\\\\

y - 10 = 3x - 12\\\\

y = 3x - 12+ 10\\\\

y = 3x - 2\\\\

3x - y - 2 =0

\)

If the p-value is smaller than α, we reject the null hypothesis; otherwise, we fail to reject it.

To approximate the p-value, we use the t-distribution because the population variance is unknown.

(a) t0 = 2.05:

To calculate the p-value, we need to find the area under the t-distribution curve beyond the test statistic in both tails. Since our alternative hypothesis (H1) is μ ≠ 7, we need to consider both tails of the distribution.

Using a t-table or statistical software, we can find the p-value associated with t0 = 2.05 and degrees of freedom = 19. Let's assume the p-value is P1.

P-value for t0 = 2.05 (P1) = 2 * (1 - P(Z < |t0|)), where P(Z < |t0|) is the cumulative probability of the standard normal distribution at |t0|.

Note: Since we have a two-tailed test, we multiply the probability by 2 to account for both tails.

(b) t0 = -1.84:

Similarly, for t0 = -1.84, we calculate the p-value by finding the area under the t-distribution curve beyond the test statistic in both tails. Since our alternative hypothesis (H1) is μ ≠ 7, we consider both tails.

Using a t-table or statistical software, we can find the p-value associated with t0 = -1.84 and degrees of freedom = 19. Let's assume the p-value is P2.

P-value for t0 = -1.84 (P2) = 2 * P(Z < |t0|)

(c) t0 = 0.4:

For t0 = 0.4, we calculate the p-value in a similar manner as before, considering both tails of the t-distribution.

Using a t-table or statistical software, we can find the p-value associated with t0 = 0.4 and degrees of freedom = 19. Let's assume the p-value is P3.

P-value for t0 = 0.4 (P3) = 2 * P(Z > |t0|)

Once you have the p-values (P1, P2, and P3) for each test statistic, you can compare them to the significance level (α) chosen for the hypothesis test. The significance level represents the threshold below which we reject the null hypothesis.

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Complete Question:

For the hypothesis test H0: μ = 7 against H1: μ ≠ 7 with variance unknown and n = 20, approximate the P-value for each of the following test statistics. (a) t0 = 2.05 (b) t0 = − 1.84 (c) t0 = 0.4

Cost of one rubber is £0.5 and cost of one pen is £0.75.

What is Cost?

The sum paid, levied, or equal amount for something: price. the investment or expenditure (as of labor or sacrifice) made to obtain a thing; the average cost of a college education has increased significantly.

Given that;

4p + 5r = £5.75

p + 4r = £3.5

⇒p = 3.5 - 4r

⇒4(3.5-4r)+5r=5.75

⇒14-16r+5r=5.75

⇒14-11r=5.75

⇒-11r=-8.25

⇒r=0.75

Therefore, cost of one rubber is £0.75.

Now calculation for the one pen we have ;

p+4(0.75)=3.5

⇒p+3=3.5

⇒p = 3.5 - 3

⇒p=0.5

Therefore, cost of one pen is £0.5.

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The prosecutor claims that there is a 1% chance that the defendant would have the crime blood type if he were innocent, and thus, there is a 99% chance that he is guilty.

This is a fallacy known as the prosecutor's fallacy.The prosecutor's fallacy is an error in statistical reasoning that occurs when the probability of an event occurring given a particular hypothesis is incorrectly equated with the probability of the hypothesis given the event.

It is a common mistake in legal proceedings and forensic science.According to the prosecutor's argument, the probability of the defendant being innocent given the blood evidence is only 1%, while the probability of him being guilty is 99%. This argument is invalid because it equates the conditional probability of the hypothesis (the defendant being innocent or guilty) given the evidence with the inverse probability of the evidence given the hypothesis.

In other words, the prosecutor has taken the likelihood of observing the blood evidence given that the defendant is innocent and used it as evidence that the defendant is guilty. This is a logical fallacy, as it fails to take into account other factors that could account for the presence of the blood evidence and ignores the possibility that the defendant may be innocent. Therefore, the prosecutor's argument is wrong, and his conclusion that the defendant is guilty cannot be justified by the evidence.

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The statement that is always true among the given options is (3) ΔBAG ~ ΔΑΕΒ.

In the given diagram, we have AB || DFC, EDA || CBG, and EFB and AG are drawn. We need to determine which statement is always true among the options provided: (1) ADEF = ACBF, (2) ABAG = ABAE, (3) ΔBAG ~ ΔΑΕΒ, or (4) ADEF ~ AAEB.

Let's analyze each statement:

(1) ADEF = ACBF: This statement is not always true. Since AB || DFC, the angles ADE and ACB are not necessarily equal. Therefore, the corresponding angles of the quadrilateral ADEF and ACBF are not always equal.

(2) ABAG = ABAE: This statement is not always true. Although ABAG and ABAE share a common side AB, the angles AG and AE are not necessarily equal. Hence, the two triangles ABAG and ABAE are not necessarily congruent.

(3) ΔBAG ~ ΔΑΕΒ: This statement is always true. Given that AB || DFC and EDA || CBG, we can conclude that the corresponding angles BAG and ΑΕΒ are equal by alternate interior angles. Additionally, the angles BGA and BEA are equal as vertical angles. Therefore, ΔBAG ~ ΔΑΕΒ by the Angle-Angle (AA) similarity criterion.

(4) ADEF ~ AAEB: This statement is not always true. The quadrilateral ADEF and the triangle AAEB do not have a definite relationship based on the given information. We cannot determine their similarity or congruence without additional details.

In conclusion, the statement that is always true among the given options is (3) ΔBAG ~ ΔΑΕΒ.

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