(lesson 4.2.5) Find g(-5) given g(x) = x³ - 2​

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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Answer: 3+2×(8-5)+6 =15

\(\sf\purple{15}\) ✅

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\(3 + 2 \times (8 - 5) + 6 \\ \\ = 3 + 2 \times 3 + 6 \\ \\ = 3 + 6 + 6 \\ \\ = 15\)

\(\sf\purple{BODMAS\: rule.}\)

B = Brackets

O = Orders

D = Division

M = Multiplication

A = Addition

S = Subtraction

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Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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Answer:

2x+1=4x-19

20=2x

x=10

The following weights (in pounds) are within 1.5 units of the standard deviation of the mean:

A. 4.4

B. 4.6

D. 5.2

E. 6.9

F. 7.6

The mean weight of the chickens in this population is 6.3 pounds, and the standard deviation is 1.2 pounds. To be within 1.5 units of the standard deviation, we need to look at the range of weights that are 1.2 +/- 1.5, which is 4.7 to 7.9 pounds.

This means that the weights within this range are 4.4, 4.6, 5.2, 6.9, 7.6, and any other weights that fall within the range. Therefore, the weights within 1.5 units of the standard deviation of the mean are:

A. 4.4, B. 4.6, D. 5.2, E. 6.9, and F. 7.6.

The standard deviation measures the spread of the data from the mean. In this case, the mean is 6.3 pounds and the standard deviation is 1.2 pounds. This means that the data points on either side of the mean will be 1.2 pounds away from it.

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Answer:

0%

Step-by-step explanation:

We have the following information:

mean (m) = 208 days

standard deviation (s) = 15 days

We have that the z value would be:

z = (x - m) / sd

replacing we have:

z = (308 - 208) / 15

z = 6.66

However,

P (x> 308) = 1 - (x <308)

P (x> 308) = 1 - (z <6.66)

if we look for this value of z in the table we assume that it is 1, since the table reaches 3 and the value is 1. Therefore:

P (x> 308) = 1 - 1

P (x> 308) = 0

Which means that the probability is 0%, therefore it is a very unusual pregnancy.

Answer: x=44

Step-by-step explanation: hope this helps

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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\( \frac{55}{100} = 0.55\)

Answer:

  11/20

Step-by-step explanation:

  \(\dfrac{55}{100}=\dfrac{5\cdot11}{5\cdot20}=\boxed{\dfrac{11}{20}}\)

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

w = 8 ft

l = 15 ft

total area (paint) = ?

Step 02:

rectangle area

A = l * w

A1 = 15 ft * 8 ft = 120 ft²

circle area

A = π r²

half circle area

A = (π r²) / 2

A2 = (π * (4ft)²) / 2

A2 = 25.13 ft²

total area = A1 + A2 = 120 ft² + 25.13 ft² = 145.13 ft²

The answer is:

They will used 145.13ft² of paint.

Answer:

It would be 0.41 ft^3

Step-by-step explanation:

Alright, to start, lets get the volume of the entire cinder block and the holes within it.

1.31 * 0.66 * 0.66 ---> 0.5706...

Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.

0.33 * 0.39 * 0.66 ---> 0.0849...

Since there's two of them: 0.1698...

To finish it, subtract the hole volume from the total volume;

0.5806 - 0.1698 = 0.4108

Rounds to 0.41 ft^3

Answer:

midsegment = 23

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = \(\frac{18+28}{2}\) = \(\frac{46}{2}\) = 23

The required solution of the given inequality 2x < 8 is x < 4.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given  inequality is

2x < 8

According to given question we have

Write inequality

2x < 8

Divide both sides by 2 we get,

x < 4

Therefore, the required solution of the given inequality 2x < 8 is x < 4.

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Answer:

A, B, C.

Step-by-step explanation:

Answer:

P = 48 in²

Step-by-step explanation:

Given: A rectangle; Width = 9 inches, length = 15 inches, enlarged by a scale factor of \(\frac{3}{2}\)

To find: Perimeter of the dilated rectangle

Formula: \(P=2(l+w)\)

Solution: After a dilation with a scale factor of one-half, then the lengths on the image would be one-half , one-half , and one-half . To find the perimeter of an enlarged figure, you can multiply the original figure's perimeter by the scale factor.

\(P=2(l+w)=2\) × \((15+9)=48in\)

Therefore, the perimeter of the detailed rectangle that was enlarged is 48 in²

Answer:

it's 9in

Step-by-step explanation: i got it right on my test

The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

Ans : 36

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the radius of the circle is √91 units and its centre is (-3,2) .

We know that the standard equation of circle is,

\(\longrightarrow (x-h)^2+(y-k)^2=r^2 \\\)

where,

On substituting the respective values, we have;

\(\longrightarrow \{ x-3\}^2+\{ y-(-2)\}^2= (\sqrt91)^2 \\\)

Simplify,

\(\longrightarrow \red{ (x-3)^2+(y+2)^2=91} \\\)

This is the required equation of the circle.

Answer:

(x - 3)² + (y + 2)² = 91

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (3, - 2 ) and r = \(\sqrt{91}\) , then

(x - 3)² + (y - (- 2) )² = ( \(\sqrt{91}\) )² , that is

(x - 3)² + (y + 2)² = 91 ← equation of circle

Therefore , the solution of the given problem of linear equation comes out to be x =4 spirit blankets were sold.

A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. Even though y and y are separate parts, the above phrase is commonly referred to as a "mathematical equation with two variables." The only variables in bivariate linear equations are two. There are never any solutions toward the application areas of linear equations. Y=mx+b is the formula for a single series of equations, where m denotes the gradient and b the y-intercept.

Here,

Given :

Sprit blanket cost = $20

hot chocolate = for $2 per cup.

Let x be the number of spirit blanket sold:

=> 7x

and

Hot chocolate sold

=> 7x + 8

So,

=>  2(7x + 8) + 20 * 7x = 560

=> 14x + 16 + 140x= 560

=> 154x  = 560-16

=> 154x = 544

=> x  = 544/154

=> x = 3.567 or approx x =4

Therefore , the solution of the given problem of linear equation comes out to be x =4 spirit blankets were sold.

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Answer:

Jane must pay $ 5,947.2 over 12 months. Of that amount, $ 637.2 will correspond to interest generated by the loan, which will be paid in 12 installments of $ 495.6.

Step-by-step explanation:

Jane Windsor acquired a ski boat for $ 5,900, paying a down payment of 10% and financing the remainder of the price at an annual interest rate of 12%.

Thus, since 5,900 x 0.1 is equal to 590, the financed amount arises from the subtraction between 5,900 minus 590, which yields a financed amount of $ 5,310.

Therefore, the amount to be paid monthly arises from the following calculation:

5,310 x 1.12 = Amount with interest

5,947.2 = Amount with interest

5,947.2 - 5,310 = Interest

637.2 = Interest

5,947.2 / 12 = Monthly payments

495.6 = Monthly payments

Therefore, Jane must pay $ 5,947.2 over 12 months. Of that amount, $ 637.2 will correspond to interest generated by the loan, which will be paid in 12 installments of $ 495.6.

Step-by-step explanation:

The graphs are not give but the graph looks like the above picture.

The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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The angle is 16 degrees or 164 degrees.

Any triangle that is not a right triangle is said to be oblique. There are two types of triangles: acute triangles, in which all three angles are less than right angles, and obtuse triangles (one of the three angles is greater than a right angle). Actually, right triangles could equally well be included in the category of "oblique triangles" for trigonometric purposes. In that case, studying oblique triangles is basically studying all triangles.

Given, the area of an oblique triangle which is going to be used as an area of the formula backward to find a missing measure.

We know two side lengths of the triangular region 60 ft and 1 20 ft

Area = 1000-square-foot

A= 1/2*60*120=1000

A=3600=1000

Dividing both sides with 3600,

We get an angle of 16 degrees.

But it is also possible that the area will be the same. If we use this in supplementary angle as well we get,

180-16 = 164 degrees.

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Answer:

Number of small candles = 12

Number of large candles = 16

Step-by-step explanation:

Total candles = 28

x + y = 28 ---------------(I)

Cost of 'x' small candles = 4 *x = 4x

Cost of 'y' large candles = 6 *y = 6y

Total amount = $144

4x + 6y = 144 -------------(II)

Multiply equation (I) by (-4) and then add the equation. So, x will be eliminated and we can find the value of 'y'

(I) * (-4)            -4x - 4y = -112

(II)                    4x  + 6y = 144              {Now, add}

                               2y = 32

                                y = 32/2

y = 16

Plug in y = 16 in equation (I)

x + 16 = 28

       x = 28 - 16

x = 12

Answer:

small candles-x

large -y

144-4x=6y

28-x=y

28-y=x

(28-x)6+4x=144

168-6x+4x=114

-2x=-54

2x=54

x=27

27 small and 1 large