PLSS HELP ITS THE LAST QUESTION

Answer:

1,920

Step-by-step explanation:

288/3 = 96

96 x 20 = 1920

Answer:

1920 eggs

Step-by-step explanation:

make a ratio and cross multiply

20/3=x/288

3x=5760

x=1920

Answer:

Its 67.9 but technically its 67.912 *hope this helps

Step-by-step explanation:

Right scalene triangle.

Sides: a = 66   b = 16   c = 67.912

Area: T = 528

Perimeter: p = 149.912

Semiperimeter: s = 74.956

Angle ∠ A = α = 76.373° = 76°22'23″ = 1.333 rad

Angle ∠ B = β = 13.627° = 13°37'37″ = 0.238 rad

Angle ∠ C = γ = 90° = 1.571 rad

Height: ha = 16

Height: hb = 66

Height: hc = 15.55

Median: ma = 36.674

Median: mb = 66.483

Median: mc = 33.956

Inradius: r = 7.044

Circumradius: R = 33.956

Vertex coordinates: A[67.912; 0] B[0; 0] C[64.142; 15.55]

Centroid: CG[44.018; 5.183]

Coordinates of the circumscribed circle: U[33.956; 0]

Coordinates of the inscribed circle: I[58.956; 7.044]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 103.627° = 103°37'37″ = 1.333 rad

∠ B' = β' = 166.373° = 166°22'23″ = 0.238 rad

∠ C' = γ' = 90° = 1.571 rad

Answer:

im not sure if this is what you're looking for but g=x^4 and the y intercept is g(0)=0

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.

Probability of dropouts next year being exactly 305: 0

Probability of dropouts next year being less than 305: 0.68

Probability of dropouts next year being greater than 305: 0.32

Probability of dropouts next year being within one standard deviation of 305: 0.95

The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.

The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Answer:

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

Step-by-step explanation:

Given: The curved line represented by the function \(f(x)\) crosses the x-axis at \((-2,0),(1,0),(3,0)\) and y-axis at \((0,-6)\)

To find: value of x for which \(f(x)=0\)

Solution:

\(f(x)=0\) gives those values of x for which the curve represented by the given function cuts the x-axis.

According to question, the curve cuts the x-axis at \(x=-2,1,3\)

The values of x, when f(x) = 0 are the y-intercepts of the graph, and the values are -2, 1 and 3

The points on the function on the graph are given as:

\((x,y) = \{(-2,0), (1,0), (3,0), (0,-6)\}\)

In the above ordered pairs, the points where y or f(x) equals 0 are:

\((x,y) = \{(-2,0), (1,0), (3,0)\}\)

Remove the y-values

\(x = \{-2, 1, 3\}\)

The above set represents the values of x, when f(x) = 0.

Hence, the values of x, when f(x) = 0 are -2, 1 and 3

Read more about y-intercepts at:

https://brainly.com/question/25683754

Answer:

Step-by-step explanation:

Answer:

y=31x/15 < y=27x/13 < y=15x/7 < y=13x/6 < y=11x/5 < y=21x/9 (=7x/3) < y=19x/8

Step-by-step explanation:

since all equations base on a linear, simple expression of x, we can simply compare the fractions.

in general, the bigger the number at the bottom, the smaller the individual fraction. that is our first indicator.

we then notice that many fractions represent the value of 2 plus one fraction.

31/15 = 2 1/15

27/13 = 2 1/13

15/7 = 2 1/7

13/6 = 2 1/6

11/5 = 2 1/5

the only exceptions are 21/9 and 19/8

but 21/9 is actually 7/3 = 2 1/3

and fits therefore into the list above.

that leaves 19/8 = 2 3/8.

the list above can be sorted based on the single fraction at the end (remember, the bigger the number at the bottom, the smaller the value). so, from least to greatest :

2 1/15 (31/15)

2 1/13 (27/13)

2 1/7 (15/7)

2 1/6 (13/6)

2 1/5 (11/5)

2 1/3 (7/3 = 21/9)

where did now 2 3/8 fit in ?

well, 3/8 is almost 1/2 (so, relatively big), and we start our comparison with the biggest number in the list so far :

1/3 (from 2 1/3).

what is bigger - 1/3 or 3/8 ?

let's find the smallest number that can be divided by 3 and by 8. that would be 24. so now we bring both fractions to the same base of 24.

1/3 = 8/24

3/8 = 9/24

=> 3/8 > 1/3

and therefore, 19/8 is the largest value and at the end of the list.

By mathematical induction, T(n) = nlog(n) for all n that are exact powers of 2.

We will prove by mathematical induction that T(n) = nlog(n) for all n that are exact powers of 2.

Base case: For n = 2, we have T(2) = 2 as given.

Inductive hypothesis: Assume that T(\(2^k\)) = \(2^k\) × log(\(2^k\)) for some positive integer k.

Inductive step: We need to show that T(\(2^{(k+1)}\)) = \(2^{(k+1)}\) × log(\(2^{(k+1)}\)).

Using the recurrence relation, we have:

T(\(2^{(k+1)}\)) = 2T(\(2^k\)) + \(2^{(k+1)}\)

Substituting T(\(2^k\)) = \(2^k\) × log(\(2^k\)) from the inductive hypothesis, we get:

T(\(2^{(k+1)}\)) = 2(\(2^k\) × log(\(2^k\))) + \(2^{(k+1)}\)

      = \(2^{(k+1)}\) × k × log(2) + \(2^{(k+1)}\)

      = \(2^{(k+1)}\) × (k+1)

      = \(2^{(k+1)}\) × log(\(2^{(k+1)}\))

For every n that are precise powers of 2, T(n) = nlog(n) is the result of mathematical induction.

Learn more about mathematical induction at

https://brainly.com/question/29503103

#SPJ4

The unit vector normal to the plane defined by a and b is λ = -32i/49 + 49j/49 - 44k/49.

To find the unit vector normal to a plane defined by two non-collinear vectors, we can use the cross product. The cross product of two vectors a and b produces a vector that is orthogonal to both a and b, and has a magnitude equal to the area of the parallelogram defined by a and b.

To obtain a unit vector, we divide the cross product by its magnitude.

Given that a = 7i + 8j - 2k and b = 9i - 4j - 5k, we can find the cross product as follows:

a x b = det( i j k)

7 8 -2

9 -4 -5 )

= (8 x (-5) - (-2) x (-4)) i

- (7 x (-5) - (-2) x 9) j

+ (7 x (-4) - 8 x 9) k

= 18i + 59j + 50k

To obtain the unit vector normal to the plane, we need to divide this vector by its magnitude:

|18i + 59j + 50k| = √(18^2 + 59^2 + 50^2) = √(6885)

So, the unit vector normal to the plane is:

λ = (18i + 59j + 50k)/√(6885)

= (-32i + 49j - 44k)/49

We can see that this matches the given result, so we can conclude that the unit vector normal to the plane defined by a and b is λ = -32i/49 + 49j/49 - 44k/49.

For more such questions on vector

https://brainly.com/question/3184914

#SPJ4

The store should have 445 picks remaining, not 450 as estimated by the manager. To determine if the store manager's estimate is reasonable, let's analyze the situation.

The store initially has 500 guitar picks. They order 15 boxes, and each box contains 9 picks. So the total number of picks they receive from the order is:

15 boxes * 9 picks/box = 135 picks

Next, the store sells 19 boxes, with each box containing 10 picks. Therefore, the total number of picks sold is:

19 boxes * 10 picks/box = 190 picks

To find the remaining number of picks, we can subtract the sold picks from the received picks:

Total remaining picks = Initial picks + Received picks - Sold picks

Total remaining picks = 500 + 135 - 190 = 445 picks

According to the calculations, the store should have 445 picks remaining, not 450 as estimated by the manager.

However, it's important to note that we are working with whole numbers, so there might be some rounding involved in the manager's estimate. It's possible that the manager rounded up to 450 for simplicity or other reasons.

Given the small discrepancy of 5 picks between the calculated value and the manager's estimate, it is reasonable to conclude that the manager's estimate is close enough to the actual number of picks. The discrepancy could be due to rounding or a small counting error. It's unlikely to have a significant impact on the store's operations or inventory management.

In summary, while the manager's estimate of 450 guitar picks may not be exactly accurate, it is reasonably close to the actual remaining number of picks based on the given information.

Learn more about estimate here:

https://brainly.com/question/30250563

#SPJ11

Answer:

I think that number one is 26, two is -4, and three is -4

Step-by-step explanation:

To solve for number one replace 8 with (x) so 3(8) + 2. 3 x 8 = 24 and 24+2 = 26

Numbers 2 and 3 appear to be the same problem so just do 3(-2) + 2 (Because you replace the number with the x) 3(-2) = -6 + 2 = -4!

I hope that helped!

Step 1. The party will be thrown by Steve, Jo, Lucy, Max, and Alex --> 5 people.

On Monday, each invites 3 friends. So for, the number of people invited is:

Step 2. On Tuesday, the friends that were invited (15) invited 3 more people each. The number of people invited now is:

Step 3. On Wednesday, the 45 people invited on Tuesday, each invite 3 more people. The number of people invited again multiplies by 3:

Step 4. The trend continues so for Thursday, the number of people invited on the previous day multiplies by 3:

Step 5. On Friday the number of people invited is:

Step 6. Finally, on Saturday, the day of the party, the number of people invited is multiplied one last time by 3:

Answer:

3,645

Answer:

the answer is 76.8

Step-by-step explanation:

multiple of the number

The cosine of angle X is given as follows:

cos(X) = 4/5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For angle X, we have that:

Hence the cosine of angle X is obtained as follows:

cos(X) = 32/40

cos(X) = 4/5.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The function of the power series f(x) = 6ln(1+x) = ∑=1 , ∞ 6(-1)⁽ⁿ⁻¹⁾xⁿ/n.

And a_n = 6(-1)⁽ⁿ⁻¹⁾xⁿ/n.

The common ratio is the distance between each number in a geometric series. The proportion of a number or two consecutive numbers. The common ratio, which is the same for all numbers or common, is the number divided by the number that comes before it in the sequence.

To find the power series for f(x), we first need to find the power series for g(x) = 6/(1+x):

g(x) = 6/(1+x) = 6(1 - x + x² - x³ +...) (geometric series with common ratio -x)

Next, we integrate term by term:

∫ g(x) dx = ∫ 6(1-x+x²-x³+...) dx

= 6(x - x²/2 + x³/3 - x⁴/4 + ...) + C , where C is a constant.

Since we're only interested in finding the coefficients of the power series, we can ignore the constant term.

Thus, the power series for f(x) is:

f(x) = 6ln(1+x) = 6(x - x²/2 + x³/3 - x⁴/4 + ...) = ∑=1 , ∞ 6(-1)⁽ⁿ⁻¹⁾xⁿ/n

where a_n = 6(-1)⁽ⁿ⁻¹⁾xⁿ/n.

Therefore, f(x) = 6ln(1+x) = ∑=1 , ∞ 6(-1)⁽ⁿ⁻¹⁾xⁿ/n.

To learn more about the power series visit-

brainly.com/question/29888415

#SPJ4

Option a, adjacency matrix. An adjacency matrix is a two-dimensional array that represents a graph's edges, where the rows and columns correspond to the vertices of the graph. If there is an edge between two vertices, the corresponding element in the matrix is set to 1, otherwise it is set to 0. This implementation is useful for dense graphs, where the number of edges is close to the maximum possible number of edges.

An adjacency matrix is a simple and efficient way to represent graphs that have a large number of vertices and edges. It allows for fast lookups of the existence of an edge and is useful for various algorithms that require graph representation. However, it is not suitable for sparse graphs, where the number of edges is much smaller than the maximum possible number of edges. In such cases, an adjacency list would be more appropriate.

The common implementation of a graph that uses a two-dimensional array to represent the graph's edges is called an adjacency matrix.

To know more about array representation,visit:

https://brainly.in/question/5489688

#SPJ11

The base area is 3x² + 10x  + 40  + 145 / (x -4).

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Given:

Volume of prism = 3x³-2x²-15

and, height = x-4

Now, Volume of prism = Base area x height

3x³-2x²-15 = (x- 4) x b

b =  3x³-2x²-15/ (x -4)

Now,

b =  3x³-12x² +10x² -40x +40x -160 + 145/ (x -4)

b= 3x²( x -4)+ 10x (x- 4) + 40(x -4) + 145

b = 3x² + 10x  + 40  + 145 / (x -4)

Hence, the base area is 3x² + 10x  + 40  + 145 / (x -4).

Learn more about volume of prism here:

https://brainly.com/question/21308574

#SPJ1

To find the number of three-letter initials with none of the letters repeated, we need to consider the number of choices for each position in the initials.

To determine the number of three-letter initials with none of the letters repeated, we can analyze each position in the initials. For the first letter, we have 26 choices since there are 26 letters in the English alphabet.

After selecting the first letter, for the second letter, we have 25 choices remaining since we cannot repeat the letter used in the first position. Similarly, for the third letter, we have 24 choices remaining since we cannot repeat either of the previous letters.

Therefore, the total number of three-letter initials with none of the letters repeated can be found by multiplying the number of choices for each position: 26 * 25 * 24 = 15,600. Hence, there are 15,600 different three-letter initials that people can have if none of the letters are repeated.

To learn more about multiplying click here:

brainly.com/question/23536361

#SPJ11

A trapezoid is a plane figure bounded by four sides. Therefore, the required answers are given below;

a) ΔADE = ΔBCF (Side-Angle-Side congruent property)

b) DE = 5 cm and CF = 5 cm

c) AE = 12 cm

Plane figures are shapes that are formed by straight boundaries referred to as sides. Examples include; square, rectangle, trapezium, etc.

A trapezoid is a family of quadrilaterals., these are figures that have four straight sides.

In the given question, the required answers are:

a) To prove that ΔADE = ΔBCF

Thus,

AE ⊥ DC  (given)

BC ⊥ DC  (given)

<AED = <BFC = \(90^{o}\)

AE = BF (height of the trapozoid)

<ADE ≅ <BCF (congruent property of two triangles)

Therefore, it can be concluded that;

ΔADE = ΔBCF (Side-Angle-Side congruent property)

b) Given that AB = 8 cm, and DC = 18 cm.

Then,

CD = DE + EF + FC

18 = DE + 8 + FC   (since EF = AB)

18 - 8 = 2 DE     (since DE = FC)

DE = 5 cm

Thus, DE = 5 cm and CF = 5 cm

c) To determine the value of AE, we have to apply the Pythagoras theorem. So that;

\(/Hyp/^{2}\) = \(/Adj 1/^{2}\) + \(/Adj 2/^{2}\)

\(13^{2}\) = \(AE^{2}\) + \(5^{2}\)

169 - 25 =  \(AE^{2}\)

\(AE^{2}\) = 144

AE = \(\sqrt{144}\)

     = 12

AE = 12 cm

For more clarifications on the measure of the sides of a trapezoid, visit: https://brainly.com/question/28007759

#SPJ 1

9514 1404 393

Answer:

  p(x) = x^3 +x^2 -82x +80

Step-by-step explanation:

If a polynomial function has a zero at x=a, then (x -a) is a factor. Your list of zeros means the factors are ...

  p(x) = (x -8)(x +10)(x -1) . . . . . . . . factored form

When this is multiplied out, it becomes ...

  p(x) = x^3 +x^2 -82x +80 . . . . . . standard form

_____

The factored form can be multiplied out using the distributive property.

  = ((x(x +10) -8(x +10))(x -1)

  = (x^2 +10x -8x -80)(x -1)

  = (x^2 +2x -80)x -(x^2 +2x -80)

  = x^3 +2x^2 -80x -x^2 -2x +80

  = x^3 +x^2 -82x +80

The rate of inflating is r=30% per month.

The bill of food after three months can be determined as,

Thus, the bill after three months will be $263.64.

Answer:

3(b/150)

I think I got it right, where's my second supporter?

Answer:

,

Step-by-step explanation:

,...

Answer:

10^11

Step-by-step explanation:

This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.

Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.

10 ^ (8+3)

= 10^11

see image

Answer:

54 students

Step-by-step explanation:

42 / 7 = 6

9 x 6 = 54

42 : 54 = 7 : 9

Observe that

\(\left(\sqrt x - \dfrac1{\sqrt x}\right)^2 = \left(\sqrt x\right)^2 - 2\sqrt x\dfrac1{\sqrt x} + \left(\dfrac1{\sqrt x}\right)^2 = x - 2 + \dfrac1x\)

Now,

\(x = 9 - 4\sqrt5 \implies \dfrac1x = \dfrac1{9-4\sqrt5} = \dfrac{9 + 4\sqrt5}{9^2 - \left(4\sqrt5\right)^2} = 9 + 4\sqrt5\)

so that

\(\left(\sqrt x - \dfrac1{\sqrt x}\right)^2 = (9 - 4\sqrt5) - 2 + (9 + 4\sqrt5) = 16\)

\(\implies \sqrt x - \dfrac1{\sqrt x} = \pm\sqrt{16} = \pm 4\)

To decide which is the correct value, we need to examine the sign of \(\sqrt x - \frac1{\sqrt x}\). It evaluates to 0 if

\(\sqrt x = \dfrac1{\sqrt x} \implies x = 1\)

We have

\(9 - 4\sqrt5 = \sqrt{81} - \sqrt{16\cdot5} = \sqrt{81} - \sqrt{80} > 0\)

Also,

\(\sqrt{81} - \sqrt{64} = 9 - 8 = 1\)

and \(\sqrt x\) increases as \(x\) increases, which means

\(0 < 9 - 4\sqrt5 < 1\)

Therefore for all \(0 < x < 1\),

\(\sqrt x - \dfrac1{\sqrt x} < 0\)

For example, when \(x=\frac14\), we get

\(\sqrt{\dfrac14} - \dfrac1{\sqrt{\frac14}} = \dfrac1{\sqrt4} - \sqrt4 = \dfrac12 - 2 = -\dfrac32 < 0\)

Then the target expression has a negative sign at the given value of \(x\) :

\(x = 9-4\sqrt5 \implies \sqrt x - \dfrac1{\sqrt x} = \boxed{-4}\)

Alternatively, we can try simplifying \(\sqrt x\) by denesting the radical. Let \(a,b,c\) be non-zero integers (\(c>0\)) such that

\(\sqrt{9 - 4\sqrt5} = a + b\sqrt c\)

Note that the left side must be positive.

Taking squares on both sides gives

\(9 - 4\sqrt5 = a^2 + 2ab\sqrt c + b^2c\)

Let \(c=5\) and \(ab=-2\). Then

\(a^2+5b^2=9 \implies a^2 + 5\left(-\dfrac2a\right)^2 = 9 \\\\ \implies a^2 + \dfrac{20}{a^2} = 9 \\\\ \implies a^4 + 20 = 9a^2 \\\\ \implies a^4 - 9a^2 + 20 = 0 \\\\ \implies (a^2 - 4) (a^2 - 5) = 0 \\\\ \implies a^2 = 4 \text{ or } a^2 = 5\)

\(a^2 = 4 \implies 5b^2 = 5 \implies b^2 = 1\)

\(a^2 = 5 \implies 5b^2 = 4 \implies b^2 = \dfrac45\)

Only the first case leads to integer coefficients. Since \(ab=-2\), one of \(a\) or \(b\) must be negative. We have

\(a^2 = 4 \implies a = 2 \text{ or } a = -2\)

Now if \(a=2\), then \(b=-1\), and

\(\sqrt{9 - 4\sqrt5} = 2 - \sqrt5\)

However, \(\sqrt5 > \sqrt4 = 2\), so \(2-\sqrt5\) is negative, so we don't want this.

Instead, if \(a=-2\), then \(b=1\), and thus

\(\sqrt{9 - 4\sqrt5} = -2 + \sqrt5\)

Then our target expression evaluates to

\(\sqrt x - \dfrac1{\sqrt x} = -2 + \sqrt5 - \dfrac1{-2 + \sqrt5} \\\\ ~~~~~~~~~~~~ = -2 + \sqrt5 - \dfrac{-2 - \sqrt5}{(-2)^2 - \left(\sqrt5\right)^2} \\\\ ~~~~~~~~~~~~ = -2 + \sqrt5 + \dfrac{2 + \sqrt5}{4 - 5} \\\\ ~~~~~~~~~~~~ = -2 + \sqrt5 - (2 + \sqrt5) = \boxed{-4}\)

If the null space of a 7 × 9 matrix is 3-dimensional, we can determine the rank of matrix A, the dimension of the row space of A, and the dimension of the column space of A.

The rank of a matrix is equal to the number of linearly independent columns or rows in the matrix. Since the null space is 3-dimensional, the rank of A would be 9 - 3 = 6.

The dimension of the row space, also known as the row rank, is equal to the dimension of the column space, or the column rank. Therefore, the dimension of the row space and the dimension of the column space of A would also be 6.

The rank of matrix A would be 6, and both the dimension of the row space and the dimension of the column space of A would also be 6.

Learn more about matrix here: brainly.com/question/28180105

#SPJ11