2/3 of a number is 20 less than the original number. Find the original number

The answer is 19 : 2.

Since chips are drawn at random so possible number of outcomes is

\(C(7,2)=\frac{7 !}{2 ! 5 !}=21\)

Following table shows all possible outcomes and the corresponding sum :

Outcomes Sum

1 2         3

1 3        4

1 4        5

1 5        6

1 6        7

1 7       8

2 3       5

2 4       6

2 5       7

2 6       8

2 7       9

3 4       7

3 5       8

3 6       9

3 7      10

4 5      9

4 6     10

4 7      11

5 6      11

5 7      12

6 7       13

Out of 21 outcomes, 2 shows sum 6.

That is outcome in favor are 21-2=19 and against are 2.

The odds are the sum of the numbers on the two selected slips is not 6 is 19 : 2.

What is Probability?

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Option a, Yes players with future transfer plans do experience significant points variance if those plans have an impact on their point performance.

There are two probable conclusions: (a) players with a future transfer plan do indeed have a greater point variance, and (b) players with a future transfer plan do indeed have a higher point median.

The presentation of players with and without move expectations ought to be analyzed, jumbling variables ought to be considered, and factual tests ought to be rushed to survey the legitimacy of these speculations.

The outcome of this research would ultimately establish whether or not the possibility of a future transfer plan had an impact on a player's point production.

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The rectangle maximum area will be A=9 square units with the length=3 and the width=3.

Area is defined as the space occupied by a plane or rectangle having length and width in two dimensional plane.

It is given that the perimeter of rectangle is P=12

So from the formula of perimeter of rectangle

2(L+W)=12

L+W=6

L=6-W

Now the area of rectangle will be

A=LxW

A=(6-W)W

Now for maximum area we will find the derivative and equate to zero.

\(A=(6W-W^2})\)

\(A'=6-2W=0\)

\(W=3\)

\(L=6-W=6-3=3\)

So the area will be

\(A=3\times 3=9 \ square \ units\)

Hence the rectangle maximum area will be A=9 square units with the length=3 and the width=3.

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Using trigonometric identities, If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is; 1

We are told that sinA + sin² A = 1.

Now, we want to find (cos²A + cos⁴A).

From trigonometric identities, we know that;

cos²A = 1 -  sin² A

Thus;

cos²A + cos⁴A = 1 -  sin² A + cos⁴A

Similarly, using trig identities on the given expression;

From sinA + sin² A = 1, we can say that;

sinA = 1 - sin² A

Since cos²A = 1 -  sin² A, then we can say that;

sinA = cos²A

Thus;

sin²A = cos⁴A

Thus;

cos²A + cos⁴A = 1 -  sin² A +  sin²A

= sinA +  sin²A= 1

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Correct question is;

If sinA + sin² A = 1, then the value of the expression (cos²A + cos⁴A) is

Answer:

x=\(-\frac{4}{3}\)

Step-by-step explanation:

The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

The perimeter of the triangle is 31 feet when the value if y is 3 feet.

Perimeter of the triangle:

Perimeter of the triangle is obtained by the total distance around the edges of a triangle.

The standard form for the perimeter of the triangle is

P = a + b + c.

where

a, b and c refers the edges of the triangle.

Given,

Here we have the triangle with the side values are (y + 5) feet, (3y + 5) feet, and (4y - 3) feet.

Then we have to find the perimeter of the triangle when the value of y is 3 feet.

We know formula of the perimeter of triangle, so first we have to calculate the side values of it, by apply the value of y as 3,

Apply the value of y as 3 feet then we get the value of the edges are

=> y + 5 => 3 + 5 = 8 feet

=> 3y + 5 => 3(3) + 5 = 14 feet

=> 4y - 3 => 4(3) - 3 = 9 feet.

Therefore, the edges of the triangle are 9ft, 14 ft and 9 ft.

Now, we have to apply the values on the formula of the perimeter of the triangle is, then we get

=> P = 8 + 14 + 9

Then the value of P = 31

Therefore, the value of the perimeter of the triangle is 31 feet.

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Answer:

67

Step-by-step explanation:

When two angles are complimentary, it means that, together, they make a 90 degree angle.

/_A + /_B must equal 90°

The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>

A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.

In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.

To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.

The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.

Therefore, the matrix equation can be written as Ax = 40 27 32.

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Chantal's careful measurements and consideration of the bungee cord's length, stretching capacity, and brake anchor placement contribute to a safe and enjoyable bungee jumping experience.

Chantal's decision to measure 16 feet away from the base of the tree is due to the length of the bungee cord being 16 feet long. She wants to ensure that the cord is fully stretched when in use, providing the proper tension and safety during the activity.

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Answer:

The solution of the equation is (3,1)

Step-by-step explanation:

Hope it helps:)

When the residual is negative it represents the predicted value is very much high.

Therefore, the negative residual value on the regression line represents the predicted value is very much high.

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Answer:

It's either 1:3 or 1:3

Step-by-step explanation:

A scale factor is times, calculate and, a reinduced PEMDAS

Congruent shapes have congruent corresponding sides.

The true statement is (d) Corresponding parts of congruent figures are congruent

From the question, we have the following corresponding sides

When the rectangle is reflected, the corresponding sides remain unchanged.

This means that corresponding parts of corresponding figures are equal.

Hence, the true statement is (d)

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Answer: since LP is half a line and PN is also half a line, then LP and PN are equal

So PN=6

Answer:

M=-1/4

Step-by-step explanation:

Use the slope intercept form y=mx+b to find the slope m.

Answer:

The slope of the equation: y=-1/4x+7 is -1/4

The slope of the equation: y=-3x+5 is -3

Step-by-step explanation:

It is easier to think of the slope at the number behind the x variable. But algebraically, y=mx+b is the formula and the number that is in the value of m is the slope of the linear function.

It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.

Non-exponential form:

To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.

Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.

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Answer:

The surface area of this prism is 800 ft^2

Step-by-step explanation:

To get this answer you need to add all the base edges, which will equal to 40. Then you times 40 with 20 which will equal to 800 ft^2. Hope this helps!

Answer:

520ft^2

Step-by-step explanation:

triangles

A=1/2bh

A=60

since both those half triangles make one trianlge there is no need to multipply 60 by 2

back rectangular

A= l x w

A= 8x20

A= 160

face rectangle

A= l x w

A=20 x 17

bottom rectangle

A=lxw

A = 300

add it all up

60+160+300=520ft^2

LET ME KNOW IF I MADE A MISTAKE

Answer:

AC is not equal to BC

AB=BC

Answer:

Step-by-step explanation:

The conclusion is that the null hypothesis is not true

Answer:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

So, substituting the values given in the question, we get:

(x - 3)² + (y + 5)² = 3²

Simplifying, we get:

(x - 3)² + (y + 5)² = 9

Therefore, the correct option is A) (x - 3)² + (y + 5)² = 9.

Step-by-step explanation:

The probability of the stick hitting a line is always 1 or 100%.

The probability that the stick will hit a line depends on the length of the stick compared to the spacing between the lines.

Since the spacing between the lines is 1, the stick will hit a line if its length is greater than or equal to 1.

Let's assume that the stick is randomly thrown and can land at any position on the plane with equal probability.

If we place the stick at any point on the plane, it will hit a line if its length is greater than or equal to the distance between the two closest lines on either side of it. Since the lines are spaced 1 unit apart, the distance between the two closest lines on either side of the stick will always be less than or equal to 1.

Therefore, the probability that the stick will hit a line is equal to the ratio of the length of the stick to the spacing between the lines, which is 1/1 = 1.

So, the probability that the stick will hit a line is 1 or 100%.

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The depth of the dirt in the raised gardening bed is 6 inches.

The volume of the dirt is given as 24 cubic feet, and the dimensions of the bed are provided as 6 feet in width and 8 feet in length. To find the depth of the dirt in inches, we need to calculate the area of the bed first.

The area of the bed is calculated by multiplying its width and length:

Area = 6 feet * 8 feet = 48 square feet.

To find the depth of the dirt, we divide the volume of the dirt by the area of the bed:

Depth = Volume / Area = 24 cubic feet / 48 square feet.

To convert the result to inches, we need to multiply it by the conversion factor of 12 inches per foot:

Depth = (24 cubic feet / 48 square feet)  12 inches/foot.

Simplifying the expression, we have:

Depth = 6 inches.

Therefore, the depth of the dirt in the raised gardening bed is 6 inches.

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Answer:

1/3x + 1/2

Step-by-step explanation:

combine like terms 1/3x plus 2/3x equals 3/3x - 2/3x = 1/3x

and 3/4-1/4 = 2/4.

Answer:

1/3x+1/2

Step-by-step explanation:

1/3x+2/3x-2/3x+3/4-1/4      eliminated +2/3x-2/3x

1/3x+3/4-1/4

1/3x+2/4    simplify 2/4 to 1/2

1/3x+1/2

The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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Answer:

A ∆ with an exterior angle :116° & two interior angles 7x+6 & 4x

The value of angle 7x+6

we know that ,

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non adjacent interior angles of the triangle.

so,

\(7x + 6 + 4x= 116 \\ 11x + 6 = 116 \\ 11x = 116 - 6 \\ 11x = 110 \\ x = 110 \div 11 \\ x = 10\)

so ,the measure of green angle would be

\(7x + 6 \\ placing \: the \: value \: of \: x \: as \: 10 \\ 7 \times 10 + 6 \\ = 70 + 6 \\ = 76\)

To verify our answer ,the sum of the resultant value of green angle and 4x should be 116°(the exterior opposite angle)

so,

\(7x + 6 + 4x = 116 \\ 7 \times 10 + 6 + 4 \times 10 = 116 \\ 70 + 6 + 40 = 116 \\ 76 + 40= 116 \\ 116 = 116 \\ \\ hence,\: verified\)

Solution:

Note that:

Simplify the equation to find x.

Substitute the value of x into the measure of the green angle.

The measure of the green angle is 76°.

distance= rate * time

distance/rate=time

(2.4 *10^20)/ (1.2*10^5)  = 2 * 10^15 seconds