Can we draw a triangle with sides 3cm 3.5 cm and 6.5 cm?

After factoring the value of y^x = 5 or -4.

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators (such as +, -, x, ÷). These expressions can be evaluated to determine their numerical value, but they can also be simplified, factored, and manipulated using the rules of algebra. Examples of algebraic expressions include 2x + 3, x^2 - 4, and (x + y)^2.

Given expression,

y^2x - y^x - 20 = 0

Let y^x = t .

t^2 - t - 20

t^2-5t+4t-20 = 0

t (t-5) + 4 (t-5) = 0

(t-5) (t+4) = 0

so, t-5 = 0

we get , t = -4

and t+4 = 0

so we get , t = 5

Hence, the value of y^x = 5 or -4.

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The total number of possible combinations would be 2,598,960.

The sample space for this experiment would be all possible combinations of 5 cards from a deck of 52 cards. This would include all possible combinations of 5 cards of the same suit (e.g. 5 spades, 5 hearts, etc.), all possible combinations of 4 cards of one suit and 1 card of another suit (e.g. 4 spades and 1 heart, 4 hearts and 1 spade, etc.), all possible combinations of 3 cards of one suit and 2 cards of another suit, and so on. The total number of possible combinations would be 2,598,960.

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The probability mass function (pmf) of x is:

                    = 0.0020      for x = 1

                    = 0.1459       for x = 2

P(X = x) {      = 0.8825       for x = 3

                    = 0.5883       for x = 4

                    = 0                otherwise

In this question we have been given that after shuffling a deck of 52 cards, a dealer deals out 5. let x = the number of suits represented in the five-card hand.

We need to find the pmf of x.

here, sample space n = 52,

and x = 5.

Let x = the number of suits represented in the five - card hand.

So, all possible outcomes for above event would be,

N = 52C5

N = 2598960

For x = 1 (all are spades)

Then the number of ways to get 5 spades would be 13C5 = 1287

so there are 1287 hands of 5S.

Since there are 4 suits, we multiply 1287 by 4C1

Then P(x = 1) = (4 * 1287)/2598960

                     = 0.0020

For x = 2 (only spades and hearts with at least one of each suit)

Then we can have 4S and 1H; 3S and 2H; 2S and 3H; or 1S and 4H.

And the number of possible outcomes would be,

(13C4 * 13C1) + (13C3 * 13C2) + (13C2 * 13C3) + (13C1 * 13C4)

= 2[(13C4 * 13C1) + (13C3 * 13C2)]

= 2(715 * 13 + 286 * 78)

= 63206

We're choosing 2 suits from the 4, so we multiply this by 4C2 = 6

Then P(x = 2) = (6 * 63206)/2598960

                     = 0.1459

For x = 3  (a hand with S, H, and clubs (C))

Then we can have 3S, 1H, and 1C; 1S, 3H, and 1C; 1S, 1H, and 3C; 2S, 2H, and 1C; 2S, 1H, and 2C; or 1S, 2H, and 2C.

Using combination formula,

3[(13C3 * 13C1 * 13C1) + (13C2 * 13C2 * 13C1)]

= 3 [(286 * 13 * 13) + (78 * 78 * 13)]

= 382278

We're choosing 3 suits from the 4, so we multiply this by 4C3 = 6

Then P(x = 3) = (6 * 382278)/2598960

                     = 0.8825

For x = 4  (2 spades ∩ one of each other suit)

For this case the possible outcomes would be,

13C2 * 13C1 * 13C1 * 13C1

= 78 * 13 * 13 * 13

= 171366

Then we can have 3S, 1H, and 1C; 1S, 3H, and 1C; 1S, 1H, and 3C; 2S, 2H, and 1C; 2S, 1H, and 2C; or 1S, 2H, and 2C.

Using combination formula,

3[(13C3 * 13C1 * 13C1) + (13C2 * 13C2 * 13C1)]

= 3 [(286 * 13 * 13) + (78 * 78 * 13)]

= 382278

Then P(x = 4) = (4 * 382278)/2598960

                     = 0.5883

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The complete question is:

After shuffling a deck of 52 cards, a dealer deals out 5. let x = the number of suits represented in the five-card hand.

(a) find the pmf of x.

[hint: p(1) = 4p(all are spades), p(2) = 6p(only spades and hearts with at least one of each suit), and p(4) = 4p(2 spades ∩ one of each other suit)](round your answers to five decimal places.)

Answer:

r=17/3

Step-by-step explanation:

Given -17=-3r

Divide both sides by -3

-17/-3=r=17/3

r=17/3

Hope this helps :)

Answer:

Slope (m) = 2
y = 2x

Step-by-step explanation:

Change in y / Change in x
-1 becomes 1 (positive)

1 + 1 = 2
1 - 5 = 4
4/2 = 2

y = 2x

Check the picture below.

Answer:

270

Step-by-step explanation:

He read 45 pages an hour.  If we go back to hour 0, we would add 45 pages to 225

Answer:

270 pages

Step-by-step explanation:

In the attachment, we can see that Aiden read 45 pages per hour. Therefore, since he already read for an hour, we need to add 45 to 225

45+225=270

So, Aiden's book has a total of 270 pages.

The polygonal shape of the hexacontakaienneagon has 69 sides.

A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Polygons include shapes like triangles, hexagons, pentagons, and quadrilaterals.

The hexacontakaienneagon shape's number of sides is indicated by the name. For instance, a triangle has three sides, whereas a quadrilateral has four. A two-dimensional closed figure with three or more straight sides is called a polygon. A polygon is any shape with straight edges, such as a triangle or rectangle. Figures with open sides or any curved sides are not considered to be polygons.

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Answer:

True.

Step-by-step explanation:

In a reflection, the orientation of a figure changes. This means that the direction of the shape is reversed, as if it were being viewed in a mirror. For example, if a figure is facing to the right, it will appear to be facing to the left after it has been reflected. The shape itself is not altered by the reflection, only its orientation.

Answer:

(4.) 4(3 + 9)

(5.) 5(n + 7)

(6.) 7(11 + 3)

(7.) 8(5+n)

Step-by-step explanation:

(4.) The area of a rectangle is length * width.  Because there are two rectangles, the areas must be combined in order to find the total area.

The area of the first rectangle is 4*3 and the area of the second is 9*4 so the total area would be 4*3 + 4*9.  We can factor out the 4 and simply add the 9 and 3 to get area = 4(3 + 9).

(5.) The total area before using the distributive property is 5 * n + 5 * 7.  We factor out the 5 and add the n and 7 to get area = 5(n + 7)

(6.) We need two numbers whose product is 77 and two numbers whose product is 21. Also, one of the numbers must be the same (namely the width, since the width of both rectangles is equal and doesn't change).  

We can use 7*11 for the first rectangle and 7*3 for the second rectangle.  We factor out the 7 and add the 3 and 11 to get area = 7(3 + 11).

(7.) We need two numbers whose product is 5n and two numbers whose product is 40.  Like number 6, the width of both rectangles must be the same.  Since we already have 8 for the first rectangle, we can use 8 * n and 8 * 5.

We factor out the 8 and add the 5 and n to get 8(5 + n).

The segment lengths for this triangle are given as follows:

Similar triangles are triangles that share these two features given as follows:

There are three triangles in this problem, all of which are similar.

The length of segment PX can be obtained with triangles PQR and PXY, as follows:

PX/30 = 10/40

PX/30 = 1/4

4PX = 30

PX = 7.5.

The length of segment XQ is found applying the segment addition postulate, as follows:

PQ + XQ = 30

7.5 + XQ = 30

XQ = 22.5.

The length of segment XY can also be obtained with the similarity of triangles PXY and PQR, as follows:

XY/36 = 10/40

XY/36 = 1/4

4XY = 36

XY = 9.

The length of segment ZW is obtained with the similarity of triangles PZW and PQR, as follows:

ZW/36 = 24/40

ZW/36 = 0.6.

ZW = 36 x 0.6

ZW = 21.6.

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Answer: D

Step-by-step explanation:

No, we cannot. We must perform a t-test to determine whether or not the difference in the means is statistically significant.

We must perform a t-test to determine whether or not the difference in the means is statistically significant. First, we must calculate the difference in the means, which is

199 - 187

= 12.

Then, we must calculate the standard error of the difference in means, which is the square root of

(6^2/7 + 9^2/12).

Then, we must calculate the t-statistic, which is the difference in means divided by the standard error. Finally, we must compare the t-statistic to the critical t-value at the 0.01 level of significance. If the t-statistic is greater than the critical t-value, we can reject the null hypothesis that there is no difference in the means and conclude that the mean number of days before remission after treatment 1 is greater than the mean number of days before remission after treatment 2.

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Lilly is travelling at a faster speed.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Distance travelled by Spencer = 4/5 mile

Time taken to travel the distance = 1 1/3 minutes = 4/3 minutes

Speed = Distance / Time = (4/5) / (4/3) = 3/5 = 0.60 mile per minute

Distance travelled by Lilly = 3/4 mile

Time taken to travel the distance = 1 1/8 minute = 9/8 minutes

Speed = (3/4) / (9/8) = 2/3 = 0.67 mile per minute

Hence Lilly is travelling at a greater speed of  0.67 mile per minute.

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The two pair of linear equations are 2x+6y=30 and x+y=7.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Each, x, table cover cost $2 and each, y, center piece cost $6.

Karl spent $30 decorating for the annual holiday party.

So, the equation is 2x+6y=30 --------(I)

Karl bought 7 items total.

Now, x+y=7 --------(II)

From equation (II), x=7-y

Substitute, x=7-y in equation (I), we get

2(7-y)+6y=30

14-2y+6y=30

14+4y=30

4y=16

y=4

Substitute y=4 in equation (II), we get

x=3

Therefore, the two pair of linear equations are 2x+6y=30 and x+y=7.

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Step-by-step explanation:

The account starts at 2000$

2000$×0.06(same as 6%)= 120$

The account gains 120$ yearly

A. After 4yrs that would be 480$ interest

120$×4= 480$

2000$+480$= 2480$ after 4yrs

B. Aftee 16yrs that would be 1920$ interest

120$×16= 1920$

1920$+2000$= 3920$

C. 2500$-2000$= 500$

500$÷120$= 4.16yrs

It will take about 4.2 years for the account to reach 2500$

D. 3000$-2000$= 1000$

1000$÷120$= 8.33yrs

It will take about 8.3yrs for the account to reach 3000$

Answer:

9

Step-by-step explanation:

What you do if first you draw your rectangle. You name length as x (as told in the question) and width as x-3 (since the width is 3 feet less). To obtain the area you have to do x × (x-3) because to find area you do length × width right.

So area is x(x-3) and it also tells you that area is 54 there

That's how you get x(x-3)=54

Now to solve it, you have to expand

x(x-3)=54

x²-3x-54 = 0 (you have to factorise this now)

(x+6) or (x-9) = 0

x = -6 or x = 9

As you can see you have two answers there. We have to eliminate the -6 because length can never be negative. The logic is simple, any length you take for example on a ruler (it has to be 0 or above) you can measure 1 feet, 2 feet, even 100 feet but you can't measure less than 0 right?

So the final answer is that x=9 and x represents the length

So length = 9

The system of linear equations with our defined variables are 2x + 2y = 62 ...eq(i) and x + 4y = 70 ...eq(ii)

A system of linear equations is a collection of two or more linear equations that use the same set of variables. The solution of a system of linear equations is the set of values for the variables that make all of the equations in the system true.

In this problem, let's define our variables as;

The equations can be written as;

2x + 2y = 62 ...eq(i)

x + 4y = 70 ...eq(ii)

Which is synonymous to option D in the question

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Answer: The answer is -34 3/16

Step-by-step explanation:

−51/2 + 63/4(−41/4)

=−51/2 + −2583/16

= −2991/16

= -34 3/16

On solving the provided question, we can say that - by the unitary method  price of the each drink will be $4

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

she spent $20  = on 5 cases

so of each will be 20/5 = $ 4

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The value of angle x is 73⁰

You should be aware that a point where two or three straight lines intersect forms an angles.

The parameters that will help us to determine the value of x are

Line B is a straight line. then the sum of angles on a straight line is 180.

⇒110 + b = 180

Making b the subject we have

b = 180 - 110

This means that  b = 70°

Also, a = 52° (Opposite angles)

The sum of all interior angles of a triangle is 180.

This means that a + b + c = 180

substitute for a and b to get c

52 + 70 + c = 180

122 + c = 180

Making c the subject of the relation

c = 180 - 122

⇒c = 58°

On the other hand c + d + e = 180

Substitute for c and d to have 58 + 49 + e = 180

107 + e = 180

Making e the subject of the relation we have

e = 180 - 107

e = 73°

But x = e (opposite angles)

There the value of x is 73⁰

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The two functions are not inverses of one another.

A relation is a function if it has only One y-value for each x-value.

The given two functions are F(x)=5x+2

G(x) = x-2/5

Now we need to verify whether these two are inverses of one another

F(G(x)=F(x-2/5)

=5(x-2/5)+2

=5x-2+2

=5x

Now G(F(x))=G(5x+2)

=5x+2-2/5

=5x+8/5

F(G(x) is not equal to G(F(x)).

Hence, the two functions are not inverses of one another.

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For the table, we have that the rate between the output and the input is given as follows:

12/3 = 16/4 = 28/7 = 32/8 = 4.

Meaning that this is a proportional relationship, and that one employee can help 4 customers, which is the constant of proportionality.

The graph has a constant slope and an intercept of zero, meaning that it also represents a proportional relationship, with the rate given as follows:

k = 8/1 = 8.

The data is given by the image presented at the end of the answer.

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The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

We use the formula

n= (zc/E)2σ2

Where,

n = sample size

zc = The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

E = margin of error

σ = standard deviation

Substituting the given values,

n= [(1.96*0.95)/1]2*5.72

n= 95.29

Therefore, the minimum sample size n equals 96 (rounded up to the nearest whole number).

The minimum sample size needed to estimate μ for the given values of c, o, and E is 100

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The logarithm rules and the matching equation is as follows

equation                         logarithm rule

[tex]log_{3}(\frac{(x-4)}{(x-1)})[/tex]                      quotient rule

[tex]log_{2}x(x+2})[/tex]                    product rule

[tex]log(x+2)^{3} x^{3}[/tex]                   product rule and power rule

[tex]log_{3}(x-4)-log_{3}(x+4)[/tex]  quotient rule

3 log (x + 2) - 3 log (x)     product rule and power rule

The laws of logarithm are generally rules that describes how problems involving logarithm is being solved

The quotient rule refers to when there is a division, the rul when applied changes division to subtraction.

The power rule takes care if exponents and places the number in the exponents to be just before the log sign

The product rule is used to deal with duplication, it changes multiplication to addition

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Answer:

the minimum sample size required is 139

Step-by-step explanation:

To construct a 95% confidence interval with a maximum error of 0.19 reproductions per hour, we need to use the t-distribution. The t-distribution is used when the population variance is unknown and the sample size is small.

To find the minimum sample size required, we need to use the following formula:

n = (t_(α/2,df) * s / E)^2

where:

n is the minimum sample size

t_(α/2,df) is the critical value of the t-distribution for a confidence level of 95% (α = 0.05) and df is the degrees of freedom

s is the standard deviation of the population

E is the maximum error allowed

We are given that the mean is 12.6 reproductions and the variance is 3.61. The standard deviation is the square root of the variance, so the standard deviation is 1.9.

To find the critical value of the t-distribution, we need to know the degrees of freedom. The degrees of freedom is equal to the sample size minus 1. Since we don't know the sample size yet, we will use a symbol (let's use "df") to represent the degrees of freedom in the formula.

Plugging the values into the formula, we get:

n = (t_(0.025,df) * 1.9 / 0.19)^2

To find the critical value of the t-distribution, we need to use a t-table or a computer program. Looking up the critical value in a t-table or using a computer program, we find that the critical value for a 95% confidence level and df = 9 is 2.262.

Plugging this value into the formula, we get:

n = (2.262 * 1.9 / 0.19)^2

Simplifying the expression, we get:

n = (11.868)^2

n = 138.7

The minimum sample size required is 138.7. Since we can't have a fractional number of samples, we need to round up to the next integer, which is 139.

Therefore, the minimum sample size required is 139.

Answer:

Each DC cost $18.49.

Step-by-step explanation:

[tex](\frac{79.94 - 5.94)}{4}[/tex]  Subtract out the shipping cost of 5.98 from the total cost of $79.94 and divide that amount by 4.  That will get you 18.49 which is the cost of each DVD.

False, sample evidence cannot prove that a null hypothesis is true.

Sample evidence can be used to infer whether a null hypothesis is true or not, but it cannot prove it to be true. The null hypothesis is a statement of no effect or no difference, and it is typically used as a starting point for statistical hypothesis testing. When sample data is collected, it is used to calculate a test statistic, which is then used to make a decision about the null hypothesis.

If the test statistic falls within the acceptance region, meaning that it is not unlikely to occur if the null hypothesis is true, then the null hypothesis is not rejected. However, if the test statistic falls in the rejection region, meaning that it is unlikely to occur if the null hypothesis is true, then the null hypothesis is rejected. The conclusion is that the sample evidence provides a probability that the null hypothesis is true or not, but it cannot prove it to be true.

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Common factor

8x+4

4(2x +1)

∴ Solution is 4 (2x+1)

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Answer: y = -4

Step-by-step explanation: