determine the general solution of cos2X -7cosX -3=0​

Answer:

the answer of r is 8 i hope it will help

[tex] \frac{ - 15}{23} + \frac{30}{ - 46} \\ = \frac{ - 15}{23} + \frac{(2) \times (15)}{(2) \times ( - 23)} \\ = \frac{ - 15}{23} + \frac{15}{ - 23} \\ = \frac{ - 15}{23} - \frac{15}{23} \\ = \frac{ -3 0}{23} \\ = - 1.3[/tex]

Answer:

19.3 miles per gallon

Step-by-step explanation:

First, subtract 54,042.8-53,737.7. The answer is 305.1

Then, find the unit rate. 305.1/15.8

You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.

That's your answer!

Answer: x>1

Step-by-step explanation:

To solve for x, we want to isolate x.

3x+7>10       [subtract both sides by 7]

3x>3             [divide both sides by 3]

x>1

Therefore, we know that x>1.

Answer:

Step-by-step explanation:

3x + 7 > 10

3x > 10 - 7

3x > 3

x > 1

x ∈ ( 1, ∞ )

Answer:

23 / 400 = 0.0575

Step-by-step explanation:

Given the distribution :

_____shops__ free park. food _: location total

male 88 24 40 21 173

female 110 38 56 23 227

total 198 62 96 44 400​

From the table of the distribution Given, we obtain :

n(Female n location) = 23

n(Total) = 400

Hence, the probability that a female who chose location gets the prize will be ;

n(Female n location) / n(Total) = 23 / 400 = 0.0575

9514 1404 393

Answer:

  ≈ 1000√10∠-129.04464° = -1992 -2456i

Step-by-step explanation:

  3 -i = √(3³+(-1)²)∠arctan(-1/3) ≈ √10∠-18.4349°

Then (3-i)^7 = 10^(7/2)∠(7×-18.4349°) = 1000√10∠-129.04464°

  = 1000√10(cos(-129.04464°) +i·sin(-129.04464°))

  = -1992 -2456i

......hope it helps......

Answer:

yes,.to obtain sinx as 1 the angle must be 90degrees

so the answer is correct

but there are more solutions like when the cosine angle is 45 the answer is 1

and when x is 450 still sinx = 1..that is to say sin450= 1

Answer:

A 1/2

Step-by-step explanation:

Ratio of short length to hypotenuse

= cos60

= 1/2

Answer:

Angle formed by the sector measuring x% will be 126°.

Step-by-step explanation:

Since, sum of all sectors formed in a circle is 100%.

By adding the measures of all the sectors,

x + x + 21 + 9 = 100

2x + 30 = 100

2x = 70

x = 35%

Now we know sum of all the central angles formed at the center of a circle = 360°

Therefore, angle formed by x% = 360° × 35%

                                                    = [tex]\frac{360\times 35}{100}[/tex]

                                                    = 126°

Answer:

A and F

Step-by-step explanation:

A and F both represent instances of division of 14/5

B represent multiplication

C represent the reciprocal of the problem, 5/14

D represent addition

40

Step-by-step explanation:

Each number is followed by a number that is half its value, so the sequence goes like

320, 160, 80, 40, 20, 10.

Answer:

3

Step-by-step explanation:

x 1，2，3，4

y-3，-5，-7，-9

[tex]y = - 3 - (x - 1) \times 2[/tex]

The linear function is given by y = 7x - 4

A linear function is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept

From the table, using the points (1, 3) and (4, 24):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{24-3}{4-1}(x-1)\\\\ y=7x-4[/tex]

The linear function is given by y = 7x - 4.

Find out more on linear function at: https://brainly.com/question/4025726

Answer:

A a vertex

Step-by-step explanation:

When rays meet they form a point is formed known as the vertex.

Answer:

2/15

Step-by-step explanation:

(-3/5) (-2/9)

Rewriting

-3/9 * -2/5

-1/3 * -2/5

A negative times a negative is a positive.

2/15

Answer:

The sales tax on a 320 dollars purchase is of $29.6.

Step-by-step explanation:

State sales tax y is directly proportional to retail price x.

This means that:

[tex]y = cx[/tex]

In which c is the constant of proportionality.

An item that sells for 156 dollars has a sales tax of 14.42 dollars.

This means that [tex]x = 156, y = 14.42[/tex]. We use this to find c. So

[tex]y = cx[/tex]

[tex]14.42 = 156c[/tex]

[tex]c = \frac{14.42}{156}[/tex]

[tex]c = 0.0924[/tex]

Then

[tex]y = 0.0924x[/tex]

What is the sales tax on a 320 dollars purchase?

y when [tex]x = 320[/tex]. So

[tex]y = 0.0924(320) = 29.6[/tex]

The sales tax on a 320 dollars purchase is of $29.6.

Answer:

the operating characteristics have been solved below

Step-by-step explanation:

we have an average of 10 minutes per customers

μ = mean service rate = 60/10 = 6 customers in one hr

the average number of customers that are waiting in line

mean arrival λ = 2.5

μ = 6

[tex]Lq = \frac{2.5^{2} }{6(6-2.5)} \\[/tex]

= 6.25/21

= 0.2976

we calculate the average number of customers that are in the system

[tex]L=Lq+\frac{2.5}{6}[/tex]

= 0.2976+0.4167

= 0.7143

we find the average time that a customer spends in waiting

[tex]Wq=\frac{0.2976}{2.5}[/tex]

= 0.1190 hours

when converted to minutes = 0.1190*60 = 7.1424 minutes

[tex]0.1190+\frac{1}{6}[/tex]

=0.2857

probability that arriving customers would wait for the service

= 2.5÷6 = 0.4167

Answer:

[tex]E(x)=\$9.118[/tex]

Step-by-step explanation:

From the question we are told that:

Available bills

 [tex]\$5=N0 9\\\\\$10=N0 5[/tex]

 [tex]\$20=N0 3[/tex]

Therefore

Total Bills

 [tex]n=5+9+3[/tex]

 [tex]n=17[/tex]

Probability of selecting each bill

 [tex]For\$5[/tex]

 [tex]P(\$5)=\frac{9}{17}[/tex]

 [tex]For\$10[/tex]

 [tex]P(\$10)=\frac{5}{17}[/tex]

 [tex]For\$20[/tex]

 [tex]P(\$20)=\frac{3}{17}[/tex]

Generally the equation for Expected winning is mathematically given by

 [tex]E(x)=\sum(X)*P(X)[/tex]

 [tex]E(x)=5*\frac{9}{17}+10*\frac{5}{17}+20*\frac{3}{17}[/tex]

 [tex]E(x)=\$9.118[/tex]

Answer: 9 feet

Step-by-step explanation:

From the information given, we have already been given the equation which is x(x-3)=54. Therefore we will find the value of x which will be:

x(x-3)=54

x² - 3x - 54

x² - 9x + 6x - 54

x(x - 9) + 6(x - 9)

Therefore,

(x - 9) = 0

x = 0 + 9

x = 9

The length is 9 feet

The width will be:

x - 3 = 9 - 3 = 6 feet

Answer:

71 feet

Step-by-step explanation:

94×2=188

330-188=142

142÷2=71

Answer:

3+ 0 = 3

( 4+7) + 3.0 × 1 = 4 + (7+3)

9 + 8 = 8 + 9

Answer:

1 71years

Step-by-step explanation:

x+10=81

x=71

2. x+8=49

x=41

3. x+11=100

x=99

Answer:

this is the answer I got! i don't know if it helps, but I hope it does

Answer:

Step-by-step explanation:

Answer:

1326

Step-by-step explanation:

[tex]{52\choose2}=\frac{52!}{(52-2)!2!}=\frac{52!}{50!*2!}=1326[/tex]

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

Answer:

[tex]Pr= 0.00725[/tex]

Step-by-step explanation:

Given

[tex]p = 0.05[/tex] ---- probability that each component fails

[tex]n = 3[/tex]

Required

[tex]P(System\ Overheats)[/tex]

We understand that the system will overheat if at least 2 component fails; Assume the components are: x, y and z

The events that the system will overheat are: xyz', xy'z, x'yz and xyz

Where ' means that the component did not fail, and the probability is 1 - p (i.e. complement rule)

So, we have:

[tex]xyz' \to 0.05 * 0.05 * (1 - 0.05) = 0.002375[/tex]

[tex]xy'z \to 0.05 * (1 - 0.05)* 0.05 = 0.002375[/tex]

[tex]x'yz \to (1 - 0.05)* 0.05 * 0.05 = 0.002375[/tex]

[tex]xyz \to 0.05 * 0.05 * 0.05 =0.000125[/tex]

So, the required probability is:

[tex]Pr= 0.002375 +0.002375 +0.002375 + 0.000125[/tex]

[tex]Pr= 0.00725[/tex]

Hello,

there are 5 differents sums:

16,18,20,22,24.

-------------------------------------------------------

Dim i As Integer, j As Integer, k As Integer, l As Integer, u As Integer, v As Integer, nb As Integer

Dim mat(4, 4) As Integer

nb = 0

For i = 1 To 4

   For j = 1 To 4

       If j <> i Then

           For k = 1 To 4

               If k <> j And k <> i Then

                   l = 10 - k - j - i

                   If l > 0 And l < 5 And l <> i And l <> j And l <> k Then

                       mat(1, 1) = i

                       mat(1, 2) = j

                       mat(1, 3) = k

                       mat(1, 4) = l

                       For u = 2 To 4

                           For v = 1 To 4 - u + 1

                               mat(u, v) = mat(u - 1, v) + mat(u - 1, v + 1)

                           Next v

                       Next u

                       'Call visu(mat())

                       nb = nb + 1

                       Print nb,

                       mat(4, 1)

                   End If

               End If

           Next k

       End If

   Next j

Next i

End

Sub visu (m() As Integer)

   Dim i As Integer, j As Integer

   For i = 1 To 4

       For j = 1 To 4 - i + 1

           Print m(i, j);

       Next j

       Print

   Next i

End Sub