What value of x makes this equation true?
x/6-7 = - 4

Answer:

x^2-2x+1

Step-by-step explanation:

We can solve this by using FOIL

First, Outside, Inside, Last

Multiply the x with the x to get x^2

Then x times -1 for the outside numbers to get -x

Then -1 times x for the inside numbers to get -x

And finally -1 and -1 for the last numbers to get 1

Add the two -x to get -2x.

Put it all together

x^2-2x+1

Answer:

[tex]x^2-2x+1[/tex]

Step-by-step explanation:

=> (x-1)(x-1)

USING FOIL

=> [tex]x^2-x-x+1[/tex]

=> [tex]x^2-2x+1[/tex]

Answer:

Mark has 24

Don has 79

Step-by-step explanation:

Let x = marbles mark has

don has 3x+7

Together they have 103

mark + don = 103

x+ (3x+7) = 103

Combine like terms

4x+7 = 103

Subtract 7

4x = 96

Divide by 4

x = 96/4

x =24

Mark has 24

Don has 103 -24

Done has 79

Answer:

The answer to this equation is 3 5/6

Step-by-step explanation:

in order to solve this problem, we must first turn these fractions into improper fractions. We can do this by multiplying the base number with the denominator and adding the numerator to that number.

6 1/2 = 13/2

2 2/3 = 8/3

Now, set up your equation.

13/2 - 8/3

Change the denominators to the same number so it will be easier to subtract.

39/6 - 16/6

Now subtract.

23/6 = 3 5/6

Answer:

3 5/6

Step-by-step explanation:

6 1/2 - 2 2/3 = 13/2 - 8/3

(39 - 16)/6 = 23/6 = 3 5/6

Answer:

-7.2

Step-by-step explanation:

Answer:

prime factors in ascending order of 1729 is 7 , 13 , 19

relation between  consecutive prime factors is 6

Step-by-step explanation:

given data

number = 1729

solution

we get here factors of 1729

1729 = 7 × 13 × 19

so that required prime factors in ascending order of 1729 is 7 , 13 , 19

and

now we get relation between these prime factors is the difference between consecutive prime factors is

13 - 7 =  6

19 - 13 = 6

so relation between  consecutive prime factors is 6

Step-by-step explanation:

Prime factors of the number 1729 are 7,13,19

i.e. 1729 =7×13×19

The factors in ascending order are 7,13,19.

Clearly we can see that each consecutive prime factors​ have difference of 6.

13-7=6

19-13=6

Answer:

3/7

Step-by-step explanation:

We have 7 possible outcomes. Of those 7, we are looking for 4 ≤ x < 7. Since only 3 of those values work (4, 5, 6), our answer is 3/7.

the answer is 24cm^2.

hope it helped..

Answer: x =21

Step-by-step explanation:

x +2 = 3x -40  They both have the same angle measures so they have to equal each other to solve for x

x + 2 = 3x -40

-x         -x  

   2 = 2x -40

 +40        +40

42 = 2x

x = 21

Answer:

The maximal area will be "1093.5 square feet".

Step-by-step explanation:

Let,

Length = L feet

Breadth = b feet

Given Total fencing = 162 feet

According to the question,

 [tex](2\times L)+(3\times b)=162[/tex]

              [tex]2L+3B=162[/tex]

                         [tex]L=\frac{162-3b}{2}[/tex]

                         [tex]L=81-\frac{3}{2}b[/tex]

As we know,

 [tex]Area=Length\times breadth[/tex]

          [tex]=(81-\frac{3}{2}b)\times b[/tex]

          [tex]=81b-\frac{3}{2}b^2[/tex]

Now, we required to decrease or minimize the are. So for extreme points:

 [tex]\frac{dA}{db}=0[/tex]

or,

 [tex]\frac{dA}{dB}=\frac{d}{db}(81-\frac{3}{2}b^2 )=0[/tex]

       [tex]81-\frac{3}{2}\times 2\times b=0[/tex]

                            [tex]b=\frac{81}{3}[/tex]

                            [tex]b=27 \ feet[/tex]

Now on putting the value of b, we get

 [tex]l=81-\frac{3}{2}\times 27[/tex]

   [tex]=81-40.5[/tex]

   [tex]=40.5 \ feet\\[/tex]

So that the dimensions will be:

⇒  40.5 feet by 27 feet

Therefore when the dimension are above then the area will be:

=  [tex]81\times 27-\frac{3}{2}\times 27\times 27[/tex]

=  [tex]2187-\frac{3}{2}\times 729[/tex]

=  [tex]2187-1093.5[/tex]

=  [tex]1093.5 \ square \ feet[/tex]

Answer:

270 tiles.

Step-by-step explanation:

The kitchen is 15 x 18 feet. If we multiply we find the area is 270 square feet. one square foot is a 12 x 12 inch square, so we can fit one tile per square foot, giving us 270 tiles.

Answer:

a and c

Step-by-step explanation:

Answer:

a and c

Step-by-step explanation:

Answer:

x=∛4 x

Step-by-step explanation:

Let the number be x.

According to the question,

x^3=4 x

x=∛4 x

This is the only answer we can conclude from the information given in the question.

The required expression is x³ + 4x.

Given that,

The cube of a number increased by 4 times the same number is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Let the number be x,
cube of number = x³
4 time of number = 4x
The cube of a number increased by 4 times the same number, which implies,
x³ + 4x

Thus, the required expression is x³ + 4x.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

Option B

Step-by-step explanation:

We are given the following system of equations -

[tex]\begin{bmatrix}-5x+2y-2z=26\\ 3x+5y+z=-22\\ -3x-5y-2z=21\end{bmatrix}[/tex]

Now by Cramer's Rule, we would first write down the matrix of the coefficients , replacing each column with the answer column -

[tex]\begin{bmatrix}-5&2&-2\\ 3&5&1\\ -3&-5&-2\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}26\\ -22\\ 21\end{bmatrix}[/tex]

Replace each column of the coefficients shown at the top, with the answer column at the bottom respectively -

[tex]\begin{bmatrix}-5&2&26\\ 3&5&-22\\ -3&-5&21\end{bmatrix}[/tex]

Now solve through Cramer's Rule -

x = Dx / D = - 6,

y = Dy / D = - 1,

z = Dz / D = 1

Solution = ( - 6, - 1, 1 ) = Option B

-5 x + 2 y - 2 z = 263 x + 5 y + z = -22 - 3 x - 5 y - 2 z = 21

Answer is x=-6,\:z=1,\:y=-1

Answer:

Step-by-step explanation:

8P3=8*7*6=336

Answer:

If we have a growing exponential relation, we can write it as:

f(x) = A*r^x

Where A is the initial amount, r is the rate of growth, in this case, r > 1 (because is a growing exponential relation)

Now, the "slope" of the graph in x, is equal to the derivate of f(x) in that point, and we have:

f'(x) = A*(r^x)*ln(r)

Now, remember that r > 1, then ln(r) > 0.

then, f'(x) is a growing function as x grows, and f'(x) grows exponentially, this means that the slope of the graph also grows exponentially as x grows.

Answer:

Length=17 yds, Width=14 yds

Step-by-step explanation:

62=x+x+(x+3)+(x+3)

4x+6=62

4x=56

x=14

x+3=17

Answer:

  0 ≤ g(x) < ∞

Step-by-step explanation:

The range is all non-negative numbers.

___

g(x) is an even-degree polynomial with a positive leading coefficient, so it opens upward. There is no added constant, so its minimum value is zero. The function can take on all values zero or greater.

  range: [0, ∞)

Answer:

100/3 cubic feet.

Step-by-step:

In this case, if you observe the sphere, the height is simply two times the radius.

The formula to find the volume of a sphere is π * r^2 * h. The height is basically just 2r. And so, the edited formula becomes π * r^2 * 2r = 2 * π * r^3.

2 * π * r^3 = 50

π * r^3 = 25

r^3 = 7.957747155

r = [tex]\sqrt[3]{7.957747155}[/tex]

r = 1.996472712

Now that we have the measure of the radius, we can find the volume of the sphere!

(4 / 3) * π * r^3

(4/3) * π * (1.996472712)^3

= (4/3) * π * 7.957747155

= (4/3) * π * (25 / π)

= (4/3) * 25

= 100/3 cubic feet.

Hope this helps!

Answer:

100/3

Step-by-step explanation:

Answer:

The given equation has two solutions

[tex]v = (-5.29, \: 5.29)[/tex]

Step-by-step explanation:

The given equation is

[tex]3v^2 - 84 = 0[/tex]

Let’s solve the equation

[tex]3v^2 - 84 = 0 \\\\3v^2 = 84 \\\\v^2 = \frac{84}{3} \\\\v^2 = 28 \\\\[/tex]

Take the square root on both sides

[tex]\sqrt{v^2} = \sqrt{28} \\\\v = \sqrt{28} \\\\v = \pm 5.29 \\\\[/tex]

So the equation has two solutions

[tex]v = (-5.29, \: 5.29)[/tex]

Also refer to the attached graph of the equation where you can verify that the equation has two solutions.

Note:

It is a very common mistake to consider only the positive value and not the negative value.

Consider the square root of 25

[tex]\sqrt{25} = \pm 5 \\\\Since \\\\5 \times 5 = 25 \\\\-5 \times -5 = 25 \\\\[/tex]

That is why we have two solutions for the given equation.

Answer:

2.19 km

Step-by-step explanation:

If x is the distance she walks down the road before turning, then the total time is:

t = x/8 + √((3 − x)² + 2²) / 3

t = x/8 + √(9 − 6x + x² + 4) / 3

24t = 3x + 8√(13 − 6x + x²)

24t = 3x + 8(13 − 6x + x²)^½

Take derivative of both sides with respect to x.

24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

When t is a minimum, dt/dx = 0.

0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)

-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)

3 / (6 − 2x) = 4(13 − 6x + x²)^-½

3 / (24 − 8x) = (13 − 6x + x²)^-½

(24 − 8x) / 3 = (13 − 6x + x²)^½

(24 − 8x)² / 9 = 13 − 6x + x²

576 − 384x + 64x² = 117 − 54x + 9x²

459 − 330x + 55x² = 0

Solve with quadratic formula.

x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)

x = (330 ± √7920) / 110

x = 2.19 or 3.81

Since 0 < x < 3, x = 2.19.

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $600

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $600

(b) When H0 cannot be rejected, we conclude that the manager's claim is correct.

(c) When H0 can be rejected, we conclude that the manager's claim is wrong.

Step-by-step explanation:

We are given that the manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less.

The accountant will use a sample of weekend guest bills to test the manager's claim.

Let [tex]\mu[/tex] = population mean guest bill for a weekend

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $600

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $600

Here null hypothesis states that the mean guest bill for a weekend is $600 or less.

On the other hand, alternate hypothesis states that the mean guest bill for a weekend is more than $600.

(b) When the null hypothesis ([tex]H_0[/tex]) cannot be rejected, then the correct conclusion would be: We conclude that the mean guest bill for a weekend is $600 or less which means that the manager's claim is correct.

(c) When the null hypothesis ([tex]H_0[/tex]) can be rejected, then the correct conclusion would be: We conclude that the mean guest bill for a weekend is more than $600 which means that the manager's claim is wrong.

Answer: 12600

Step-by-step explanation:

We are given the function that f(x) = 12000 * 1.05x

the x in f(x) is the amount of years that passed in the city of Peachwood, and the f(x) is the total population of Peachwood

These are two key elements in this function,

Therefore after 1 year the equation would be f(1) = 12000*1.05(1)

or f(1) = 12600

Answer:

1,050 workers

Step-by-step explanation:

25% = 0.25

0.25 × 1400 = 350

1400 - 350 = 1050

Hope this helps.

Answer:

1/5

Step-by-step explanation:

The number 5 or greater than 4 is 5.

1 number out of 5 total parts.

= 1/5

P(5 or greater than 4) = 1/5

Answer:

a. the probability of a type II  error is 0.5319

b. the required sample size to satisfy and the type II error probability  is 59.4441

Step-by-step explanation:

From the information given; we have:

sample size n = 25

Population standard deviation [tex]\sigma[/tex] = 4

true average lifetime = Sample Mean [tex]\bar X[/tex] = 62

We can state our null hypothesis and alternative hypothesis as follows:

Null hypothesis:

[tex]\mathbf{H_o : \mu = 60}[/tex]

Alternative hypothesis

[tex]\mathbf{H_1 : \mu \neq 60}[/tex]

Where ;

∝ = 0.01

From the standard normal tables at critical value ∝ = 0.01 ; the level of significance is -2.575 lower limit and 2.575 upper limit

The z statistics for the lower limit is:

[tex]lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]-2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}[/tex]

[tex]-2.575= \dfrac{\bar x - 60 }{0.8}}}[/tex]

[tex]-2.575*0.8= {\bar x - 60 }{}}}[/tex]

[tex]-2.06= {\bar x - 60 }{}}}[/tex]

[tex]\bar x = 60-2.06[/tex]

[tex]\bar x = 57.94[/tex]

The z statistics for the upper limit is:

[tex]lower \ limit = \dfrac{\bar X - \mu }{\dfrac{\sigma}{\sqrt {n}}}[/tex]

[tex]2.575= \dfrac{\bar x - 60 }{\dfrac{4}{\sqrt 25}}}[/tex]

[tex]2.575= \dfrac{\bar x - 60 }{0.8}}}[/tex]

[tex]2.575*0.8= {\bar x - 60 }{}}}[/tex]

[tex]2.06= {\bar x - 60 }{}}}[/tex]

[tex]\bar x = 60-(-2.06)[/tex]

[tex]\bar x = 60+2.06[/tex]

[tex]\bar x = 62.06[/tex]

Thus; the probability of a type II error is determined as follows:

β = P (  [tex]57.94 < \bar x < 62.06[/tex] )

[tex]= P ( \dfrac{57.94 -62 }{\dfrac{4}{\sqrt{25}}}<\dfrac{62.06 -62 }{\dfrac{4}{\sqrt{25}}})[/tex]

[tex]= P ( \dfrac{-4.06 }{0.8}}<\dfrac{2.06 }{0.8})[/tex]

= P ( -5.08 < Z < 0.08 )

= P ( Z < 0.08) - P ( Z < - 5.08)

Using Excel Function: [ (=NORMDIST (0.08)) - (=NORMDIST(-5.08)) ] ; we have:

= 0.531881372 - 0.00000001887

= 0.531881183

≅ 0.5319

b.

What is the required sample size to satisfy and the type II error probability of b(62) = 0.1

Recall that:

The critical value of ∝ = 2.575  ( i. e   [tex]Z_{1 - \alpha/2 } = 2.575[/tex]  )

Now ;

the critical value of β is :

[tex]Z _{1- \beta} = 1.28[/tex]

The  required sample size to satisfy and the type II error probability  is therefore determined as :

[tex]n = [\dfrac{(Z_{1 - \alpha/2} + Z_{1 - \beta} ) \sigma }{\delta}]^2[/tex]

[tex]n = [\dfrac{(2.575+1.28 ) 4 }{2}]^2[/tex]

[tex]n = [\dfrac{(3.855 ) 4 }{2}]^2[/tex]

[tex]n = [\dfrac{(15.42 ) }{2}]^2[/tex]

n = 7.71 ²

n= 59.4441

Thus; the required sample size to satisfy and the type II error probability  is 59.4441

A)

In order to calculate the Type II Error, we proceed with stating the factors:

Hypothesized Mean is given as  =  μ[tex]_{0} [/tex]        = 60

True Mean  is given as                 =  μa        = 62

Standard Deviation  is given as  = σ           = 4

Sample Size                                   = n           = 25

Standard error of mean                = σx          =σ/[tex]\sqrt{\\} [/tex]σ               =  0.80

given 0.01 level and two tailed test critical value Zσ             ±  2.58 or approximately 3

Acceptance region is

given as:   = μ - Z∝ * σx ≤ Π ≤ μ+Z∝⇄            =57.9360 ≤x≤   62.0640

Type II Error = probability of not rejecting β    = P(57.94-μa/σx))     <Z< (62.064-μa)/σx))

                                      = P (-5.08   <Z<    0.08)
                                      = 0.5319-0)

                                      = 0.532

B

Hypothesized mean                        = μ₀             =        60

True Mean                                        =μₐ               =       62          

Standard Deviation                          =σ                 =      4

for 0.01 level and two-tailed test critical value Z∝/2              ± 2.58

for 0.01 level of type II error critical value Z[tex]\beta [/tex]                         = 1.28

Required sample size    = n                                       = ([tex]Z_{\alpha /2} [/tex] + [tex]Z_{\beta } [/tex])²σ²/(μ₀-μ₀)²
                                                                                    = 60


See the link below for more about two-sided tests:
https://brainly.com/question/8170655

Answer:

6

Step-by-step explanation:

12*5=60

6*3=18

1*7=7

hope this help

Answer:

[tex] P(Head) = \frac{65}{100}=0.65[/tex]

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

And for this case the probability that in the next flip we will get a tail would be:

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

Step-by-step explanation:

For this case we know that a coin is toss 100 times and we got 65 heads and 35 tails.

We can calculate the empirical probabilities for each outcome and we got:

[tex] P(Head) = \frac{65}{100}=0.65[/tex]

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

And for this case the probability that in the next flip we will get a tail would be:

[tex] P(Tail) = \frac{35}{100}=0.35[/tex]

Answer:

H=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

S=4lw+2wh

Put S as 136, l as 6, w as 4, and solve for h.

136 = 4(6)(4)+2(4)H

136 = 8h + 96

-8h = 96 - 136

-8h = -40

h = -40/-8

h = 5

Answer:

2 units.

Step-by-step explanation:

In this question we use the Pythagorean theorem which is shown below:

Given that

The right triangle OMP

The hypotenuse i.e OM is the circle radius =5 units.

The segment MP = 4 units length

Therefore

[tex]OP^2 + MP^2 = OM^2[/tex]

[tex]OP^2 + 4^2 = 5^2[/tex]

[tex]OP^2 + 16 = 25[/tex]

So OP is 3

Now as we can see that ON is also circle radius so it would be 5 units

And,

ON = OP + PN

So,

PN is

= ON - OP

= 5 units - 3 units

= 2 units

Answer:

2

Step-by-step explanation:

Answer:

x= 2.25

y=6.5

Step-by-step explanation:

2x+5y=37 y=11-2x

2x+5(11-2x)=37

2x+55-10x=37

-8x+55=37

-55       -55

-8x=-18

÷-8   ÷-8

x= 2.25

y=11-2x

y=11-2(2.25)

y=11-4.5

y=6.5

Answer: x= 18/8 y = 13/2

Step-by-step explanation:

We know that y = 11-2x

So, you want to do the substitution method.

The equation states : 2x+5y  = 37

So, you would substitute the y in the equation for 11-2x

2x+5(11-2x) = 37

2x+55-10x = 37  (combine like terms)

-8x +55 = 37 (subtract 55 from each side)

-8x = -18 ( divide -8 from each side)

x = 18/8

Now, we need to solve for y. For that, we just need to substitute the x in the y equation.

It would look like this: 11-2(18/8) =y

Now we solve.

11-18/4 = 13/2 (6.5)

So, y equals 13/2. Now to check , plug in each for the equation and see if it is correct.