Suppose Grant is going to build a playlist that contains 6 songs. In how many ways can Grant arrange the 6 songs on the playlist?
Grant can arrange the 6 songs on the playlist in
different ways.

Answer:

16

Step-by-step explanation:

6*2 = 12

12 + 4 = 16

Answer:

(4, -3)

Step-by-step explanation:

the equation f(x-5) is a translation of the equation f(x) by 5 units to the right.

So, if all points of the equation f(x) are shifted 5 units to the right, the minimum point of the graph is also shifted 5 units to the right, so to find the minimum point of y = f(x - 5), we just need to sum 5 units to the x-coordinate:

Minimum point = (-1 + 5, -3) = (4, -3)

So the minimum point of y = f(x - 5) is (4, -3).

The minimum point on the graph of y = f(x - 5) is (-6,3)

On the graph of the equation y = f(x);

The minimum point is given as (-1,-3)

The graph of y = f(x - 5) means that, f(x) is shifted to the right by 5 units

So, the corresponding point of (x,y) of f(x) on the graph of f(x - 5) is:

[tex](x,y) \to (x - 5,y)[/tex]

This gives

[tex](-1,-3) \to (-1 - 5,3)[/tex]

Subtract 5 from -1

[tex](-1,-3) \to (-6,3)[/tex]

Hence, the minimum point on the graph of y = f(x - 5) is (-6,3)

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Answer: 6 cm, V=48π or V=150.8 cm³

It appears the question is asking for the radius, but below I have shown how to find the volume.

Step-by-step explanation:

The radius is half of the diameter. The diameter of the cone of 12 cm. Half of 12 is 6. Therefore, the radius is 6 cm.

The formula to find the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]. Now that we have the radius from above, we can use that to plug into the equation along with the given height.

[tex]V=\pi (6^2)\frac{4}{3}[/tex]                    [expand the exponent]

[tex]V=36\pi \frac{4}{3}[/tex]                       [combine like terms]

[tex]V=48\pi[/tex] or [tex]V=150.8 cm^3[/tex]            

Answer:

560 km

Step-by-step explanation:

350x8/5=

350x1.6=

560

Answer:

0.0499

Step-by-step explanation:

The p-value can be calculated using technology. The p-value is computed by using F distribution right tailed excel function. The excel function "F.DIST.RT(4.76,3,6)" gives desired p-value which is 0.0499.

The p-value shows that the for 5% level of significance the null hypothesis can be rejected.

Answer:

[tex]x=-\frac{11}{6}[/tex]

Step-by-step explanation:

8x2=6x=5

16+6x=5

6x=5-16

6x=-11

[tex]x=-\frac{11}{6}[/tex]

Answer:

See below.

Step-by-step explanation:

[tex]8x^2+6x=5[/tex]

Reformat this so the equation equals zero:

[tex]8x^2+6x-5=0[/tex]

[tex]a=8, b=6, c=-5[/tex]

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]x=\frac{-(6)\pm\sqrt{(6)^2-4(8)(-5)} }{2(8)}[/tex]

[tex]x=\frac{-6\pm\sqrt{36+160} }{16}[/tex]

[tex]x=\frac{-6\pm\sqrt{196} }{16}[/tex]

[tex]x=\frac{-6\pm14 }{16}[/tex]

[tex]x=\frac{-6+14}{16}=8/16=1/2[/tex] or

[tex]x=\frac{-6-14}{16}=-20/16=-5/4[/tex]

Answer:

work is shown and pictured

Answer:

Step-by-step explanation:

tan(pi\4+A)tan(3pi\4+A) =-1

using the tangent sum of angle formula

Answer:

5x 10 ^-5

Step-by-step explanation:

UHM that would be

NaN × [tex]10^{0}[/tex]

I hope this helps!

so my reasoning...  Any number that can be written in the decimal form between 1.0 to 10.0 multiplied by the power of 10.  

Answer:44

Step-by-step explanation:the two triangles are congruent , so we deduce from that the angle B=angle E =48

So, x+4=48 , x=44 degree

The formula C = π2r

Is used for the circumference.

We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:

C/d = π

And remember that the diameter is twice the radius, so we can write:

d = 2r

Then we can rewrite the equation for the circumference as:

C = π2r

Then we conclude that the correct option is B.

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Answer:

The price before tip was 35

Step-by-step explanation:

Let x = original amount

x * 20% = 7

Change to decimal form

x * .20 = 7

Divide each side by .20

x*.20/.20 = 7/.20

x =35

Answer:

x=3

Step-by-step explanation:

Use the Pythagorean Theorem to write an equation.

x^2+y^2=z^2

Substitute values from the problem.

x^2 + 6^2 = 9^2

Solve for what you know.

x^2 + 36 = 81

Square root it.

x+6=9

Subtract 6 from both sides.

x=3

In the future, if you see a right triangle with an unknown side, and the other two sides are either 3, 6, or 9, you know that the other one is the missing value out of 3/6/9. This is called a 3/6/9 triangle.

Answer:

Step-by-step explanation:

Hypotenuse (h) = 9

base (b) = X

Perpendicular (p) = 6

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]

[tex] {b}^{2} = {(9)}^{2} - {(6)}^{2} [/tex]

[tex] {b}^{2} = 81 - 36[/tex]

[tex] {b}^{2} = 45[/tex]

[tex]b = \sqrt{45} [/tex]

[tex]b = 6.7[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

ln(2000) = 7.601

Step-by-step explanation:

For this we need to know the rules of logarithms, specifically the product rule and the power rule.  The product rule is simply ln(a*b) = ln(a) + ln(b).  The power rule is simply ln(a^b) = b ln(a).

With these rules, let's begin to simplify the expression:

4 ln(2) + 3 ln(5)

= ln(2^4) + ln(5^3)

= ln(16) + ln(125)

= ln(16 * 125)

= ln(2000)

= 7.601

Hope this helps.  Cheers.

A logarithm is a power to which a number must be raised in order to get some other number.

The value of the expression 4 log 2 + 3 log 5 as a single number is 3.30102.

A logarithm is a power to which a number must be raised in order to get some other number.

Example:

log 10 = 1

log 100 = log 10² = 2 log 10 = 2 x 1 = 2
log 1000 = log 10³ = 3 log 10 = 3 x 1 = 3

log 0 = undefined

log 1 = 0

We have,

Some formulas for log:

log[tex]x^{n}[/tex] = n log x

log mn = log m + log n

Given,

4 log 2 + 3 log 5

= log [tex]2^{4}[/tex] + log [tex]5^{3}[/tex]

= log 16 + log 125

= log (16 x 125)

= log 2000

= 3.30102

Thus the value of the expression 4 log 2 + 3 log 5 as a single number is

3.30102.

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Answer:

[tex]\tan A=\frac{10}{24}=\frac{5}{12}[/tex]

Step-by-step explanation:

The easiest way to remember sine, cosine, and tangent ratios is to use SOH-CAH-TOA as an acronym.

SOH - Sine: Opposite over hypotenuse

CAH - Cosine: Adjacent over hypotenuse

TOA - Tangent: Opposite over adjacent

Note that these are referring to the position of the sides relative to the angle you are looking at. In this case, that is angle A. Since it's tangent, we have:

[tex]\tan A=\frac{10}{24}=\frac{5}{12}[/tex]

Answer:

C. surface area of 5 rectangular prisms.

Step-by-step explanation:

The table in the given figure as shown above has a rectangular flat top that has a solid shape of rectangular prism.

It also has 4 legs that are also rectangular in shape. The legs are rectangular prisms.

To determine the quantity of paint Kimberly would need, she needs to make use of the surface area of the table.

The surface area of the table = surface area of the top + surface area of the 4 legs = surface area of 5 rectangular prisms.

Answer:

C

Step-by-step explanation:

Answer:

A. Yes, the triangles are congruent by SAS.

Step-by-step explanation:

EF = FG and DF = FH-> Given

angle EFD = angle HFG -> Vertical angles are congruent

DE F = HGF -> SAS Triangle Congruence Theorem

We can prove  ∠DE F = ∠HGF by SAS congruency.

Hence option A is correct.

In the given triangle,

DE = GE

DF = FH

We know that,

SAS congruency stands for "Side-Angle-Side" congruence,

Which is a rule used in geometry to prove that two triangles are congruent or equal in size and shape.

This rule states that if two sides and the angle between them of one triangle are congruent to the corresponding two sides and angle of another triangle, then the two triangles are congruent.

Since the triangles

DE,GE and DF, FH are the corresponding sides and

DE = GE

DF = FH

Since DEF and FHG are congruent.

Therefore,

∠DE F = ∠HGF

Hence proved.

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Answer

187.5 ml/hr

Step-by-step explanation:

1500ml/8hrs=187.5ml/hr

Answer:

[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

Step-by-step explanation:

We can use Heron’s formula to determine the area of a triangle when three side lengths of a triangle are given.

[tex]s=\frac{a+b+c}{2}[/tex]

[tex]s : \mathrm{semi \: perimeter}[/tex]

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]A : \mathrm{area}[/tex]

Answer:

Heron's formula gives the area of a triangle when the length of all three sides are known. Use Heron's formula to find the area of triangle ABC, if AB=3,BC=2,CA=4 . Substitute S into the formula . Round answer to nearest tenth.

Step-by-step explanation:

Answer in fraction form = 9/8

Answer in decimal form = 1.125

note: the improper fraction 9/8 converts to the mixed number 1 & 1/8

To get this answer, we divide both sides by 8 to isolate n. The expression 8n really means "8 times n". We divide to undo the multiplication.

Answer:

350 pairs

Step-by-step explanation:

If the ratio of Athletics, Boots, and Dress shoes is 5 to 2 to 3, it means that for every 2 pairs of Boots they have 5 pairs of Athletics shoes and 3 pairs of dress shoes.

So, if they have 70 pairs of boots, we can calculate the number of Athletics as:

[tex]\frac{5*70}{2} =175[/tex]

And if they have 70 pairs of boots, the number of dress shoes are:

[tex]\frac{3*70}{2}=105[/tex]

Finally, they have 70 pairs of boots, 175 pairs of athletics, and 105 pairs of dress shoes. It means that they have 350 pairs in total.

70 + 175 + 105 = 350

Answer:

1) 18

2) P

Step-by-step explanation:

1) Multiply the top number by itself and then reverse the digits!

9*9 = 81 reversed is 18

2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.

Answer:

P

Step-by-step explanation:

2.

The number of strokes of the letter that come to an end.

The bottom of the A has two sticks that come to an end.

A = 2

The B has no sticks coming to an end.

B = 0

The C and an upper and a lower stroke coming to an end.

C = 2

D has none.

D = 0

E has 3 sticks coming to an end.

E = 3

etc.

M has 3.

N has 2.

O has 0.

P has 1 stick coming to an end.

Q has none.

R has 2.

S has 2.

T has 3.

U has 2.

V has 2.

W has 3.

X has 4.

Y has 3

Z has 2.

Of all letters after L, only P has exactly 1 stroke coming to an end.

Answer: P

Answer:

minimum sample size = 97

Step-by-step explanation:

Margin of error = 20

standard deviation = 100

sample size = n

standard error = 100/sqrt(n)

confidence level, alpha = 95%

Using the standard rule for 95% confidence

standard error <= sample mean [tex]\pm[/tex] 1.96 standard error, or

20 <= 1.96*100 / sqrt(n)

n >= (1.96*100/20)^2 = 9.8^2 = 96.04  

=>

n >= 97

Answer:

52 green, 15 orange

Step-by-step explanation:

g + o = 67   g = green, o = orange, x = total

g = 3o + 7

use substitution: (3o + 7) + o = 67

solve for o:

4o + 7 = 67

4o = 60

o = 60/4 = 15

solve for g:

g + 15 = 67

g = 52

Answer:

Step-by-step explanation:

[tex]\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}[/tex]

Domain:

[tex]x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3[/tex]

solution:

[tex]\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}[/tex]

use (a - b)(a + b) = a² - b²

[tex]\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}[/tex]

multiply both sides by (x - 3) ≠ 0

[tex]\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}[/tex]

cancel (x - 3)

[tex]\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3[/tex]

subtract [tex]\frac{4(x-3)}{x}[/tex] from both sides

[tex]\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}[/tex]

cross multiply

[tex](4)(x)=(x+3)(-x+12)[/tex]

use FOIL

[tex]4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36[/tex]

subtract 4x from both sides

[tex]0=-x^2+12x-3x+36-4x[/tex]

combine like terms

[tex]0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36[/tex]

change the signs

[tex]x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0[/tex]

The product is 0 if one of the factors is 0. Therefore:

[tex]x-9=0\ \vee\ x+4=0[/tex]

[tex]x-9=0[/tex]            add 9 to both sides

[tex]x=9\in D[/tex]

[tex]x+4=0[/tex]          subtract 4 from both sides

[tex]x=-4\in D[/tex]

Answer:

  17

Step-by-step explanation:

A graphing calculator is useful for writing a linear equation from a table of values. The one shown below says the table can be represented by the equation ...

  y = 2x -3

The graph of the two equations shows the solution is (10, 17).

  The y-value of the solution is 17.

Answer:

17 is correct

Step-by-step explanation:

Answer:

-6.

Step-by-step explanation:

The equation is y = -7x - 6.

The initial value is found when x = 0.

y = -7(0) - 6

y = 0 - 6

y = -6

Hope this helps!

Rewriting the Equation:

Answer:

7x+y=-33

Step-by-step explanation:

1.) Combine Like Terms: y=-7x-33

2.) Move the variable to the left side and use the inverse operation:

y+7x=-33

3.) Reorder terms using commutative property since x comes before y:

7x+y=-33

If you want to find the function then tell me.

Answer:

We have the measure of both angles as  55 degrees and 35 degrees

Step-by-step explanation:

We know that there are three angles in a right-angled triangle. One of which is 90. FOr now, the other two are unknown, so we would designate them to be x and y.

We now set up an equation using the information we are given about the problem.

From this statement "The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle." we can set up the following equation:

x =2y -15 -------- equation 1

similarly, we know that the sum of angles in a triangle = 180 degrees. Hence, we can use this to set up another equation as follows:

x + y + 90 = 180

x+ y = 90 ------------- equation 2

we can now solve the two equations simultaneously as

x -2y =-15

x+ y = 90

from this, we have that

x = 55 and y = 35

We have the measure of both angles as  55 degrees and 35 degrees

The lowest common denominator is lcm(5, 3), which is 15.

The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or [tex]5\frac{1}{15}[/tex].

Answer:

In this question it is given that:

The cash account of a company had an ending balance of $6750. During the last month, the account was debited for a total of $11,350 and credited for a total of $10,500.

And we have to use the formula

Substituting the values , we will get

Therefore beginning cash balance is