find both the number combinations in the number of permutations for 9 objects taken 7 at a time

The equation for the hourly rate is 55x = 1578.5

For double hourly rate for overtime, it is 55 x 2x= 1578.5

Given

Antonia makes X dollars for regular hours

And 2x dollars for over time

Since he works 55 hours this week he works 8 hours a day

Hence the equation is as follows

55x = 1578.5

x= $28.7

In case of double payment during overtime

He gets double amount as following equation

55 x 2x

55 x 2(28.7) =  $3157

Hence the equation to find his hourly rate is 55x = 157.85

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Answer:

Length = 15

Step-by-step explanation:

The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation

90 feet / 6 pieces

Which equals

90 feet / 6 pieces = 15 feet/piece        (15 feet per peice)

Hope this helps :)

he needs 3 pints of mango

Answer:3

Step-by-step explanation:

If the ratio is 1:5 that means that the number of pints of apple juice is multiplied by 5 to get the nimber of pints of mango juice

Answer:

1. 5- (-8) = 13

2. -3 1/2 - 4 1/2 = -7 1/2

3. -7 - 4 = -11

4. -0.5 - 3.5 = -4

Step-by-step explanation:

1. 5- (-8) =

5 + 8

13

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

-7 1/2

3. -7 - 4 =

-11

4. -0.5 - 3.5 =

-4

The value of x if T is the midpoint segment XY is 14.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints.

The midpoint is halfway between the two end points.

Therefore, the end point of the segment is XY.

The midpoint is T.

Hence,

XY = XT + YT

XT = 3x - 14 = YT

XY = 8x - 56

Let's find the value x.

Therefore,

8x - 56  = 3x - 14 + 3x - 14

8x - 56 = 6x - 28

8x - 6x = -28 + 56

2x = 28

divide both sides by 2

x = 28 / 2

x = 14

Therefore, the value of x is 14

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Answer:

u= 30

Step-by-step explanation:

the sum of all angles on a triangle is 180* so u add the others (120+30)

that brings it to 150 then 180-150=30*

Using simple interest, the amounts invested into each account are given as follows:

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = P(1 + rt)

In which:

The amount of interest after t years is given by:

I(t) = Prt

You invest $8,000 in 3 investment accounts, hence:

[tex]P_1 + P_2 + P_3 = 8000[/tex]

From the rates of the account, we have that:

The amount invested in the glass account was double the amount invested in the metal account, hence:

[tex]P_3 = 2P_2[/tex]

The yield was a total of $280 at the end of one year, hence:

[tex]I_1 + I_2 + I_3 = 280[/tex]

[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]

From the first and the third equations, we have that:

[tex]P_1 + P_2 + P_3 = 8000[/tex]

[tex]P_1 + 3P_2 = 8000[/tex]

[tex]P_1 = 8000 - 3P_2[/tex]

Hence the amount of the metal investment can be found as follows:

[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]

[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]

[tex]0.08P_2 = 120[/tex]

[tex]P_2 = \frac{120}{0.08}[/tex]

[tex]P_2 = 1500[/tex]

Hence the other investments are given as follows:

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The rate of interest is 10% and the sum is Rs 10,1000.

The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.

The compound interest formula is given by

Compound Interest = Amount – Principal

Here, the amount is

[tex]A=P(1+\frac{r}{100} )^{n}[/tex]  where,

A = amount

P = principal

r = rate of interest

n = time (in years)

Given:

C.I. of a sum of money in 3 years = Rs 13310

C.I. of a sum of money in 4 years = Rs 14641

Let the principal be P and the rate of interest be r%

Then, according to the question,

For 3 years:

[tex]13310=P(1+\frac{r}{100} )^{3}[/tex]       ..... (1)

For 4 years:

[tex]14641=P(1+\frac{r}{100} )^{4}[/tex]       ..... (2)

Dividing equation (2) by (1), we obtain

[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]

⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]

⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]

⇒[tex]r=\frac{100}{10}[/tex]

⇒ r = 10%

Now, substituting r in equation (1),

[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]

⇒[tex]13310=P(\frac{1331}{1000} )[/tex]

⇒P = Rs 10,000

Therefore, the rate of interest is 10% and the sum is Rs 10,1000.

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Answer: 6, 48 and 7, 56 and 9, 72 and 10,80

Step-by-step explanation:

By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.

So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.

Now, solve for y when the value of x is 489.

Rounding off: y = $215

Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.

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the answer is this

4 4/8.

Answer:

$3337.92

Step-by-step explanation:

$3.66 x 912 = $3337.92

We have to find the length of FH.

We know that G is on the line, and we know the length FG and GH, so we can represent this as:

We then, we can apply the rule that states that the length of a segment is equal to the length of the segments that are part of it:

Answer: FH = 15

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

[tex]18-51=36x+45-18x-60\\18x-51=36x-18x+45-60\\18x-51=18x-15\\18x-18x=-15+51[/tex]

∴ 18x-18x≠-15+51

THERE IS NO SOLUTION FOR THIS EQUATION

Answer: 11

Step-by-step explanation:

8x + 7 = 9x - 4

7 = x - 4

11 = x

Answer:

y = 5, 3

x = 155, 171

(y = 5, x = 155)

(y = 3, x = 171)

Step-by-step explanation:

(8y - 15) = (y²)

-8y + 15          -8y + 15

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

y² - 8y + 15 = 0

(y - 5) (y - 3) = 0

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

y = 5, 3

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

y² + x = 180

(5)² + x = 180

25 + x = 180

-25         -25

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

x = 155

(3)² + x = 180

9 + x = 180

-9            -9

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

x = 171

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

I really hope this helps!

Step-by-step:

n(x) = -1 - x + 4

n(-2) = -1 - (-2) + 4

  = -1 + 2 + 4

  = 5

___________________________

n(0)= -1 - 0 + 4

  = 3

___________________________

n(5)= ​-1 - 5 + 4

  = -2

The most appropriate choice for Independent event and multiplicative counting rule will be given by

This is known as multiplicative counting rule.

What is Independent event and multiplicative counting rule?

Event that is not dependent on any other event is called independent event.

Let A and B be two independent events.

P(A∩B) = P(A) [tex]\times[/tex] P(B)

If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.

Here,

Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on

Also assuming that the events are independent

The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways

This is known as multiplicative counting rule.

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Answer:

9

Step-by-step explanation:

[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]

Answer:

I believe it should be

f(1.7) = 2.8

f(-3.4) = -17.6

f(9.8) = 35.

Step-by-step explanation:

Simply plug-in the different numbers for x.

We can conclude that the probability of the randomly selected person does not use any facility is 0.

So, the probability that the selected person does not uses any facility:

Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.

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The equation best compares the slopes of two functions is,

Slope of function B = 2 × Slope of function A

Given,

The function A, f(x) = x - 9

We have to find slope of Function B

The function is in the form of y = mx + b

Here, m is the slope.

y = x - 9

m is 1 and b is -9

Now, lets consider the graph of line passing through points (-1, -3) and (2, 3)

That is,

(x₁, y₁) = (-1, -3)

(x₂, y₂) = (2, 3)

Now we can find the slope of the line:

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - (-3)) / (2- (-1))

m = (3 + 3) / (2 + 1)

m = 6/3

m = 2

That is, the slope of function B is 2

Here,

Slope of function A is 1.

That is, slope of function B is twice the slope of function A.

Therefore, the equation best compares the slopes of two functions is,

Slope of function B = 2 × Slope of function A

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Answer:

f(4) = 11

Step-by-step explanation:

f(x) = 3 x -1

Let x = 4

f(4) = 3*4 -1

     = 12-1

     = 11

f (x) = 3x - 1

f (4) = 3 × 4 - 1

f (4) = 12 - 1

f (4) = 11

Hope Helpful :-;

Answer:

c because if the number next to the underlined is above 5 u round up under 4 u round down

Step-by-step explanation:

Answer: c. 76

Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.

Answer:

20

Step-by-step explanation:

The sum of the exterior angles of a polygon add to 360.  360 divided by 18 is 20.

Answer:

26000:48000

26000/48000

26/48(cancel the zeros)

13/24

fractional form=13/24

Answer:

s=3

Step-by-step explanation:

So you have the equation: [tex]\frac{6}{s}=2[/tex]

If we multiply both sides by this "s" value we should maintain equality, and it conveniently cancels out our division by "s" on the left side giving us the following equation: [tex]6=2s[/tex]

The only "operation" on the value "s" is the coefficient of 2, which is multiplying the value of "s" by 2.

To undo this multiplication of 2, we simply divide by 2, since 2/2 = 1, and now we have a coefficient of 1 for the "s", which is the same as isolating "s"

But we want to divide both sides by 2 to maintain equality, so let's write out our expression

[tex]\frac{6}{2}=\frac{2s}{2}\implies3=\frac{2}{2}*s\implies 3=s[/tex]

We can double check this by plugging in this value for "s" in the original equation: [tex]s=3, \ \frac{6}{s}=2\implies \frac{6}{3}=2\implies 3=3[/tex] which is indeed true, so we have our solution!