Eight people are going for a ride in a boat that seats eight people. One person will drive, and only three of the remaining people are willing to ride in the two bow seats. How many seating arrangements are possible?

Answer:

301.59

Step-by-step explanation:

your answer was almost right you just forgot to multiply by 9

Answer:  12.22 ft/sec²

Step-by-step explanation:

An increase from 26 to 51 is an increase of 51 - 26 = 25 mi/hr

We need to do this in 3 seconds -->   25 mi/hr ÷ 3 sec

Note the following conversion: 1 mile = 5280 ft

[tex]\dfrac{25\ miles}{hr}\times \dfrac{1}{3\ sec}\times \dfrac{5280\ ft}{1\ mile}\times \dfrac{1\ hr}{60\ min}\times \dfrac{1\ min}{60\ sec} \\\\\\=\dfrac{5280(25)\ ft}{3(60)(60)\ sec^2}\\\\\\=\large\boxed{12.22\ ft\slash sec^2}[/tex]

The constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².

Acceleration can be defined as the rate of change of the velocity of an object with respect to time.

[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]

As the velocity that is given to us is 51 miles/hour and 26 miles/hour, therefore, we first need to convert the units of the velocity in order to get the acceleration in  ft/s².

[tex]\rm Final\ velocity= 51\ mi/hr = \dfrac{51\times 5280}{3600} = 74.8\ m\s^2[/tex]

[tex]\rm Initial\ velocity= 26\ mi/hr = \dfrac{26\times 5280}{3600} = 38.134\ m\s^2[/tex]

Now, acceleration is written as the ratio of the difference between the velocity and the time needed to increase or decrease the velocity of the object.

[tex]\rm Acceleration=\dfrac{Final\ velocity- Initial\ Velocity}{Time}[/tex]

Substituting the values we will get,

[tex]\rm Acceleration = \dfrac{74.8-38.134}{3} = 12.22\ \ ft/s^2[/tex]

Hence, the constant acceleration that is required to increase the speed of a car from 26 mi/h to 51 mi/h in 3 seconds is 12.22 ft/s².

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P + 127 = 550        P = 423

Answer:

P = 423  

P + 127 = 550

Step-by-step explanation:

Answer:

$3.60 per gallon.

Step-by-step explanation:

First, we look for the gallon of gas that will be used for a 172.5 mile trip:

30 miles = 1 gallon of gas

172.5 miles = ?

172.5 ÷ 30 = 5.75 gallons of gas

Let's find the approximate cost of gas in dollars per gallon:

5.75 gallons of gas = $20.70

1 gallon of gas = $?

20.70 ÷ 5.75 = $3.60

The answer is $3.60 per gallon.

Answer:

[tex]\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2-3x[/tex]

[tex]f(x)=y[/tex]

[tex]y=2x^2-3x[/tex]

Switch variables.

[tex]x=2y^2-3y[/tex]

Solve for y.

Multiply both sides by 8.

[tex]8x=16y^2-24y[/tex]

Add 9 on both sides.

[tex]8x+9=16y^2-24y+9[/tex]

Take the square root on both sides.

[tex]\sqrt{8x+9} =\sqrt{16y^2-24y+9}[/tex]

Add 3 on both sides.

[tex]\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3[/tex]

Divide both sides by 4.

[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}[/tex]

Simplify.

[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}[/tex]

[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}[/tex]

[tex]\frac{\sqrt{8x+9}+3}{4}=y[/tex]

Inverse y = [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}[/tex]

Answer:

[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]

Step-by-step explanation:

[tex] f^{-1}(x) = 2x^2 - 3x [/tex]

Change function notation to y.

[tex] y = 2x^2 - 3x [/tex]

Switch x and y.

[tex] x = 2y^2 - 3y [/tex]

Solve for y.

[tex] 2y^2 - 3y = x [/tex]

Complete the square on the left side. We must divide both sides by 2 to have y^2 as the leading term on the left side.

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

1/2 of 3/2 is 3/4. Square 3/4 to get 9/16.

Add 9/16 to both sides to complete the square.

[tex] y^2 - \dfrac{3}{2}y + \dfrac{9}{16} = \dfrac{x}{2} + \dfrac{9}{16} [/tex]

Find common denominator on right side.

[tex] (y - \dfrac{3}{4})^2 = \dfrac{8x}{16} + \dfrac{9}{16} [/tex]

If X^2 = k, then [tex] X = \pm \sqrt{k} [/tex]

[tex] y - \dfrac{3}{4} = \pm \sqrt{\dfrac{1}{16}(8x + 9)} [/tex]

Simplify.

[tex] y = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]

Back to function notation.

[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]

Answer:

The algebraic expression is v = 2x

v is the volume of the sugar syrup and

x is the mass of sugar in grams.

Step-by-step explanation:

Let x be the mass of sugar in grams and v be the volume of sugar syrup.

So, mass of sugar in grams/volume of sugar syrup × 100 % = 50 %

x/v × 100 % = 50 %

x/v = 50/100

x/v = 1/2

v = 2x

So, the algebraic expression required is v = 2x where v is the volume of the sugar syrup and x is the mass of sugar in grams.

Answer:

[tex]\boxed{k = 7 }[/tex]

Step-by-step explanation:

Given Condition is:

[tex]\frac{k}{1} = 7[/tex]

Multiplying both sides by 1

k = 7*1

k = 7

Answer:

The percentage of hatchbacks that run on gasoline: 78%

The percentage of diesel vehicles that are hatchbacks: 21 %

Step-by-step explanation:

The given table represents the following:

Hatchbacks that run on Gasoline = 18

Hatchbacks that run on Diesel = 5

Total number of hatchbacks = 23

Sedan that run on Gasoline = 15

Sedans that run on Diesel = 12

Total number of sedans = 27

SUVs that run on Gasoline = 3

SUVs that run on Diesel = 7

Total number of SUVs = 23

Total number of gasoline vehicles = 36

Total number of Diesel vehicles = 24

To find:

the percentage of hatchbacks that run on gasoline

the percentage of diesel vehicles that are hatchbacks

Solution:

[tex]\text{Percentage of hatchbacks that run on gasoline = } \dfrac{\text{Number of hatchbacks on gasoline}}{\text{Total number of hatchbacks}}\times 100\\\Rightarrow \text{Percentage of hatchbacks that run on gasoline = } \dfrac{18}{23}\times 100 \approx 78\%[/tex]

[tex]\text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{\text{Number of hatchbacks that run on diesel}}{\text{Total number of diesel vehicles}}\times 100\\\Rightarrow \text{Percentage of diesel vehicles that are hatchbacks = } \dfrac{5}{24}\times 100 \approx 21\%[/tex]

So, the answer is:

The percentage of hatchbacks that run on gasoline: 78%

The percentage of diesel vehicles that are hatchbacks: 21%

Answer:

I used a calculator and this is what can up with

Step-by-step explanation:

Answer:

WX = 8 mm

Step-by-step explanation:

To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].

We use the law of sines in the blue triangle to do such:

[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]

Now we can use this value in the larger right angle triangle where WX is the opposite side to angle  [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:

[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]

which rounded to the nearest integer gives

WX = 8 mm

Answer:

The expression for the shaded region is 10x² + 12x .

Step-by-step explanation:

First, you have to find the area of both rectangles using the formula :

[tex]area = length \times height[/tex]

Small rectangle,

[tex]area = x \times (5x - 2)[/tex]

[tex]area = 5 {x}^{2} - 2x[/tex]

Large rectangle,

[tex]area = (3x + 2) \times 5x[/tex]

[tex]area = 15 {x}^{2} + 10x[/tex]

In order to find the shaded region, you have to subtract the smaller from the larger one :

[tex]area \: of \: shaded = large - small[/tex]

[tex]area = 15 {x}^{2} + 10x - 5 {x}^{2} + 2x [/tex]

[tex]area = 10 {x}^{2} + 12x[/tex]

Answer:

x=46 degrees

Step-by-step explanation:

first find the size of the other angles(let call z and y)

the sum of a straight angle is 180:

180=130+z

z=180-130=50

y=180-96=84

sum of angles of triangle =180

x+y+z=180

50+84+x=180

x=180-134=46 degrees

Answer:

46°

Step-by-step explanation:

Angle of a line = 180°

To find the other side of 130°

The other side = 180° - 130° = 50°

To find the other side of 96°

The other side = 180° - 96° = 84°

To find x°

Total angle of a triangle = 180°

180° = x° + 50° + 84°

x° = 180° - 134°

x° = 46°

Answer:

Step-by-step explanation:

diameter=2×5=10 cm

32/10=3.2≈3

128/10=12.8≈12

total number of squares=12×3=36

Answer: D) Front - $35.00 Back - $22.50

Step-by-step explanation:

b+12.5=f

600f+450b=31,125

Substitute

600(b+12.5)+450b=31,125

Distribute

600b+7500+450b=31,125

Combine like terms

1050b+7500=31125

Subtract 7500

1050b=23625

Divide by 1050

b=22.5

Thus, the back tickets cost $22.50.

Hope it helps <3

Answer:

Combining statement 1 and statement 2 is sufficient

Step-by-step explanation:

There are 3 items purchased

Most expensive item=20% discount

The other two items=10% discount each

Statement 1: The average (arithmetic mean) of the regular prices of the 3 items was $30.

Assume:

The 3 items cost: $40, $30 and $20 respectively,

Total discount =20% of $40 + 10% of $30 + 10% of $20

=$8 + $3 + $2

= $13

Assume

The 3 items cost: $50, $30 and $10 respectively,

Total discount = 20% of $50 +10% of $30 + 10% of $10

=$10 + $3 + $1

= $14

Therefore, statement 1 is INSUFFICIENT

Statement 2: The most expensive item was $50

The discount for the most expensive item at $50 = 20% of $50

= 0.2*$50

=$10

But we don't know the price of the other 2 items, so we can't determine the discounts.

Therefore, Statement 2 is also INSUFFICIENT

Combining statement 1 and 2

1) The average (arithmetic mean) of the regular prices of the 3 items was $30.

So, the SUM of the 3 items = $90

2) The most expensive item is $50

So the OTHER 2 items sum up to $40

$50 item gets 20% discount and the other two items ($40) each get 10% discount

The discount = 20% of $50 + 10% of $40

=0.20*50 + 0.1*40

=$10 + $4

=$14

Combining the two statements is sufficient

Answer:

10.5 cm^2

Step-by-step explanation:

Since we have two sides and the angle between those sides, we can use the alternative area formula:

[tex]A=\frac{1}{2}ab\sin(C)[/tex]

a and b are the two sides while C is the angle in between the two sides.

Plug in the numbers:

[tex]A=\frac{1}{2}(7)(6)\sin(150)[/tex]

Recall the unit circle. Sin(150) is 1/2.

[tex]A=21(\frac{1}{2})[/tex]

[tex]A=21/2=10.5cm^2[/tex]

Answer:

Step-by-step explanation:

There are 2^10 = 1024 bit strings of length 10.

a) There are 10C2 = 45 ways to have exactly two 1-bits in 10 bits

  p(2 1-bits) = 45/1024

__

b) Of the four (4) possibilities for beginning and ending bits (00, 01, 11, 10), exactly one (1) of those is 00.

  p(b0=0 & b9=0) = 1/4

__

c) There are 10C7 = 120 ways to have seven 1-bits in the bit string.

  p(7 1-bits) = 120/1024 = 15/128

__

d) ∑10Ck {for k=0 to 4} = 386 is the total of the number of ways to have 0, 1, 2, 3, or 4 1-bits in the string. If there are more than that, there won't be more 0-bits than 1-bits

  p(more 0 bits) = 386/1024 = 193/512

__

e) The string will have two 1-bits if it starts with 1 and there is a single 1-bit among the other 9 bits. There are 9 ways that can happen, among the 512 ways to have 9 remaining bits.

  p(2 1-bits | first is a 1-bit) = 9/512

Answer:

Step-by-step explanation:

[tex]24\% \: of \: 800[/tex]

By definition of p% = p/100

[tex] = \frac{24}{100} \times 800[/tex]

Reduce the numbers with Greatest Common Factor 100

[tex] = 24 \times 8[/tex]

Multiply the numbers

[tex] = 192[/tex]

Hope I helped!

Best regards!!

Answer:

c

Step-by-step explanation:

Answer:

b > 3 2/15

Step-by-step explanation:

To make it easier to solve convert the mixed fraction to a fraction.

2 3/5 = 13/5

Now, multiply the fraction by 3/3 so that you will have a common denominator.

13/5 × 3/3 = 39/15

Now you solve for b.

39/15 < b - 8/15

39/15 + 8/15 < (b - 8/15) + 8/15

47/15 < b

b > 47/15

Convert the fraction to a mixed fraction to find the answer

47/15 = 3 2/15

b > 3 2/15

Answer:

Allison will owe $10,888.50 in 3 years

Step-by-step explanation:

FV=PV(1+r/n)^nt

Where,

PV=$7000

r=15%=0.15

n=quarterly=4

t=3 years

FV=PV(1+r/n)^nt

=7000(1+0.15/4)^4*3

=7000(1+0.0375)^12

=7000(1.0375)^12

=7000(1.5555)

=10,888.50

To 2 decimal places=$10,888.50

Allison will owe $10,888.50 in 3 years

Answer:

$10,888.20

Step-by-step explanation:

Order of Operations: BPEMDAS

Compounded Interest Rate Formula: A = P(1 + r/a)ᵃᵇ

A = Final Amount

P = Initial Amount

r = rate

a = Compounded number

b = time

Step 1: Define

P = 7000

r = 15% = 0.15

a = 4

b = 3 years

Step 2: Solve for A

At the end of the 3 years that elapsed, Allison will have to pay a final debt of $10,888.20.

Answer:

20 cars

Step-by-step explanation:

Solve for x!

10000+1000x(the first company)=20000+500x (the second company)

-10000              -10000

1000x=10000+500x

-500x              -500x

500x=10000

divide by 500 on both sides,

x=20

Check!

First company: 10000+1000(20)=10000+20000=30000

Second company: 20000+500(20)=20000+10000=30000!

30000=30000

Hope this helped!

Number of cars would need to be sold to make the total pay same is 20

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context

Given,

The first company pays a salary of $10,000 plus a commission of $1,000 for each car sold

therefore the expression is

10000+1000x

where x is the number of car sold

The second pays a salary of $20,000 plus a commission of $500 for each car sold

Then the expression will be

20000+500x

How many cars would need to be sold to make the total pay the same is

10000+1000x=20000+500x

1000x-500x=20000-10000

500x=10000

x=20

Hence, the number of cars would need to be sold to make the total pay the same is 20

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Answer:

24.5 oz

Step-by-step explanation:

First lets calculate the blood tests, 3/4 oz of solution.

3/4 multiplied by four tests= 3. (.75*4=3)

So 3 oz of Blood Tests were performed, now lets calculate the amount of tissue staining tests for performed.

1/2 multiplied by five tests= 5/2 or 2.5 oz of tests. (.5*5=2.5)

3oz+2.5=5.5oz

Now let's subtract that amount by 30.

30-5.5=24.5

Answer:

According to the graph, when y = 0, x = -0.4 and 2.3 .

Answer:

Step-by-step explanation:

when y=0,curve cuts x-axis and it cuts x-axis where x=-0.4

and x=2.3

Hey there! I'm happy to help!

To find the volume of a rectangular prism, you simply multiply each of the three different sides!

18×9×17=2754

Therefore, the volume of this rectangular prism is c. 2754 units cubed.

Now you can find the volume of a rectangular prism! Have a wonderful day!

Answer: The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Step-by-step explanation:

There are three measures of the center: 1) Mean   2) Median  3) Mode

Mean : Average value of the data

Mode = The most repeated value.

Median is the middlemost value in a well-ordered data.

It measures the center of the data.

Hence, the completed statement would be:

The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Answer:

First ____ is median

Second ____ is center

Step-by-step explanation:

The median is the middle value of a set of numbers, and is found in the center.

Answer:

C. y = 0.5x + 5

Hope that helps.

Answer:

112

Step-by-step explanation:

Define the variables:

x = number of French students sent by the school

Write the equation:

x / 21 = 1 / 3

Solve:

x = 7

The school sent 7 French students and 21 German students, for a total of 28 students.

The other 3 schools also sent 28 students.  So the total number of students sent is:

4 × 28 = 112

Answer:

Step-by-step explanation:

French students=F

[tex]\frac{F}{21} =\frac{1}{3} \\F=\frac{1}{3} \times 21 =7\\Total~ students~ of ~one~ school=21+7=28\\Total~language~students=28 \times 4=112[/tex]

Answer:

Volume of the sphere is 66.67r/h

Step-by-step explanation:

Hello,

Volume of a sphere = ⁴/₃πr³

Volume of a cylinder = πr²h

The volume of the cylinder = 50ft³

But the cylinder and sphere both have the same radius and height

Volume of a cylinder = πr²h

50 = πr²h

Make r² the subject of formula

r² = 50/πh

Volume of a sphere = ⁴/₃πr³

Put r² into the volume of a sphere

Volume of a sphere = ⁴/₃π(50/πh)r

Volume of a sphere = ⁴/₃ × 50r/h

Volume of a sphere = ²⁰⁰/₃ r/h

Volume of a sphere = 66.67r/h

The volume of the sphere is 66.67r/h

Answer:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex]

Step-by-step explanation:

[tex]\frac{7}{16} *\frac{-6}{13} = \frac{-42}{208}[/tex] . First multiply 7*-6=-42.

Then do 16*13=208.

Simplify by dividing both by 2.

You get [tex]\frac{-42}{208}=\frac{-21}{104}[/tex].

Your final simplified answer is [tex]\frac{-21}{104}[/tex]

I hope this helps!