Combine like terms.

3p2q2-3p2q3+4p2q3-3p2q2+pq

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:

x=7/10

Step-by-step explanation:

2/5=4/10

11/10=x+4/10

11/10-4/10=x

7/10=x

Answer:

x=7/10 or 0.7

Step-by-step explanation:

I turned the fractions into decimals

so

1.1=x+0.4

subtract 0.4 from 1.1 to get 0.7

Turn it into a fraction which is 7/10

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!

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: A) 1/2

Step-by-step explanation:

Answer:

If you flip a coin three times in the air, what is the probability that tails lands up all three times?

Step-by-step explanation:

1/2

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:

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:

$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:  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.

Learn more about Acceleration:

https://brainly.com/question/12134554

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

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!

P + 127 = 550        P = 423

Answer:

P = 423  

P + 127 = 550

Step-by-step explanation:

Answer:

C. y = 0.5x + 5

Hope that helps.

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

Learn more about Equation and Expression here

https://brainly.com/question/10413253

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Answer:

348 km³

Step-by-step explanation:

The volume of the triangular prism can be calculated using the formula, Volume = base area of the prism*the length of the prism

Base area of the prism = area of triangle =  ½*base of the triangle*height of the triangle

Base of the triangle = 12 km

Height of the traingle = 5.8

Therefore,

Base area = ½*12*5.8

= 6*5.8

Base area = 34.8 km²

Length of prism = 10 km

Volume of prism = base area*prism length

= 34.8*10

Volume of triangular prism = 348 km³

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:

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:

A. Intern

Step-by-step explanation:

Usually as a intern, you go around gaining experience about something. For example, if your a fresh graduate , you would first be hired as an intern to gain experience in the job you want.

Answer:

B:Mentor

Step-by-step explanation:

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:

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:

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

Answer:

c

Step-by-step explanation:

Answer:

tanФ = 2.6363636

Step-by-step explanation:

To find the tangent of the angle in-between the lines we will follow the steps below:

We are going to use the formula;

tanФ = |m₂ - m₁  / 1 + m₁m₂|

We can get the slope m₁ from the first equation

2x+3y–5=0

we will re-arrange it in the form y=mx + c

3y = -2x + 5

Divide through by 3

y = -[tex]\frac{2}{3}[/tex]x + [tex]\frac{5}{3}[/tex]

comparing the above equation with y=mx + c

m₁ =  -[tex]\frac{2}{3}[/tex]

We will proceed to find the second slope m₂ using the second equation

5x=7y+3

we will re-arrange it in the form y=mx + c

7y = 5x -3

divide through by 7

y = [tex]\frac{5}{7}[/tex] x -  [tex]\frac{3}{7}[/tex]

comparing the above with y=mx + x

m₂ = [tex]\frac{5}{7}[/tex]

we can now go ahead and substitute into the formula

tanФ = |m₂ - m₁  / 1 + m₁m₂|

tanФ = | [tex]\frac{5}{7}[/tex] -  (-[tex]\frac{2}{3}[/tex] ) / 1 +  (-[tex]\frac{2}{3}[/tex]₁)( [tex]\frac{5}{7}[/tex])|

tanФ = | [tex]\frac{5}{7}[/tex] +[tex]\frac{2}{3}[/tex]  / 1 -  [tex]\frac{10}{21}[/tex]|

tanФ = | [tex]\frac{29}{21}[/tex] / [tex]\frac{11}{21}[/tex]|

tanФ = | [tex]\frac{29}{21}[/tex] × [tex]\frac{21}{11}[/tex]|

21 will cancel-out 21

tanФ =[tex]\frac{29}{11}[/tex]

tanФ = 2.636363

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:

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:

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:

301.59

Step-by-step explanation:

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

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:

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.