SIMPLE ALGEBRAICE FRACTIONS
A computer shop displays a total of 50 type A and type B mice. The cost of a type A mouse is $6 and that of a type B mouse is $13. If the total cost of both types of mice is $433, find the number of type A mice displayed.​

Answer:

Option D: x = -2; x = 3/4

Step-by-step explanation:

Hello!

We can factor this expression and then find the zeroes to find our solutions.

We have to factor by grouping. Multiply the 1st and last term, 4x² and -6 is -24x², and find two factors that equal to -24x² and add up to the second term, 5x. 8x and -3x work for this.

Now, set the equation equal to zero.

Remember, if two numbers, a and b, multiply to 0, either a or b or both numbers must be zero. So now we set both factors to zero, hence the zero-product property.

And the next one:

The solutions are x = -2, and x = 3/4, or Option D

Answer:

B as the number of molecules increases the volume increases

Step-by-step explanation:

Using the combination formula, it is found that there is a 0.1 = 10%  probability of randomly choosing the correct pair of answer options

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 2 answers are chosen from a set of 5, hence the total number of options is given by:

[tex]C_{5,2} = \frac{5!}{2!3!} = 10[/tex]

Only one pair is correct, hence the probability of randomly choosing the correct pair of answer options is given by:

p = 1/10 = 0.1 = 10%.

More can be learned about the combination formula at https://brainly.com/question/25821700

Answer:

[tex]\frac{x^{2} }{21}[/tex]

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Eliminate quotient in numerator

3. Multiply the numbers

Solution: [tex]\frac{x^{2} }{21}[/tex]

Answer:

When we multiply 4\7, 5\3 and 3\4, then the answer will be 5\7.

A poll worker analyzing the ages of voters found that μ = 65 and σ = 5. The possible voter age that would give her zx = 1.14 is 71.

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of a population

N = number of observations of population

X = mean

μ = population mean

It is given that the random variable,

X = The ages of voters

μ = The analysis is having mean of 65

Standard deviation = 5

X = normal (65,5) Now, we will convert it into Z-score concept ,

Z = x - 65/ 5

z = 1.14

X = 65 + 5z

So, X = 65 + 5(1.14)

         = 65 + 5.7

         = 70.70

Therefore, We can also write it by rounding off the value,i.e.=71

The possible voter age that would give her zx = 1.14 is 71.

Learn more about standard deviation

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Answer:

C, 71

Step-by-step explanation:

quiz edge

Answer:

7/15

Step-by-step explanation:

2/3 of those means 2/3 of the 7/10 books sold by the used book store

2/3 of 7/10 means 2/3 * 7/10 = 14/30 = 7/15

Hope this helps :)

Have a nice day!

Answer:

It's 1,560,000

Step-by-step explanation:

You can just put it into a calculator.

Answer:

1,560,000

Step-by-step explanation:

When you multiply 1,200 by 1,300, you would get 1,560,000.

Answer:

The answer is 3. 1. There is '0' point of intersection, that means they do not intersect. This only possible when the lined are parallel to each other.

'c' can be any real number except 4 for which the considered system would have no solution.

When both the lines(represented by both the equations) are parallel and not coincident, then that system of linear equations have no solutions as there is no common point on both line.

If they are coincident (lying over each other), then there will have infinite solution since in that case, they will have infinite points in common.

Thus, if two lines are not in any of above case, they intersect at single point and in that case, the considered system of equation has unique single solution.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:

[tex]y = mx +c[/tex]

Parallel lines(non-coincident) have same slope but different y-intercept.

Converting these equations to slope-intercept form, we get:

For first line:

[tex]\dfrac{1}{2}x + \dfrac{1}{5}y = 2\\\\ \dfrac{1}{5}y = 2 - \dfrac{1}{2}x\\\\y = 10 - \dfrac{5}{2}x\\\\y = -\dfrac{5}{2}x + 2[/tex]

and

For second line:

[tex]5x + 2y = c\\\\y = \dfrac{1}{2}c - \dfrac{5}{2}x\\\\y = -\dfrac{5}{2}x + \dfrac{c}{2}[/tex]

For no-solution, we need both lines to stay parallel but not coincident so that there is no common point (solution of this system) between those two lines.

Thus, we get:

[tex]2 \neq \dfrac{c}{2}\\\\\text{Multiplying 2 on both the sides}\\\\c \neq 4[/tex]

Since 'y' assumes real numbers assumingly, so 'c' can be any real number except 4 for which the considered system would have no solution.

Below is image attached of those parallel lines when c = 10.

Thus,  'c' can be any real number except 4 for which the considered system would have no solution.

Learn more about the case of 'no solution' here:

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Answer:

I would be 3 8/10

Step-by-step explanation:

hope this helps

Answer:

V= 22800 unit^3

Step-by-step explanation:

hope this helps :)

Answer:

10 meters is equivalent to 1000 cm and 0.01 kilometers

Step-by-step explanation:

The expression that models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds is d=9cosine[(π/2)t] option second is correct.

It is defined as the number of waves that crosses a fixed point in one second, known as frequency. The unit of frequency is per second.

The pendulum takes 2 seconds to swing a horizontal distance of 18 inches from right to left.

For swing back from left to right, it takes again 2 seconds to cover a horizontal distance of 18 inches.

The total time to complete the one cycle = 4 seconds

Thus, the frequency is the reciprocal of the time

f = 1/4

The expression for the angular speed is:

w = 2πf

w = 2π(1/4)

w = π/2

The distance of the pendulum from the center A = half the horizontal                                  

                                                                                 distance of 18 inches

A = 18/2

A = 9 inches

We know the cosine function for the pendulum is given by:

d = Acosine(wt)

d = 9cosine(πt/2)  or

d = 9cosine[(π/2)t]

Thus, the expression that models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds is d = 9cosine[(π/2)t]

Learn more about the frequency here:

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Answer:

Given that the p-value is greater than 0.05, rejecting the null hypothesis and concluding that the mean time was not greater than 60 minutes

Step-by-step explanation:

I got it right on AP Classroom

Answer:

ans below

Step-by-step explanation:

when rectangle is rotated, hemisphere is formed with r =12cm

volume = 2/3πr^3

= 1152π cm^3

Answer:

525

Step-by-step explanation:

So its 25 a day and hes doing it for 21 days because 7*3=21.

so 25*21= 525

Answer:

10+51+17=78

Step-by-step explanation:

Alright, so at first I just took a random number and kept on working it out until I got the exact answer as 78. Finally, i got the third number as 17. Now, i know the third number is 7 more than the first so I have to subtract 17 and 7, 17-7=10. So the first number is 10. Ok, now i know that the second number is 3 times the third number (17) so you should multiply, 17x3=51. 51 is the 2nd number.

1st number=10

2nd number=51

3rd number=17

Add them, 10+51+17=78.

Answer:

Step-by-step explanation:

In the question we are given ,

So , we are assuming that ,

We are finding the solution by adding all these term and equating it with 78 because sum of these three numbers is equal to 78 .

Here we go ,

[tex] \longrightarrow \: x + 3(x + 7) + x + 7 = 78[/tex]

Step 1 : Solving the bracket part :

[tex] \longrightarrow \: \blue{x }+ \blue{ 3x} + \red{21} + \blue{ x} + \red{7 }= 78[/tex]

Step 2 : Adding like terms :

[tex] \longrightarrow \:5x + 28 = 78[/tex]

Step 3 : Transposing 28 to right hand side :

[tex] \longrightarrow \:5x = \green{78} - \green{28}[/tex]

Step 4 : Subtracting 28 from 78 :

[tex] \longrightarrow \:5x = 50[/tex]

Step 5 : Transposing 5 to right hand side :

[tex] \longrightarrow \:x = \cancel \frac{50}{5} [/tex]

Step 6 ; Cancelling 50 with 5 :

[tex] \longrightarrow \: \purple{\boxed{x = 10}}[/tex]

Therefore value of ,

Verification :

We are verifying our answer by adding the three numbers and it must be equal to 78 .

Therefore , our answer is correct .

Answer:

0.1s + 125 < 180

Answer:

ask your classmates what is there shoe sizes are

Step-by-step explanation:

The number of pounds of peaches is 6 pounds and the number of pounds of apples is 18 pounds

Given:

cost of peaches per pound = $4

cost of apples per pound = $2

Total amount spent = $60

Total pounds bought = 24

let

x = number of peaches

y = number of apples

x + y = 24 (1)

4x + 2y = 60 (2)

multiply (1) by 2

2x + 2y = 48 (3)

4x + 2y = 60 (2)

subtract (3) from (2)

4x - 2x = 60 - 48

2x = 12

x = 12/2

x = 6

substitute x = 6 into (1)

x + y = 24 (1)

6 + y = 24

y = 24 - 6

y = 18

Therefore, the number of pounds of peaches is 6 pounds and the number of pounds of apples is 18 pounds

Answer:

So, a.0, b.1/10, c.81, d.1/64

Step-by-step explanation:

Part A, anything raised to the power of zero is equal to zero. So suppose we have a constant, b, and we raise it to the power of zero, so b^0, it'll always be 0.

Part B, a negative power essentially means that you'll have to inverse the number. Once again, if we have a constant, b, and we raise it to the power of -1, it'll end up being 1/b. So b^-1 = 1/b.

Part C, its simply just multiplying 3 with itself four times.

Part D, as mentioned before, anything raised to a negative power means that you need to inverse the number. So 4^-3 is equal to 1/4^3, meaning that its just 1/64.

Answer:

The graph g(x) is shifted vertically up by 3 units.

The graph of g(x) is shifted horizontaly left by 2 units.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it a because it there the right answer

Answer:

[tex]y =\dfrac{-1}{2}x +4[/tex]

Step-by-step explanation:

Equation of the line: y = mx +b

y = 2x + 7

m = 2

Slope of the perpendicular line = [tex]-\frac{1}{m}[/tex]

   [tex]\sf m_1 =\dfrac{-1}{2}[/tex]

Equation of the perpendicular line:

             [tex]y= \dfrac{-1}{2}x + b[/tex]

This line is passing throught (2 ,3). Substitute the x & y coordinate in the above equation and now we can obtain the value of b (y-intercept)

           [tex]\sf 3 = \dfrac{-1}{2}*2+b\\\\3 = -1 + b\\[/tex]

   3  +  1 = b

          4 = b

Equation:

      [tex]y =\dfrac{-1}{2}x +4[/tex]

Korey’s gross profit margin last month will be equal to 55.7%.

The gross profit margin is a profitability ratio. Profitability ratios measures the efficiency with which a company generates profit from its asset. Gross profit margin measures the return on sales.

Gross profit margin = net income / gross profit

$1850 / 3320 = 0.557 = 55.7%

To learn more about profit margin, please check: brainly.com/question/26208770

Answer:

The answer is actually a. 42.5%

Step-by-step explanation:

Correct on edg. 2022

When multiplying two powers, if their bases are the same, then you simply add the exponents:

   [tex]\frac{8^5*8^3*8^2}{8^8} =\frac{8^{5+3+2}}{8^8} =\frac{8^{10}}{8^8}[/tex]

When dividing two powers, if their bases are the same, you simply minus the exponents.

  [tex]\frac{8^{10}}{8^8}=8^{10-8}=8^2[/tex]

Thus when the expression is simplified, the answer as a power is [tex]8^2[/tex]

Answer: 8^2

Hope that helps!

Answer:

y=0.75x

Step-by-step explanation:

$3 for every 4 hours

$0.75 for every hour

y=0.75x

The equation relating the total cost (y) to the number of hours (x) is y = 0.75x.

The equation that relates the total cost (y) to the number of hours (x) can be derived from the given information. We know that the cost is $3 for 4 hours of feeding kookaburras.

The cost is proportional to the number of hours, and we can represent this relationship using a linear equation:

Cost = Rate × Hours

In this case, the rate is the cost per hour, which is $3 / 4 hours = $0.75 per hour.

Therefore, the equation relating the total cost (y) to the number of hours (x) is:

y = 0.75x

Here, "y" represents the total cost, and "x" represents the number of hours. This equation reflects the linear relationship between the total cost and the number of hours of feeding kookaburras in the zoo.

To know more about equation:

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Thus its an obtuse angle triangle.

=============================

Acute triangle means they measure less than 90°

Right triangle means a triangle with 90°

Obtuse triangle has one angle greater than 90°

Obtuse

Check one angle is streched like it's greater than 90°

So

it's an obtuse triangle