Value times frequency equals product.
True or False

Final answer:

To ensure there are no solutions to the compound inequality x < 5 and x > c, we can choose c to be 5 or larger, such as c = 6, making the inequality impossible.

Explanation:

To determine a value of c such that the compound inequality x < 5 and x > c has no solutions, we need to choose a value of c that makes the inequality impossible to satisfy.

One way to ensure there are no solutions is to choose c so that it is greater than or equal to 5.

If c is 5 or any number larger than 5, then there is no real number x that can be both greater than c and at the same time less than 5.

For example, if we choose c = 6, then the set of values greater than 6 (x > 6) does not intersect with the set of values less than 5 (x < 5).

Therefore, c = 6 would ensure that there are no solutions to the compound inequality.

The linear equation for squirrel y = 12x.

The linear equation for mouse  y = 8x

The distance covered by the squirrel is 36km at time 3hours.

The distance covered by the squirrel is 24km at time 3hours.

A linear equation is an "algebraic equation is of the form y=mx + b where 'm' is the slope of the line and 'b' is the y - intercept".  

According to the question,

Animal            Mouse       Squirrel

Speed(mph)         8                12

"x" the time goes along with x-axis and "y" is  the distance covered by the animal.

The mouse time and distance would  plot the graph (1,8)(2,16)(3,24)....

The squirrel time and distance  would plot the graph (1,12)(2,24)(3,36)....

Let us consider the track is straight line and shorter distance is 50 meters.

Formula for straight line equation y = mx + b  where 'b' is the base value, 'x' is the time and 'y' is the distance.

The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.

The linear equation for mouse  y = 8x + b  and the mouse starts at 0 meters.  so the equation becomes y = 8x.

Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by mouse and the squirrel.

y =12x

y = 12(3)

y = 36.

The distance covered by the squirrel is 36km at time 3hours.

For mouse, at time x = 3 hours.

y = 8(3)

y=24.

The distance covered by the squirrel is 24km at time 3hours.

Hence, The linear equation for squirrel y = 12x.

The linear equation for mouse  y = 8x

The distance covered by the squirrel is 36km at time 3hours.

The distance covered by the squirrel is 24km at time 3hours.

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Answer:

Its actually 11  1/3

Step-by-step explanation:

Answer:

i think it is 54

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

To find the number of students studying each language, assign variables, write equations based on the given information, and solve the system of equations.

To solve this problem, let's assign variables. Let x represent the number of students taking Spanish, and y represent the number of students taking French.

According to the given information, the number of students taking French is 2/3 of the number taking Spanish. So, we can write this as an equation:
y = (2/3)x

The total number of students taking French and Spanish is 310. So, we can write another equation:
x + y = 310

Now, we can solve these two equations to find the values of x and y. Substituting the value of y from the first equation into the second equation, we get:
x + (2/3)x = 310
(5/3)x = 310
x = (3/5) * 310
x = 186

Substituting x = 186 back into the first equation, we find:
y = (2/3) * 186
y = 124

Therefore, there are 186 students taking Spanish and 124 students taking French.

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Answer:

1/9, 1/8 and 1/4

Step-by-step explanation:

multiply the both given numerators (top numbers) and both given denominators (bottom numbers) given bellow

1/3 x 1/3 = 1/9  because 1 x 1 = 1 and 3 x 3 = 9

1/4 x 1/2 = 1/8 because 1 x 1 = 1 and 4 x 2 = 8

3/4 x 1/3 = 3/12 or 1/4 simplified because 3 x 1 = 3 and 4 x 3 = 12. when you simplify you divide the denominator by the numerator and 12 divided by 3 is 4 and you the 4 stays as the denominator and make the numerator of 1

Final answer:

By setting up and solving an equation based on the monthly membership and per-session training costs at both Silver Gym and Fit Factor, it's determined that Sarah would need to buy 3 personal training sessions for the total cost at the two gyms to be equal.

Explanation:

To find how many personal training sessions Sarah would have to buy to make the total cost at Silver Gym and Fit Factor equal, we'll set up an equation. Let x be the number of personal training sessions.

At Silver Gym, the total cost is $45 (membership) + $25x (personal training sessions).

At Fit Factor, the total cost is $75 (membership) + $15x (personal training sessions).

Setting these two expressions equal to each other gives us the equation:
45 + 25x = 75 + 15x.

To solve for x, first subtract 15x from both sides, giving: 10x = 30. Then divide both sides by 10 to isolate x, resulting in x = 3.

Therefore, Sarah would have to buy 3 personal training sessions in one month for the total costs at both gyms to be equal.

Answer:

  3 sessions

Step-by-step explanation:

You want to know the number of personal training sessions Sarah would have to buy to make the total costs the same at Silver Gym and Fit Factor. Silver Gym costs $45 per month and $25 per session, while Fit Factor costs $75 per month and $15 per session.

Silver Gym costs $25 -15 = $10 more per personal training session, but $75 -45 = $30 less for the monthly fee. This means it takes $30/$10 = 3 sessions for the difference in fees to be made up by the difference in session costs.

Sarah would have to buy 3 sessions for the total cost to be the same.

If you need to see this using equations, we can write the cost equations as ...

  S = 45 +25x . . . . . . . . cost for x sessions at Silver Gym

  F = 75 +15x . . . . . . . . . cost for x sessions at Fit Factor

Setting these equal, we have ...

  S = F

  45 +25x = 75 +15x

  25x -15x = 75 -45 . . . . . . . subtract 45+15x from both sides

  10x = 30

  x = 30/10 = 3 . . . . sessions for equal cost

Sarah would have to buy 3 sessions for the total cost to be the same.

__

Additional comment

These "break even" problems usually have a higher fixed cost associated with a lower per use cost, and vice versa. The costs are the same when the number of uses, multiplied by the difference in use cost, comes to the same amount as the difference in fixed costs. Here, the $10 difference in session cost, times 3 sessions, is equal to the $30 difference in monthly membership fee.

Answer:

The area of given trapezoid is 68.8 cm²

Step-by-step explanation:

Given: A trapezoid with height 6.4 cm and parallel base is 12.9 cm and 8.6 cm.

We have to find the area of area of this trapezoid.

Area of trapezoid = [tex]\frac{1}{2}\times \text{sum of parallel sides}\times height[/tex]

Given : Height = 6.4 cm

and parallel base is 12.9 cm and 8.6 cm.

Substitute, we have,

Area of trapezoid = [tex]\frac{1}{2}\times (12.9+8.6)\times 6.4[/tex]

Simplify, we have,

Area of trapezoid = [tex]\frac{1}{2}\times 21.5\times 6.4[/tex]

Area of trapezoid = 68.8 cm²

Thus, The area of given trapezoid is 68.8 cm²

Answer: 28 square inches

Step-by-step explanation:

We know that the area of a triangle is given by :-

[tex]\text{A}=\dfrac{1}{2}*b*h[/tex], where b is base and h is the height of the triangle.

From the given picture, it cam be seen that alll the traingles area of same measure, the base of the triangle = 2 inches

The height of the triangle = 6 inches

Now, the area of a triangle is given by :-

[tex]\text{A}_1=\dfrac{1}{2}*6*2=6\ in^2[/tex]

Area of the square in the center =[tex](side)^2=(2)^2=4\ in^2[/tex]

Now, the total surface area of the pyramid is given by :-

[tex]\text{S.A.}=4+4(6)=28\ in^2[/tex]

Answer:

Shane's total sales is $6000.

Step-by-step explanation:

It is given that the Shane earns 13% commission on his sales and the Shane's commission this month is $780.

Let the Shane's total sales be x. So, 13% of x is $780.

[tex]x\times \frac{13}{100}=780[/tex]

Solve the above equation to find the value of x.

[tex]x=780\times \frac{100}{13}[/tex]

[tex]x=6000[/tex]

The value of x is 6000, therefore Shane's total sales is $6000.

They sold 3 left handed gloves and 9 right handed gloves.

To solve this problem, we have to write a system of equations.

Data given;

[tex]x + y = 12...equation (i)\\ 45x + 52y = 561 equation (ii)[/tex]

From equation (i)

[tex]x + y = 12\\ x = 12 - y...equation (iii)[/tex]

Substitute equation (iii) into equation (ii)

[tex]45x + 52y = 561\\ x = 12 - y\\ 45(12- y) + 52y = 561\\ 540 - 45y +52y = 561\\ 540 + 7y = 561\\ 7y = 21\\ y = 3[/tex]

Put y = 3 in equation (i)

[tex]x + y = 12\\ x + 3 = 12\\ x = 9[/tex]

From the calculations above, they sold 9 right handed gloves and 3 left handed gloves

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