A breakfast bar comes in two sizes. The 5-ounce bars come in a box of 10. A box of the 7-ounce has 6 bars. The 5-ounce bar contains 15 grams of dietary fiber. How many grams of dietary fiber are in one box of the 7-ounce bars?​

\(\frac{10}{4}\) = \(\frac{x}{20}\) proportion can be used to find the actual distance 'x' represented by 20 centimeters on the map.

The unitary method is used to find the value of a single unit from a given multiple.

For example: 50 boxes are of 500 rupees so what will be the price of 1 box

50 boxes → Rs. 500

1 box → 500/50

1 box → Rs. 10

This method is mostly used for ratio and proportion concept.

Here, we have given that the scale on a map shows that 10 kilometers is represented by 4 centimeters.

so,

4 centimeters → 10 kilometers

1 centimeter → 10/4 kilometers         ------- ( i )

for 20 centimeters

20 centimeter → x kilometers

1 centimeter → x / 20 kilometers       ------- ( ii )

on equating both the equations ( i ) and ( ii )

x / 20 = 10 / 4

x = 50 kilometers

Hence, \(\frac{10}{4}\) = \(\frac{x}{20}\) proportion can be used to find the actual distance 'x' represented by 20 centimeters on the map.

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The simplified form of the given expression is x raise to the power of one-thirty.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Simplifying indices expressions

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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The lowest form of 6/42 is 1/7 and,

the lowest form of 14/28 is 1/2.

What is the lowest form of fraction?

When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form. This is also known as its Lowest form.

In fraction 6/42, both denominator and numerator have common factor as 6, So we divide the denominator and numerator by 6.

Hence, we get 1/7.

Similarly, In fraction 14/28, both denominator and numerator have common factor as 14, So we divide the denominator and numerator by 14.

Hence, we get 1/2.

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Answer:

The choice C. x = -7/2

Step-by-step explanation:

\( - 4x = 14 \\ \\ x = \frac{14}{ - 4} \\ \\ x = - \frac{14 \div 2}{4 \div 2} \\ \\ x = - \frac{7}{2} \)

Answer:

\(\huge\boxed{\sf{\displaystyle-\frac{7}{2} }}\)

Step-by-step explanation:

Hello.

Divide both sides by -4 in order to isolate the variable (x):

-4x=14

\(\dfrac{14}{-4}}\)

This fraction can be reduced:

\(\dfrac{7}{-2}\)

or

\(-\dfrac{7}{2}\)

I hope it helps.

Have a great day.

\(\boxed{imperturbability}\)

9514 1404 393

Answer:

  C)  Peta, because she invests the most

Step-by-step explanation:

The additional $70 that Peta invests is equivalent to more than 2 years' interest at either of the other rates. Not only does Peta invest more money, she does so at a higher interest rate.

Peta will have the most money in her account when she closes it.

__

The balances will be ...

  Joan $490.02

  Peta $548.21

  Linda $420.00

Answer:

x=E

Step-by-step explanation:

The total number of students who graduated from the Cincinnati universities and colleges are 15382.

We are given that 6.76 % of Cincinnati college and university graduates majored in Registered Nursing.

The number of the Cincinnati college and university graduates who majored in Registered Nursing = 1026.

We need to find the total number of students that graduated from the Cincinnati universities and colleges altogether in 2016.

Let the total number of students be x.

ATQ:

6.67 % x = 1026

6.67 x = 102600

667 x = 10260000

x = 10260000 / 667

x = 15382.309

Rounding off to the nearest whole number is:

x = 15382.

Therefore, we get that the total number of students who graduated from the Cincinnati universities and colleges are 15382.

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Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

a) z* = -1.97

b) z* = -2.33

c) z* = -1.65

d) z* = 2.04

e) z* = 2.33

f) z* = -1.25.

Step-by-step explanation:

Z-score:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

a. P(z < z*) = 0.0244

We have to look at the ztable, and find z which has a pvalue of 0.0244. So it is z* = -1.97

b. P(z < z*) = 0.0098

We have to look at the ztable, and find z which has a pvalue of 0.0098. So it is z* = -2.33

c. P(z < z*) = 0.0496

We have to look at the ztable, and find z which has a pvalue of 0.0496. So it is z* = -1.65

d. P(z > z*) = 0.0204

We have to look at the ztable, and find z which has a pvalue of 1 - 0.0204 = 0.9796. So z* = 2.04

e. P(z > z*) = 0.0098

We have to look at the ztable, and find z which has a pvalue of 1 - 0.0098 = 0.9902. So z* = 2.33

(f) P(z > z* or z < -z*) = 0.201

This is z which has a pvalue of 0.201/2 = 0.1055. So it is z* = -1.25.

Answer: Increases in X tend to be accompanied by increases in Y

Step-by-step explanation:

The option given that indicates a positive value for a correlation is that an increases in X tend to be accompanied by increases in Y.

When two variables are said to be positively correlated, it simply means that the variables move along the same direction. As one variable increase, the other variable too will slow increase and vice versa.

Answer: 5/2187

Step-by-step explanation: The equation for geometric sequence is (a (subroot) n = a (subroot) 1) x ratio^(n-1).

Answer:v=-4

Step-by-step explanation:We move all terms to the left:

-5v+6-(26)=0

We add all the numbers together, and all the variables

-5v-20=0

We move all terms containing v to the left, all other terms to the right

-5v=20

v=20/-5

The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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Answer: 20

Step-by-step explanation: just do 100/5=20 so do 100/20=5 hope this helps!!

Answer:

20

Step-by-step explanation:

the guy above me ∧ is correct! Hope this helps! :)

Answer:

Step-by-step explanation:

\(\bold{2x^2 + 5x= 5x +50}\\\\{}\ \ -5x\qquad -5x\\\\\bold{2x^2\ =\ 50}\\\\\div2\quad\ \ \div2\\\\\bold{x^2=25}\\\\\bold{x=5\quad\vee\quad x=-5}\)

Check the picture below.

so we really have a trapezoid and a rectangle, let's get their area and sum them up.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel ~sides}{bases}\\[-0.5em] \hrulefill\\ h=5\\ a=7\\ b=14 \end{cases}\implies A=\cfrac{5(7+14)}{2}\implies A=\cfrac{105}{2} \\\\\\ \stackrel{\textit{\large areas}}{\stackrel{trapezoid}{\cfrac{105}{2}}~~ +~~\stackrel{rectangle}{(12\cdot 14)}}\implies \cfrac{105}{2}+168\implies \cfrac{241}{2}\implies 120\frac{1}{2}\)

The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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C. The equation is

An equation is in slope-intercept form if it is in the form

Expressing the given equation in slope-intercept

This gives

Divide through by -6

This gives

Therefore, the slope-intercept form of the given equation is

Where

slope = 2/3

y-intercept = -3

Answer:

Already answered on the other one

Step-by-step explanation:

#1

\(\\ \rm\Rrightarrow (gof)(-1)\)

\(\\ \rm\Rrightarrow g(f(-1))\)

\(\\ \rm\Rrightarrow g(2(-1)^2-(-1))\)

\(\\ \rm\Rrightarrow g(2+1)\)

\(\\ \rm\Rrightarrow g(3)\)

\(\\ \rm\Rrightarrow 3+1\)

\(\\ \rm\Rrightarrow 4\)

#2

\(\\ \rm\Rrightarrow (fog)(-1)\)

\(\\ \rm\Rrightarrow f(g(-1))\)

\(\\ \rm\Rrightarrow f(-1+1)\)

\(\\ \rm\Rrightarrow f(0)\)

\(\\ \rm\Rrightarrow 2(0)^2-0\)

\(\\ \rm\Rrightarrow 0\)

#3

\(\\ \rm\Rrightarrow (gof)(x)\)

\(\\ \rm\Rrightarrow g(f(x))\)

\(\\ \rm\Rrightarrow g(2x^2-x)\)

\(\\ \rm\Rrightarrow 2x^2-x+1\)

#4

\(\\ \rm\Rrightarrow (fog)(x)\)

\(\\ \rm\Rrightarrow 2(x+1)^2-x\)

\(\\ \rm\Rrightarrow 2(x^2+2x+1)-x\)

\(\\ \rm\Rrightarrow 2x^2+4x+2-x\)

\(\\ \rm\Rrightarrow 2x^2+3x+2\)

#5

No they are not equal

Simplifying

10x + -8 = ax + b

Reorder the terms:

-8 + 10x = ax + b

Solving

-8 + 10x = ax + b

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1ax' to each side of the equation.

-8 + -1ax + 10x = ax + -1ax + b

Combine like terms: ax + -1ax = 0

-8 + -1ax + 10x = 0 + b

-8 + -1ax + 10x = b

Add '8' to each side of the equation.

-8 + -1ax + 8 + 10x = 8 + b

Reorder the terms:

-8 + 8 + -1ax + 10x = 8 + b

Combine like terms: -8 + 8 = 0

0 + -1ax + 10x = 8 + b

-1ax + 10x = 8 + b

Reorder the terms:

-8 + -1ax + -1b + 10x = 8 + b + -8 + -1b

Reorder the terms:

-8 + -1ax + -1b + 10x = 8 + -8 + b + -1b

Combine like terms: 8 + -8 = 0

-8 + -1ax + -1b + 10x = 0 + b + -1b

-8 + -1ax + -1b + 10x = b + -1b

Combine like terms: b + -1b = 0

-8 + -1ax + -1b + 10x = 0

The solution to this equation could not be determined.

Answer:

a = 10 and b = 8

Step-by-step explanation:

comparing the two equations

Answer:

The angle Sita here is called Amplitude

Answer:

The radius is \( 2\sqrt{15} \)

The center is (3, 3)

Step-by-step explanation:

Equation of circle in standard form with center at (h, k) and radius r:

\( (x - h)^2 + (y - k)^2 = r^2 \)

We need to complete the square in x and y.

\( x^2 + y^2 - 6x - 6y = 42 \)

Separate x-terms and y-terms:

\( x^2 - 6x + ~~~~~y^2 - 6y + ~~~~~ = 42 + ~~~~~ + ~~~~~ \)

To complete the square, you square half of the linear term's coefficient.

Linear term in x: -6x

Coefficient: -6

Half of the coefficient: -3

Square half of the coefficient: 9

We need to add 9 to both sides to complete the square in x.

The linear term in y is -6y, so we do the same and we also need to add 9 to both sides to complete the square in y.

\( x^2 - 6x + 9 + y^2 - 6y + 9 = 42 + 9 + 9 \)

\( (x - 3)^2 + (y - 3)^2 = 60 \)

Now that we have the equation in standard form, we can get the radius and center of the circle.

\( r^2 = 60 \)

\( r = \sqrt{60} \)

\( r = \sqrt{4 \times 15} \)

\( r = 2\sqrt{15} \)

The radius is \( 2\sqrt{15} \)

The center is (3, 3)

Answer:

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

Here is the solution:

Answer:

Step-by-step explanation:

\(x + x = x\)

Cancel x on both sides:-

\(x=0\)

-Hope this helps!

Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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A square and a regular heptagon are coplanar and share a common side overline{ad}. The degree measure of exterior angle BAC is

A square is a closed two-dimensional figure with four sides and four corners. The four sides are all equal in length and the four angles are also equal in degree. A square is characterized as a quadrilateral all of whose angles are 90°. The properties of the angles in a square are as follows:

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

\(\frac{180(n-2)}{n}\)

where, n is the number of sides.  

Since, the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

\(\frac{180(7-2)}{7}\) = 128 7/4

Hence, ∠A  will be 128\(\frac{7}{4}\) degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

   ∠BAC = 360 - (∠A + 90)

⇒ ∠BAC = 360 - (128\(\frac{7}{4}\) +90)

⇒ ∠BAC = \(141\frac{3}{7}\)°

Hence the degree measure of exterior angle BAC is \(141\frac{3}{7}\) .

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Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

Answer:

Step-by-step explanation:

Substitute the x and y coordinate into both equations and check to see if they work is a best way to determine whether a given point is a solution to a system of equations.

One or many equation having same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

The best way to determine whether a given point is a solution to a system of equations is to substitute the  x and y coordinate into both equations and check to see if they satisfy the equation.

And if the solutions do not satisfy the equation that means given x , y are not the solutions.

And if the unknowns are the solutions of system of the equation that

means the pair of point lies in the graph.

Therefore the answer is option C.

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