a) A furniture store can sell 40 chairs per week at a price of sh. 80 each. The manager estimates that for each and sh. 5 price reduction, she can sell five more chairs per week. The chairs cost the store sh. 30 each. If x stands for the number of sh. 5 per price reduction, find price of the chairs and the quantity that maximize profit.

Answer: [tex]10^4[/tex]

Step-by-step explanation:

Assuming we are using the common log (base 10),

[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]

Answer:

Multiply the top equation by -3 and the bottom equation by 2

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}[/tex]

To solve the given system of equations by addition, make one of the variables in both equations sum to zero.  To do this, the chosen variable must have the same coefficient, but it should be negative in one equation and positive in the other, so that when the two equations are added together, the variable is eliminated.

To eliminate the variable y:

Multiply the top equation by -3 to make the coefficient of the y variable 6:

[tex]\implies -3(4x-2y=7) \implies -12x+6y=-21[/tex]

Multiply the bottom equation by 2 to make the coefficient of the y variable -6:

[tex]\implies 2(3x-3y=15) \implies 6x-6y=30[/tex]

Add the two equations together to eliminate y:

[tex]\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}[/tex]

Solve for x:

[tex]\implies -6x=9[/tex]

[tex]\implies x=-\dfrac{9}{6}=-\dfrac{3}{2}[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\implies 3\left(-\dfrac{3}{2}\right)-3y=15[/tex]

[tex]\implies -\dfrac{9}{2}-3y=15[/tex]

[tex]\implies -3y=\dfrac{39}{2}[/tex]

[tex]\implies y=-\dfrac{39}{2 \cdot 3}[/tex]

[tex]\implies y=-\dfrac{13}{2}[/tex]

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Answer:

A. True

Step-by-step explanation:

The ratio 1000 grams=1kilogram is correct.

The function that's illustrated in the graph is function D.

First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.

Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.

The answer that illustrates the information explained is D.

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Answer:

B.

Step-by-step explanation:

An open circle means to exclude the point.

A closed circle means to include the point.

In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.

A parabola has an x squared in the equation.

The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.

The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.

The answer is B.

Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart

Step-by-step explanation:  On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches

Answer:

See below    

Step-by-step explanation:

Remember... when you square a negative number, you get a positive result

  AND you cannot divide by zero AND you cannot have the sqrt of a negative number  so:

-2 > x > 2     (looks like 'D'   but there is a negative sign missing)

Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.

Percentage is simply number or ratio expressed as a fraction of 100.

It is expressed as;

Percentage = ( Part / Whole ) × 100%

Given the data in the question;

We substitute the given values into the above equation.

Percentage = ( Part / Whole ) × 100%

Percentage = ( 4554 / 9900 ) × 100%

Percentage = ( 0.46 ) × 100%

Percentage = 46%

Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.

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Answer:

I.Q.R = 11 - 3

I.Q.R = 9

the interquartile range = 9

Answer:
[tex]\pi[/tex][tex]14^{2}[/tex] or [tex]\pi 196\\[/tex]

Step-by-step explanation:

  The circle V has the radius of 14 (r=14)
The formula of area is (A=[tex]\pi r^{2}[/tex])

So we insert the value of (r=14)
[tex]A=\pi 14^2[/tex]
[tex]A=\pi 196[/tex]
And that's the answer, The exact value is 615.752...

Answer: 196 pi

Step-by-step explanation:

The test statistic based on the probability illustrated is -3.22.

Based on the information, the test statistic will be:

= (0.4 - 0.5)/[✓0.5(1 - 0.5)/260]

= -3.22

The p value using the distribution table is 0.0012.

The conclusion is to reject the null hypothesis as there's sufficient evidence to warrant rejection.

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The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400

The ratio based on the information given will be:

= 1200/600

= 2

Therefore, the constant ratio is 2.

In 6 years, the population will be:

= 600 × 2^6

= 600 × 64

= 38400

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The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13

y = -14x² + 1035x - 10266

-14x² + 1035x - 10266 = 0

x = -b ± √b² - 4ac / 2a

= -1035 ± √1035² -4(-14)(-10266) / 2(-14)

= -1035 ± √1071225 - 574896 / -28

= -1035 ± √496329 / -28

x = 1035 / 28 ± √496329 / 28

x = 11.80 or 62.13

The maximum value of x is 62.13

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Answer:

x = 5

Step-by-step explanation:

Since the line is vertical,

the equation of the line then is x = (some value).

Since this particular line passes throught (5,-4), where the x coordinate is 5, we can deduce the equation of this line to be x = 5.

answer: 200, 2 hundred, two hundred

Hello,

If we want to factor the expression, we have to solve

3x² + 10x + 8 = 0

a = 3 ; b = 10 ; c = 8

∆ = b² - 4ac = 10² - 4 × 3 × 8 = 4 > 0

x1 = (-b - √∆)/2a = (-10 - 2)/6 = -12/6 = -2

x2 = (-b + √∆)/2a = (-10 + 2)/6 = -8/6 = -4/3

Factor :

a (x - x1)(x - x2)

= 3(x + 2)(x + 4/3)

= (x + 2)(3x + 4)

Answer: 2.25 inches

Step-by-step explanation:

The radius of a circle is half the diameter.

In accordance with the graph of the cubic function, the roots are - 2, - 1, 3.

In this question we have a graph of a cubic equation, the roots are the points of the curve that pass through the x-axis. Cubic equations have at least a real root and at most three. In accordance with the graph of the cubic equation, the roots are - 2, - 1, 3.

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Answer:

14

Step-by-step explanation:

The equation would be R = 5(4) - 6. Multiply 5 by 4 to get 20, then subtract 6 to get 14.

The containers must be spheres of radius = 6.2cm

We know that the shape that minimizes the area for a fixed volume is the sphere.

Here, we want to get spheres of a volume of 1 liter. Where:

1 L = 1000 cm³

And remember that the volume of a sphere of radius R is:

[tex]V = \frac{4}{3}*3.14*R^3[/tex]

Then we must solve:

[tex]V = \frac{4}{3}*3.14*R^3 = 1000cm^3\\\\R =\sqrt[3]{ (1000cm^3*\frac{3}{4*3.14} )} = 6.2cm[/tex]

The containers must be spheres of radius = 6.2cm

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Answer:

41.12 ft

Step-by-step explanation:

10 + 6 = 16

2 x pi x r = 25.12

16 + 25.12 = 41.12

Answer:

Step-by-step explanation:

find the outer perimeter of this figure

r = diameter : 2 = 8 : 2 = 4

2π4 =

8π=

8 × 3.14 = 25.12 ft

find figure perimeter

25.12 + 6 + 10 =

41.12 ft

Answer:

D.

Step-by-step explanation:

the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.

The linear function y = 3 · w - 1 represents the number of sea shells found in each week.

The speed of the driven gear is 180 rounds per minute.

In the first problem we have an example of linear progression, in which the number of sea shells is increased linearly every week. After a quick analysis, we conclude that the linear function y = 3 · w - 1, a kind of direct relationship.

In the second problem, we must an inverse relationship to determine the speed of the driven gear. Please notice that the speed of the gear is inversely proportional to the number of teeths. Then, we proceed to calculate the speed:

[tex]\frac{v_{1}}{v_{2}} = \frac{N_{2}}{N_{1}}[/tex]

If we know that [tex]v_{2} = 60\,rpm[/tex], [tex]N_{2} = 60[/tex] and [tex]N_{1} = 20[/tex], then the speed of the driven gear is:

[tex]v_{1} = v_{2}\times \frac{N_{2}}{N_{1}}[/tex]

[tex]v_{1} = 60\,rpm \times \frac{60}{20}[/tex]

[tex]v_{1} = 180\,rpm[/tex]

The speed of the driven gear is 180 rounds per minute.

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Explanation:

These are the steps to focus on

step 3: -6x - 8 < -2

step 4: -6x < 6

The move from the third step to the fourth step has us adding 8 to both sides. Therefore, we use the addition property of inequality.

That property has four forms

It's similar to the idea of starting with a = b, then adding c to both sides to get a+c = b+c

We add the same thing to both sides to keep things balanced.

Answer:

It is necesary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator

Step-by-step explanation:

Answer:

484

Step-by-step explanation:

because a=22² , which is equal to 484

because a=22² , which is equal to 484, but a=c hence C is equal to 484

Using the Fundamental Counting Theorem, it is found that:

The 2 people can arrange themselves in 40 ways.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

With one people in the aisle and one in the normal seats, the parameters are:

n1 = 4, n2 = 7

With both in the aisle, the parameters is:

n1 = 4, n2 = 3

Hence the number of ways is:

N = 4 x 7 + 4 x 3 = 28 + 12 = 40.

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Answer:

90 kilo per hour

Step-by-step explanation:

hope that helps!!

The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

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