Janet has three times as many dimes as nickels and twice as many quarters as nickels. If she has $3.40 in all, how many nickels, dimes, and quarters does she have?
If n represents the number of nickels Janet has, which of the following equations could be used to solve the problem?

5n + 10n + 25n = 340
n + 3n + 2n = 340
5n + 30n + 50n = 340

The statement "The value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16" is FALSE.

To determine whether the value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16, we need to check if the function has any real roots greater than 3.

One way to approach this is by analyzing the behavior of the function as x approaches infinity. We can check the sign of the leading coefficient (-3) and the constant term (16) to determine the overall behavior of the function.

Leading coefficient:

The leading coefficient of -3 indicates that the highest power of x in the function is negative. This means that as x approaches infinity, the function will decrease without bound.

Constant term:

The constant term of 16 indicates that the function intersects the y-axis at y = 16.

Considering these observations, we can infer that the function starts at a positive value (y = 16) and approaches negative infinity as x increases. This implies that the function f(x) = -3x^3 + 20x^2 - 36x + 16 will have at least one real root greater than 3.

Therefore, the statement "The value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16" is FALSE.

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Final answer:

The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.

Explanation:

To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.

The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.

we can re-write our expression as:

-3a^2+27a+1200=0

-3(a^2-9a-400)=0

a^2-9a-400=0

factorizing the above we have:

a^2+16a-25a-400=0

a(a+16)-25(a+16)=0

(a+16)(a-25)

thus replacing back x^2 we have:

(x^2+16)(x^2-25)

=(x^2+16)(x-5)(x+5)

factorizing (x^2+16) we get

x^2=+/-√-16

x=+/-4i

thus the zeros of the expression are:

x=-5, x=5 , x=-4i, x=4i

Answer:

  P(z < 1.45) ≈ 0.92647

Step-by-step explanation:

Several forms of technology are available for finding the area under the standard normal curve. There are probability apps, web sites, spreadsheets, and calculator functions.

The area under the standard normal curve between two values of z is given on many spreadsheets and by many calculators using the normalcdf(a,b) function. In this form, 'a' is the lower bound, and 'b' is the upper bound of the z-values for which the area is wanted.

For the problem at hand, the value of 'a' is intended to be negative infinity. A calculator allows input of no such value, so some "equivalent" value must be used. (At least one calculator manual suggests -1e99.)

The area of the normal curve below z=-8 is less than 10^-11, so -8 is a suitable stand-in for -∞ on a calculator that displays a 10-decimal-digit result. All the decimal digits shown are accurate, not affected by our choice of lower bound.

The attachment shows the value of the expression is about ...

  P(z < 1.45) ≈ 0.92647

Answer with explanation:

We have to find , P (z< 1.45).

 Breaking ,z value into two parts, that is , In the column,the value at, 1.40 and in the row ,value at , 0.05,the point where these two value coincide,gives value of Z<1.45.

The value lies in the right of mean.

So, P(z<1.45)=0.9265

In the,Normal curve, at the mid point of the curve

Mean =Median =Mode

Z value at Mean = 0.5000

→So, if you consider , the whole curve,

P(Z<1.45)= 0.9265 × 100=92.65%=92%(approx) because we don't have to consider ,z=1.45.

→But, if you consider, the curve from mean ,that is from mid of the normal curve

P (z<1.45)=92.65% - 50 %

           =42.65% =42 %(approx) because we don't have to consider ,z=1.45.

Each economic term is matched with its appropriate description as follows:

OLIGOPOLY ||  There are no barriers to entry in the market.

MONOPOLY ||  There is a single seller in the market.

COLLUSION ||  Three companies secretly enter into a price agreement.

PERFECT COMPETITION ||  Every company in this market structure is aware of the actions of the other companies.

There are no barriers to entry in the market is the match of - Oligopoly (The market is shared by many sellers )

There is a single seller in the market is the match of - Monopoly

Three companies secretly enter into a price agreement is the match for - Collusion

Every company in this market structure is aware of the actions of the other companies is the match for Perfect Competition.

Answer:

Larry has 1525 cents or 15.25 dollars.

Step-by-step explanation:

The following are the values for each of the coins:

1 Nickel=5 cents

1 Dime = 10 cents

1 Quarter = 25 cents

1 Fifity-cent = 50 cents

So the total value of the Larry's have is

Total money = 62*5 cents + 24*10 cents + 17*25 cents + 11*50 cents

Total money = 310 cents + 240 cents + 425 cents + 550 cents

Total money = 1525 cents

This is equal to 15.25 dollars.

The answer to this should be 13

Substitute the value of the variable into the expression and simplify

Substitute: |-2^2 + -3^2|

Simplify: |-2^2|= 4, |-3^2|= 9

Solve: 4 + 9 = 13

Given a = 5, b = -3, and c = -2, the absolute value of |c2 + b2| is calculated by squaring the values of c and b, adding them, then taking the absolute value, resulting in 13.

The question asks us to evaluate the expression |c2 + b2|, given that a = 5, b = -3, and c = -2. The vertical bars indicate that we are dealing with the absolute value, which means we want the positive result of the expression inside the bars.

First, substitute the given values into the expression, we get |-22 + (-3)2| which is |4+9|.

Second, add the squares of c and b together to get 13.

Finally, since the absolute value of 13 is still 13, this is our answer, corresponding to option D.

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We have to find the missing value to the nearest whole number of tan x° =0.9.

Since, tan x° =0.9

To evaluate the missing value of 'x', we will take [tex] \arctan (0.9) [/tex]

So, [tex] x^{\circ}=\arctan (0.9) [/tex]

Now, we will find the value of [tex] \arctan (0.9) [/tex]using the calculator, we get,

[tex] x^{\circ}=\arctan (0.9)=41.9^{\circ}=42^{\circ} [/tex]

So, the missing value of 'x' to the nearest whole number is [tex] 42^{\circ} [/tex].

Answer:

[tex]114.8\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=\frac{1}{2}(b1+b2)h[/tex]

In this problem we have

[tex]b1=12\ ft[/tex]

[tex]b2=15\ ft[/tex]

[tex]h=8.5\ ft[/tex] ----> the height of the trapezoid is the perpendicular distance between the bases

substitute the values

[tex]A=\frac{1}{2}(12+15)(8.5)[/tex]

[tex]A=\frac{1}{2}(27)(8.5)=114.75\ ft^{2}[/tex]

Round to the nearest tenth

[tex]114.75=114.8\ ft^{2}[/tex]

Answer:

114.8 is the answer

Step-by-step explanation:

got it on edgen

Answer:

Option C is correct.

Step-by-step explanation:

Given is :

The value of Ari's rolls of coins is = $113

The coins are pennies, dimes, nickels and quarters.

Total money is represented by = penny + nickle + dime + quarter  All values in dollars are represented by:

113 = .01* pennies + .05* nickles + 0.1* dimes + 0.25* quarters  

Further calculating we get,

113 = .01* 50*penny rolls + .05 * 40*nickle rolls + .1 * 50*dime rolls + .25 * 40*quarter rolls  

[tex]113=.5p+2n+5d+10q[/tex]

where p is the number of penny rolls, n is the number of nickle rolls, d is the number of dime rolls, and q is the number of quarter rolls  

Now checking all the options by putting values.

A. [tex]113=.5(5)+2(8)+5(4)+10(7)[/tex]

[tex]113\neq 108.5[/tex]

B. [tex]113=.5(4)+2(8)+5(7)+10(5)[/tex]

[tex]113\neq 103[/tex]

C. [tex]113=.5(4)+2(8)+5(5)+10(7)[/tex]

[tex]113=113[/tex]

D. [tex]113=.5(5)+2(8)+5(7)+10(4)[/tex]

[tex]113\neq 93.5[/tex]

Therefore, option C is the right option.

The answer to question 13 is (B). [tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]

The answer to question 14 is (A). [tex]\(x - 9\) and \(x + 3\)[/tex]

The answer to question 15 is (A). [tex]\((x - 6)\) and \((x - 5)\).[/tex]

The answer to question 16 is (A). [tex]\((x + 6y)(x + 4y)\).[/tex]

The answer to question 17 is (A).[tex]\(2x - 5\) and \(3x + 4\).[/tex]

The answer to question 18 is (B). [tex]\((5x + 7)\) and \((x - 2)\).[/tex]

To find a simpler form of the product [tex]\((4x - 6y^3)^2\)[/tex], we apply the formula for squaring a binomial, which is [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]. Here, [tex]\(a = 4x\)[/tex] and [tex]\(b = 6y^3\).[/tex]

So, [tex]\((4x - 6y^3)^2 = (4x)^2 - 2(4x)(6y^3) + (6y^3)^2\).[/tex]

Calculating each term, we get:

[tex]\((4x)^2 = 16x^2\),[/tex]

[tex]\(-2(4x)(6y^3) = -48xy^3\),[/tex]

[tex]\((6y^3)^2 = 36y^6\).[/tex]

Putting it all together, we have:

[tex]\(16x^2 - 48xy^3 + 36y^6\).[/tex]

To find the possible dimensions of the rectangle, we need to factor the trinomial [tex]\(x^2 + 6x - 27\).[/tex] We look for two numbers that multiply to -27 and add up to 6. These numbers are 9 and -3.

So, [tex]\(x^2 + 6x - 27 = (x + 9)(x - 3)\).[/tex]

We factor the trinomial [tex]\(x^2 + x - 30\)[/tex] by finding two numbers that multiply to -30 and add up to 1. These numbers are 6 and -5.

So, [tex]\(x^2 + x - 30 = (x - 6)(x + 5)\).[/tex]

To factor [tex]\(x^2 - 10xy + 24y^2\)[/tex], we look for two numbers that multiply to \[tex](24y^2\)[/tex] and add up to -10y. These numbers are -6y and -4y.

So, [tex]\(x^2 - 10xy + 24y^2 = (x - 6y)(x - 4y)\)[/tex].

To find the possible dimensions of the barnyard, we factor the trinomial [tex]\(6x^2 + 7x - 20\).[/tex] We need two numbers that multiply to [tex]\(6 \times -20 = -120\)[/tex] and add up to 7. These numbers are 15 and -8. We then split the middle term accordingly and factor by grouping:

[tex]\(6x^2 + 15x - 8x - 20 = 0\),[/tex]

[tex]\(3x(2x + 5) - 4(2x + 5) = 0\),[/tex]

[tex]\((3x - 4)(2x + 5)\).[/tex]

We factor the trinomial [tex]\(5x^2 - 3x - 14\)[/tex] by finding two numbers that multiply to [tex]\(5 \times -14 = -70\)[/tex] and add up to -3. These numbers are -10 and 7. We then split the middle term accordingly and factor by grouping:

[tex]\(5x^2 - 10x + 7x - 14 = 0\),[/tex]

[tex]\(5x(x - 2) + 7(x - 2) = 0\),[/tex]

[tex]\((5x + 7)(x - 2)\).[/tex]

Final answer:

The value of y, which directly varies with x, is found by first determining the constant of variation when x = 9 and y = 5.4. Using this constant, we calculate the value of y for x = -10, resulting in y = -6.

Explanation:

The value of y directly varies with x, which means the relationship between x and y can be described by the equation y = kx, where k is the constant of variation. Since y = 5.4 when x = 9, we first find the constant of variation as follows: k = y/x = 5.4/9 = 0.6. Now, to find y when x is -10, we use the constant of variation k in the equation: y = kx = 0.6(-10) = -6.

The relationship between y and x is one of direct variation, represented by the equation y = kx, where k is the constant of variation. Given that y = 5.4 when x = 9, the constant k is calculated as 0.6. Applying this constant, when x = -10, the value of y is found to be -6. This process showcases the direct variation principle in determining y based on the given x values and the constant of variation.

The sale price of the chair including tax is $185.5.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, Miles is buying a chair that regularly costs $250.

Today the chair is on sale for 30% off

So, the new cost is 250-30% of 250

= 250 - 30/100 ×250

= 250-75

= $175

The tax rate is 6%

Sale price = 175+6% of 175

= 175+6/100 ×175

= 175+0.06×175

= $185.5

Therefore, the sale price of the chair including tax is $185.5.

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The range is 24 and the interquartile range is the difference between the median of the second-half to the first-half is 8.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The data set below represents the total number of touchdowns a quarterback threw each season for 10 seasons of play.

29, 5, 26, 20, 23, 18, 17, 21, 28, 20

Arrange in ascending order, we have

5, 17, 18, 20, 20, 21, 23, 26, 28, 29

The range will be given as

→ Range = 29 - 5 = 24

The interquartile range will be given as

→ Interquartile range = median of second-half - median of first-half

→ Interquartile range = 26 - 18

→ Interquartile range = 8

The range is 24 and the interquartile range is 8.

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Answer:

Table 1

Step-by-step explanation:

We have the function [tex]f(x)=8(\frac{1}{4})^{x}[/tex].

Now, the function g(x) is obtained by reflecting f(x) across y-axis.

i.e. g(x) = f(-x)

i.e. [tex]g(x)=8(\frac{1}{4})^{-x}[/tex]

So, substituting the values of x in f(x) or g(x), we will discard some options.

2. For x=0, the value of [tex]f(0)=8(\frac{1}{4})^{0}[/tex] i.e. f(0) = 8.

As in table 2, f(0) = 0 is given, this is not correct.

3. For x=0, the value of [tex]g(0)=8(\frac{1}{4})^{-0}[/tex] i.e. g(0) = 8.

As in table 3, g(0) = -8 is given, this is not correct.

4. For x=0, the value of [tex]g(0)=8(\frac{1}{4})^{-0}[/tex] i.e. g(0) = 8.

As in table 3, g(0) = 0 is given, this is not correct.

Thus, all the tables 2, 3 and 4 do not represent these functions.

Hence, table 1 represents f(x) and g(x) as the values are satisfied in this table.

We have been given that the formula for the force of gravity pulling on the bob is given by [tex] F=m\times g\times sin(\theta) [/tex]), where g is equal to[tex] 9.8m/s^2 [/tex].

Now, we have been given that the mass of the bob of the pendulum is 0.01 kg and that the pendulum makes 22.5 degree angle with the vertical.

Thus, applying the given values in the formula of the given in the question, we get the formula to be:

[tex] F=m\times g\times sin(\theta)=0.01\times9.8\times sin(22.5^{\circ}) [/tex]

[tex] \therefore F\approx0.0375 [/tex] N

Answer: 10

Step-by-step explanation:

Solution :

Given that, Celia earned $5.00.

She saved $1.00 and spent the rest.

To find the ratio of the amount saved to the amount spent , we must first calculate the amount spent.

To calculate the amount spent, subtract the amount saved from the total money earned.

Amount spent by Celia = amount earned - amount saved [tex] = 5-1 = 4 [/tex]

[tex] ratio= \frac{amount\:saved}{ amount\:spent} =\frac{1}{4} \\
\\
ratio= 1:4 [/tex]

Hence, 1:4 is the ratio of the amount saved to the amount spent.

Answer:

2475 cm

Step-by-step explanation:

We are given that Roberto's toy car travels 40 cm/sec at high speed and 25 cm/sec at low speed.

We have to find that the distance would have the car traveled

Speed of car at high speed=40 cm/sec

Speed of car at low speed=25 cm/sec

If car  takes time to travel at high speed=30 seconds

If car takes time to travel  at low speed=51 seconds

[tex]Distance=speed\times time[/tex]

Using this formula

Distance traveled by the car at high speed=[tex]40\times 30=1200 cm[/tex]

Distance traveled by the car at low speed=[tex]51\times 25=1275 cm[/tex]

Total distance traveled by the car =1200+1275=2475 cm

Hence, the distance  would have traveled by the car=2475 cm

Answer:  B

Step-by-step explanation: