Josie buys o purse that costs $64.95. If the sales tax is 5.5%, what is the cost of the tax.​

let's firstly convert the mixed fractions to improper fractions.

\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)

Answer:

f(4)=9

Step-by-step explanation:

The given function is

F(x)=3x-3

so,

f(4)=3*4-3

f(4)=12-3

f(4)=9

putting 4 in place of x we get answer of the question.

Answer:

TWO CRACKERS

Step-by-step explanation:

I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.

Hope this helped

Using the exponential function T = 18 + 68e^(-t/8), the initial temperature is 86°C, the time the temperature will reach 35°C is 11.1 minutes

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form f(x) = aˣ

In the question given, the exponential function given shows an exponential decay

T = 18 + 68e^(-t/8)

a) The initial temperature when the tea was poured would be (t = 0)

T = 18 + 68e^(-0/8)

T = 16 + 68 = 86°C

b) The temperature of the tea at 35°C

35 = 18 + 68e^(-t / 8)

T = 11.1

c) The reason why the the tea will never reach 15°C is because there's no solution for the expression.

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Answer: \(V=x^3-2x^2+13x-12\)

Step-by-step explanation:

Given

The area of the base is given by \(b(x)=x^2-x+12\)

The height of the container is \(h(x)=x-1\)

The volume of the cylindrical container is

\(V=Area\times height\)

Insert the values

\(\Rightarrow V=\left( x^2-x+12\right)\cdot \left(x-1\right)\\\Rightarrow V=x^3-x^2+12x-x^2+x-12\\\Rightarrow V=x^3-2x^2+13x-12\)

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

\( { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} \)

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

\( \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}\)

- Therefore, the equation is;

\({ \boxed{ \tt{y = - 2x}}}\)

- What is x when y is 15

\({ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}\)

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = \(\frac{-15}{3}\)

                        x = -5

Therefore, when y = 15, x = -5.

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Answer:

D

Step-by-step explanation:

When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"

If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))

Answer:

  II.  2198₁₆

Step-by-step explanation:

You want the product of D7 and 28 in hexadecimal.

  D7₁₆ × 28₁₆ = D7₁₆ × 20₁₆ + D7₁₆ × 8

  = 1AE0₁₆ +6B8₁₆ = 2198₁₆

__

Additional comment

A suitable calculator can figure this for you.

Here the multiplication can take advantage of the limited number of '1' bits in the binary representation of 28₁₆. Effectively, we only need to double D70 and halve D70 and add those values together.

The relevant decimal equivalents are A=10, B=11, D=13, E=14.

As with any place-value number system, numbers 1 place to the left have 16 times their value before shifting, where the base of the number system is 16.

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The Distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

The distance the handler will move from the starting point to the return point when creating an arc of a circle with a radius of 70 feet, we need to find the length of the arc.

The formula to calculate the length of an arc is given by:

Length of arc = (θ/360) * 2πr

Where:

θ is the central angle of the arc (in degrees)

r is the radius of the circle

In this case, since the handler is creating a full circle, the central angle is 360 degrees.

Length of arc = (360/360) * 2π * 70

Length of arc = (1) * 2π * 70

Length of arc = 2π * 70

Length of arc = 140π

To find the approximate value in feet, we can use the approximation π ≈ 3.14159.

Length of arc ≈ 140 * 3.14159

Length of arc ≈ 439.8204 feet

Therefore, based on the given theory and using a circle with a radius of 70 feet, the distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

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Pareto chart is a type of bar graph which often displays the data in descending order of frequency.

It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.

For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.

Toga: 6

Hayride: 6 + 4 = 10

Beer Bash: 10 + 8 = 18

Masquerade: 18 + 2 = 20

The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.

Toga: 6 (30%)

Hayride: 10 (50%)

Beer Bash: 18 (90%)

Masquerade: 20 (100%)

Hence, the Pareto chart for the given data is as follows:

Toga: 30%

Hayride: 20%

Beer Bash: 40%

Masquerade: 10%

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Answer:

0.05%

Step-by-step explanation:

Answer:

zero ( 0)

Step-by-step explanation:

The number that best represents sea level has always been 0. This is because sea level is meant to represent where the initial point where dry land meets the sea all around the world. Seeing since 0 is the universal neutral number which is neither positive or negative, it acts as the perfect number for sea level. Any elevation above sea level is in the positives while elevations under sea level would be in the negatives since it is lower than sea level and lower than 0 is negatives.

Here, we are required to suggest a number which might be a good representation for the sea level.

Such quantifications may

fall below or above sea

level.

Therefore, a number which might be a good representation for the sea level is zero (0).

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Answer:

The 48-ounce carton is the cheapest

Step-by-step explanation:

The question gives us the prices of different sizes of bottles of orange juice. It then asks us to calculate the price per ounce for each size and to find which size is the cheapest.

In order to calculate the price per ounce for each size, we have to divide the price of each size by its size:

• 8-ounce bottle:    \(\mathrm{\frac{\$ 0.90}{8 \ oz}}\) = $0.113 / oz

• 18-ounce bottle:  \(\mathrm{\frac{\$ 1.50}{18 \ oz}}\) = $0.083 / oz

• 48-ounce bottle:  \(\mathrm{\frac{\$ 2.50}{48 \ oz}}\) = $0.052 / oz

• 64-ounce bottle:  \(\mathrm{\frac{\$ 3.75}{64 \ oz}}\) = $0.059/ oz

As we can see from the calculation above, the price per ounce of the 48-ounce carton is the lowest, at $0.052 / oz.

As per the circumference of a circle, the length of the paper is 176 mm.

The circumference of a circle is the total arc length of it.

The diameter of the pencil is(d) 7 mm

Therefore, the radius of the pencil is(r)

\(= \frac{d}{2} \\= 7/2 mm\\= 3.5 mm\)

Now, the circumference of the cross-section of the pencil is

\(= 2\)(π)r units

\(= (2) (22/7) (3.5) mm\\= 22 mm\)

Therefore, the length of the paper is

= (circumference of the cross-section of the pencil) × 8 units

\(= (22) (8) mm\\= 176 mm\)

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Answer:

28

Step-by-step explanation:

-3 * (x-11) = -51

x-11 = 17

x = 28

Answer:

A=(n * s * a) 2A=(n*s*a)2

Step-by-step explanation:

A=(n * s * a) 2A=(n*s*a)2 where n is the number of sides, s is the length of one side and a is the apothem

Answer:

2.38

Step-by-step explanation:

William wish1wish woman weeks whereby when wishful willful

As you may know, the 8 would be located in the hundreaths place.

2.3892

If the number right of 8 is five for less, it says the same. If it's 5 or more, then 8 would change. In this case, 9 is more than 5 meaning that 8 becomes 9. However, we aren't quite finished yet. 9 and everything left of that number must become 0.

Your answer would be 2.39.

Answer:

the answer to that question is 6x squared.

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

12x and 18x3

first, simplify 18x3

12x and 54x

Now, cancel the x, we'll add it on in the end

12 and 54

Factor it!

(2 * 3 * 2) and (2 * 3  * 3 * 3)

2 and 3 remain common, so multiply = 6

Add on x from before.

6x is the answer.

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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Answer:

n=4 x=4

Step-by-step explanation:

3-5 = -2

12-20 = -8

find their what they have in common = 4

12·4= 48

3·4= 12

rearrange = 48-20 = n (12-5)

we should end up with 28 = n · 7

now we just need to figure out what ? · 7 = 28 which is 4

n = 4

I'm not sure if I did this correctly but I hope it helps

The percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The total number of water bottles the company manufactured in February, March, and April.

In February, the company manufactured 4,100 water bottles. In March, the company manufactured 7% more water bottles than in February, which is 7/100 * 4,100 = 287 water bottles.

Therefore, the total number of water bottles the company manufactured in March is 4,100 + 287 = 4,387 water bottles. In April, the company manufactured 500 more water bottles than in March, which is 4,387 + 500 = 4,887 water bottles.

This is calculated as (4,887 - 4,100) / 4,100 = 0.195 or 19.5%.

Therefore, the percent change in the number of water bottles the company manufactured from February to April is 19.5%, to the nearest percent.

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1. The difference in the distance of Jupiter from the sun than Mercury will be 4.816.

2. The difference in the distance of Neptune from the sun than Mars will be

3. The greatest distance between Earth and Uranus is Uranus.

4. The greatest distance between Venus and Saturn is Saturn

From the information, the average distance from the sun to each planets have been given. The difference in the distance of Jupiter from the sun than Mercury will be:

= 5.203 - 0.387

= 4.816

The difference in the distance of Jupiter from the sun than Mars will be:

= 30.07 - 1.524

= 28.546

The greatest distance between Earth and Uranus is Uranus and the greatest distance between Venus and Saturn is that of Saturn.

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Answer:

a

\(0.0028  < p_1 - p_2  < 0.0288\)

b

The  interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack  and the non-Vioxx users (the placebo group  ) who suffered from heart attack  lie within the interval

The  use of Vioxx drug should be stopped

Step-by-step explanation:

From the question we are told that

   The sample size for Vioxx users is  \(n_1 = 3025\)

   The second sample size for placebo is  \(n_2 =  2875\)

   The number of Vioxx users that suffered heart attack is  \(k  = 334\)

     The number of non-Vioxx users that suffered heart attack is  \(g  = 272\)

    Generally the  sample proportion for Vioxx users is mathematically represented as

      \(\r p_1 =  \frac{k}{n_1}\)

=>   \(\r p_1 =  \frac{334}{3025}\)

=>   \(\r p_1 =  0.11041 \)

    Generally the  sample proportion for placebo users is mathematically represented as

       \(\r p_2 =  \frac{g}{n_2}\)

=>   \(\r p_2 =  \frac{272}{2875}\)

=>   \(\r p_2 =  0.09461 \)  

Generally the confidence level is 90% , then the level of significance is  \(\alpha =  (100-90)\%\)

=>   \(\alpha =  0.10\)

Generally the critical value of  \(\frac{\alpha }{2}\) from the normal distribution table  is  

     \(Z_{\frac{\alpha }{2} } =  1.645\)

Generally the standard error is mathematically represented as

      \(SE =  \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }\)

=>  \(SE =  \sqrt{\frac{0.11041 (1- 0.11041)}{3025} + \frac{0.09461 (1-0.09461)}{2875} }\)

=>  \(SE = 0.0079\)

Generally the margin of error is mathematically represented as

    \( E=  Z_{\frac{\alpha }{2} } *  SE\)

=>  \( E=  1.645  *  0.0079\)  

=>  \( E=  0.013\)  

Generally the 90%  confidence interval is mathematically represented as

     \(0.11041 - 0.09461- 0.013 < p_1 - p_2  < 0.11041 - 0.09461+ 0.013 \)

=>       \(0.0028  < p_1 - p_2  < 0.0288\)

The  interval means that there is 90% confidence that the true difference between the proportion of Vioxx users who suffered from heart attack  and the non-Vioxx users (the placebo group  )  lie within the interval

Looking at the interval we see that proportion of Vioxx users who suffered is  more compared to  non-Vioxx users (the placebo group  )[i.e the both limit of the interval is  positive ] hence the  use of Vioxx drug should be stopped

The value of the limit \(h(x)=\frac{(x-2)^{8}}{x^2+1}\)using the squeeze theorem is 0.

A function rule is an equation-based relationship between dependent and independent variables. How to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, is explained by the function rule of a particular function.

A function that is trapped between two other functions has its limit determined by the squeeze theorem. In calculus and mathematical analysis, the squeeze theorem is frequently applied to verify a function's limit through comparison with two other functions whose limits are known.

As per this theorem, if we are required to find the limit \(\lim_{x \to c} h(x)\) and if we have f ( x ) ≤ h ( x ) ≤ g ( x ) and the limits \(\lim_{x \to c} f(x)= \lim_{x \to c} g(x)=L\) . Then the required limit is given as \(\lim_{x \to c} h(x)=L\).

Consider the expression,

\(h(x)=\frac{(x-2)^{8}}{x^2+1}\)

Now the value of the limit:

\(0\leq h(x)\leq x\\0\leq \frac{(x-2)^{8}}{x^{2}+1}\leq x\)

\(\lim_{x \to 2} h(x)= \lim_{x \to 2} \frac{(x-2)^{8}}{x^2+1}\)

\(\lim_{x \to 2} \frac{(x-2)^{8}}{x^2+1}= \lim_{x \to 2} \frac{(2-2)^{8}}{2^2+1}\)

\(\lim_{x \to 2} \frac{(x-2)^{8}}{x^2+1}= \lim_{x \to 2} \frac{(2-2)^{8}}{4+1}\)

\(\lim_{x \to 2} \frac{(x-2)^{8}}{x^2+1}= 0\)

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Answer: 46 miles

Step-by-step explanation:

times the amount of miles driven in one hour by 2