Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings.

Hey!

91 ÷ 7 = 13

So, we know that Luke paints one portrait every week.

13 × 4 = 52

So, Luke paints 52 portraits in 4 weeks.

First, we can calculate the number if portraits he can paint in one week.
We can do this by simply dividing the total portraits by the weeks needed.

91 ÷ 7
=13

Now, to calculate the number of portraits he can paint in 4 weeks, just multiply the total number of paintings he can do in a week by 4.

13 x 4
=52
So the answer is 52 portraits.

The amount earned per hour

The number of hours would be the independent (x-value), while the total amount you earn is the dependent variable.

Okay. So, 1,000 = 1 kilometer. To find the speed in meters, do 96.5 * 1,000. When you do that, you get 96,500 meters. The cheetah's speed is 96,500 meters per hour. But, it asks for the speed per second, so we're not done yet. 3,600 seconds equal 1 hour. Let's do 96,500/3,600. The quotient for that problem is 26.80555556 as shown on the calculator or 26.8 when rounded to the nearest tenth. The cheetah's speed in meters per second is 26.8.

20 students....mean score of exam was 81...

x / 20 = 81
x = 81 * 20
x = 1620....this is the total of all the grades added up

(1620 - x) / 19 = 85
1620 - x = 85 * 19
1620 - x = 1615
-x = 1615 - 1620
-x = - 5
x = 5 <=== weird answer...but thats what I am getting

The value of the unreadable score is [tex]5[/tex]

It should be noted that the mean of numbers simply means the average of the numbers.

Since the mean score of the 20 students was 81, then the total score will be: [tex]= 20 * 81= 1620[/tex]

Then, since the mean score of the 19 students was 85, their total scores will be: = [tex]19 * 85 = 1615[/tex]

The value of the unreadable score will be:

[tex]= 1620 - 1615 = 5[/tex].

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[tex]\bf \cfrac{\quad \frac{9}{y}\quad }{\frac{6}{y-7}}\implies \cfrac{9}{y}\cdot \cfrac{y-7}{6}\implies \cfrac{9}{6}\cdot \cfrac{y-7}{y}\implies \cfrac{3}{2}\cdot \cfrac{y-7}{y}\implies \cfrac{3y-21}{2y}[/tex]

[tex]\bf cos\left(\cfrac{{{ \theta}}}{2}\right)=\pm \sqrt{\cfrac{1+cos({{ \theta}})}{2}}\\\\ -------------------------------\\\\ \cfrac{\pi }{12}\cdot 2\implies \cfrac{\pi }{6}\qquad therefore\qquad \cfrac{\quad \frac{\pi }{6}\quad }{2}\implies \cfrac{\pi }{12}\qquad then \\\\\\ cos\left( \frac{\pi }{12} \right)\implies cos\left( \cfrac{\frac{\pi }{6}}{2} \right)=\pm\sqrt{\cfrac{1+cos\left( \frac{\pi }{6} \right)}{2}}[/tex]

[tex]\bf cos\left( \cfrac{\frac{\pi }{6}}{2} \right)=\pm\sqrt{\cfrac{1+\frac{\sqrt{3}}{2}}{2}}\implies cos\left( \cfrac{\frac{\pi }{6}}{2} \right)=\pm\sqrt{\cfrac{\frac{2+\sqrt{3}}{2}}{2}} \\\\\\ cos\left( \cfrac{\frac{\pi }{6}}{2} \right)=\pm\sqrt{\cfrac{2+\sqrt{3}}{4}}\implies cos\left( \cfrac{\frac{\pi }{6}}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{\sqrt{4}} \\\\\\ cos\left( \cfrac{\frac{\pi }{6}}{2} \right)=\pm\cfrac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Answer:

[tex]\cos \left(\frac{\pi }{12}\right)=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Step-by-step explanation:

To find the exact value of [tex]\cos \left(\frac{\pi }{12}\right)[/tex] using half angle identities you must:

Write [tex]\cos \left(\frac{\pi }{12}\right)[/tex] as [tex]\cos \left(\frac{\frac{\pi }{6}}{2}\right)[/tex]

Using the half angle identity [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]

[tex]\cos \left(\frac{\frac{\pi }{6}}{2}\right)=\sqrt{\frac{1+\cos \left(\frac{\pi }{6}\right)}{2}}[/tex]

Use the following identity: [tex]\cos \left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}[/tex]

[tex]\sqrt{\frac{1+\cos \left(\frac{\pi }{6}\right)}{2}}=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}[/tex]

Join [tex]1+\frac{\sqrt{3}}{2}[/tex]

[tex]1+\frac{\sqrt{3}}{2}=\frac{1\cdot \:2}{2}+\frac{\sqrt{3}}{2}=\frac{2+\sqrt{3}}{2}[/tex]

[tex]\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}=\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2} } =\sqrt{\frac{2+\sqrt{3}}{4}} =\frac{\sqrt{2+\sqrt{3}}}{\sqrt{4}}=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

Therefore,

[tex]\cos \left(\frac{\pi }{12}\right)=\frac{\sqrt{2+\sqrt{3}}}{2}[/tex]

The common ratio of the geometric sequence is: 2/3.

Common Ratio of a Geometric Sequence

Common ratio, r = a term divided by the consecutive term in the series.

Given the geometric sequence, 54,36,24,16...

common ratio (r) = 16/24 = 2/3.

24/36 = 2/3.

36/54 = 2/3.

Therefore, the common ratio of the geometric sequence is: 2/3.

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If Justin sold 300 liters of soda, then he would have sold 300000 milliliters of soda. 1 liter= 1000 milliliters

Answer:

300,000 mililiters

Step-by-step explanation:

Remember that in international system the convertions are really easy because they are done 10 by 10, so from liters to mili, there are 3 spots, 1000, so there are 1000 mili-liters in a liter, so you just need to multiply the 300 liters of soda by 1000, which is 300,000 mililiters and that is what Justin sold at the baseball game in mililiters.

Final answer:

The equation of the central street PQ can be found by using the negative reciprocal of the slope of the given street and a point on the central street. The equation is y - 4 = (-3/7)(x + 1).

Explanation:

To find the equation of the central street PQ, we need to determine the slope and y-intercept of the given equation. The equation -7x + 3y = -21.5 can be rearranged to y = (7/3)x - 21.5/3, which means the slope is 7/3 and the y-intercept is -21.5/3. Since the central street is perpendicular to the given street, its slope will be the negative reciprocal of 7/3, which is -3/7. Using the point-slope form of a line equation, we can write the equation of the central street PQ using point P(-1, 4) as follows:

y - 4 = (-3/7)(x + 1)

We can simplify this equation further if required.

Final answer:

To find the equation of street PQ, one must understand that parallel streets share the same slope, while perpendicular streets have slopes that are negative reciprocals. The given street AB has a slope of 7/3. The slope of PQ will either be 7/3 (if parallel) or -3/7 (if perpendicular), and additional information is needed to determine its y-intercept.

Explanation:

The subject question involves finding the equation of a street that is either parallel or perpendicular to another street, given in the form of a linear equation. The given equation of the street passing through points A and B is -7x + 3y = -21.5. To determine the equation of the central street PQ, which is either parallel or perpendicular, we need to use concepts of slope.

In the case of a parallel street, the slope must be the same as the slope of the given street, while for a perpendicular street, the slope would be the negative reciprocal of the given street's slope. Since we're not given additional information about the relationship between AB and PQ, we can only speculate based on the slope. The slope-intercept form of an equation, y = mx + b where 'm' represents the slope and 'b' represents the y-intercept, is useful in determining the proper equation for street PQ.

For the given equation, -7x + 3y = -21.5, we first need to rewrite it in slope-intercept form to identify the slope: 3y = 7x - 21.5, which simplifies to y = (7/3)x - 7.17. Here, the slope of the line is (7/3). Thus, the slope of street PQ will be either (7/3) if it's parallel, or -3/7 if it's perpendicular. To find the exact equation, we would need a point that street PQ passes through.

15/8 = 1.875 ft per piece....so each piece is just short of 2 ft

Divide 15 by 8 to get 1.875. Each piece is 1.875 feet long.

Please give me brainliest answer.

Final answer:

The probability that a chosen ball came from Urn B, given that it was a yellow ball, is 20%, which isn't reflected in any of the provided options, making (f) None of the above the right answer.

Explanation:

To answer the question, we first need to calculate the total number of yellow balls in all urns, which is, 8 (from Urn A) + 3 (from Urn B) + 4 (from Urn C) = 15. But we are interested only in the case where the yellow ball came from Urn B, the number of which is 3. So, the probability that a yellow ball came from Urn B represents the ratio of the number of yellow balls in Urn B to the total number of yellow balls. Thus, the probability would be calculated as 3 (yellow balls in Urn B) / 15 (total yellow balls) = 0.20 or 20%. Therefore, the correct answer in the given options is (f) None of the above.

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Answer:

[tex]\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta) = 0[/tex]

General Formulas and Concepts:

Pre-Calculus

Unit Circle

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta)[/tex]

Step 2: Evaluate

Limit Rule [Variable Direct Substitution]:                                                    [tex]\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta) = \sin(0) \cdot 0 + tan(0)[/tex]Simplify:                                                                                                         [tex]\displaystyle \lim_{\theta \to 0} \sin (3\theta)\theta + \tan (4\theta) = 0[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Assuming that   4^2-6(2^x)-16=0   is correct, we can rearrange it as:

-6(2^x) + 4^2 - 16=0

Are you sure it's not   6(2^x) + 4^2 - 16=0  ?

If   6(2^x) + 4^2 - 16=0    is correct, then

6(2^x) + 4^2 - 16=16 - 16 = 0, that is,   6(2^x) = 0.  Then x = 0 (answer)

The answer is the option B. rotate 90 degrees counterclokwise and then rotate 270 degrees counterclockwise.

See that two consecutive rotations counterclockwise are equivalent to one single roration counterclockwise as long as the angles sum up the same.

Given that 90° + 270 ° = 360° means that the two rotaions are equivalent to one 360° rotation, and so the final figure will be the same as the original figure.

The answer for this question would be B) Identify property of multiplication or the second option because since the result 20 is the same as the 20 multiplied against 1. * I take no credit for the image below I just found it off google. ✅

Final answer:

The equation 20 x 1 = 20 demonstrates the Identity Property of Multiplication, which states that multiplying any number by one keeps its original value.

Explanation:

The property shown in the following equation 20 x 1 = 20 is the Identity Property of Multiplication. This property states that any number multiplied by one remains unchanged or that the number keeps its identity. The option B, Identify property of multiplication, is a typo, and it likely means to refer to the Identity Property of Multiplication. The options A, C, and D describe different properties that do not apply to this equation.

The Zero Property of Multiplication involves a multiplication where any number times zero is zero. The Negative One Property of Multiplication is not a standard mathematical property and seems to be a non-existent or misspelled option. The Identity Property of Division is not applicable as there is no division taking place in this equation.

To answer your first question: Whenever you convert from rectangular to polar coordinates, the differential element will *always* change according to

[tex]\mathrm dA=\mathrm dx\,\mathrm dy\implies\mathrm dA=r\,\mathrm dr\,\mathrm d\theta[/tex]

The key concept here is the "Jacobian determinant". More on that in a moment.

To answer your second question: You probably need to get a grasp of what the Jacobian is before you can tackle a surface integral.

It's a structure that basically captures information about all the possible partial derivatives of a multivariate function. So if [tex]\mathbf f(\mathbf x)=(f_1(x_1,\ldots,x_n),\ldots,f_m(x_1,\ldots,x_n))[/tex], then the Jacobian matrix [tex]\mathbf J[/tex] of [tex]\mathbf f[/tex] is defined as

[tex]\mathbf J=\begin{bmatrix}\mathbf f_{x_1}&\cdots&\mathbf f_{x_n}\end{bmatrix}=\begin{bmatrix}{f_1}_{x_1}&\cdots&{f_m}_{x_n}\\\vdots&\ddots&\vdots\\{f_m}_{x_1}&\cdots&{f_m}_{x_n}\end{bmatrix}[/tex]

(it could be useful to remember the order of the entries as having each row make up the gradient of each component [tex]f_i[/tex])

Think about how you employ change of variables when integrating a univariate function:

[tex]\displaystyle\int2xe^{x^2}\,\mathrm dr=\int e^{x^2}\,\mathrm d(x^2)\stackrel{y=x^2}=\int e^y\,\mathrm dy=e^{r^2}+C[/tex]

Not only do you change the variable itself, but you also have to account for the change in the differential element. We have to express the original variable, [tex]x[/tex], in terms of a new variable, [tex]y=y(x)[/tex].

In two dimensions, we would like to express two variables, say [tex]x,y[/tex], each as functions of two new variables; in polar coordinates, we would typically use [tex]r,\theta[/tex] so that [tex]x=x(r,\theta),y=y(r,\theta)[/tex], and

[tex]\begin{cases}x(r,\theta)=r\cos\theta\\y(r,\theta)=r\sin\theta\end{cases}[/tex]

The Jacobian matrix in this scenario is then

[tex]\mathbf J=\begin{bmatrix}x_r&y_\theta\\y_r&y_\theta\end{bmatrix}=\begin{bmatrix}\cos\theta&-r\sin\theta\\\sin\theta&r\cos\theta\end{bmatrix}[/tex]

which by itself doesn't help in integrating a multivariate function, since a matrix isn't scalar. We instead resort to the absolute value of its determinant. We know that the absolute value of the determinant of a square matrix is the [tex]n[/tex]-dimensional volume of the parallelepiped spanned by the matrix's [tex]n[/tex] column vectors.

For the Jacobian, the absolute value of its determinant contains information about how much a set [tex]\mathbf f(S)\subset\mathbb R^m[/tex] - which is the "value" of a set [tex]S\subset\mathbb R^n[/tex] subject to the function [tex]\mathbf f[/tex] - "shrinks" or "expands" in [tex]n[/tex]-dimensional volume.

Here we would have

[tex]\left|\det\mathbf J\right|=\left|\det\begin{bmatrix}\cos\theta&-r\sin\theta\\\sin\theta&r\cos\theta\end{bmatrix}\right|=|r|[/tex]

In polar coordinates, we use the convention that [tex]r\ge0[/tex] so that [tex]|r|=r[/tex]. To summarize, we have to use the Jacobian to get an appropriate account of what happens to the differential element after changing multiple variables simultaneously (converting from one coordinate system to another). This is why

[tex]\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]

when integrating some two-dimensional region in the [tex]x,y[/tex]-plane.

Surface integrals are a bit more complicated. The integration region is no longer flat, but we can approximate it by breaking it up into little rectangles that are flat, then use the limiting process and add them all up to get the area of the surface. Since each sub-region is two-dimensional, we need to be able to parameterize the entire region using a set of coordinates.

If we want to find the area of [tex]z=f(x,y)[/tex] over a region [tex]\mathcal S[/tex] - a region described by points [tex](x,y,z)[/tex] - by expressing it as the identical region [tex]\mathcal T[/tex] defined by points [tex](u,v)[/tex]. This is done with

[tex]\mathbf f(x,y,z)=\mathbf f(x(u,v),y(u,v),z(u,v))[/tex]

with [tex]u,v[/tex] taking on values as needed to cover all of [tex]\mathcal S[/tex]. The Jacobian for this transformation would be

[tex]\mathbf J=\begin{bmatrix}x_u&x_v\\y_u&y_v\\z_u&z_v\end{bmatrix}[/tex]

but since the matrix isn't square, we can't take a determinant. However, recalling that the magnitude of the cross product of two vectors gives the area of the parallelogram spanned by them, we can take the absolute value of the cross product of the columns of this matrix to find out the areas of each sub-region, then add them. You can think of this result as the equivalent of the Jacobian determinant but for surface integrals. Then the area of this surface would be

[tex]\displaystyle\iint_{\mathcal S}\mathrm dS=\iint_{\mathcal T}\|\mathbf f_u\times\mathbf f_v\|\,\mathrm du\,\mathrm dv[/tex]

The takeaway here is that the procedures for computing the volume integral as opposed to the surface integral are similar but *not* identical. Hopefully you found this helpful.

what function can you post it please and thank you

Final answer:

To find local maxima, minima, and saddle points, find critical points using the first derivative test and then apply the second derivative test.

Explanation:

To find the local maxima, local minima, and saddle points of a function, we first need to find the critical points. These are the points where the derivative of the function is either zero or undefined. To check whether each critical point is a local maxima, local minima, or saddle point, we use the second derivative test.

The second derivative test states that if the second derivative is positive at a critical point, then the point is a local minimum. If the second derivative is negative, then the point is a local maxima. If the second derivative is zero, the test is inconclusive.

By applying the second derivative test to each critical point, we can determine whether it is a local maxima, local minima, or saddle point.

2/5 are in band...of those, 1/4 play saxophone....so 1/4 of 2/5 play saxophone....." of " means multiply

1/4 * 2/5 = 2/20 which reduces to 1/10 <== 1/10 play saxophone

Answer:

1/10=10%

Step-by-step explanation:

In order to calculate this you just have to multiply the fraction of kids of your class that are in the ban by the number of kids that play the saxophone from those kids that are in the band:

[tex]\frac{2}{5} *\frac{1}{4}\\\frac{2*1}{4*5}\\\frac{2}{20}=\frac{1}{10}  \\\frac{1}{10}[/tex]

So we know that 1/10 or 1 out of 10 kids in your class play saxophone in the band, or 10%of the class plays saxophone in the band.

Given

A road trip with these parameters

total distance 2240 midistance per day 650 micost per night for lodging $85mileage 28 mpggas price $3/galFind1/4 of the cost of gas and lodgingSolution

The cost of gas is ...

... (2240 mi)/(28 mi/gal)·($3/gal) = $240

The cost of lodging is

... ($85/day)·floor(2240 mi/(650 mi/day)) = $85·3 = $255

Total cost of gas and lodging is $240 +255 = $495.

The cost for a 1/4 share is $495/4 = $123.75.

(10 1/2) / (1 3/4) =
10.50 / 1.75 =
6 <== he can make 6 banners

Answer:

6

Step-by-step explanation:

I took the k12 2.12 Quiz: Divide Fractions

B is the correct answer. If you use the distributive property correctly you will see why.

(4x+3)(2x+1)= 8x^2+4x+6x+3
= 8x^2+10x+3


please vote my answer brainliest. thanks!

east bound train = x

westbound train = x-20 ( 20 miles slower than east bound)

5x + 5(x-20) = 750

5x +5x -100=750

10x -100 = 750

10x =850

x = 850/10 = 85

east bound train is 85 mph

west bound train is 85-20 = 65 mph

check: 85*5 = 425

65*5 = 325

325+425 = 750

Supposing, for the sake of illustration, that the mean is 31.2 and the std. dev. is 1.9.

This probability can be calculated by finding z-scores and their corresponding areas under the std. normal curve.  
                                                                     34 in - 31.2 in
The area under this curve to the left of z = -------------------- = 1.47 (for 34 in)
                                                                           1.9
                                                                      32 in - 31.2 in
and that to the left of 32 in   is               z = ---------------------- = 0.421
                                                                             1.9

Know how to use a table of z-scores to find these two areas?  If not, let me know and I'll go over that with you.


My TI-83 calculator provided the following result:

normalcdf(32, 34, 31.2, 1.9) = 0.267  (answer to this sample problem)

Take that pi = 3.142

pi r = 9.42
r = 9.42/3.142 = 2.998
d = 2 x 2.998 = 5.996
Cricumference = 3.142 x 5.996 = 18.839 cm

You need to get the radius then multiply by 2 to get the diameter then you can get the circumference.

The answer would be A! :)

Hello there~

-18x - 45 = -12

Let's start by adding 45 to both sides

-18x - 45 + 45 = -12 + 45

-18x = 33

Then divide both sides by -18

-18x/-18 = 33/-18

x = -11/6

I hope this helps!

The exact average speed when x = 56 seconds is approximately 30.86 mph.

To use linear approximation to approximate a person's average speed if they travel one mile in 56 seconds, we'll first find the derivative of the function [tex]\( s(x) = \frac{3600}{60 + x} \)[/tex] with respect to x.

[tex]\[ s'(x) = -\frac{3600}{(60 + x)^2} \][/tex]

Now, we'll evaluate the derivative at x = 0 to find the slope of the tangent line at that point, which will be our linear approximation.

[tex]\[ s'(0) = -\frac{3600}{(60 + 0)^2} = -\frac{3600}{3600} = -1 \][/tex]

So, the slope of the tangent line at x = 0 is -1.

Now, using the point-slope form of the equation of a line, we'll find the equation of the tangent line at x = 0:

y - s(0) = s'(0)(x - 0)

[tex]\[ y - s(0) = -1 \cdot x \][/tex]

y = -x + s(0)

We know that s(0) is the exact speed at x = 0, so we'll substitute x = 0 into the original function to find it:

[tex]\[ s(0) = \frac{3600}{60 + 0} = 60 \text{ mph} \][/tex]

So, the equation of the tangent line is:

y = -x + 60

Now, to approximate the average speed when x = 56, we'll substitute x = 56 into the equation of the tangent line:

y = -56 + 60 = 4

So, the approximate average speed when x = 56 seconds is 4 mph.

To find the exact speed, we'll substitute x = 56 into the original function s(x):

[tex]\[ s(56) = \frac{3600}{60 + 56} = \frac{3600}{116} \approx 30.86 \text{ mph} \][/tex]

So, the exact average speed when x = 56 seconds is approximately 30.86 mph.

Give me a heart and I'll tell you the answer

Answer:

5/2

Step-by-step explanation:

Start by eliminating parentheses.

... 2n +4 +6 = -9 +8n +4

... 10 = -5 +6n . . . . subtract 2n

... 15 = 6n . . . . . . . add 5

... 15/6 = n = 5/2

_____

Check

(2·5/2 +4) +6 = -9 +4(2·5/2 +1)

5 +4 +6 = -9 +4(5 +1)

15 = -9 +24 . . . . . true, so the answer checks OK

Answer:

THE ANSWER IS 1

Step-by-step explanation:

Final answer:

To calculate the second moment of area for a 4-inch diameter shaft about the x-x and yy axes, we use the formula I = π * d^4 / 64 and find that I = 4 * π in´ for both axes.

Explanation:

The student is asking for the calculation of the second moment of area, also known as the moment of inertia, for a shaft with a 4-inch diameter about both the x-x and yy axes.

The moment of inertia of a circular cross-section about its centroidal axis is calculated using the formula I = π * d^4 / 64, where d is the diameter of the shaft. In this case, the diameter d is given as 4 inches.

To calculate the second moment of area for the 4-inch diameter shaft, we substitute the diameter into the formula to get:

I = π * (4 in)^4 / 64 = π * 256 in´ / 64 = 4 * π in´.

So, the moment of inertia for both the x-x and yy axes would be the same and equal to 4 * π in´, since the shaft is symmetrical about these axes.

Answer and explanation included in the photo