A merchant has coffee worth $60 a pound that she wishes to mix with 50 pounds of coffee worth $90 a pound to get a mixture that she will sell for $70 a pound. How many pounds of the &60 coffee should be used?

Answer:

  1. the range of f^-1(x) is {10, 20, 30}.

  2. the graph of f^-1(x) will include the point (0, 3)

  3. n = 8

Step-by-step explanation:

1. The domain of a function is the range of its inverse, and vice versa. The range of f^-1(x) is {10, 20, 30}.

__

2. See above. The domain and range are swapped between a function and its inverse. That means function point (3, 0) will correspond to inverse function point (0, 3).

__

3. The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

You are given a1 = 2, a12 = 211, so ...

  211 = 2 + d(12 -1)

  209/11 = d = 19 . . . . . solve the above equation for the common difference

Now, we can use the same equation to find n for an = 135.

  135 = 2 + 19(n -1)

  133/19 = n -1 . . . . . . . subtract 2, divide by 19

  7 +1 = n = 8 . . . . . . . . add 1

135 is the 8th term of the sequence.

The answer is:

There will be necessary 13 ounces of salad dressing.

Why?

Since we already know that there will be needed 0.56 ounces of salad dressing per cup, and the recipe calls 2.1 cups of lettuce per person, we need to calculate the total ounces of salad dressing per each person, and then, calculate it for 11 persons.

So, calculating we have:

[tex]SaladDressingPerPerson=Cups*SaladDressing=2.1*0.56oz\\\\SaladDressingPerPerson=1.176oz[/tex]

Therefore, we know that there will be needed 1.176 ounces of salad dressing per person.

Then, calculating the ounces of dressing for 11 dinner guests, we have:

[tex]TotalOunces=SaladDressingPerPerson*NumberOfPersons\\\\TotalOunces=1.176ounces*11=12.94ounces=13ounces[/tex]

Hence, we have that there will be necessary 13 ounces of salad dressing.

Have a nice day!

Answer:

the answer is D

Step-by-step explanation:

The tire has a circumference [tex]24\pi[/tex] inches, or [tex]2\pi[/tex] feet. It has a linear speed of 60 mph, or 88 feet/second. This means that any point on the rim of the tire will have traveled 88 feet in 1 second. We have

[tex]\dfrac{88}{2\pi}=\dfrac{44}\pi\approx14.006[/tex]

which means the tire completes a little over 14 revolutions in 1 second. One complete revolution corresponds to a rotation of 360º. Then its angular speed in degrees per second is

[tex]\left(\dfrac{44}\pi\dfrac{\rm rev}{\rm s}\right)\dfrac{360\,\rm deg}{1\,\rm rev}}=5042\dfrac{\rm deg}{\rm s}[/tex]

Given the car's speed of 60 mph and the tires' diameter of 24 inches, we can convert them to more standard units of meters and seconds. Using the physical concept that the angular speed equals the rate of change of angular displacement, we calculate the angular speed of the tires in radians per second. The result is then converted back to the desired unit of degrees per second, yielding an approximate angular speed of 5041 deg/sec.

To determine the angular speed of the tires, we need to understand some basic physics. First, we should calculate the linear velocity in more standard units. As we know 1 mile is approximately 1609.34 meters, and 1 hour is 3600 seconds, thus we can convert 60 mph into approximately 26.82 meter per second.

Next, the diameter of the tire is given as 24 inches, which is approximately 0.61 meters (as 1 inch = 0.0254 meters), so the radius r of the tire will be half of that, which is about 0.305 meters. The linear speed v of the edge of the tire is equal to the speed of the car, v = 26.82 meter per second.

The angular velocity w is defined as the rate of change of angular displacement with respect to time, which can also be expressed in terms of linear velocity and radius of the circular path as w = v/r. Plugging in our values, we can calculate w to be approximately 87.9 rad/sec.

Now, to convert to degrees per second, we should know that 1 radian is equal to approximately 57.2958 degrees. Therefore, the angular speed of the tire in degree per second is approximately 5041 degrees per second, or rounded to the nearest degree per second, it's approximately 5041 deg/sec.

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Answer:

The total area covered by students is 40 yd x 40 yd = 1600 yd^2

24 students covered 8 ft x 8ft  or (8 ft x 1 yd/3 ft)^2 = [(8/3) yard]^2 = (64/9) yd^2

Therefore, you need the amount of students per yard or 24 students/(64/9) yd^2

and multiply (students/yd^2)  x  (area covered by students) = number of total students present

Therefore:   number of students present = 24 students/(64/9) yd^2 x 1600 yd^2 = 5400 students

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

22.20 is the correct answer! Hope I helped.

The measure of angle A is 22.19°.

A triangle is a polygon with three sides, vertices, and angles.

The length of the sides of a triangle ABC is

AB = 12 cm

BC = 5 cm

CA = 9 cm

The angle of the law of cosines has to be used to determine the value of angle A

b² = a²+c² - 2 ac cos A

Substituting the values

5² = 12² + 9² -2 * 12 *9 cos A

cos A = 0.9259

A = 22.19°

Therefore, the measure of angle A is 22.19°.

To know more about Triangle

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Answer:

The answer is C.

Step-By-Step Explanation:

Once you combine the like terms of 5x^2-8x-7 and 2x^2-3x-7 you get 7^2-11x-5. Then you need to subtract x^2-9x-4 from 7^2-11-5x. Then you will get the answer which is C.

Answer:

  C.  6x² -2x -1

Step-by-step explanation:

You want the sum of ...

  (5x² -8x +2) + (2x² -3x -7) - (x² -9x -4)

Eliminating parentheses gives ...

  5x² -8x +2 +2x² -3x -7 -x² +9x +4

Grouping like terms, we have ...

  (5x² +2x² -x²) + (-8x -3x +9x) + (2 -7 +4)

Then combining like terms gives ...

  6x² -2x -1 . . . . matches choice C

Answer:

P' (−11, 13), Q' (−17, −19), R' (23, 27)

Step-by-step explanation:

When we reflect a point across the x-axis, we negate the y-coordinates to obtain the image points.

The mapping for the reflection across the x-axis is

[tex](x,y)\to (x,-y)[/tex]

The vertices of the given figure are;

P(−11,−13), Q(−17,19), and R(23,−27)

We apply the rule to obtain:

[tex]P(-11,-13)\to P'(-11,13)[/tex]

[tex]Q(-17,19)\to Q'(-17,-19)[/tex]

[tex]R(23,-27)\to R'(23,27)[/tex]

The correct option is P' (−11, 13), Q' (−17, −19), R' (23, 27)

Answer:

The work shown in the simplification below is incorrect.

Step-by-step explanation:

To start; we have to know  what csc(t) and sec(t) is.

csc(t) = 1/sin(t)      and    sec(t)= 1/cos(t)

So in the above simplification it was all mixed up, csc(t) was substituted with 1/cos(t) instead of 1/sin(t) and sec(t) was substituted with 1/sin(t) instead of 1/cos(t).

So, we are going to solve it the right way;

csc(t) sec(t) = [tex]\frac{1}{sin(t)}[/tex]   ÷   [tex]\frac{1}{cos(t)}[/tex]

                   =  [tex]\frac{1}{sin(t)}[/tex]   ×   [tex]\frac{cos(t)}{1}[/tex]

                    =[tex]\frac{cos(t)}{sin(t)}[/tex]

                    = cot(t)

Therefore csc(t) sec(t) = cot(t)   and not tan(t).

The simplification shown is not correct because the steps used are incorrect and the resulting expression is not equivalent to the original. The correct simplification is csc(t) sec(t) = 1/(sin(t) * cos(t)).

The simplification shown is not correct. Let's break it down step by step:

To simplify the expression correctly, we can use the reciprocal identities: csc(t) = 1/sin(t) and sec(t) = 1/cos(t). When multiplying these together, we get:

csc(t) * sec(t) = (1/sin(t)) * (1/cos(t)) = 1/(sin(t) * cos(t)).

So, the correct simplification is csc(t) sec(t) = 1/(sin(t) * cos(t)).

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Answer:

  29°

Step-by-step explanation:

  ∠1 ≅ ∠8

  3x+25 = 4x -17

  42 = x . . . . . . . . . . add 17-3x

Now, we can find the measure of ∠1:

  m∠1 = 3(42) +25 = 151

Angle 2 is the supplement to this, so has measure ...

  m∠2 = 180° -151° = 29°

Answer:

45

Step-by-step explanation:

So more than 3 people.

Families with 4 =245

Families with 5=125

Families with 6=66

Families with 7=10

Families with 8=4

Add up (this will be our numerator)

Add up all the frequency numbers to get your denominator.

So the answer is =450/1000=45/100=45%

[tex]\bf \textit{volume of a cube}\\ V=s^3~~ \begin{cases} s=&side's\\ &length\\ \cline{1-2} V=&64 \end{cases}\implies 64=s^3\implies \sqrt[3]{64}=s\implies \boxed{4=s} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{scaling all sides by a factor of 5}}{V=s^3\implies V=(4\cdot 5)^3}\implies V=20^3\implies V=8000[/tex]

Answer:

8,000

Step-by-step explanation:

When the sides of the cube are scaled by a factor of k, the volume increases by a factor of k3. Here, the new volume is 64 cubic meters × 53 = 8,000 cubic meters.

Answer:

  4√41 ≈ 25.61 feet

Step-by-step explanation:

The shortest route is the one that crosses the longest edge between room surfaces. In this case, that is the 16-foot edge between the floor and wall opposite the amplifier, or the 16-foot edge between the ceiling and the wall adjacent to the amplifier.

The length of the required wire is ...

  √((8+12)² +16²) = √656 = 4√41 ≈ 25.61 . . . feet

Answer:

√((8+12)² +16²) = √656 = 4√41 ≈ 25.61 feet

Step-by-step explanation:

Answer:

(-8, 135°)

Step-by-step explanation:

(8, -45°) has magnitude 8 and direction -45°.

If we add 180° to the direction and change the sign of the magnitude, we'll have the same point.

(-8, -45° + 180°) = (-8, 135°)

Answer:

  C. Has held several jobs in the last three years

Step-by-step explanation:

Stable employment is a positive with respect to creditworthiness. Changing jobs frequently is considered a negative.

__

The lack of credit history other than one credit card can also detract from Penny's creditworthiness. Lenders like to see that a few other lenders have extended you credit, and that all your payments have been "as agreed."

Answer:

P= 3

Q= -14

R= -5

Step-by-step explanation:

Just solve the equation on the right side, you'll get:

=3x^2 -15x +x -5

=3x^2 -14x -5

Now compare it to the equation on the left side,

The coefficient of x^2 on the left is "p", on the right that we just solved is 3.

Same for "q" which is the coefficient on the left, on the right it's -14.

And for "r" it's -5 from the equation on the right.

Expanding the right side of the equation (3x + 1)(x - 5), we get 3x^2 - 14x - 5. Matching coefficients, we find that p = 3, q = -14, and r = -5.

To solve for the values of p, q, and r that will make the equation px2 + qx + r = (3x + 1)(x - 5) true, we need to expand the right side and then compare coefficients. Expanding the right side, we have:

3x2 - 15x + x - 5

This simplifies to:

3x2 - 14x - 5

Now, we match the coefficients from the expanded form to the left side of the equation:

p must match the coefficient of x2, which is 3.

q must match the coefficient of x, which is -14.

r must match the constant term, which is -5.

Therefore, the correct values are:

A. p = 3

D. q = -14

E. r = -5

Answer:

They should put $6750 in the bank account and $20,250 in the stock fund.

Step-by-step explanation:

Consider the provided information that Avery and Caden have saved $27000.

Let x is the money deposit in the bank and y is the money deposit in stock fund.

Therefore,

x + y = 27000

x  = 27000 - y

The bank account will pay 2.4% annual interest.

[tex]\frac{2.4}{100}x+x=1.024x[/tex]

Stock fund pays 7.2% annual interest.

[tex]\frac{7.2}{100}y+y=1.072y[/tex]

Therefore,

1.024 x + 1.072 y = 1.06 × 27000

Substitute the x  = 27000 - y in above equation.

1.024 (27000 − y) + 1.072 y = 1.06 × 27000

27648 − 1.024 y + 1.072 y = 28620

0.048 y = 28620-27648

0.048 y = 972

y = 20250

Now, substitute the y = 20250 in x  = 27000 - y.

x = 27000 − 20250

x = 6750

Hence, they should put $6750 in the bank account and $20,250 in the stock fund.

Answer:

Step-by-step explanation:

The total number of orders for large is 27

the probability of ordering something hot is 22/27=0.8148

to convert to percentage, multiply by 100: 0.8148*100=81.48%. rounded = 81%

There are 27 people total who are buying large drinks. 22 of those large drinks are hot drinks.

To figure out what percentage 22 is of 27, divide 22 by 27.

22/27= .814... or 81% or 80%.

81% of large drinks bought are hot.

Hope this helps!

Answer:

  A.  $3.63

Step-by-step explanation:

You can choose the correct answer simply by estimating.

The almonds are about $5.50 for each of the 2 kg, so will total about $11. Since the total amount paid is just over $25, the amount paid for cashews is about $25 -11 = $14.

That amount pays for 4 kg of cashews, so 1 kg will be half of half that amount, or about $3.50 -- certainly, less than $7.26.

_____

If you want to write an equation, you can write ...

  2(5.49) +4(c) = 25.50

  4c = 14.52 . . . . . . . . . . . . subtract 10.98

  14.52/4 = c = 3.63 . . . . . divide by the coefficient of c

1 kg of cashews has a price of $3.63.

Answer:

  $24,153

Step-by-step explanation:

Jan's monthly income from commissions is ...

  4.15% × $48,500 = $2012.75

Multiplied by 12 months in the year, that is ...

  $2012.75 × 12 = $24,153 . . . . gross annual income from commissions

Answer:

2 root 21

Step-by-step explanation:

14 + 6 equals 20

Add x is 21

2 root21

Answer:

B. 2sqrt(30)

Step-by-step explanation:

The three right triangles are similar.

In the left right triangle, the short leg measures 6, and the hypotenuse measures x.

In the large triangle, the short leg measures x, and the hypotenuse measures 6 + 14 = 20.

Since all three triangles are similar, the ratios of the lengths of corresponding sides are equal.

6/x = x/20

x^2 = 6 * 20

x^2 = 120

x = sqrt(120)

x = sqrt(4 * 30)

x = 2sqrt(30)

Answer: B. 2sqrt(30)

Step-by-step explanation:

(x+2)^(-1/5) - (x+2)^(-6/5)

Factor out (x+2)^(-1/5):

(x+2)^(-1/5) [ 1 - (x+2)^(-5/5) ]

(x+2)^(-1/5) [ 1 - (x+2)^-1 ]

(x+2)^(-1/5) [ 1 - 1/(x+2) ]

Common denominator:

(x+2)^(-1/5) [ (x+2)/(x+2) - 1/(x+2) ]

(x+2)^(-1/5) [ (x+2-1)/(x+2) ]

(x+2)^(-1/5) [ (x+1)/(x+2) ]

[tex](x+2)^{-\frac{1}{5}}-(x+2)^{-\frac{6}{5}}[/tex]

[tex]\dfrac{1}{(x+2)^{\frac{1}{5}}}-\dfrac{1}{(x+2)^{\frac{6}{5}}}[/tex]

[tex]\dfrac{1}{\sqrt[5]{x+2}}-\dfrac{1}{(x+2)\sqrt[5]{x+2}}[/tex]

[tex]\boxed{\dfrac{x+1}{\sqrt[5]{x+2}\cdot(x+2)}}[/tex]

Hope this helps.

r3t40

Answer:

I think it's -13 and 3.i hope this answer helps

Answer: Y = 4x - 14

Step-by-step explanation:

See paper attached. (:

Answer:

  A. 8

Step-by-step explanation:

The length of the remaining side will be between the sum and difference of the given sides:

  5 + 13 = 18 . . . . upper limit of 3rd side length

  13 - 5 = 8 . . . . . lower limit of 3rd side length

The only answer choice in this range is 8.

_____

Comment on question and answers

Please note that this would not be an allowed answer for some triangle inequality questions. Some authors insist that the sum of the two shortest sides be greater than the longest side, so the triangle has non-zero area. Other authors allow the sum to be greater than or equal to the longest side. The only viable answer choice here is one that makes use of the "or equal to" condition. The 5-8-13 triangle will look like a line segment of length 13. It will have no area.

Answer:

THE CORRECT ANSWER IS 10, PLEASE DO NOT CHOOSE 8, IT WAS WRONG FOR ME SO THE CORRECT ANSWER IS 10

Step-by-step explanation:

Answer:

[tex]A_{(x)}[/tex] = 150 - 25x

Step-by-step explanation:

Let Leanne uses gas for x weeks.

Since expenditure on gas for one week = $25.00

Therefore, Leanne will spend on gas for x weeks = $25x

It is given in the question that she has total amount = $150.00

So the amount Leanne is left with after x weeks = 150 - 25x

If we represent amount left, by [tex]A_{(x)}[/tex]

so the recursive formula will be

[tex]A_{(x)}[/tex] = 150 - 25x

Now for x = 1 week

[tex]A_{(1)}[/tex] = 150 - 25 = $125

Therefore, Leanne will have $125 in her gas card after the first week.

a = acceleration = dv/dt ~ delta v/ delta t.

a = ( 12 m/s - 6 m/s ) / ( 1 s ) = 6 m/s^2

Done.

Answer:

it doesnt say the prices on here

Step-by-step explanation:

Answer:

A'(-1, -1)

Step-by-step explanation:

Dilation about the origin multiplies each individual coordinate value by the dilation factor.

A' = (1/3)A = (1/3)(-3, -3) = (-1, -1)

Answer:

(-1, -1)

Step-by-step explanation:

When you figure scale factor, it's always a number that's multiplied into the coordinates of the pre-image.  The coordinates of A are (-3, -3), so multiplying in the scale factor of 1/3 divides each of those coordinates by 3.  -3/3 = -1

width = w

length = 2w - 5

Perimeter = 26

The formula for perimeter is:

P = l + l + w + w

Plug in corresponding values into this equation...

26 = (2w - 5) + (2w - 5) + w + w

Now you must solve for w

26 = 2w - 5 + 2w - 5 + w + w

Combine like terms

26 = 2w - 5 + 2w - 5 + w + w

26 = 6w - 5 - 5

26 = 6w - 10

Bring -10 to the other side by adding it to both sides

26 + 10 = 6w + (-10 + 10)

36 = 6w + 0

36 = 6w

Isolate w by dividing 6 to both sides

36/6 = 6w/6

6 = w

Width is 6 cm

To find length plug 6 in for w in the equation 2w - 5

2(6) - 5

12 - 5

7

Length is 7 cm

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  [tex]-4r^3-3r^2+2rs-5[/tex]

Step-by-step explanation:

The terms have powers of r that are 2, 0, 1, and 3 (in the order shown here). You want to rearrange those terms so the powers have order 3, 2, 1, 0. The above answer shows that arrangement.

Ordering a polynomial in descending powers of r involves arranging the terms from the highest to the lowest exponent of r. When squaring exponentials, square the digit and double the exponent. For large r compared to d, d can be disregarded.

Ordering a polynomial in descending powers of r involves organizing the terms from highest to lowest exponent of the variable r. For example, for a polynomial of r as 6r^4 - 2r + 7r^2 - 3, we would arrange it as 6r^4 + 7r^2 - 2r - 3. Note that the polynomial starts with the term with the highest power of r (r^4), followed by the term with the next highest power (r^2). The process continues down to the term with the lowest power of r (r), and lastly, the constant term (-3). Remember to retain the corresponding coefficients while reordering terms.

When dealing with terms involving the squaring of exponentials, remember to square the digit as usual and double the exponent. For instance, (r^3)^2 would be r^6.

Also, comparisons of terms such as r » d (meaning r is much larger than d), we disregard d as its contribution to the final polynomial will be negligible.

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