The Coffee Counter charges ​$8 per pound for Kenyan French Roast coffee and ​$7 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for ​$7.30 per​ pound?

Answer:

see explanation

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3   8   14   19   22   29   33   37   43   49

                            ↑ middle is between 22 and 29

median = [tex]\frac{22+29}{2}[/tex] = [tex]\frac{51}{2}[/tex] = 25.5

The upper quartile [tex]Q_{3}[/tex] is the middle value of the data to the right of the median.

29   33   37   43   49

               ↑

[tex]Q_{3}[/tex] = 37

The lower quartile [tex]Q_{1}[/tex] is the middle value of the data to the left of the median.

3   8   14   19   22

           ↑

[tex]Q_{1}[/tex] = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3,  14,  25.5,  37,  49

Answer:

d - 12.50 = 17

add 12.50 to both sides to get d alone.

d = 12.50 + 17

Answer:

It's B d= 17 + 12.50

Step-by-step explanation:

Got it right on edg

Answer:

Step-by-step explanation:

Given that:

If C(x) =  the cost of producing x units of a commodity

Then;

then the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

We are to consider a given function:

[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]

And the objectives are to determine the following:

a) the total cost at a production level of 1000 units.

So;

If C(1000) = the cost of producing 1000 units of a commodity

[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]

[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]

[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]

[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]

[tex]C(1000) = $310491.1064[/tex]

[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]

(b) Find the average cost at a production level of 1000 units.

Recall that :

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

SO;

[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]

Using the law of indices

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]

c(1000) =$ 310.49 per unit

(c) Find the marginal cost at a production level of 1000 units.

The marginal cost  is C'(x)

Differentiating  C(x) = 54,000 + 130x + 4x^{3/2} to get  C'(x) ; we Have:

[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]

[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]

[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]

[tex]C'(1000) = 319.7366596[/tex]

[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]

(d)  Find the production level that will minimize the average cost.

the average cost per unit is c(x)  = [tex]\dfrac{C(x)}{x}[/tex]

[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]

the production level that will minimize the average cost is c'(x)

differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]

Also

[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]

[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]

[tex]x^2 = 27000\sqrt{x}[/tex]

[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]

x= 0;  or  [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900

Since  production cost can never be zero; then the production cost = 900 units

(e) What is the minimum average cost?

the minimum average cost of c(900) is

[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]

c(900) = 60 + 130 + 4(30)

c(900) = 60 +130 + 120

c(900) = $310 per unit

Answer:

The  90%  confidence interval for population mean is   [tex]14.7 < \mu < 19.1[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 16.9[/tex]

    The confidence level is  [tex]C = 0.90[/tex]

     The sample size is  [tex]n = 45[/tex]

     The standard deviation

Now given that the confidence level is  0.90 the  level of significance is mathematically evaluated as

       [tex]\alpha = 1-0.90[/tex]

       [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex]  from the standardized normal distribution table. The values is  [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The  reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex]  instead of  that of  [tex]\alpha[/tex]  is because [tex]\alpha[/tex]  represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%)  did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex]  is just considering the area of one tail which is what we required calculate the margin of error

  Generally the margin of error is mathematically evaluated as

        [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]

         [tex]MOE = 2.207[/tex]

The  90%  confidence level interval is mathematically represented as

      [tex]\= x - MOE < \mu < \= x + MOE[/tex]

substituting values

     [tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]

    [tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]

     [tex]14.7 < \mu < 19.1[/tex]

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

Answer:

x < -( 8-2b) /a  a > 0

Step-by-step explanation:

−ax + 2b > 8

Subtract 2b from each side

−ax + 2b-2b > 8-2b

-ax > 8 -2b

Divide each side by -a, remembering to flip the inequality ( assuming a>0)

-ax/-a < ( 8-2b) /-a

x < -( 8-2b) /a  a > 0

Answer: [tex]x<\frac{-8+2b}{a}[/tex]

                  [tex]a>0[/tex]

Step-by-step explanation:

[tex]-ax+2b>8[/tex]

[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]

[tex]-ax>8-2b[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]

[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]

[tex]ax<-8+2b[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}a[/tex]

[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]

[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]

Answer:

70

Step-by-step explanation:

You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.

Answer:

4 boys

Step-by-step explanation:

Let x represent boys and y represent girls

Hence, x : y = 3 : 2

x/y = 3/2  

2x = 3y ------ (1)

x/y + 4 = 3/3

3x = 3(y + 4)

3x = 3y + 12 --------- (2)

From (1): x = 3y/2

Substitute x into (2) we have:

9y/2 = 3y + 12

9y = 6y + 24

9y - 6y = 24

3y = 24

∴ y = 8

From (2) : 3x = 24 - 12 = 12

∴ x = 4

Hence there Four boys

Answer:

-3

Step-by-step explanation:

2x + 3 +7x = -24

Add the X together

9x +3 = -24

Bring over the +3. [when you bring over change the sign]

9x = -24 -3

9x = -27

-27 divide by 9 to find X

therefore answer is

x= -3.

Hope this helps

Answer:

x = -3

Step-by-step explanation:

question is

2x + 3 + 7x = -24

First you combine the like terms

2x and 7x you can add them so it will be 9x

so it will then it will be like this:

9x + 3 = -24

now you take the 3 and send it to the other side, and right now the 3 is positive so when it goes to the other side it will turn into -3

so

9x = -24 -3

again now you combine the like terms

-24 -3 = - 27

now you have

9x = -27

now just divide each side by 9

x = -27/9

x = -3

Sorry if this doesnt help

Answer:

Option (D)

Step-by-step explanation:

In the picture attached,

An obtuse angle triangle ABC has been given.

By applying Sine rule in the triangle,

[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]

Since, m∠A + m∠B + m∠C = 180°

45° + 110° + m∠C = 180°

m∠C = 180°- 155° = 25°

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]

[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]

[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]

b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]

b = 15.56

b ≈ 15.56

[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]

a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]

a = 11.712

a = 11.71

Therefore, Option (D) will be the answer.

Answer:

a) Central area = 0.95, df = 10 t = (-2.228, 2.228)

(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)

(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)

(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)

(e) Upper-tail area = 0.01, df = 30 t= 2.457

(f) Lower-tail area = 0.025, df = 5 t= -2.571

Step-by-step explanation:

In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;

We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.

The following are the answers obtained from the table;

a) Central area = 0.95, df = 10 t = (-2.228, 2.228)

(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)

(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)

(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)

(e) Upper-tail area = 0.01, df = 30 t= 2.457

(f) Lower-tail area = 0.025, df = 5 t= -2.571

Answer:

462.61 yards.

Step-by-step explanation:

To solve, you need to find the measurement of the angle that forms a 90 degree angle with the 23.9 degree angle.

90 - 23.9 = 66.1 degrees.

Now that you have the angle, you can use TOA to solve for x (TOA = Tangent; Opposite over Adjacent).

tan(66.1) = x / 205

x / 205 = tan(66.1)

x = tan(66.1) * 205

x = 2.256628263 * 205

x = 462.6087939

So, you are about 462.61 yards from the cabin.

Hope this helps!

Answer:

[tex]\boxed{V=lwh}[/tex]

Step-by-step explanation:

The formula for volume of a cuboid is:

[tex]V=lwh[/tex]

[tex]volume = length \times width \times height[/tex]

Answer:

V = l w h

Step-by-step explanation:

Volume of a Cuboid = Length × Width × Height

Where l = length, w = width and h = height

Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Answer:

(3) x ≥ -3

(4) 2.5 gallons

(4) -12x + 36

Step-by-step explanation:

Hey there!

1)

Well its a solid dot meaning it will be equal to.

So we can cross out 1 and 2.

And it's going to the right meaning x is greater than or equal to -3.

(3) x ≥ -3

2)

Well if each milk container has 1 quart then there is 10 quarts.

And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.

(4) 2.5 gallons

4)

16 - 4(3x - 5)

16 - 12x + 20

-12x + 36

(4) -12x + 36

Hope this helps :)

Answer: A, (0, -3)

Step-by-step explanation:

Inequalities, once graphed, take the form of the image you attached:

Linear inequalities are straight lines, sometimes dotted and sometimes solid, with shading on one side of the line.

Any point in the shading is a correct solution to the inequality.

In this case, the line is solid, so any point on the line is a solution to the inequality.

Looking at answer choice A: (0, -3), it lies on the line as the y-intercept.

The correct choice is A.

Answer:

The mean for all such groups randomly selected is 0.09*800=72.

Step-by-step explanation:

The value of the standard deviation is 7.

Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.

The standard deviation is calculated by using the formula,

[tex]\sigma = \sqrt{Npq}[/tex]

N = 600

p = 9%= 0.09

q = 1 - p= 1 - 0.09= 0.91

Put the values in the formulas.

[tex]\sigma = \sqrt{Npq}[/tex]

[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]

[tex]\sigma[/tex] = 7

Therefore, the value of the standard deviation is 7.

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Answer:

8 and 9

Step-by-step explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8.  So the two integers are 8 and 9.

Answer:

acute isosceles triangle

vertex angle, y =  44.0 degrees. (smallest angle)

Step-by-step explanation:

If the sides are in the ratio 4:4:3,

two of the sides have equal lengths, so it is an isosceles triangle.

Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.

To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.

The base angle x is given by the ratio

cos(x) = 1.5/4 = 3/8

Consequently the base angle is  arccos(3/8) = 68.0 degrees.

The vertex angle equals twice the complement of 68.0

vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)

Answer:

The sample size is 30.

Step-by-step explanation:

The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set

From the question the frequency is given as

Frequency = 2 4 6 8 10

The sample size n =

2 + 4 + 6 + 8 + 10

= 30

Therefore the sample size n of the data set = 30

Answer:

1024

Step-by-step explanation:

4 * 4 * 4 * 4 * 4

Answer:

Step-by-step explanation:

Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.

Volume of a cone V = πr²h/3

If the diameter and the height are equal, then r = h

V = πh²h/3

V = πh³/3

If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min

Using chain rule to get the expression for dV/dt;

dV/dt = dV/dh * dh/dt

From the formula above, dV/dh = 3πh²/3

dV/dh =  πh²

dV/dt = πh²dh/dt

20 = πh²dh/dt

To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.

20 = π(11)²dh/dt

20 = 121πdh/dt

dh/dt = 20/121π

dh/dt = 20/380.133

dh/dt = 0.0526ft/min

This means that the height of the pile is increasing at  0.0526ft/min

Answer:

[tex] -3n - 7 [/tex]

Step-by-step explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]

[tex] m = \frac{-13 + 10}{1} [/tex]

[tex] m = \frac{-3}{1} [/tex]

[tex] m = -3 [/tex]

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

[tex] y = mx + b [/tex]

[tex] -10 = -3(1) + b [/tex]

[tex] -10 = -3 + b [/tex]

Add 3 to both sides:

[tex] -10 + 3 = -3 + b + 3 [/tex]

[tex] -7 = b [/tex]

[tex] b = -7 [/tex]

The equation of the given linear function can be written as:

[tex] y = -3x - 7 [/tex]

Or

[tex] f(x) = -3x - 7 [/tex]

Therefore, if the input is n, the output would be:

[tex] f(n) = -3n - 7 [/tex]

the ancient Greek used the golden ratio

Answer:

An important proportion that the Ancient Greeks used was the Golden Mean, the a0

Step-by-step explanation:

Also known as Golden Ratio, Divine Proportion, or Golden Section

Answer:

hope you get it....sorry for any mistake calculations

Answer:

1

Step-by-step explanation:

[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]

When the wavelength of a diffraction grating is decreased,  the distance between lines decreases.

The diffraction grating is used to carry out interference experiments. It consists of a  number of small lines that are constructed to be close to each other and produce an interference pattern.

The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.

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Answer: 54 mL

Step-by-step explanation:

Simply do 9(number of containers)*6(Syrup per container) to get 54 mL of syrup.

Hope it helps <3

Answer:

False

Step-by-step explanation:

To find <A, we can do 5x - 80 = 3x + 20.

As we simplify, we will get 2x = 100, which is x = 50

Therefore, <A will be 50 degrees and not 45 degrees.

Also, if you need y, you can do:

3y - 7 = y + 7

2y = 14

y = 7