A nut store normally sells cashews for​ $4.00 per pound and peanuts for​ $1.50 per pound. But at the end of the month the peanuts had not sold​ well, so, in order to sell 10 pounds of​ peanuts, the manager decided to mix the 10 pounds of peanuts with some cashews and sell the mixture for $3.50 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the​ revenue?

The value of the function is 157.5

The function is given as:

f(80)=1000(0.5)^(80/30)

Evaluate the quotient

f(80)=1000(0.5)^(8/3)

Evaluate the exponent

f(80)=1000 * 0.15749013123

Evaluate the product

f(80) = 157.49013123

Approximate

f(80) = 157.5

Hence, the value of the function is 157.5

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If the price of a barrel of crude oil went up to $75, the amount that would be paid per barrel is $75.

The U.S. dollar is the main currency for trade around the world which includes the trade of crude oil.

This means barrels of crude oil are denominated in dollars. An increase of crude oil to $75 per barrel means that Americans would be $75 because they already use the currency that the oil is denominated in.

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Answer:

14) 21.136505024965 m

15) 43.076759215619 km

Step-by-step explanation:

14)

let h be the height of the lighthouse:

tan(41.3) = 18.7/h

Then

h = 18.7÷tan(41.5)

  = 21.136505024965 m

………………………………………

15)

90-71.4 =18.6

Let s be the distance that the plane flew

towards the south:

tan(90 - 71.4) = s/128

Then

tan(18.6) = s/128

Then

s = tan(18.6)×128

  = 43.076759215619 km

14.)

See the diagram below.

Here use tan rule:

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(41+ \frac{30}{60} ) = \dfrac{18.7}{adjacent}[/tex]

[tex]\sf adjacent = \dfrac{18.7}{tan(41.5)}[/tex]

[tex]\sf adjacent = 21.14[/tex]

The height of the lighthouse is 21.14 m.

15.)

See the diagram below.

Here use tan rule:

[tex]\sf tan(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf tan(18.6) = \dfrac{opposite}{128}[/tex]

[tex]\sf opposite = 128 tan(18.6)[/tex]

[tex]\sf opposite = 43.08[/tex]

The plane travelled 43.08 km far south.

Answer:

26

Step-by-step explanation:

[tex]f(x)=3x^{2} -5x+4\\f(-2)=3(-2)^{2} -5(-2)+4\\=3(4)+10+4\\=12+10+4\\=26[/tex]

Answer:

26

Step-by-step explanation:

3(-2)^2 = 12

5(-2) = -10

So 12 - (-10) + 4 = 26

The volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².

The volume of a substance is the total space occupied by a three-dimensional object.

The volume of a right circular cylinder with a radius of r units and a height of h units is given by the formula V = πr²h square units.

We are asked to find the volume of the right circular cylinder with a radius of 6 m and a height of 9 m.

Substituting these values in the formula, we get Volume,

V = π(6)²(9) m² = 324π m² = 1017.876 m² ≈ 1018 m².

Therefore, the volume of the right circular cylinder with a radius of 6 m and a height of 9 m is 1018 m².

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f td d,ts#=#=sr#=rs$/,% gu gu hijkojibgu yf ,tdts$_, %_g g hu

Using the normal distribution, it is found that 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 20.66, \sigma = 2.4[/tex]

The proportion of students that are 21 or older is one subtracted by the p-value of Z when X = 21, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21 - 20.66}{2.4}[/tex]

Z = 0.14

Z = 0.14 has a p-value of 0.5557.

1 - 0.5557 = 0.4443 = 44.43% of students are 21 or older and thus old enough to legally order alcohol at Griff's.

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Answer:

Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. There are many types of inferential statistics and each is appropriate for a specific research design and sample characteristics

Step-by-step explanation:

hope this helps (﹡ˆ﹀ˆ﹡)♡

C is the right answer.

Trust me char!!

Na bakla na yswa!

Answer: Recognize the equation as that of a vertical line passing through the x-axis at −3

The common ratio of the associated geometric sequence is 4

The table of values is given as:

x y

1 9

2 36

3 144

4 576

5 2304

The common ratio is calculated as:

Ratio = y(2)/y(1)

This gives

Ratio = 36/9

Divide

Ratio - 4

Hence, the common ratio is 4

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If the angles of a convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex] then the smallest angle is 21°.

Given The exterior angles of convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex]

and we have to find the value of smallest angle.

The sum of the  angles of a convex octagon is 360°

so to calculate the smallest angle we need to find out the value of x first and which is calculated by summing up all the exterior angles and put them equal to 360.

(2x+6)+(x+13)+(2x-1)+(2x+12)+(2x-17)+(3x-4)+(3x-10)+4x=360

2x+6+x+13+2x-1+2x+12+2x-17+3x-4+3x-10+4x=360

2x+x+2x+2x+2x+3x+3x+4x+6+13-1+12-17-4-10=360

19x-1=360

19x=360+1

19x=361

x=361/19

x=19

Putting the value of x in all the angles and we will find the following:

2x+6=2*19+6=44

x+13=19+13=32

2x-1=2*19-1=37

2x+12=2*19+12=50

2x-17=2*19-17=21

3x-4=3*19-4=51

3x-10=3*19-10=47

4x=4*19=76

Hence among all the exterior angles the smallest angle is 21°.

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The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).

Since the expression is √7x² ÷ √3x

So, one need to  rationalize the denominator and thus:

√7x² ÷ √3x  x √3x  ÷ √3x  

or write as √7x² x√3x ÷ √3x

or write as√(21x³)/3x

or write as √3*7*x³/3x

or write as √3*7*x/3

= √7x/√3

Therefore, The choice that is equivalent to the quotient values of X in √7x² ÷ √3x is Option C : (√7x/3).

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Answer:

[tex]x^2[/tex]

Step-by-step explanation:

Hello!

The HCF or the highest common factor (sometimes also known as the greatest common factor, GCF), is the greatest factor between terms.

First, let's expand both terms:

If we keep them on top of another, we can see that the overlapping variables are [tex]x*x[/tex], meaning that the greatest common factor between them is [tex]x^2[/tex].

Hello !

Answer:

[tex]z {}^{ - 6} [/tex]

Step-by-step explanation:

[tex] \frac{z {}^{3} }{z {}^{9} } = z {}^{3 - 9} = z {}^{ - 6} [/tex]

It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated

1. Part A:

Since the points in the scatter plot show a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.

The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to  1.

Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with negative slope.

r =  + 1 is a perfect positive correlation: the points will ajdust perfectly to a line with positive slope.

r = 0 means that the variables are not correlated at all.

Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows other thing.

Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.

2. Part B.

A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.

Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.

Thus, the scenario could be:

Amout of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

        50                                                     40

        25                                                     80

        12.5                                                  160

        6.25                                                 320

The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.

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Answer:

[tex]2261.9cm^{2}[/tex]

Step-by-step explanation:

Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]

Note: Do not get tricked by the 24cm (taking 24cm as the radius), that is the diameter.

To find r, radius = [tex]\frac{1}{2} d[/tex]

                          =[tex]\frac{1}{2} (24)\\[/tex]

                          = 12cm

Now we know r = 12cm, h = 18cm

Now we substitute r and h into the formula to find the total surface area.

Total Surface Area of Cylinder = [tex]2\pi (12)(18)+2\pi (12)^{2} \\=432\pi +288\pi \\=720\pi cm^{2} \\=2261.9cm^{2}[/tex]

Answer:

  D, E

Step-by-step explanation:

A set of ordered pairs represents a function if no x-value is repeated in the set.

{(-1,6), (4,4), (7, 13), (4,8)} . . . . . not a function

{(3,6), (3, 5), (9, 12), (0, -3)} . . . not a function

{(-5,0), (6, 8), (3,-5), (-5,-3)} . . . . not a function

{(7,9), (8,4), (-2,4),(-3, 14)} . . . . no repeated x-values; is a function

{(8,3), (3, 7), (6,4), (5,4)} . . . . . .no repeated x-values; is a function

Answer:

Step-by-step explanation:

let the consecutive even integers be 2x,2x+2

8×2x=7(2x+2)

16x=14x+14

16x-14x=14

2x=14

x=14/2=7

so numbers are 2×7,2×7+2

or

14,16

Answer:

The probability that a selected randomly rail bridge will exhibit structural distress given that it is old

= (200/520) * 0.5 * 0.7 * 100

= 0.1346154 * 100

= 13.46154 %

Answer:

Step-by-step explanation:

let the numbers be x& y

y=4x+17

xy=-18

x(4x+17)=-18

4x²+17x+18=0

4x²+8x+9x+18=0

4x(x+2)+9(x+2)=0

(x+2)(4x+9)=0

x=-2

x=-9/4 (rejected as it is not an integer.)

y=4×(-2)+17=-8+17=9

so numbers are -2,9

The number of cakes Mrs Darby can decorate in a 30-hour week is 22.5 cakes.

Time conversion

1 hour = 60 minutes

1 1/3 hours = 60 × 1 1/3

= 60 × 4/3

= 240/3

= 80 minutes

30 hours = 30 × 60

= 1800 minutes

Number of cakes decorated = 1800 / 80

= 22.5 cakes

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Answer:

Square Root of 7 = 7^1/2    = 2.646

Cubed Root of 7 = 7^1/3    = 1.913

Square Root of 7^3 = 7^3/2     = 3.659

Answer:

$72

Step-by-step explanation:

100%-$60

1%-$0.60

100%-30%=70%

70%-$0.60x70=$42

the inequality in the number-line is:

x ≤ -1.5

We know that we have a closed circle at -1.5, this means that the value is a solution of the inequality.

Then we have a line that goes to the left of that circle, so the inequality will have solutions that are less than or equal to -1.5

Then the inequality is:

x ≤ -1.5

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Answer:c

Step-by-step explanation:

trust me

If the bet is done 762 times then expected value is that we may have a loss of $1562.1if the bet is that is heart comes we will get $16 and lose $3 if not comes.

Given We will get $16 if hearts come and lose $3 when not comes and bet is made 762 times. We have to calculate the expected win after 762 times.

We know that there are 13 hearts in the standard deck of cards.

Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:

Probability= number of items/ total number of items.

When two cards are chosen at random without replacement then the probability of getting two hearts is 13/52*12/51

=156/2652

=0.05

When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-0.05

=0.95

When  bet is made only 1 time expected value will be 0.05*16-0.95*3

=0.8-2.85

=-2.05 means we are expecting to lose $2.05.

When bet is made 762 times then the expected value will be -2.05*762=-1562.1.

Hence the expected value when bet is made 762 times is that we will lose $1562.1 .

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Answer:

9x^3-15x

Step-by-step explanation:

The mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069

Mean is the study of central tendency of a data set. The average value of the data points is the mean.

It is given that

The probability that the students have the student loan is  = 62% = 0.62

The probability that the students do not have student loan is

   1 - p

= 1 - 0.62

= 0.38

Total number of students is

n = 50

1) [tex]\rm \mu \;\hat p[/tex] = p = 0.62

2) [tex]\rm \sigma\hat p[/tex]  = [tex]\rm \sqrt {p ( 1 - p ) / n}[/tex]

=  [tex]\rm \sqrt {(0.62 * 0.38) / 50}[/tex]

= 0.069

Therefore the mean of the distribution sample is 0.62 and the standard error of the distribution sample is 0.069.

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Answer: [tex]8\sqrt{5}[/tex]

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{y}{16}=\frac{4}{y}\\\\y^{2}=64\\\\y=8[/tex]

So, by the Pythagorean theorem,

[tex]8^2 + 16^2 = x^2\\\\320=x^2\\\\x=\boxed{8\sqrt{5}}[/tex]