The Nutty Professor sells cashews for $7.40 per pound and Brazil nuts for $4.80 per pound. How much of each type should be used to make a 28 pound mixture that sells for $6.19 per pound?

Based on the calculations, the formula of this sinusoidal function is equal to f(x) = 6cos(2x) + 4.

Mathematically, the standard equation of a cosine function is given by:

y = Acos(Bx - C) + D

Where:

For the amplitude, we have:

A = maxline - midline

A = 10 - 4

Amplitude, A = 6.

Since the maxline to the midpoint is euqal to π/4, we have:

¼ × P = π/4

4P = 4π

P = π

For the value of B, we have:

B = 2π/P

B = 2π/π

B = 2.

Since there isn't any phase shift, the value of C is equal to zero (0) and D is equal to 4.

Next, we would substitute the parameters into the cosine function:

y = Acos(Bx - C) + D

y = 6cos(2x - 0) + 4

f(x) = y = 6cos(2x) + 4.

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If the perpendicular from chord is x, the length of cord is 11.3 and diameter be 15.5 then the value of x is 4.54.

Given Perpendicular from center to chord is x. The length of cord be 11.3 and the diameter be 15.5.

Perpendicular means a line on other line making an angle of 90 degrees. Cord is the length of line joining two points on a circle and is different from radius or diameter. We know that the formula of calculating the length of chord is as under:

l=[tex]2\sqrt{r^{2} -d^{2} }[/tex]

now put the value of l=11.3 and r=15.5/2=7.25

11.3=[tex]2\sqrt{7.25^{2} -x^{2} }[/tex]

11.3/2=[tex]\sqrt{52.5625-x^{2} }[/tex]

5.65=[tex]\sqrt{52.5625-x^{2} }[/tex]

squaring both sides

[tex]5.65^{2} =52.5625-x^{2}[/tex]

31.9225=52.5625-[tex]x^{2}[/tex]

31.9225-52.5625=-[tex]x^{2}[/tex]

-20.64=-[tex]x^{2}[/tex]

20.64=[tex]x^{2}[/tex]

x=4.54

Hence if the length of cord is 11.3 and diameter is 15.5 then the value of x is 4.54.

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So Explicit formula for 2nd one

Or general formula as per Geometric progression

For 50 years there are 365(50)=18250days excluding leap years (We will check for leap year if neck to neck situation arises)

Now find sum

Sum of 18250 terms

[tex]\\ \rm\Rrightarrow \dfrac{a(r^n-1)}{r-1}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1(2^{18250}-1)}{2-1}[/tex]

1 from both denominator and numerator cancels out

[tex]\\ \rm\Rrightarrow 2^{18250}-1[/tex]

[tex]\\ \rm\Rrightarrow 6.272214002E5493[/tex](Accurate)

It's far more than 1 M so second option would give you more penny

Answer:

4

Step-by-step explanation:

divide the numbers

subtract the numbers

final answer:
= 4

Answer:

9

Step-by-step explanation:

35(a) / 7 = 5

28(b) / 7 = 4

a + b = 35 + 28

35 + 28 = 63

63 / 7

= 9

Hope that helps! :)

Answer:

[tex]\huge\boxed{\sf 64}[/tex]

Step-by-step explanation:

[tex]f(x) = 8^x[/tex]

Put x = 2

[tex]f(2) = 8^2\\\\f(2) = 8 \times 8\\\\f(2) = 64\\\\\rule[225]{225}{2}[/tex]

Answer:

(1, 2)

Step-by-step explanation:

So you can solve this systems of equations by substitution. Substitution involves "finding" the value of one of the variables and then substituting that into the other equation

In this example I'll try to define an equation equal to that of "2x" using the first equation and then substitute that into the second equation

Given:

[tex]x-3y=-5[/tex]

Add 3y to both sides

[tex]x=3y-5[/tex]

Multiply both sides by 2

[tex]2x = 6y-10[/tex]

Given:

[tex]2x+5y=12[/tex]

Substitute 2x as (6y-10)

[tex](6y-10)+5y=12[/tex]

Simplify

[tex]11y-10=12[/tex]

Add 10 to both sides

[tex]11y = 22[/tex]

Divide both sides by 11

[tex]y=2[/tex]

Plug 2 in as y (works for either given equation)

[tex]x-3(2)=-5[/tex]

simplify

[tex]x-6=-5[/tex]

add 6 to both sieds

x=1

Using scientific notation, the correct statement is given by:

C. Corporation C owns the most land. Corporation A owns 8 times more land than corporation B.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

Considering the amounts in scientific notation, the standard amounts in acres of each corporation are given as follows:

Hence corporation C owns the most land. 320,000/40,000 = 8, hence Corporation A owns 8 times more land than corporation B, and statement C is correct.

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The value of x has a positive sign and the value of y has a negative sign. Option C

An angle in the unit circle of angle α with a radius of 1 with the set of points;

cos α and sin α

In the given problem, we have the angle as -60º, which is equal to an angle of 360 - 60 to give us 300º

Also, it is in the fourth quadrant, where the cosine is positive and the sine is negative.

Thus, the value of x has a positive sign and the value of y has a negative sign.

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Answer:

[tex]21 \frac{1}{3}[/tex] fit into the product

Step-by-step explanation:

so you want to convert [tex]2 \frac{2}{3}[/tex] into a fraction by multiplying 2 by 3 and adding it to the 2. This will give you (3 * 2) = 6 => 6+2=8 which is the numerator. So the fraction becomes [tex]\frac{8}{3}[/tex] and since the two fractions are equal they both become this. So now you have [tex]\frac{8}{3} * \frac{8}{3}[/tex] which can be calculated by multiplying the numerators and denominators. This gives you [tex]\frac{8*8}{3*3} = \frac{64}{9}[/tex]. Now this just gives you the product but the question is asking you how many one thirds is the product. This is essentially saying how many 1/3 fit into the product or in other words what is the product divided by 1/3. This gives you the equation [tex]\frac{64}{9} \div \frac{1}{3}[/tex] which can be calculated by changing the sign to multiplication and flipping the second fraction (1/3 => 3/1) This gives you the equation [tex]\frac{64}{9} * \frac{3}{1} = \frac{64 * 3}{3 * 3} = \frac{64}{3}[/tex]. I rewrote the 9 as 3 * 3 in the equation so you can see that we can just cancel out the 3. Since if have a number and multiply it by "x" and divide by "x" you just have the original number. So now you have 64/3 which simplifies to [tex]21 \frac{1}{3}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2\dfrac{2}{3}\times 2 \dfrac{2}{3}}[/tex]

[tex]\mathsf{= \dfrac{2\times3+2}{3}\times\dfrac{2\times 3 + 2}{3}}}[/tex]

[tex]\mathsf{= \dfrac{6 + 2}{3}\times \dfrac{6 + 2}{3}}[/tex]

[tex]\mathsf{= \dfrac{8}{3}\times\dfrac{8}{3}}[/tex]

[tex]\mathsf{= \dfrac{8\times8}{3\times3}}[/tex]

[tex]\mathsf{= \dfrac{8 + 8 + 8 + 8 + 8 + 8 + 8 + 8}{3 + 3 + 3}}[/tex]

[tex]\mathsf{= \dfrac{16 + 16 + 16 + 16}{6 + 3}}[/tex]

[tex]\mathsf{= \dfrac{32 + 32}{9}}[/tex]

[tex]\mathsf{= \dfrac{64}{9}}[/tex]

[tex]\mathsf{= 7 \dfrac{1}{9}}[/tex]

[tex]\approx{\mathsf{21 \dfrac{1}{3}}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Step-by-step explanation:

The value of x is 1.56ft.

The Pythagoras theorem states that the sum of the squares of the base and height is equal to the square of the hypotenuse of the right-angle triangle.

If p is the height, b is the base and h is the hypotenuse then according to the Pythagoras theorem

p²+b²=h²

Here given that the radius of the circle is r=2.1 ft

the perpendicular distance from the center of the circle to the line =1.4ft

that perpendicular line will bisect the line of length 2x.

Foe which each half of the line will be x.

Applying Pythagoras theorem in the right-angle triangle,

1.4²+x²=2.1²

⇒1.96+x²=4.41

⇒x²= 4.41-1.96

⇒x²= 2.45

⇒x= 1.56 ft

Therefore the value of x is 1.56ft.

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Answer:

7

Step-by-step explanation:

When x = 5, 2x³ - 12x² + 11x + 2 = 7.

The independent variable is brush strokes

The statement is given as:

"I did 60 brush strokes in 1 minute"

The independent variable is the action that is done.

From the statement.

The action is the strokes of brush

Hence, the independent variable is brush strokes

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Answer:

A

Step-by-step explanation:

Complex roots of quadratic functions occur when the discriminant is negative.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0[/tex]

Evaluate the discriminant of each of the given equations.

[tex]\textsf{A.} \quad 3x^2+2=0[/tex]

[tex]\implies a=3, \quad b=0, \quad c=2[/tex]

[tex]\implies b^2-4ac=0^2-4(3)(2)=-24[/tex]

As -24 < 0 the equation will have complex roots.

[tex]\textsf{B.} \quad 2x^2+1=7x[/tex]

[tex]\implies 2x^2-7x+1=0[/tex]

[tex]\implies a=2, \quad b=-7, \quad c=1[/tex]

[tex]\implies b^2-4ac= (-7)^2-4(2)(1)=41[/tex]

As 41 > 0 the equation does not have complex roots.

[tex]\textsf{C.} \quad 3x^2-1=6x[/tex]

[tex]\implies 3x^2-6x-1=0[/tex]

[tex]\implies a=3, \quad b=-6, \quad c=-1[/tex]

[tex]\implies b^2-4ac=(-6)^2-4(3)(-1)=48[/tex]

As 48 > 0 the equation does not have complex roots.

[tex]\textsf{D.} \quad 2x^2-1=5x[/tex]

[tex]\implies 2x^2-5x-1=0[/tex]

[tex]\implies a=2, \quad b=-5, \quad c=-1[/tex]

[tex]\implies b^2-4ac=(-5)^2-4(2)(-1)=33[/tex]

As 33 > 0 the equation does not have complex roots.

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Answer:

The transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

If f(x) = x³ and g(x) = -2x³, then the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

Hence, the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.

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Answer:

146

Step-by-step explanation:

arrange your values in descending order then cancel out last value with the first value.

the middle value would be your answer.

hope it was helpfull.please give me a thanks

Option A. The answer to the question is Marcelina spends the intended amount of money and buys the intended amount of corn.

We can see a point that takes us to the amount that the corn was bought and the quantity that was obtained.

This shows that she is in range of what she was asked to buy. E shows us the amount that was spent as 12 dollars and the quantity of 50kg.

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Answer:

1

Step-by-step explanation:

So the sum of a finite geometric series can be defined as: [tex]S_n = \frac{a_1-a1*r^n}{1-r}[/tex] where r is the constant ratio or how much more greater the current term is, compared to the previous term (how much it's being multiplied by), and the n is the number of terms in the series. So with the given information you have the equation:

[tex]1365=\frac{a_1-a_1*4^6}{1-4}[/tex]

Simplify:

[tex]1365=\frac{a_1-4096a_1}{-3}[/tex]

Multiply both sides by -3

[tex]-4095 = a_1-4096a_1[/tex]

Subtract coefficients

[tex]-4095=-4095a_1[/tex]

Divide both sides by -4095

[tex]1 = a_1[/tex]

Answer:

Step-by-step explanation:

2 over 6 = Y over 9 Fraction equation is required

2/6 = y/9

y = 2/6 * 9

y = 3

check

2/6 = 3/9

1/3 = 1/3

the answer is good

Answer:

Pure substance

Step-by-step explanation:

A pure substance is matter that is uniform throughout and has consistent properties

Answer:

The amount of gross profit earned by Abbey Co. on the above transactions is $7,554.00

Step-by-step explanation:

What is the gross profit of Abbey Co?

Note that after sales of goods of $29,300 whose cost is $20,510 to Gomez Co, Gomez returned goods whose selling price is $2,500 and cost originally $1,800 to Abbey Co.

The implication of such goods returned is that $2,500 would be deducted from selling price and $1,800 would be deducted from cost of goods sold.

selling price=$29,300-$2,500

selling price=$26,800.00

cost of goods sold=$20,510-$1,800

cost of goods sold=$18,710.00

Note again that Gomez paid the invoice within the discount period, which means that net sales is the selling price of $26,800.00  minus 2% discount(2/15 means a discount of 2% is available if credit sales is settled in cash within the first 15 days of making sales0

net sales=$26,800.00*(1-2%)

net sales=$26,264.00

The gross profit is net sales minus the cost of goods sold

gross profit= $26,264.00-$18,710.00

gross profit=$7,554.00

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The critical value and the conclusion are mathematically given as

z_{0.05}=1.960 and  z<Zcritical, therefore we Reject H_o

a)Test statistic  z=-3.32

Claim: p< 0.5

a=0.05

critical value z_{0.05}

z_{0.05}=1.960

b)

z<Zcritical,

Beause z=-3.32< z_{0.05}=1.960 Reject H_o

In conclusion,

z_{0.05}=1.960 and  z<Zcritical, therefore we Reject H_o

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Answer:

D (2, 1)

Step-by-step explanation:

Fir an in-detailed representation, image below

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Hello

Answer:

Look at the picture.

The solution to the given proportion (x-1)/5 = (x-1)/2 is equal to x = 1.

To solve the proportion (x-1)/5 = (x-1)/2, we need to find the value of x that satisfies the equation. Cross-multiplication is a common method used to solve proportions.

First, cross-multiply the equation:

2(x - 1) = 5(x - 1)

Now, distribute the values on both sides:

2x - 2 = 5x - 5

Next, isolate the variable x on one side of the equation. Let's move all terms containing x to the left side of the equation by subtracting 2x from both sides:

2x - 2 - 2x = 5x - 5 - 2x

-2 = 3x - 5

Now, let's move the constant term (-5) to the other side of the equation by adding 5 to both sides:

-2 + 5 = 3x - 5 + 5

3 = 3x

Finally, to find the value of x, divide both sides by 3:

3/3 = 3x/3

1 = x

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Answer:

36

Step-by-step explanation:

1/6(216/1)

A common discrete distribution used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that the golfer will miss at least one of his next eight 5-foot putts is 0.4523.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

A.) The probability that this kicker will successfully make all of his next eleven extra-point kicks is,

P(x=11) = ¹¹C₁₁ (0.988¹¹) (0.012⁰)

           = 0.8756

B.) The probability that the kicker will miss at least one of his next eleven extra point kicks is,

P(X<11) = 1 - P(X=11)

           = 1 - 0.8756

           = 0.1243

C.) The probability that this golfer will successfully make all of his next eight 5-foot putts is,

P(x=8) = ⁸C₈ (0.9275⁸) (0.0725⁰)

          = 0.5477

D.) The probability that the golfer will miss at least one of his next eight 5-foot putts is,

P(X<8) = 1 - P(X=8)

          = 1 - 0.5477

          = 0.4523

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Answer:

logarithmic

Step-by-step explanation:

I'm jujust that good to help you

Answer:

Yes, they are congruent

Step-by-step explanation:

The triangles are congruent as they follow the ASA rule or, Angle Side Angle.

All the angles AND sides are corresponding, so they are congruent.

Hope this helped (: