one serving of almonds is 1/3 cup. booker bought 2 and 2/3 cups of almonds how many servings of almonds did booker buy

x + y = 48

x = 3y + 12

48 - y = 3y + 12

36 = 4y

y = 9

x = 39

#1 had 39, #2 has 9

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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The basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

The given piecewise-defined function f(x) has different expressions for different intervals. For x greater than or equal to zero, f(x) takes the value of x. For x less than zero, f(x) is equal to -x. We need to find a basic function that captures this behavior.

Among the options provided, f(x) = |x| is equivalent to the given piecewise function. The absolute value function, denoted by |x|, returns the positive value of x regardless of its sign. When x is non-negative, |x| equals x, and when x is negative, |x| is equal to -x, mirroring the conditions of the piecewise-defined function.

The function f(x) = |x| represents the absolute value of x and matches the behavior of the given piecewise-defined function, making it the equivalent basic function.

In summary, the basic function equivalent to the piecewise-defined function f(x) = x if x ≥ 0 and -x if x < 0 is f(x) = |x|, which represents the absolute value of x.

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Answer:

15

Step-by-step explanation:

Answer:

\(\sqrt{41}\)

Step-by-step explanation:

Calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2 -y_{1})^2 }\)

with (x₁, y₁ ) = (- 1, - 1 ) and (x₂, y₂ ) = (3, - 6 )

d = \(\sqrt{(3-(-1))^2+(-6-(-1))^2}\)

  = \(\sqrt{(3+1)^2+(-6+1)^2}\)

  = \(\sqrt{4^2+(-5)^2}\)

  = \(\sqrt{16+25}\)

  = \(\sqrt{41}\)

Answer:

7^-22

Step-by-step explanation:

Exponent laws.

Answer:

60 minutes make an hour

Step-by-step explanation:

Because 1 hour = 60 minutes

Answer:

The original price would be 112.8125

Step-by-step explanation:

I multiplied 90.25 by 1.25.

Answer:

$120.33

Step-by-step explanation:

hope this helps:))

Answer:

Step-by-step explanation:

what do u mean i domt rlly inderdstnd

Answer:

14

Step-by-step explanation:

So we need to do 21-7. This is 14. So the other addend is 14.

Answer:

14

Step-by-step explanation:

First, we'll mark our unknown addend as a variable.

How about x?

So, now our equation is 7+x=21

Now we have to figure out what x is.

You could have done this in a number of ways.

Option 1: The Sub-Add

21-7=x

Option 2: Basic Addition (First Grade Edition)

21+x=7

Option 3: The really hard thing that could be avoided by doing one and two and is also really long to say so just don't do it

x+7=21

so x will equal the addend

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21

Now count up all of the numbers past seven.

There are fourteen.

So x equals 14.

Told ya it was hard.

I hope this helped! Contact me for more!

The probability of household views between 5 and 11 hours will be 0.7653. Number of hours needed in order to be in top 3% will be 13.03 hours. Probability of views more than 3 hours will be 0.9838.

a) The probability of television views between than 5 and 11 hours.

 P( 5≤X≤11) = P[ (5-μ)/σ ≤ (X-μ)/σ ≤ (11-μ)/σ]

                   = P [ (5-8.35)/2.5 ≤ z ≤ (11-8.35)/2.5)

                    = P ( -1.34 ≤ z ≤ 1.06)

                    = P ( z≤ 1.06) - P(z ≤ -1.34)

Substituting values from the z-table

   P ( 5≤X≤11) = 0.85543 - 0.09012 = 0.76531

Probability that household views between 5 and 11 hours is  0.7653.

b) Hours needed to be in top 3% of all households.

 P( X> h) = 0.03

 P[ (X-μ)/σ > (h-μ)/σ] = 0.03

P ( z >h-8.35/2.5) = 0.03

P ( z ≤ h-8.35/2.5) = 0.97

From the table

  (h - 8.35)/ 2.5 = 1.87

   h = (1.87× 2.5) + 8.35

      = 13.025 = 13.03 hours

So if the viewing time is more than 13.03, the household will be in the top 3%.

c) Probability of viewing more than 3 hours

 P(X> 3) = P[ (X-μ)/σ > (3-μ)/σ]

               = P( z < -2.14) = 0.9838

So probability the household will have views more than 3 hours will be 0.9838.

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The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

Using slope intercept form,

y = mx + b

where

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

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1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Answer:  The graph is shown below. It is nonlinear

==========================================================

Explanation:

I used GeoGebra to make the graph. Desmos is another option I recommend.

The equation we graph is y = (1/2)^x since we're splitting the paper in half each time. This is an exponential decay function. Note how the curve slopes downhill when moving to the right.

It appears the curve touches or crosses the x axis; which is misleading. Instead, the curve is getting closer and closer to this horizontal asymptote. It will never reach the x axis. Think of it like an electric fence.

As the graph indicates, we don't have a straight line. Therefore, the function isn't linear. It's a nonlinear curve.

Find the circumference:

8km x 2 x 3.14 = 50.24 km

Arc length = 50.24 x 225/360 = 31.4 km

answer: C. 10 pi or 31.4 km

The area of quadrilateral AMNO is approximately 2.4 square inches.

To find the area of quadrilateral AMNO, we can use the formula for the area of a general quadrilateral, which states that the area can be calculated as half the product of the diagonals multiplied by the sine of the angle between them. In this case, the diagonals are AM and NO, and the angle between them is ZO.

Given that m = 1.3 inches and n = 2.1 inches, we can use these values to calculate the area.

First, we need to find the length of the diagonals AM and NO. Using the Pythagorean theorem, we can find the length of AM:

AM = √(AO^2 + OM^2)

= √(m^2 + n^2)

= √(1.3^2 + 2.1^2)

≈ √(1.69 + 4.41)

≈ √6.1

≈ 2.47 inches

Similarly, the length of NO is also 2.47 inches.

Now, we can calculate the area of AMNO using the formula:

Area = (1/2) * AM * NO * sin(ZO)

Plugging in the values, we have:

Area = (1/2) * 2.47 * 2.47 * sin(138°)

Using a calculator, we find that sin(138°) ≈ 0.9401.

Substituting the values, we get:

Area ≈ (1/2) * 2.47 * 2.47 * 0.9401

≈ 2.4267 square inches

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The equation for the maximum number of yards per second that can be run is y = 5/3 s.

A direct variation measurement between distance covered and time taken can be composed as:

y=kx,

where,

This is because the athlete's distance travelled directly varies with the amount of time it takes.

Find k using the given values:

y=kx,

10 = k(6)

k = 10/6

k = 5/3

As a result, the equation for the maximum number of yards per second is y = 5/3 s.

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Answer:

55.56% is the answer

Step-by-step explanation:

...

Answer:

What is the percent increase from 45 to 70

Step-by-step explanation:

You're welcome.

Answer:

34.0522° N, 118.2437° W

Step-by-step explanation:

Answer:

The Complex fourth roots of 4  is \(\sqrt2 i, \ - \sqrt2 i, \ \sqrt2 \ and \ - \sqrt2\) .

Step-by-step explanation:

Complex fourth roots of 4 can be obtained by solving \(x^4 = 4\).

\(x^4 = 4 \implies x^4-4 = 0\)

\((x^2)^2 - (2)^2 = 0\)

By using the algebraic identity \(a^2 - b^2 = (a + b)(a - b)\),

     \((x^2)^2 - (2)^2 = 0 \implies (x^2 - 2)(x^2 + 2) = 0\)

\(\implies (x^2 + 2) = 0 \ or \ (x^2 - 2) = 0\)

\(\implies x^2 = -2 \ or x^2 = 2\)

\(\implies x = \pm\sqrt-2 \ or \ x = \pm\sqrt2\\\implies x = \pm\sqrt2 i \ or \ x = \pm\sqrt2\)

\(\therefore\) The Complex fourth roots of 4  is \(\sqrt2 i, \ - \sqrt2 i, \ \sqrt2 \ and \ - \sqrt2\) .

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Answer:

y = 4 (x - 9/2) +0

Step-by-step explanation:

hope ot helps you

Answer:

here

Step-by-step explanation:

The sum of these numbers is 45 + x.

Let x be the smallest of the three numbers.

Then the median of the three numbers, given as 15, must be either the second largest number or the smallest number.

Now, we have two possible cases:

Case 1: The median is the second largest number.

Since the median is the second largest number, the second largest number is 15.

Therefore, the three numbers can be written as follows: x, 15, y, where y is the largest number.

Then, we know that the mean of the three numbers is 20 more than the least of the numbers and 10 less than the greatest.

Mathematically, this can be written as:x + 15 + y / 3 = x + 20y - x - 15 = 30y - x = 45

Now, we can solve for y by substituting y - x = 45 into the expression for the mean:

x + 15 + y / 3 = x + 20y - x - 15

= 30y - x

= 45y

= 30

Therefore, the three numbers are x, 15, and 30.

Their sum is:

x + 15 + 30 = 45 + x

So the sum of these numbers is 45 + x.

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Answer:

The value of the second expression is 14, so the expressions are equivalent.

Step-by-step explanation:

x=5

6+2(5)-2=

6+10-2=

16-2=

14

The other expression also came out to be 14, so they are equivalent.

Answer:

The value of the second expression is 14, so the expressions are equivalent.

Step-by-step explanation:

The square root of any natural number is either an integer or irrational. To prove this, let's first consider natural numbers that are perfect squares. A perfect square is a number that is the result of multiplying an integer by itself, i.e., \(x^2 = y\). In this case, the square root of y is an integer and can be expressed as x. For example, the square root of 16 is 4 since 4 x 4 = 16.  

Now let's consider a number that is not a perfect square, such as 25. This number cannot be expressed as the result of multiplying an integer by itself, i.e.,\(x^2 ≠ 25\). In this case, the square root of 25 is irrational. To illustrate this, let's assume that the square root of 25 is an integer, i.e., x. Since the square root of 25 is an integer, we can say that \(x^2 = 25\). Solving for x, we get x = ±5. Therefore, we can conclude that the square root of 25 is either 5 or -5. However, since 5 x -5 = -25 and -5 x -5 = 25, this contradicts our assumption that the square root of 25 is an integer, and so we can conclude that the square root of 25 is an irrational number.  

In conclusion, the square root of any natural number is either an integer or irrational, and this has been demonstrated by considering both perfect squares and non-perfect squares.

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Answer:

Company A:

Company B:

Company C:

Least cost         |        Medium cost     |     Greatest cost

Company A       |          Company C     |      Company B

Answer:

A, 32.005

Step-by-step explanation:

Sum means the value or result of addition. So this means we need to add 89.355 and 235.65.

89.355 + 235.65 = 325.005.

So, the sum of 89.355 and 235.65 is 325.005

Julia should consider buying the rug with a radius of 5 feet, as it has the potential to cover a larger percentage of her floor.

A simple approach to determine which rug Julia should buy is to compare the areas covered by the rugs and choose the one that covers approximately 50% of her floor.

To start with, let us calculate the area of each rug in the options

We can tell from the options that it is a circular rug, so applying the formula of a circle will be valid.

Recall that area of a circle is:

A = πr²

where

A is the area

r is the radius

1. Rug with a radius of 5 feet:

Area = π(5)² = 25π square feet.

2. Rug with a diameter of 5 feet:

The diameter is twice the radius, so the radius of this rug is 5/2 = 2.5 feet.

Area = π(2.5)² = 6.25π square feet.

3. Rug with a radius of 4 feet:

Area = π(4)² = 16π square feet.

4. Rug with a diameter of 4 feet:

The radius of this rug is 4/2 = 2 feet.

Area = π(2)² = 4π square feet.

We cannot make an exact comparison to Julia floor since that info is missing. However, based on the given options, the rug with the largest area is the one with a radius of 5 feet (25π square feet). This rug would likely cover a larger portion of the floor compared to the other options.

Therefore, Julia should consider buying the rug with a radius of 5 feet, as it has the potential to cover a larger percentage of her floor.

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The rate of the plane in still air (p) is 576 km/h and the rate of the wind (w) is 0 km/h. This means that the airplane's speed in still air is 576 km/h and there is no wind affecting its speed.

To find the rate of the plane in still air and the rate of the wind, we can use the concept of relative motion.

Let's denote the rate of the plane in still air as "p" (in km/h) and the rate of the wind as "w" (in km/h).

When the airplane travels against the wind, its effective speed is reduced by the speed of the wind. So the rate of the airplane against the wind can be calculated as:

Rate against the wind = p - w

Similarly, when the airplane travels with the wind, its effective speed is increased by the speed of the wind. So the rate of the airplane with the wind can be calculated as:

Rate with the wind = p + w

Given that the airplane travels 3456 kilometers against the wind in 6 hours and the same distance with the wind in the same amount of time, we can set up the following equations:

3456 = (p - w) * 6   (equation 1)

3456 = (p + w) * 6   (equation 2)

We have a system of two equations with two unknowns (p and w). We can solve this system of equations to find the values of p and w.

First, let's simplify the equations:

6p - 6w = 3456   (equation 1)

6p + 6w = 3456   (equation 2)

Now, we can add the two equations together to eliminate the variable w:

12p = 6912

Dividing both sides of the equation by 12:

p = 576

Now, we can substitute the value of p back into one of the original equations to find the value of w. Let's use equation 1:

6(576) - 6w = 3456

3456 - 6w = 3456

-6w = 0

w = 0

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According to the given figure, option (A) and option (F) are correct options which better shows ∠4 ≅ ∠6 respectively.

Let's procced to solve this question.

∠4 ≅ ∠8 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠4 ≅ ∠8 by the corresponding angle postulate. It's true.

∠6 ≅ ∠8 by the definition of vertical angles. It's true.

and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B  ≅ ∠C then ∠A ≅ ∠C.

⇒ ∠4 ≅ ∠6 by the transitive property of congruence.

Hence, option (A) is correct.

Now,

∠2 ≅ ∠6 by the corresponding angle postulate because two parallel lines is cut by a transversal and ∠2 ≅ ∠6 by the corresponding angle postulate. It's true.

∠2 ≅ ∠4 by the definition of vertical angles. It's true.

and by using the transitive property of congruence that ∠A ≅ ∠B and ∠B  ≅ ∠C then ∠A ≅ ∠C.

⇒ ∠4 ≅ ∠6 by the transitive property of congruence.

Hence, option (F) is correct.

Therefore, option (A) and option (F) are correct option.

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