50 peanuts for $3.00 or 75 peanuts for $3.50. Which is the better deal?

Answer: 15

Step-by-step explanation:

Area = bh

Area = 120

Height = 8

Since you have the area and the height you need to divide:

120/8

=

15

__________________________________________________________

You can also check your answer by doing bh

15 x 8

=

120

The volumes of right prisms are listed below:

Case A: 150 cm³

Case B: 525 m³

Case C: 429 m³

The volume of right prism (V), in cubic length units, is always equal to the product of the base area (A), in square length units, and height (h), in length units:

V = A · h

There are three right prisms, whose areas are combinations of right triangles and rectangles. The area formulas are shown below:

Rectangle

A = w · l

Right triangle

A = 0.5 · w · l

Where:

The complete procedure is listed below:

Case A

A = 0.5 · (4 cm) · (5 cm) + (3 cm) · (5 cm)

A = 25 cm²

V = (25 cm²) · (6 cm)

V = 150 cm³

Case B

A = (5 m) · (8 m) + (5 m) · (7 m)

A = 75 m²

V = (75 m²) · (7 m)

V = 525 m³

Case C

A = (8 m) · (4 m) + (3 m) · (9 m) + 0.5 · (5 m) · (5 m)

A = 71.5 m²

V = (71.5 m²) · (6 m)

V = 429 m³

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A quadratic equation is an equation of degree 2 and has the standard form: ax² + bx + c = 0,  with a ≠ 0. Example: 2x² - 3x - 2 = 0, the solution is {-1/2, 2}.

A quadratic equation is an equation of degree 2. The standard form of a quadratic equation is:

ax² + bx + c = 0,  with a ≠ 0

The quadratic equations can be solved using:

- factorization

- completing the square

- abc formula

Example 1:

2x² - 3x - 2 = 0

Using factorization:

2x² - 3x - 2 = (2x +1) (x-2)

Hence,

(2x +1) (x-2) = 0

Solution:

x = -1/2  and x = 2

x = {-1/2, 2}

Example 2:

x² - 6x + 4 = 0

By completing the square:

x² - 6x + 5 = (x - 3)² - 4

Hence,

x² - 6x + 5 = 0

(x - 3)² - 4 = 0

(x - 3)² = 4

x - 3 = ± 2

The solutions are

x = 3 - 2 = 1  or

x = 3 + 2 = 5

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The p-value of the hypothesis test is a measure of the strength of the evidence. There is significant evidence to reject the null hypothesis if it is less than 0.001.

A hypothesis test is a statistical procedure used to make a decision about an underlying population based on sample data. The hypothesis test involves two hypotheses. The null hypothesis, which states that the population parameter is equal to a given value, and the alternative hypothesis, which states that the population parameter is not equal to the given value. The strength of the evidence is gauged by the p-value. A p-value of less than 0.001 indicates that the evidence is very strong, and that the null hypothesis should be rejected. This means that the data is not consistent with the null hypothesis, and the alternative hypothesis should be accepted. In other words, the population parameter is not equal to the given value.

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The decimal form of the value, 31/24 is 1.29166... The nearest hundredth form of this expression will be 1.29.

To calculate the nearest hundredth you have to examine the second number that comes after the decimal point. To get the nearest hundredth, leave the hundredth value as it is if the value after it is not up to five. If the value after the hundredth value is more than 5, then we have to add 1 to the figure that constitutes the hundredth value.

In the question given above, 9 is the hundredth value. The value after 9 is 1 and since it is less than 5, it will not be changed. Therefore, the figure when rounded off to the nearest hundredth form is 1.29.

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Linear regression is a statistical tool used in predictive analytics to identify the relationship between a dependent variable and one or more independent variables.

Linear regression is a statistical technique used in predictive analytics to identify the relationship between a dependent variable and one or more independent variables. It is used to predict future outcomes by analyzing data from the past. It works by fitting a linear equation to the data, which is then used to estimate the value of the dependent variable for any given combination of values of the independent variables. The linear equation is constructed by finding the line of best fit through the data points. Linear regression can be used to identify trends and patterns in the data, and to make predictions about future outcomes. It is a powerful tool for predicting the future, and can be used to make informed decisions about how to best use resources.

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The expression to represent the number of members in the House of Representatives is 4x + 35.

Based on the information, the question has to do with an expression. An expression shows the relationship between the variables.

In this situation, the United States House of Representatives has 35 more members than four times the number of members in the United States Senate

Let the number of members in Senate be x.

The expression will be:

(4 × x) + 35

= 4x + 35

The expression is 4x + 35.

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The maximum possible value of the largest of these five integers is 35.

Integer:

An integer is a number with or without a fractional part, including negative and positive numbers, including zero. Examples of integers are -5, 0, 1, 5, 8, 97, and 3,043. The set of integers represented as Z includes:

Positive number: A number is positive if it is greater than zero. For example: 1, 2, 3. .

Negative number: A number is negative if it is less than zero. For example: -1, -2, -3. . .

Zero: Zero is not defined as negative or positive is an integer.

According to the question:

Since the average of 5 different positive integers is 15, we can assume that all sum to 5 * 15 = 75. Median is 18. So the sum of the remaining 4 numbers is 75 − 18 = 57, meaning 2 numbers are greater than 18 and 2 numbers are less than 18.

Find : the highest possible maximum, and I want the minimum to be very low.

The fourth number is 19 because we want the largest integer maximum. This is because it is the lowest value that can be obtained and is higher than the median value. Then we have 1, 2, 18, 19 in the dataset for a total of 40.

The sum of the five numbers is 75.

Therefore, the maximum possible value of the largest five integer is

75 - 40 = 35.

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If the lease factor is given as 0. 00045 then the interest rate is that equivalent to 4.5%

The lease factor of 0.00045 is equivalent to an interest rate of 4.5%. This is because the lease factor is a measure of the interest rate a lessee pays on a lease.

It is calculated by dividing the interest rate by 2400. This means that the higher the lease factor, the higher the interest rate that the lessee pays.

For example, if the interest rate is 12%, then the lease factor would be 0.005.

In this case, the lessee would be paying an interest rate of 12%, or 0.005 as a lease factor.

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The number of terms in the given algebraic expression "2n + 5 - 3p + 4q" are four terms .

An Algebraic Expressions are defined an expression that consists of numbers, variables and joined by mathematical operator .

For example, 3x + 6 is an expression where 3x and 6 are the terms and x is the variable that is separated by the arithmetic sign "+".

The given expression is 2n + 5 - 3p + 4q ,

as we can see that the mathematical operators used are + and - .

This expression cannot be simplified further ,

So , the first term is 2n , the second term is 5 , third term is 3p and fourth term is 4q .

Therefore , the given expression has four terms .

The given question is incomplete , the complete question is

How many terms are in the expression shown to n +5 - 3p + 4q ?

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The expression consists of 3 terms: en, minus 3p, plus 4q. It can be expanded by multiplying the first term, en, by the coefficients of the other two terms. The resulting expression is en - 3pen + 4qen. The final result is en - 3pen + 4qen, which can also be written as en + 4qen - 3pen.

Step 1: Expand the expression by multiplying the first term, en, by the coefficients of the other two terms.

Step 2: The resulting expression is en - 3pen + 4qen.

Step 3: Simplify the expression to get the final result: en + 4qen - 3pen.

The expression to en +5 minus 3p plus 4q consists of 3 terms. To expand it, we need to multiply the first term, en, by the coefficients of the other two terms. This means that en needs to be multiplied by -3p and +4q to get the expanded expression.

This is the final result of the expansion. By multiplying the first term by the coefficients of the other two terms, we have been able to expand the expression to en +5 minus 3p plus 4q. This expression can now be used in calculations to solve problems.

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The  value of the given equation is, (6m⁸n⁹) (4mn⁷) =[tex]$$=24 m^9 n^{16}$$[/tex]

Simplify[tex]$\left(6 m^8 n^9\right)\left(4 m n^7\right): \quad 24 m^9 n^{16}$[/tex]

steps

[tex]$$\left(6 m^8 n^9\right)\left(4 m n^7\right)$$[/tex]

Apply exponent rule: [tex]$a^b \cdot a^c=a^{b+c}=0^{\prime}=$[/tex]

[tex]& m^8 m=m^{8+1} \\[/tex]

[tex]& =6 n^9 \cdot 4 m^{8+1} n^7[/tex]

\end{aligned}

Add the numbers: [tex]$8+1=9$[/tex]

[tex]=6 n^9 \cdot 4 m^9 n^7[/tex]

Apply exponent rule: [tex]$a^b \cdot a^c=a^{b+c}$[/tex]

[tex]& n^9 n^7=n^{9+7} \\[/tex]

[tex]& =6 \cdot 4 m^9 n^{9+7}[/tex]

Add the numbers: [tex]$9+7=16$[/tex]

[tex]$$=6 \cdot 4 m^9 n^{16}$$[/tex]

Multiply the numbers: 6 - [tex]$4=24$[/tex]

[tex]$$=24 m^9 n^{16}$$[/tex]

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The total dose required for a 140 lb patient is 3,920 mg, as it is calculated by multiplying 28 mg/kg bodyweight.

1. Calculate the patient's bodyweight in kilograms by dividing their weight in pounds (140) by

2.2: 140 ÷ 2.2

= 63.63 kg

2. Multiply the patient's bodyweight in kilograms (63.63) by the required dose per kilogram (28):

63.63 x 28

= 1,780.84 mg

3. Round this number up to the nearest whole number: 1,780.84 rounded up = 3,920 mg

The total dose required for a 140 lb patient is calculated by multiplying the amount required per kilogram of bodyweight by the patient's bodyweight in kilograms. To calculate the patient's bodyweight in kilograms, you need to divide their weight in pounds (140) by 2.2. This gives you 63.63 kg. Then, multiply the patient's bodyweight in kilograms (63.63) by the required dose per kilogram (28): 63.63 x 28 = 1,780.84 mg. Finally, round this number up to the nearest whole number: 1,780.84 rounded up = 3,920 mg. Therefore, the total dose required for a 140 lb patient is 3,920 mg.

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Answer:

Step-by-step explanation:

Given ∆PQR with ∠P = (4x-9)°, ∠Q = (6x+2)°, and ∠R = x°, you want an equation to find x, and the measures of the angles.

The equation expresses the fact that the sum of angles in a triangle is 180°.

  ∠P +∠Q +∠R = 180°

  (4x -9)° +(6x +2)° +x° = 180°

  11x -7 = 180 . . . . . . . . . . . . divide by °, collect terms

  11x = 187 . . . . . . . . . add 7

  x = 17 . . . . . . . . divide by 11

The angle measures are found by substituting for x in the angle expressions:

  ∠P = (4·17 -9)° = 59°

  ∠Q = (6·17 +2)° = 104°

  ∠R = 17°

There are 5040 different permutations of the set {a, b, c, d, e, f, g}.

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

The set {a, b, c, d, e, f, g} has seven elements, so there are 7! (7 factorial) permutations possible. The factorial of a number is the product of all the numbers up to and including that number. In this case,

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

This means that there are 5040 different permutations of the set

{a, b, c, d, e, f, g}.

A permutation is defined as an arrangement of elements in a specific order. In this case, the elements are {a, b, c, d, e, f, g} and the order can be changed in any way, as long as all elements are included. For example, one possible permutation is bfgdeca.

This is one of the 5040 possible permutations of the set.

As the set contains seven elements, there are 7! (7 factorial) possible permutations. This means that there are 5040 different permutations of the set {a, b, c, d, e, f, g}.

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4 quizzes are taken per week.

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

A linear equation is given by: y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let y represent the total number of quizzes after x weeks.

From the table we can see that when y = 12, x = 3 and when y = 20, x = 5. Hence:

Number of quizzes per week = 12/3 = 20/5 = 4

Hence, 4 quizzes are taken per week.

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Imogen  need to buy 3 packs of bread rolls for every 5 packs of Burgers packs that are sold.  

Two or more expressions with an Equal sign is called as Equation.

X= Number of Bread Roll Packs

Y= Number of Burger Packs

Therefor we can say

20X=12Y

X/Y=12/20=3/5

Therefore Imogen need to buy 3 packs of bread rolls for every 5 packs of Burgers packs that are sold.  

Hence, Imogen  need to buy 3 packs of bread rolls for every 5 packs of Burgers packs that are sold.  

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The equation of the hyperbola in standard form is y²/8² - (x-5)²/6² = 1

Given that the center of the hyperbola is (5,0) and the vertex is (5,6), we can see that the center is on the x-axis, so the y-coordinate of the center, k, is 0. The x-coordinate of the center, h, is 5.

We know that equation of Hyperbola is

(y-k)²/a² - (x-h)²/b² = 1

Where (h,k) is the center and given (h, k) = (5, 0) and b is the transverse axis and a is the conjugate axis.

Now b is the y-coordinate of vertex (5,6) ⇒b=±6

and c is the y-coordinate of focus (5,10)c=±10

And also c² = a²+b²

(±10)²=a²+(±6)²

⇒a²=100−36=64

Hence a=±8

Thus, the equation of the hyperbola is y²/8² - (x-5)²/6² = 1

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The proof of <BED = <BAC  is shown below.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

AE ⊥ BC

and, CD ⊥ AB

As, AE is perpendicular to BC then BE = EC = 1/2 BC

and, BD = AD = 1/2 AB

Now, In ΔBED and ΔBCA

<EBD = <ABC {common}

BD/AB = BE/ BC = 1/2

By ASA similarity Criteria ΔBED ~ ΔBCA

So, <BED = <BAC

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Answer:

To find the annual salary of one employee, you need to divide the total monthly salary by the number of employees and then multiply by 12 to get the annual salary.

Here's the step-by-step process:

Divide the total monthly salary by the number of employees: 710582 / 157 = 4550.85

Multiply the result by 12 to get the annual salary: 4550.85 * 12 = Rs. 54610.20

So, the annual salary of one employee is Rs. 54610.20.

Step-by-step explanation:

Answer: 4.699 ounces (72.85 %)

Step-by-step explanation: Total Quantity in bottle = 6.45

 Total quantity = quantity of fruit juice + quantity of not fruit juice.

  ATQ.

  6.45 = 1.751 + quantity of not fruit juice

quantity of not fruit juice = 4.699 ounces

in percentage it will be 4.699/6.45 × 100 = 72.85%

Inequality compares two variables, to show if one is less than, equal to or greater than the other variable being compared.

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Answer:

s

Step-by-step explanation:

your welcome!!!!!!!!!!!!!!!!!!!!!!!!!!!!

the centroid of the region bounded by the given curves is (x, y) = (15, 225).

To show that f is continuous on (−∞,∞), we need to show that the limit of f(x) as x approaches any point from the left and from the right is equal.

First, let's consider the limit of f(x) as x approaches 1 from the left.

As x approaches 1 from the left, f(x) = 1-x^2, so the limit of f(x) as x approaches 1 from the left is 1.

Now, let's consider the limit of f(x) as x approaches 1 from the right.

As x approaches 1 from the right, f(x) = ln x, so the limit of f(x) as x approaches 1 from the right is 0.

Since the limit of f(x) as x approaches 1 from the left is 1 and the limit of f(x) as x approaches 1 from the right is 0, we can conclude that f is continuous on (−∞,∞).

To find the centroid of the region bounded by the given curves, we need to calculate the area of the region and the area-weighted centroid of the region.

The area of the region is given by the integral of x3 from 0 to 10, which is equal to 1125/4.

The area-weighted centroid of the region is given by the integral of (x3*x)/(1125/4) from 0 to 10, which is equal to 15.

Therefore, the centroid of the region bounded by the given curves is (x, y) = (15, 225).

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The exact length of the curve y=ln[(e^x+1)/(e^x-1)], a ≤ x ≤ b, is equals to the ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].

The exact length of curves implies the length of arc of curve. Arc length is the distance between two points along a section of a curve, formula

Arc length = ₕ∫ᵏ√( 1 + ( y')² dx , h≤x≤k

We have a curve , y = ln[ (eˣ + 1) /(eˣ - 1) ] , a≤x≤b , a> 0

firstly, determine the first derivative of y with respect to x ..

dy/dx = y' = [ 1/(eˣ +1) /(eˣ -1)] d/dx (( eˣ + 1) /(eˣ -1) )

( apply chain rule )

= (eˣ -1 )/(eˣ +1 )[{(eˣ -1) eˣ - ( eˣ +1)eˣ}/(eˣ - 1)²]

( using quotient rule)

= (eˣ -1 )/(eˣ +1 )[(e²ˣ - eˣ - e²ˣ - eˣ)/(eˣ - 1)²]

= (eˣ -1 )/(eˣ +1 )[(- 2eˣ)/(eˣ - 1)²]

= -2eˣ /(eˣ -1 )(eˣ +1 )

dy/dx = - 2eˣ /e²ˣ -1

so, (dy/dx)² = (- 2eˣ /(e²ˣ -1) )²

= 4e²ˣ /(e²ˣ -1 )²

and 1 + (dy/dx)² = 1 + {4e²ˣ /(e²ˣ -1 )² }

= {(e²ˣ -1 )² + 4e²ˣ}/(e²ˣ -1 )²

= (e⁴ˣ + 1 - 2e²ˣ + 4e²ˣ)/(e²ˣ -1 )²

= ( e⁴ˣ + 1 + 2e²ˣ )/(e²ˣ -1 )²

1 + (dy/dx)² = (e²ˣ + 1)²/(e²ˣ -1 )²

Now plugging the value in arc length formula,

Arc length = ₐ∫ᵇ √{1 + (dy/dx)²} dx

= ₐ∫ᵇ √{(e²ˣ + 1)²/(e²ˣ -1 )²} dx

= ₐ∫ᵇ√{(e²ˣ + 1)/(e²ˣ -1 )}² dx

= ₐ∫ᵇ {(e²ˣ + 1)/(e²ˣ -1 )} dx

= ₐ∫ᵇ[eˣ(eˣ + e⁻ˣ)/eˣ(eˣ - e⁻ˣ )] dx

= ₐ∫ᵇ[(eˣ + e⁻ˣ)/(eˣ - e⁻ˣ )] dx

Arc length= ₐ∫ᵇ(cosh x)/(sinh x)dx ( using hyperbolic functions formulas )

let sinh x = t => cosh xdx = dt

and when x = a => t = sinh a

when x = b => t = sinh b

so, arc length = ₛᵢₙₕ ₐ∫ˢᶦⁿʰ ᵇ (1/t) dt

= [ ln( sinh b ) - ln(sinh a) ]

= ln( sinh b/ sinh a)

Arc length= [( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)]

Hence, length of curve is ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].

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The integral evaluates the area under a curve by taking the antiderivative of the given function and evaluating the limits of the integral. The final result is (1/3) ax3 - (1/2) b2 ax + c.

∫ (ax)2 − b2 3/2 dx = (1/3) ax3 - (1/2)b2 ax + c

The integral evaluates the area under a curve. It is calculated by taking the antiderivative of the given function and then evaluating the limits of the integral. To find the antiderivative, we use the power rule to calculate the derivative of the function and then integrate the result. In this case, the function is (ax)2 - b2 3/2. Using the power rule, we find that the derivative of this function is (3/2) ax2 - (1/2) b2 ax. We then integrate this result and add the constant of integration (c) to obtain the integral. The final result for this integral is (1/3) ax3 - (1/2) b2 ax + c.

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Answer:

[tex]-\infty \: < x < \infty[/tex]

or, in interval notation as

[tex]\left(-\infty \:,\:\infty \:\right)[/tex]

Step-by-step explanation:

The domain of a function [tex]f(x)[/tex] is the set of all values of [tex]x[/tex] for which [tex]f(x)[/tex] is real and defined

The given function is f(x) = x³ + 6x² + 5

There are no undefined points. So the domain is the set of all real numbers that can be expresses as

[tex]-\infty \: < x < \infty[/tex]

or, in interval notation

[tex]\left(-\infty \:,\:\infty \:\right)[/tex]

Answer: The answer is 16

Step-by-step explanation:

The value of x in the expression is 10

You should understand that an equation is a mathematical statement showing the equality of two things

The given equation is 1250=1/2×50×(2x+3x)

To find the value of x, we have to simplify the right hand side of the equation

This is = 1250 = 50(5x)/2

This will give us 2500 250x after cross multiplication

Then make x the subject of the relation by dividing by 250

This implies that x = 10

The expression leaves the value of x at 10

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