A manufacturer makes bags of popcorn and bags of potato chips. The average weight of a bag of popcorn is supposed to be 3.03 ounces with an allowable deviation of 0.02 ounces. The average weight of a bag of potato chips is supposed to be 5.08 ounces with an allowable deviation of 0.05 ounces. A factory worker randomly selects a bag of popcorn from the assembly line and it has a weight of 3.06 ounces. Then the worker randomly selects a bag of potato chips from the assembly line and it has a weight of 5.03 ounces. Which description closely matches the findings on the assembly line?

2.89 is the value of x in equation [tex]e^x[/tex] = 18 solved by using natural logarithms.

We have been asked to find x in [tex]e^x[/tex] = 18 using natural logarithms

⇒  [tex]e^x[/tex] = 18

⇒  x = ㏑ (18)

⇒ x = 2.89

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

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Use natural logarithms to solve each equation.

[tex]e^x[/tex] = 18

Answer:

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Answer:

-207

Step-by-step explanation:

38x - 17

38(-5) - 17

-190 - 17

-207

*Please mark brainliest answer

Answer:-173

Step-by-step explanation:

38x - -17

38 multiplied by -5 equals -190

-190 - -17 equals -173

The value of the expression 3√70 to the nearest integer will be 25.10.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 3√70

We know that the value of √70 will be 8.3666. Then the value of the expression will be given as,

⇒ 3√70

⇒ 3 x 8.3666

⇒ 25.0998 ≈ 25.10

The value of the expression 3√70 to the nearest integer will be 25.10.

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Answer:0.16=16%

Step-by-step explanation:    [tex]\frac{0.16}{100}[/tex]

the 100 is directly under the point so the zero will cancel out leaving= [tex]\frac{16}{100}[/tex]

And  [tex]\frac{16}{100}[/tex] equals to 16%

if we had a value "z", and we'd like to know how much is 16% of "z", well

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of z}}{\left( \cfrac{16}{100} \right)z}\implies 0.16z[/tex]

so we can use the "factor" of 0.16, to get the 16% of any value,

since 0.16   is the decimal representation of the percentage of 16.

hmmm what is 16% of 50 anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 50}}{\left( \cfrac{16}{100} \right)50}\implies 8[/tex]8 out of 50

how much is 16% of 25 anyway?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 25}}{\left( \cfrac{16}{100} \right)25}\implies 4[/tex]4 out of 25

Answer:North west, the roads should have stopped this answer but north alone wasn’t an option so just pretend Jenna is a lawless maniac ig‍♂️

Step-by-step explanation:

Answer:

here to try to help!

Step-by-step explanation:

346.96 why? Kerry was not payed at the overtime for extra hours hope it helped!

From the given scatter plot with x and y variables, we can say that the correlation is; Negative Correlation.

We are told that you kept the balance in your "discretionary spending" envelope.

Now, we are further told that a scatter plot shows the number of days that have passed since you were paid and the amount left in your discretionary spending envelope.

Now, In this case, the day of the salary increases the money spent, that is, the amount of money in the envelope decreases. Thus, as the variable increases and the other decreases, it is a negative correlation.

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It can be proved using the method of inverse variation.

What is inverse variation?

In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.

Given,

(x₁, y₁) and (x₂, y₂) are values from an inverse variation.

inverse function of x and y will be -

y1 = k. 1 / x1  

k = y1 / x1                                                ....(1)

y2 = k. 1 / x2  

k = y2 / x2                                              ....(2)

from (1) , (2)

we can say that,

y1 / x1    = y2 / x2

⇒ y2 / y1 = x1 / x2

Hence proved.

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Solution of this polynomial equation is x = 3

In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non  negative number as their powers are part of polynomial equation.

Types of polynomial equations :

Some examples of polynomial equation are :

According to question,

3x = 9

=> 3x / 3 = 9 /3

=> x = 3

Thus solution for given equation is x = 3.

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During the cooking class, the instructor put 1/8 of the salt in each serving

The instructor divided 1/2 of an ounce of salt evenly

The instructor needs to 4 servings in a dish

Therefore the number of salt in each serving can be calculated as follows

= 1/2 ÷ 4

change the expression to multiplication

1/2 × 1/4

= 1/8

Hence 1/8 of the salt was placed in each serving of the dish

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The velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.

Given:

To find: Velocity of the spacecraft (v) = ?

Finding:

Here, c = 2.7 km/s, t = 30s, R = 20

On substituting the values of 'R', 't', 'v', we get:

v = -0.0098 ( 30) + 2.7 ( ln (20))

=> v = - 0.294 + 2.7 (2.995)

=> v = 7.7025 km/s

Hence, the velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.

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The value corresponding to |f(i)| is √2.

The given function is f(x)=1-x.

Given f(x) = 1 - x

To find the value of |f(i)| we have to substitute x=i.

After substituting this, we get

f(i) = 1 - i

As we all know that, this is an imaginary even function in the form a + ib

The modulus of the imaginary function can be represented as √(a²+b²)

Here a = 1 and b = -1

Now, we will substitute this value in the above formula, we get

|f(i)| = √(1² + (-1)²)

|f(i)| = √(1+1)

|f(i)| = √2

Hence, the value of the given function f(x)=1-x which is equivalent to |f(i)| corresponding value is √2.

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Answer:

Step-by-step explanation:

25/3

The linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines. (Correct choice: D)

Linear equations are equations of the form y = m · x + b, where m, b are the slope and the intercept of the equation, respectively. As slopes may be positive, null or negative, then we should use absolute values to determine the grade of steepness of a linear equation, where |m| ≥ 0. A line is steeper than other line when the absolute value of the former is greater than the absolute value of the latter.

According to this criterion, the linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines.

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Descriptive statistics is the correct answer.

Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. (By the way, "data" is plural. One piece of information is called a "datum.") If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data.

Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section. Here we focus on (mere) descriptive statistics.

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The answer is 190m.

The faster train is 160 m long and crosses a lamp post in 12 seconds.

The speed of the faster train = 16012 = 403 m/s

Given that, the speed of the other train is 6 km/hr (53 m/s) less than the faster one. [we can convert speeds from km/h to m/s by multiplying with 5/18]

The speed of the slower train = 353 m/s.

Given that, the two trains cross each other in 14 seconds when running in opposite directions along parallel tracks.

tracks.

Relative speed =  total length of two trains  time taken to cross each other

25m/s = 160+ length of second train 14

Length of the second train = 190m.

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Answer:

G' (8, - 8 )

Step-by-step explanation:

since the dilatation is centred at the origin then multiply each of the coordinates by the scale factor of 4

G (2, - 2 ) → G' (4(2), 4(- 2)) → G' (8, - 8 )

The problem that can be defined by the function is:

A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount and x is the number of time periods.

Consider the modeled function y = 20(1.1)ˣ.

Now, y = 20 × ( 1 + r)ˣ

f(x) = 20 × ( 1 + r)ˣ

Comparing the above equation with A(x) = a( 1 + r)ˣ

The initial amount is 20 and it increases 1 + r = 1.1.

Therefore, r = 0.1 = 10 %

Let's say we are starting a cat breeding company. Initially, we have 20 cats.

So, the problem for the function is:

A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?

So, a = 20, x = 10, and r = 10% = 0.1

Therefore,

A(x) = a( 1 + r)ˣ

y = a( 1 + r)ˣ

y = 20( 1 + 0.1 )ˣ

y = 20( 1.1)¹⁰

y = 20 × 2.594

y = 52

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The function f(x) = ( x + 7)³ - 8 will shift left 7 units along x axis and will shift down 8 units along y axis to its parent function g(x) = x³.

By translation, we can stretch, shrink and shift graphs along the x-y coordinate.

We know a parent function is a function that is in its simplest form without any translation.

Given f(x) = (x + 7)³ - 8 and its parent function is g(x) = x³.

Now let us break this function f(x),

f(x) = ( x+ 7)³ implies x + 7 = 0 ⇒ x = -7.

So, x will shift 7 units to the left along the x-axis.

f(x) = ( x + 7)³ - 8, This will shift the function down 8 units along y-axis.

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The dimensions of the fencing is 28 ft and 37 ft respectively.

He use 130 feet of fencing to go around a rectangular pool and patio.

The length of the area is 9 more than the width.

The dimension of the fence can be found as follows:

Therefore,

perimeter of the rectangular fence = 2(l + w)

where

Hence,

l = 9 + w

perimeter of the rectangular fence = 2(w + 9 + w)

perimeter of the rectangular fence = 2(2w + 9)

130 = 4w + 18

130 - 18 = 4w

112 = 4w

w = 112 / 4

w = 28 ft

l = 9 + 28 = 37 ft

Therefore, the width and length of the fencing is 28 ft and 37 ft respectively.

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The inverse of the function y=4 x²+5  is y = √((x-5)/4).

Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.

Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.

A function (f(x)) is said to be one-to-one if each member of the range corresponds to exactly one element of the domain.

Given,

We have a function,

y=4 x²+5

subtracting 5 from each side.

⇒ y - 5 = 4 x²

Divide by 4 and then either

⇒ x² = (y - 5) / 4

⇒ x = √((y-5)/4)

Just change the labels now, x to y.

⇒ y = √((x-5)/4)

So, the inverse of given function is y = √((x-5)/4)

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The components of PQ are given by {5; 2}

The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy), where V is a vector. These are part of the vectors generated along the axis.

Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).

Due to the trigonometric relationship:

cos θ = adjacent side/hypotenuse = vx/V

sin θ = opposite side/hypotenuse = vy/V

where V is the magnitude of vector V.

So, the Component of PQ is Given by

PQ = {Bx - Ax; By - Ay} = {3 - (-2); 4 - 2} = {5; 2}

PQ= {5; 2}

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Answer:

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The dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.

Whole numbers are numbers that do not have any fractional part and represents a whole quantity.

A mixed number consist of an whole number and a proper fraction or fractional part.

Given the dimensions of the rectangular photo as, 12 11/16 cm by 8 3/4cm, convert each dimension to improper fractions:

12 11/16 would be converted to 203/16

8 3/4 would be converted to 35/4

203/16 = 12.6875 ≈ 13 [nearest whole number of cm]

35/4 = 8.75 ≈ 9 [nearest whole number of cm]

Therefore, the dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.

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10 order of small popcorn Should be made to keep  the cost same at both the theaters

The theater P charges Admission fee of $10 and small popcorn order of $4.55

The theater Q charges Admission fee of $8 and small popcorn order of $4.75

We need to find the number of order of small popcorn so that the cost remain same

Let the number of small popcorn order be x

Then we can form the algebraic equation as

10 + 4.55x = 8 + 4.75x

now we should simplify the equation

10- 8 = 4.75x-4.55x

2= .2x

x = 2/0.2

x = 10

Hence , 10 order of small popcorn Should be made to keep  the cost same at both the theaters

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