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A large container of breath mints has a mass of 50 g. A small container has a mass of 10 g. What is the percent decrease from the mass of the large container to the mass of the small container? Show your work.​

The area that she needs to cover, which is the area of the trapezoid, is given as follows:

A = 144 m².

The area of a trapezoid is given by half the sum of the bases, multiplied by the height.

The parameters of this problem are given as follows:

Hence the area of the trapezoid is given as follows:

A = 0.5 x 12 x (9 + 15)

A = 6 x 24

A = 144 m².

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Answer:

X=13

Step-by-step explanation:

Because vertical angles exist opposite to each other formed by intersecting lines, the angles would be congruent to each other. Meaning angle A is congruent to angle B.

Step 1: 8x-12=6x+14

Step 2: 2x-12=14

Step 3: 2x=26

Step 4: x=13

Answer:

yes they are equivalent

Step-by-step explanation:

25/45÷5/5=5/9

and 5/9×5/5=25/45

hope this answer helps u...

Answer:

Yes.

Step-by-step explanation:

5/9 is equivalent to 25/45. We can find this out by multiplying both the numerator and the denominator by 5 as 9 x 5 = 45.

So the result is; 5/9 = (5 x 5)/ 9 x 5 = 25/ 45

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Distance is the number of units between two points.

Tom's distance was 15 km shorter than James's

Calculate the difference between these distances

\(d = 25km -10km\)

Evaluate the differences

\(d = 15km\)

Hence, Tom's distance was 15 km shorter than James's

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The end behavior of f(x) is described as follows:

The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.

The function for this problem is given as follows:

f(x) = 4(5/7)^x.

It is an exponential function with base with absolute value less than 1, hence the end behavior is given as follows:

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84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

(a)

Given a₁ = - 2 and a₄ = 16, then

a₁ + 3d = 16 , that is

- 2 + 3d = 16 ( add 2 to both sides )

3d = 18 ( divide both sides by 3 )

d = 6

--------------

(b)

Given

\(a_{n}\) = 11998 , then

a₁ + (n - 1)d = 11998 , that is

- 2 + 6(n - 1) = 11998 ( add 2 to both sides )

6(n - 1) = 12000 ( divide both sides by 6 )

n - 1 = 2000 ( add 1 to both sides )

n = 2001

------------------

The value of the angles in the figure are:

m∠1 = 114°

m∠3 = 114°

m∠4 = 66°

To answer the question, we need some angle geometry knowledge:

We have:

m∠2 = 66°

Thus, we can find the angles in the figure as follow:

m∠1 = 180° - 66°   (sum of angles on a straight line is 180°)

m∠1 = 114°

m∠3 = m∠1 (vertically opposite angles are equal)

m∠3 =  114°

m∠4 = m∠2 (vertically opposite angles are equal)

m∠4 =  66°

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Answer:

A)  The probability that a randomly chosen car is made in Germany or Japan is 40%.

B)  The probability that a car chosen at random is not made in the United States is 60%.

C)  The probability that two randomly chosen cars are both from Japan is 9%.

Step-by-step explanation:

Supposing that 40% of cars in my area are manufactured in the US, 30% in Japan, 10% in Germany, and 20% in other countries, to determine the probabilities that a car selected at random is made in Germany or Japan, a car selected at random is not US-made and two cars are selected at random, both are from Japan, the following calculations must be performed:

A)

(30 + 10) / 100 = X

40/100 = X

0.4 = X

Therefore, the probability that a randomly chosen car is made in Germany or Japan is 40%.

B)

(30 + 10 + 20) / 100 = X

60/100 = X

0.6 = X

Therefore, the probability that a car chosen at random is not made in the United States is 60%.

C)

10/30 x 10/30 = X

0.3 x 0.3 = X

0.09 = X

Therefore, the probability that two randomly chosen cars are both from Japan is 9%.

Answer

sum of all 3 digit even number = 247050

The series is 100 + 102 + 104 + .... + 998

which by using formula Sn = N/2 ( a + an)

where N = number of terms

a = first term = 100

an = last term = 998

The population of the city after 13 years with growth rate of 3.5% per year is equal to 422268 people.

Population of the people in the city = 270,000

Population grow by 3.5% per year

Time = 13 years

We can use the formula for exponential growth,

P = P₀(1 + r)ⁿ

where P₀ is the initial population,

r is the annual growth rate as a decimal,

n is the number of years,

and P is the final population.

Using the values given in the problem, we have,

P₀ = 270,000

since the annual growth rate is 3.5%

r = 0.035

Since we want to know the population after 13 years.

n = 13

Plugging these values into the formula, we get,

P = 270,000(1 + 0.035)¹³

  = 270,000 (1.56395 )

   ≈ 422268.1

Rounding to the nearest whole number, the population after 13 years will be approximately 422268 people.

Therefore, the population of the city after 13 years is equal to 422268 people.

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Answer:

A - 35 copies

B - $4050

Step-by-step explanation:

A-

2300 + 70c = 4750

70c = 4750 - 2300

70c = 2450

c = 35

He sold 35 copies

B-

P = 2300 + 70(25)

P = 2300 + 1750

P = $4050

Total if he sold 25 copies: $4050

The simplified form of the expression is a³ which is calculated by using the properties of exponents.

Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as bⁿ. Its pronunciation is "b (raised) to the (power of) n." Exponentiation corresponds to repeated base multiplication where n is a positive integer; so, bⁿ is the result of multiplying n bases.

Typically, a superscript to the right of the base indicates the exponent. Then, bⁿ is referred to as "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most succinctly, "b to the nth."

The given expression is a³(2a² + 4bc⁴)⁰.

From the properties of exponents we know that:

a⁰ = 1

Therefore the value of the part of the expression (2a² + 4bc⁴)⁰ is 1

Therefore the total value of the exponential expression is a³

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The statement triangle BCD is a right angle triangle because an angle in a semicircle is a right angle option 1 is correct.

It is defined as the combination of points that, and every point has an equal distance from a fixed point (called the center of a circle).

We have a diagram shown in the picture.

BC is the diameter of the circle.

Point B and Point C lies on the circle.

If a point D, which is unique from points B and C, is plotted on circle A.

Then the right angle triangle will be formed because an angle in a semicircle is a right angle.

Thus, the statement triangle BCD is a right angle triangle because an angle in a semicircle is a right angle option 1 is correct.

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The amount earned if they decreased the price by $0.20 will be $2400.

From the information, they found that for every $0.20 that the price is reduced, they can get 50 more customers.

The amount earned if they decreased the price by $0.20 will be:

= ($5 - $0.20) × (450 + 50)

= $4.80 × 500

= $2400

Therefore, the amount is $2400.

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Answer:

60.72

Step-by-step explanation:

you multiply 25.3 by 2.4

The equation of the parabola with focus (3, 4) and directrix y = 1 is \(x^2 - 6x - 12y + 57 = 0.\)

To find the equation of a parabola with a given focus and directrix, we can use the standard form of the equation of a parabola:  

\(4p(y - k) = (x - h)^2\)  

where (h, k) represents the coordinates of the vertex, and p is the distance between the vertex and the focus or directrix.

In this case, the focus is given as (3, 4), which means the vertex of the parabola will also be located at (3, 4).

The directrix is given as y = 1.

First, let's find the value of p, which is the distance between the vertex and the focus (or the vertex and the directrix). In this case, p will be the distance between the vertex (3, 4) and the directrix y = 1.

Since the directrix is a horizontal line, the distance between the vertex and the directrix is the vertical distance, which is |4 - 1| = 3.

Now that we have the value of p, we can substitute it into the equation:

\(4p(y - k) = (x - h)^2\)

Plugging in the values (h, k) = (3, 4) and p = 3, we get:

\(4(3)(y - 4) = (x - 3)^2\)

Simplifying further:

\(12(y - 4) = (x - 3)^2\)

Expanding the equation:

\(12y - 48 = x^2 - 6x + 9\)

Bringing all terms to one side:

\(x^2 - 6x - 12y + 57 = 0\)

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Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Answer:

\(3 {( \frac{1 - x}{2}) }^{2} = 3 \times {(1 - x)}^{2} \div {2}^{2} \\ =3 \times (1 - 2 \times 1 \times x + {x}^{2}) \div 4 \\ = 3 \times (1 - 2x + {x}^{2} ) \div 4 \\ = \frac{3}{4} (1 - 2x + {x}^{2})\)

\( \bold \pink{ \underline{hope \: it \: helps}}\)

Answer:

1. 1/80 = 0.0125

2. 1/2 = 0.5

3. 280

4. 23.09

5. 1/2 = 0.5

Step-by-step explanation:

1. height of probability density function

\(\frac{1}{320-240} \\= \frac{1}{80}\)

= 0.0125

2. probabilty that you will win the auction given a bid of 280

= \(\frac{280-240}{320-240} \\=\frac{40}{80} \\= \frac{1}{2}\)

3. mean secret service price

\(\frac{320+240}{2} \\=\frac{560}{2} \\= 280\)

4. the standard deviation of the above

= (320-240)/12^1/2

= 23.09

5. with a new bid of 300 dollars, probability you will win auction

= [(300-280)/(320-240)]/[(320-280)/(320-240)

= (20/80) / (40 /80)

= 0.25/0.5

= 0.5

\(g(x) =8x^5 + ax^4 +5x +20 \\\\\text{If}~ x +4 ~ \text{is a factor of g(x) then,}~ \\\\g(-4)=0\\\\\implies 8(-4)^5 +a(-4)^4+5(-4) +20 = 0\\\\\implies 256a -8192 = 0\\\\\implies a = \dfrac{8192}{256} = 32\)

Answer:

Step-by-step explanation:

Given:

Find (f + g)(x):

Correct choice is C

\(\\ \tt\longmapsto (f+g)(x)=f(x)+g(x)\)

\(\\ \tt\longmapsto \dfrac{x-6}{2}+4x^2+x-4\)

\(\\ \tt\longmapsto \dfrac{x-6+8x^2+2x-8}{2}\)

\(\\ \tt\longmapsto \dfrac{8x^2+3x-14}{2}\)

\(\\ \tt\longmapsto 4x^2+\dfrac{3}{2}x-7\)

Answer:

A. x <= 2

Step-by-step explanation:

The domain of a real function should be all real numbers. In

f(x) = sqrt(2-x)

we need 2-x to be non-negative, therefore

2-x >= 0

which implies

x <= 2

Answer:

\(\Huge \boxed{{x\leq 2}}\)

Step-by-step explanation:

The function is given,

\(f(x)=\sqrt{2-x}\)

The domain of a function are all possible values of x.

There are restrictions for the value of x.

2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.

\(2-x\geq 0\)

\(-x\geq -2\)

\(x\leq 2\)

The domain of the function is x ≤ 2.

Answer:

156 M

Reasoning you add How far He has walked from his starting point

Step-by-step explanation:

Answer: 156 m here u go

Answer:

a. Using the empirical rule, approximately 68% of healthy adults have body temperatures within 1 standard deviation of the mean, or between 97.52°F and 98.70°F.

b. Using the empirical rule, approximately 99.7% of healthy adults have body temperatures between 96.34°F and 99.88°F, which is within 3 standard deviations of the mean.

Answer:

B. $254

Step-by-step explanation:

Flat Fee: $30    

Cost per hour: $28

Customer 1: 3(28) + 30 = 114

Customer 2: 5(28) + 30 = 170

Customer 3: 8(28) + 30 = 254

Answer:

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Step-by-step explanation:

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