2. Andrew filled 5 boxes in 35 minutes.
Paige worked for 75 minutes at a
faster rate than Andrew. Select all the
rates that could be Paige's.
A15 boxes in 75 minutes
B10 boxes in 75 minutes
C12 boxes in 75 minutes
D1 box in 6 minutes
E1 box in 9 minutes

We can answer the questions in the following way:

Barriers to economic development are all those things that hinder the growth and development of an economy of a nation.

Many factors act as barriers to economic development, like lack of education, healthcare, inadequate infrastructure, lack of access to capital, etc.

These barriers can hinder people's ability to achieve their full potential, and lead to lower levels of economic growth and development.

Taking care of these issues by the government is important to promoting sustainable economic development.

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Answer:

The area of this polygon is 14 square units.

Answer: $105

Step-by-step explanation:

I would take 5+2=7 then take 7×15=105

Answer is $105 to ship.

Answer:

Solution: It is given that Miguel needs to cut a board that is Two-thirds of a yard long into 3 equal pieces. It means is divided in 3 equal parts.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The option that is greater than 4 is option (a) 5. This is because 5 is a positive value that is larger than 4. Option (b) -5 is a negative value that is less than 4. Option (c) -1/2 is also negative and less than 4. Option (d) -25 is the most negative option and therefore less than 4. So, the only option that is greater than 4 in this case is 5.

Answer:

a

Step-by-step explanation:

got it right on edge

The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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Jocelyn would need to save $1333.33 each year with 7% interest.

To calculate how much Jocelyn needs to save for the down payment over the next three years, we first need to determine the total down payment required. If the down payment is stated as $4000, then that is the total amount needed.

Assuming that Jocelyn wants to make the down payment in three years, we can calculate how much she needs to save each year by dividing the total down payment by three:

$4000 / 3 years = $1333.33 per year

So Jocelyn would need to save approximately $1333.33 each year for the next three years in order to have enough for the $4000 down payment.

Correct Question :

JUST $4000 DOWN PAYMENT!

LOW 7% INTEREST RATE!

5 YEARS TO REPAY YOUR LOAN!

In order to afford the down payment, how much will Jocelyn need to save for each of the next three years

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The wheel will make one complete revolution around the circle after travelling a distance of 62.8 inches.

The distance that the wheel travels around the circle once is equal to the circumference of the circle.

The formula for circumference of a circle is given as;

D = 2πr

where;

The radius of the circle = 10 inches

The circumference of the circle is calculated as follows;

D = 2 x 3.14 x 10

D = 62.8 inches

Thus, the circumference of the circle is determined as 62.8 inches.

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To accumulate $88,000 (future value) in 17 years in a fund that attracts an APR of 4%, the monthly deposit should be $301.89

The monthly deposit can be determined from the future value using an online finance calculator.

N (# of periods) = 204 months (17 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $88,000

Results:

PMT (Monthly Deposits) = $301.89

Sum of all periodic payments = $61,585.56

Total Interest = $26,414.44

Thus, when $301.89 is deposited monthly in a fund earning 4% APR, the future value can become $88,000.

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Answer: The scale factor used to create the image is 0.8

Step-by-step explanation: To determine the scale factor used to create the image, we can divide the corresponding side lengths of the dilated polygon D' by the corresponding side lengths of the original polygon D.

For example, the top and bottom sides of polygon D have a length of 8, while the corresponding sides of polygon D' have a length of 6.4.

So, the scale factor used to create the image is:

6.4 / 8 = 0.8

Therefore, the scale factor used to create the image is 0.8.

The direction and angle of rotation include the following: C. 180° counterclockwise rotation.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point A (-6, 5)  →  Coordinates of point A' = (6, -5)

In conclusion, this transformation rule (x, y) → (-x, -y) is used for the 180° rotation of a geometric figure about the origin in a clockwise or counterclockwise (anticlockwise) direction.

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1. The volume of the pyramid = 12 mm³.

2. Slant height (x) x ≈ 4.3 mm

3. Surface area of square pyramid = 86.4 mm²

1. The volume of the pyramid (V) = 1/3*a²h, where:

a is the base edge = 3 mm

h is the height = 4 mm

Plug in the values:

The volume of the pyramid (V) = 1/3*3²*4 = 12 mm³.

2. Slant height (x) = √(1.5² + 4²)

x ≈ 4.3 mm

3. Surface area of square pyramid = 6bs + b² = 6(3)(4.3) + 3²

= 86.4 mm²

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Answer:

Almost equals 28°

Step-by-step explanation:

cos(x)= 12/18

x= cos^-1 (12/18)

So it equals 48.1896°

Answer:

Step-by-step explanation:

сosx*cosy+sinx*siny

The probability that they both select a poodle is bigger. The probability is 0.074

In the store, there are 11 puppies, and 3 of them are poodles.

If Rebeca and Aaron chose at random, then the probabilities are; for Rebbeca, there is a 3/11 probability to get a poodle ( because there are 3 poodles of eleven dogs) and the probability for Aaron is 2/10 because now there are one less poodle (and in consequence one less puppy)

now, the joint probability of these two events happening is the product of each probability, this is:

p = (3/11)*(2/10) = 6/110, that we can simplify at 3/55 if we divide both denominator and numerator by 2.

If the dog is replaced after Rebeca picked hers, then Aaron also has a 3/11 probability of picking a poodle, and in that case, the joint probability is:

q = (3/11)*/3/11) = 9/121

now, p = 3/55 = 0.055 and q = 9/121 = 0.074

Thus, this means that the probability of both of them selecting a poodle is bigger when the dog is replaced (which makes a lot of sense)

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Answer:

Therefore, the percentage change from 20 to 50 is an increase of 150%.

Step-by-step explanation:

To work out the percentage change from 20 to 50, we can use the following formula:

((New Value - Old Value) / Old Value) x 100%

Plugging in the numbers, we get:

((50 - 20) / 20) x 100%

= (30 / 20) x 100%

= 1.5 x 100%

= 150%

Brand B contains 3% saline solution by volume. Then, C is the right answer.

Percentage of saline solution in brand B, let x be.

We know that the overall volume of saline solution in the combination is 18% of 6 gallons plus x% of (18 - 6) gallons since Danielle blended brands A and B to make a total of 18 gallons of 8% saline solution.

Then the equation is given as,

0.18(6) + 0.01x(18 - 6) = 0.08(18)

Simplifying and solving for x, we get:

1.08 + 0.12x = 1.44

0.12x = 0.36

x = 3

Therefore, the percentage of saline solution in brand B is 3%.

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Answer: x = -5, 5 y= 0

Step-by-step explanation:

vertical asymptotes = x= -5, 5

horizontal asymptotes = y= 0

Answer:

  (b)  0.083

Step-by-step explanation:

You want the probability that a part is New and Passed the test, given the distribution of parts as shown in the table.

"This group" consists of all the parts described by the table. That is a total of ...

  5 + 23 + 2 + 30 = 60

parts.

Of those 60 parts, the number that is found in the table cell (New, Passed) is 5. This means 5/60 = 1/12 ≈ 0.083 of the total number of parts shown were New and Passed the test.

The probability of choosing one of those parts at random is 0.083.

__

Additional comment

This is not "coordinate algebra". It is probability.

Answer:

  9

Step-by-step explanation:

You want the least common denominator for the fraction in the sum ...

 (2/3)² -1/3

When the sum is simplified, it is ...

  4/9 -1/3

The denominator 9 is a multiple of the denominator 3, so the least common denominator of these two fractions is 9.

__

Additional comment

Using that denominator, the sum is ...

  4/9 -3/9 = 1/9

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If male and female students of section B in DPS and DAV are in ratio 3 : 2 and 4:3 respectively then male students of section B are 40% more than female students of section B considering both the schools (approx).

(A) 50% (C) 36% (B) 25% (D) 40%.

Hence, the correct option is D.

Let us assume that there are 3x male students and 2x female students in section B of DPS, and there are 4y male students and 3y female students in section B of DAV. We can set up the following equations to represent the given ratios

3x : 2x = male : female in DPS section B

4y : 3y = male : female in DAV section B

By simplifying these ratios, we get

3 : 2 = x/y for DPS section B

4 : 3 = x/y for DAV section B

Solving for x and y, we get

x = 6y for DPS section B

x = 4.5y for DAV section B

Now, let us add the male and female students in section B from both schools.

Male students = 3x + 4y = 3(6y) + 4(4.5y) = 30y

Female students = 2x + 3y = 2(6y) + 3(4.5y) = 21y

So, the ratio of male to female students in section B from both schools combined is

30y : 21y = 10 : 7

Therefore, male students are (10 - 7)/7 = 3/7 = 0.4286 (approx. 43%) more than female students in section B from both schools combined.

However, the question asks for the percentage more, so we need to multiply this answer by 100 to get a percentage.

0.4286 x 100 ≈ 42.86%

Therefore, male students in section B are approximately 42.86% more than female students in section B from both schools combined. Rounding to the nearest percent that is 40%.

Hence, the correct option is D.

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The fish tank that has a capacity of 60 gallons is given as follows:

A. Pacific.

The fish tank that has a capacity of 60 gallons obtained applying the proportions in the context of the problem.

The rate between quarts and gallons is given as follows:

1 gallon = 4 quarts.

Hence the capacity in quarts equivalent to 60 gallons is given as follows:

60 x 4 = 240 quarts.

Meaning that the Pacific fish tank has a capacity of 60 gallons.

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The third term in the expansion of the expression (5x - 7y)³ is 735xy².

Given expression is,

(5x - 7y)³

We have to expand this.

We know that,

(a + b)³ = a³ - 3a²b + 3ab² - b³

Using this,

(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³

               = 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³

               = 125x³ - 525x²y + 735xy² - 343y³

Here the third term is 735xy².

Hence the third term is 735xy².

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Part(a),

The exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^x[/tex]

Part(b),

The predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

Part(c),

The predicted total sales of food and drink in 2018 is 1756 billion dollars

Part(d),

If the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

(a) To model the total spent on food and drinks as an exponential function of the number of years since 1990, we can use the general form of an exponential function:

[tex]T = a \times b^t[/tex]

where T is the total spent in billions of dollars, t is the number of years since 1990, a is the initial amount spent in 1990, and b is the growth factor or base of the exponential function.

Using the given information, we can set up two equations:

T(0) = 641 (total spent in 1990)

T(13) = 1016 (total spent in 2003, which is 13 years after 1990)

Substituting these values into the exponential function, we get:

[tex]641 = a \timrd b^0[/tex] => a = 641

[tex]1016 = a b^{13[/tex] => [tex]b = (\dfrac{1016}{641})^{\frac{1}{13}[/tex]

Therefore, the exponential function that models the total spent on food and drinks as a function of the number of years since 1990 is:

[tex]T(x) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13})^x[/tex]

(b) To predict the amount spent in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the exponential function:

[tex]T(10) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{10[/tex] ≈ 964

Therefore, the predicted amount spent in 2000 is 964 billion dollars (rounded to the nearest integer).

(c) To predict the total sales of food and drink in 2018, we need to substitute t = 28 (since 2018 is 28 years after 1990) into the exponential function:

[tex]T(28) = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^{28[/tex] ≈ 1756

Therefore, the predicted total sales of food and drink in 2018 is 1756 billion dollars (rounded to the nearest integer).

(d) To estimate when the total sales will reach 2 trillion dollars, we need to solve for t in the exponential function when T(t) = 2000 (since 2 trillion dollars is equivalent to 2000 billion dollars):

[tex]2000 = 641 \times ((\dfrac{1016}{641})^{(\frac{1}{13}))^t[/tex]

[tex]ln(\dfrac{2000}{641}) = t \times ln((\dfrac{1016}{641})^{(\frac{1}{13})[/tex]

[tex]t = \dfrac{ln(\dfrac{2000}{641})} { ln((\dfrac{1016}{641})^{(\frac{1}{13})) }}[/tex]

t = 32.72

Therefore, if the exponential trend continues, the total sales will reach 2 trillion dollars approximately 32.72 years after 1990, which is around the year 2022.

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Suppose a trapezoid is defined as a quadrilateral with at least 1 pair of parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American or Canadian English, or a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of a trapezium are the parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

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Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001

Given information:

The mean time is, = 16.2 min.

The standard deviation = 3.4 min.

Let X' is sample mean time :

Now the sample mean time is given by the equation

Z = (X' - μ) / (σ/√n)

Where, μ population mean time

(σ) is Standard deviation

(A) Probability of random sample of 45 oil changes:

p (X' < 10) = 1 - p (Z ≤ 12.33)

Z = (10 - 16.2) / (3.4 √45)

p (X' < 10) = 1 - 0.9999

p (X' < 10) = 0.0001

Hence,

As, the highest critical value of Z is given as 4.40 which has an area of 0.9999.

Thus, Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001.

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Complete question is,

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.

(a) What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 ​minutes?

Answer:

00:00 in 12-hour clock time is equivalent to 12:00 midnight. It is the start of a new day and is the first minute of the 12-hour time cycle.