Help with 3 and show all work

Answer:

The correct option is D.

Step-by-step explanation:

The exponential function is

[tex]f(x)=3(4)^{2x-4}[/tex]

The polynomial function is

[tex]h(x)=(x+2)^3+1[/tex]

Find the values of both functions at x=-3, 0, 2, 4.

x values              f(x)                 h(x)

   -3              0.0000029           0

    0                   0.012                9

    2                      3                   65

    4                    768                217

From this table we can say that the exponential function f(x) exceeds the polynomial function g(x) at x=4.

Therefore the correct option is D.

Answer:

3/23 x 5/23 = 15/529 = 2.84%

Answer:

Categorical

Step-by-step explanation:

Take a vote and write it down, take your data and see how the results are.

Each time Kate refills her gas tank, she would consume 52 liters since it was stated in the problem that there will always be 3 liters of gas before she refills the tank. It was stated that she refilled her tank for two times which means she was able to consume 104 liters (52 liters x 2). It was stated in the problem as well that Kate uses allot the gas in the tank so she consumed the remaining 3 liters in her tank. This means that the total liter she was able to consume was 107 liters (104 liters + 3 liters). To find the distance she gets in miles, you need to multiply the distance covered per liter to the total liter consumed by Kate. Therefore, she was able to get 856 miles (107 liters x 8 kilometers per liter).

Natasha can treat a maximum of 10 people to the movies.

To determine how many people Natasha can treat to the movies, we can set up an inequality equation.

Let's say she wants to treat x number of people.

The amount she spends on tickets is $11x, and the amount she spends on popcorn and candy is $21. Since she can spend under $131, the inequality equation would be:

11x + 21 < 131.

To find the maximum number of people Natasha can treat, we need to solve this inequality:

11x + 21 < 131

11x < 110

x < 10

Natasha can treat a maximum of 10 people to the movies.

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If the x-coordinate is 7, representing 7 hexagons, the y-coordinate, representing the total number of sides, is 42. This is because each hexagon has 6 sides, and 7 hexagons have 7 * 6 = 42 sides.

To find the y-coordinate when the x-coordinate represents the number of hexagons, and the y-coordinate represents the total number of sides, we need to use the properties of a hexagon. A hexagon has 6 sides.

Given that the x-coordinate is 7, this means there are 7 hexagons. Each hexagon has 6 sides, so to find the total number of sides (which is the y-coordinate), you multiply the number of hexagons by the number of sides each hexagon has:

Thus,

y-coordinate = 7 hexagons * 6 sides per hexagon = 42 sides

Therefore, if the x-coordinate is 7, the y-coordinate is 42.

Final answer:

To share 150 pounds in the ratio of 4:1, divide the total by the sum of the parts of the ratio to find the value of one part, then multiply to find each share. The shares are 120 pounds and 30 pounds.

Explanation:

To share 150 pounds in the ratio of 4:1, you first need to add up the parts of the ratio (4 + 1 = 5 parts). Then, divide the total amount by the number of parts to find out how much one part is worth. In this case, 150 pounds ÷ 5 parts = 30 pounds per part. The ratio dictates that one share should have 4 parts and the other should have 1 part. Therefore, multiply 30 pounds by 4 to find the first share: 30 pounds × 4 = 120 pounds. The second share is just one part: 30 pounds × 1 = 30 pounds.

To summarize, the first person would receive 120 pounds and the second person would receive 30 pounds. This completes the sharing of 150 pounds in a 4:1 ratio.

Unit conversion is not directly relevant to this problem, but if you need to convert units, remember to use the proper conversion factors and set up the appropriate proportion.

To share 150 pounds in the ratio 4:1, divide the weight into 5 parts and allocate 4 parts for one ratio and 1 part for the other ratio. Each part would be equal to 30 pounds.

To share 150 pounds in the ratio 4:1, you can divide the total weight into 4 parts for one ratio and 1 part for the other ratio. To find the weight for each part, divide 150 by the sum of the ratio, which is 5 (4+1). Each part would be equal to 150/5 = 30 pounds. Therefore, in the ratio 4:1, the first part would be 4 parts x 30 pounds = 120 pounds, and the second part would be 1 part x 30 pounds = 30 pounds.

Answer:

4mph

Step-by-step explanation:

wouldn't it be 54.5 ?

Answer:

[tex]12\frac{1}{6}[/tex] cups of punch

Step-by-step explanation:

Peter is making a punch. He mixes :

Orange juice  =  [tex]4\frac{1}{2}[/tex] cups

Ginger ale   =    [tex]1\frac{1}{3}[/tex]

Strawberry lemonade =  [tex]6\frac{1}{3}[/tex]

Now we will add all the mixes

[tex]4\frac{1}{2}[/tex] +  [tex]1\frac{1}{3}[/tex] +  [tex]6\frac{1}{3}[/tex]

Now first we convert all the mixed fractions to improper.

[tex]\frac{9}{2}+ \frac{4}{3}+ \frac{19}{3}[/tex]

Now take LCM of 2,3,3 = 6

= [tex]\frac{27+8+38}{6}[/tex]

= [tex]\frac{73}{6}[/tex] =  [tex]12\frac{1}{6}[/tex]

The total number of cups of puch that peter makes is  [tex]12\frac{1}{6}[/tex]

Peter makes a total of 12 cups and 1/6 cup (or approximately 2/3 cup) of punch by mixing 4 1/2 cups of orange juice, 1 1/3 cups of ginger ale, and 6 1/3 cups of strawberry lemonade.

To find the total number of cups of punch that Peter makes,

need to add together the quantities of orange juice, ginger ale, and strawberry lemonade.

Here are the quantities given:

Orange juice = 4 1/2 cups

Ginger ale = 1 1/3 cups

Strawberry lemonade = 6 1/3 cups

Now, add these quantities together:

4 1/2 cups + 1 1/3 cups + 6 1/3 cups

To add these mixed numbers together, it's helpful to first find a common denominator, which in this case is 6.

Convert 4 1/2 to an improper fraction: 4 1/2

= (2 × 4 + 1)/2

= 9/2

Convert 1 1/3 to an improper fraction: 1 1/3

= (3 ×1 + 1)/3

= 4/3

Keep 6 1/3 as it is since it's already in mixed fraction form.

Now, add the fractions:

(9/2) cups + (4/3) cups + (6 1/3) cups

To add the fractions, first, find a common denominator of 6:

(9/2) cups + (8/6) cups + (19/3) cups

Now, all fractions have a common denominator of 6:

(27/6) cups + (8/6) cups + (38/6) cups

Now, add the fractions:

(27/6 + 8/6 + 38/6) cups

Combine the numerators:

(27 + 8 + 38)/6 cups

Now, add the numerators:

(27 + 8 + 38) = 73

So, Peter makes a total of 73/6 cups of punch. You can also simplify this fraction:

73/6 = 12 1/6

Therefore, Peter makes 12 cups and 1/6 cup (or approximately 2/3 cup) of punch in total.

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The other zero of the parabola with a vertex at (4, -2) and one zero at 1 is 7, determined by the symmetry of the parabola about its vertex.

If a parabola has its vertex at (4, -2) and one of its zeros is 1, we can find the other zero by using the concept of symmetry about the vertex. Since the axis of symmetry for a parabola with a vertical axis goes through the vertex, we know that the x-coordinate of the vertex will be exactly in the middle between the two zeros. The vertex form of a parabola's equation is typically written as y = a(x-h)² + k, where (h, k) is the vertex. In this case, the vertex is (4, -2).

Knowing that one zero is 1, we can determine that the other zero is equidistant from the vertex on the other side. This means that the distance from the vertex x-coordinate (4) to the known zero (1) is 3 units (4 - 1 = 3). So, counting 3 units in the other direction from the vertex's x-coordinate will give us the second zero: 4 + 3 = 7. Thus, the other zero of the parabola is 7.

The correct option is D. Matthew’s, Rhoda’s, and Ming’s.

Given,

Four students provide the following approximations for the square root of 0.89.

On calculating,

[tex]\sqrt{0.89} =0.943398113[/tex]

Now considering the 4 students approximations,

1. Anyah states that the square root of 0.89 is between 0.44 and 0.45 because of [tex]0.44<0.89/2<0.45.[/tex] This statement of  anyah is false because the [tex]\sqrt{0.89} =0.943398113[/tex], hence it not lies in between [tex]0.44[/tex] and [tex]0.45.[/tex]

2. Matthew states that the square root of [tex]0.89[/tex] is between 0 and 1 because of 0< 0.89<1. clearly the value of [tex]\sqrt{0.89} =0.943398113[/tex] lies in between [tex]0[/tex] and [tex]1.[/tex]So this statement is true.

3. Rhoda states that the square root of [tex]0.89[/tex] is between [tex]0.9[/tex] and [tex]1.0[/tex] because of [tex]0.9^2 <0.89<1.0^2[/tex] . this statement is true because the square of [tex]0.9[/tex] is [tex]0.81[/tex] and the square of [tex]1[/tex] is [tex]1[/tex] , and [tex]0.89\\[/tex] lies in between them. So the statement is  true.

4. Ming states that the square root of [tex]0.89[/tex] is between [tex]0.93[/tex] and [tex]0.95[/tex] because of [tex](0.93)^2<0.89<(0.95)^2[/tex]. this statement is also true.

Here only Anyah's statement is false.

Hence the correct option is D. Matthew’s, Rhoda’s, and Ming’s.

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The combination of coins Carson can have , 21 pennies, 1 dime, 2 nickels, 1 penny, 4 nickels, 1 penny

Currency is anything that is generally accepted to have value as a medium of exchange so that it can be traded for goods and services. The trading system within an economy is based on its currency, which is usually specific to a country and issued by that country's government.

2 dimes, 1 penny

21 pennies

1 dime, 2 nickels, 1 penny

4 nickels, 1 penny

Given that, Carson has 0.21 of a dollar.

So, he can have = 21 pennies [1 penny = 0.01 dollar]

= 2 dimes, 1 penny = 20 cents + 0.01 dollar = 0.21 dollar

= 1 dime, 2 nickels, 1 penny = 10 cents + 10 cents + 0.01 dollars = 0.21 dollar

= 4 nickels, 1 penny = 20 cents + 0.01 dollar = 0.21 dollar

Hence, the combination of coins Carson can have , 21 pennies, 1 dime, 2 nickels, 1 penny, 4 nickels, 1 penny

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Answer:

The amount in the account in the  beginning of the 6th year is $6375 .

Step-by-step explanation:

Formula

[tex]Simple\ interest = \frac{Principle\times Rate\ times Time}{100}[/tex]

As given

You invest $5000 in an account at 5.5% per year simple interest.

Principle = $ 5000

Rate = 5.5 %

Time = 5 years

(As calculate amount in the account for beginning of 6th year.)

Putting all the values in the formula

[tex]Simple\ interest = \frac{5000\times 5.5\times 5}{100}[/tex]

[tex]Simple\ interest = 50\times 5.5\times 5[/tex]

Simple interest = $ 1375

Amount =  Principle + Simple interest

Putting values in the above formula

Amount =  $5000 + $1375

Amount = $ 6375

Therefore the amount in the account in the  beginning of the 6th year is $ 6375 .