Tyler is 5 years younger than three times his cousin Lejla's age. Tyler is 40 years old. Let l represent Lejla’s age. During the Strategize step of the five-step problem-solving plan, which expression would you use to represent Tyler’s age?

a) 5l−3
b) 3l−5
c) 3l−40
d) 3l + 5

The required answer for 10x10x10x10x10x10 as an exponent is 10⁷.

An exponent is a number or letter written above and to the right of a mathematical expression called the base.

Now the given expression is,
10 x 10 x 10 x 10 x 10 x 10

Using the property,

a^a . a^b = a^(a+b)

Thus,

10 x 10 x 10 x 10 x 10 x 10 = 10^(1+1+1+1+1+1)

⇒ 10 x 10 x 10 x 10 x 10 x 10 = 10^7

or, 10 x 10 x 10 x 10 x 10 x 10 = 10⁷

Thus, the required answer for 10 x 10 x 10 x 10 x 10 x 10 as an exponent is 10⁷.

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Jolene invested $46,378.95 at 4 percent and $23,189.47 at 11 percent to achieve her annual interest of $4408 by setting up and solving a system of equations based on her investment strategy.

Jolene invests her savings in two different bank accounts, one with a 4 percent interest rate and another with an 11 percent interest rate. She invests twice as much in the lower-yielding account. To determine how much she invested at each rate given her annual interest of $4408, we can set up a system of equations.

Let's denote the amount invested at 4 percent as x and the amount invested at 11 percent as y. Given that she puts twice as much in the account with 4 percent, we can say that x = 2y. Furthermore, the total interest earned from both accounts is $4408, so the equation for the total interest would be 0.04x + 0.11y = 4408.

Substitute x = 2y into the interest equation to get 0.04(2y) + 0.11y = 4408. After simplification, the equation becomes 0.19y = 4408. Dividing both sides by 0.19 gives us y = 23189.47. Since x = 2y, multiply y by 2 to find x = 46378.95.

Therefore, Jolene invested $46,378.95 at 4 percent and $23,189.47 at 11 percent.

The Boomstar vine can grow up to 6 inches per day and 0.25 inches per hour, after converting from feet to inches and dividing by the number of hours in a day, respectively.

The Boomstar vine can grow up to 0.5 feet per day. To convert feet to inches, we multiply by the conversion factor of 12 inches per foot. Therefore, multiplying 0.5 feet by 12 gives us:

Next, to find out how fast it grows in inches per hour, we divide the daily growth in inches by the number of hours in a day:

The rain gauge collected a total of 7.675 inches of rain over the two-week period by adding last week's 4.3 inches to this week's 3.375 inches of rainfall.

This question demands basic understanding of mathematical operations and basic mathematical problem solving.

The question asks for the total amount of rain that filled a rain gauge over a two-week period. Last week, the rain gauge collected 4.3 inches of rain, and this week it collected an additional 3.375 inches. To find the total rainfall over the two weeks, we simply add these two amounts together:

4.3 inches (last week's rain) + 3.375 inches (this week's rain) = 7.675 inches

So, as per the above explaination, the rain gauge collected a total of 7.675 inches of rain over the two-week period.

Answer:

2.0 mph

Step-by-step explanation:

20x +5 = 24x -1

 add 1 to each side

20x+6 = 24x

subtract 20x from each side

6 = 4x

divide both sides by 4

x = 6/4 = 1.5

measure of angle: 20(1.5) +5 = 30+5 = 35 degrees

24(1.5) - 1 = 36-1 = 35 degrees

volume of original box: 3 *8 *10 = 240 cubic inches

volume of new box: 2 *7 *8 = 112 cubic inches

240 - 112 = 128

 volume is reduced by 128 cubic inches

There are 2100 cats and 210 dogs, totaling 2310 pets. Cats outnumber dogs 10 to 1.

To find the number of cats and dogs separately, let's set up a system of equations.

Let [tex]\( x \)[/tex] represent the number of cats and [tex]\( y \)[/tex] represent the number of dogs.

We're given two pieces of information:

1. There are 2100 cats and 210 dogs for a total of 2310 pets.

[tex]\[ x + y = 2310 \][/tex]

2. There are 2100 cats.

[tex]\[ x = 2100 \][/tex]

We can substitute the value of [tex]\( x \)[/tex] from the second equation into the first equation:

[tex]\[ 2100 + y = 2310 \][/tex]

Now, let's solve for [tex]\( y \):[/tex]

[tex]\[ y = 2310 - 2100 \][/tex]

[tex]\[ y = 210 \][/tex]

So, there are 210 dogs.

To summarize:

- Number of cats [tex](\( x \)):[/tex] 2100

- Number of dogs [tex](\( y \))[/tex]: 210

The number of months when the two companies charge the same amount is 5 months.

Let the number of months when the two companies charge the same amount be represented by x.

Therefore, based on the information given, the equation to solve the question will be:

75 + (20 × x) = 35 × x

75 + 20x= 35x

Collect like terms

35x - 20x = 75

15x = 75

Divide both side by 15

15x/15 = 75/15

x = 5

Therefore, the number of months when the two companies charge the same amount is 5 months.

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Answer:

3 bags of spoon and 4 bags of fork.

Step-by-step explanation:

If Susan will buy 3 bags of spoon then, the total spoon is 3 × 8 = 24 spoons

and, If he will buy 4 bags of fork then, the total fork is 4 × 6 = 24 forks.

Thus, for getting equal numbers of spoon and fork he has to buy a minimum of 3 bags of spoon and 4 bags of fork.