Damian earns $8 per hour selling lemonade. Write an equation that shows the amount of money damien earns when he works x hours.

100 (1 + 0.1)^8

= 100 (1.1)^8

= 214

Answer

214 trucks registered in the city at the end of Year 8

Answer:

x = (5 + i sqrt(15))/4 or x = (5 - i sqrt(15))/4

Step-by-step explanation:

Solve for x:

2 x^2 - 5 x + 5 = 0

Hint: | Using the quadratic formula, solve for x.

x = (5 ± sqrt((-5)^2 - 4×2×5))/(2×2) = (5 ± sqrt(25 - 40))/4 = (5 ± sqrt(-15))/4:

x = (5 + sqrt(-15))/4 or x = (5 - sqrt(-15))/4

Hint: | Express sqrt(-15) in terms of i.

sqrt(-15) = sqrt(-1) sqrt(15) = i sqrt(15):

Answer: x = (5 + i sqrt(15))/4 or x = (5 - i sqrt(15))/4

The quadratic equation has an imaginary roots, which is can be calculated using the quadratic formula.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

2x² - 5x + 5=0

Here a = 2, b = -5, and c = 5

[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(2)(5)}}{2(2)}[/tex]

[tex]\rm x = \dfrac{5 \pm\sqrt{-15}}{4}[/tex]

[tex]\rm x = \dfrac{5 \pm i \sqrt{15}}{4}[/tex]  (√(-15) = 15i; i is the iota)

The roots are:

[tex]\rm x = \dfrac{5 + i \sqrt{15}}{4} \\\\\rm x = \dfrac{5 - i \sqrt{15}}{4}[/tex]

Thus, the quadratic equation has an imaginary roots, which is can be calculated using the quadratic formula.

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Answer:

The answer is b.

Step-by-step explanation:

You could represent the phone service price with an equation that is

y = 0.07x + 18

So the intercept in y is 18 when x is zero, that is the minimum price of the phone service.

9 to the power of three, or cubed = 720 which is between 600 and 800.

The number you're looking for would be a decimal between approximately 8.375 and 8.6. When these numbers are cubed, they fall in the range of 600 to 800.

The question at hand is asking about cubing a number to get a result that is larger than 600 but smaller than 800. We are looking to find the cube root of numbers in this range. The integer cube roots closest to this range are the cube root of 512 (which is 8) and the cube root of 729 (which is 9).

However, neither of these is a number that you could cube to end up in the 600 to 800 range. Therefore, the desired number is not a whole number, but a decimal. If you estimate, any number between 8.375 and 8.6, when cubed, should meet the condition—meaning it would be larger than 600 but still less than 800.

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She takes 20 seconds

Answer: A.  20 seconds  

Step-by-step explanation:

We know that if a function has a repeating pattern then it is called a periodic function (like sine or cosine).

The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. It is the horizontal distance required for the graph of a periodic function to complete one cycle.

From the graph it can be seen that, the horizontal distance required for the graph of a periodic function= 20 .

Therefore,  it takes 20 seconds by Callie to complete one full swing.

Answer: (x - [tex]2i\sqrt{13}[/tex])(x + [tex]2i\sqrt{13}[/tex])

Step-by-step explanation:

x² + 52 = 0

x² = -52

[tex]\sqrt{x^{2} } = \sqrt{-52}[/tex]

x = +/-  [tex]\sqrt{52}[/tex]

x = +/-  [tex]i\sqrt{2*2*13}[/tex]

x = +/-  [tex]2i\sqrt{13}[/tex]

(x - [tex]2i\sqrt{13}[/tex])(x + [tex]2i\sqrt{13}[/tex]) = 0

Final answer:

To find the discount percentage, subtract the sale price from the original price, divide the difference by the original price, and multiply by 100. Paolo's hat was discounted by 20%.

Explanation:

To calculate the percentage of the discount that Paolo received on the hat, we need to find the difference between the original price and the sale price, and then divide that difference by the original price. Afterward, we multiply the result by 100 to get the percentage.

The original price of the hat was $35, and Paolo paid $28. The difference between the original price and the sale price is $35 - $28 = $7. Therefore, the discount is $7.

Now, we calculate the percentage discount: ($7 / $35) x 100 = 20%. So, the hat was discounted by 20%.

Answer:

1/6

Step-by-step explanation:

sim[le thought

Staci has vacuumed 1/6 of the entire house tonight.

The student's question concerns the portion of housework completed by Staci. As one of her chores, Staci must vacuum 1/2 of the house. She has already vacuumed 1/3 of her share tonight. To find out what part of the entire house has been vacuumed, we multiply the two fractions together.

Staci's share to vacuum is 1/2 of the house.

She has completed 1/3 of her share, which is 1/3 of 1/2.

To calculate the portion she has vacuumed, we multiply 1/2 by 1/3:

(1/2) x (1/3) = 1/6.

Therefore, Staci has vacuumed 1/6 of the entire house tonight.

Two-fifths of 1/4 acre is [tex]\(\frac{1}{10}\)[/tex]  acre planted in orange trees.

Sure, here's a detailed stepwise solution with explanation:

1. **Understand the problem**: The Avocados own a 1/4 acre orchard, and two-fifths of the orchard is planted in orange trees. We need to find the fraction of an acre planted in orange trees.

2. **Identify the fractions**: Let's represent the fractions given in the problem:

  - Fraction of the orchard planted in orange trees: [tex]\( \frac{2}{5} \) - Total acreage of the orchard: \( \frac{1}{4} \)[/tex]

3. **Multiply the fractions**: To find the fraction of an acre planted in orange trees, we multiply the fraction of the orchard planted in orange trees by the total acreage of the orchard.

4. **Perform the multiplication**: Multiply the fractions:

  [tex]\[ \frac{2}{5} \times \frac{1}{4} \] \[ = \frac{2 \times 1}{5 \times 4} \] \[ = \frac{2}{20} \][/tex]

5. **Simplify the fraction**: The fraction[tex]\( \frac{2}{20} \) can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. \[ \frac{2}{20} = \frac{1}{10} \][/tex]

6. **Interpret the result**: The simplified fraction  [tex]\( \frac{1}{10} \)[/tex] represents one-tenth of an acre planted in orange trees.

7. **Conclusion**: Therefore, one-tenth of an acre is planted in orange trees in the Avocados' orchard.

The store sold 1.25 footballs for every 2 basketballs.

To determine how many footballs were sold for every 2 basketballs, we can set up a ratio based on the information given. Let's denote the number of basketballs sold as [tex]\( B \)[/tex] and the number of footballs sold as [tex]\( F \)[/tex]. According to the problem, the store sold 2.5 times as many footballs as basketballs, which can be expressed as:

[tex]\[ F = 2.5B \][/tex]

Now, we want to find out how many footballs were sold for every 2 basketballs. To do this, we can divide both sides of the equation by 2 to find the number of footballs that correspond to 2 basketballs:

[tex]\[ \frac{F}{2} = \frac{2.5B}{2} \][/tex]

Simplifying the right side of the equation, we get:

[tex]\[ \frac{F}{2} = 1.25B \][/tex]

This means that for every 2 basketballs sold [tex](\( 2B \))[/tex], there were 1.25 footballs sold [tex](\( F \))[/tex]. Therefore, the store sold 1.25 footballs for every 2 basketballs.

Answer:

The given Expression is

[tex]4\sqrt{16x^4y^12[/tex]

= 4 × terms under square root are non negative.so we can break it into different terms.

= 4 × √16 ×[tex]\sqrt{x^4}\times\sqrt {y^{12}}[/tex]

Breaking into factors

= 4 × [tex]\sqrt{2\times2\times\times2\times2 } \times\sqrt{x \times x \times x \times x } \times \sqrt{ y \times y \timesy \times y \timesy \times y \times y \times y \times y \times y \times y \times y \times y \times y[/tex]

= 4× [tex]2 \times2 \times x \times x \times y\times y\times y\times y\times y\times y[/tex]

= 16× [tex]x^{1+1}\times y^{1+1+1+1+1+1}[/tex]

= 16 [tex]x^2 y^6[/tex]

The solution of the expression 4√(16x⁴y¹²) will be 16x²y⁶.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

The given expression is  4√(16x⁴y¹²). The expression will be solved as:-

E =  4√(16x⁴y¹²)

E = 4 √ [( 4 x 4 ) ( x² x x² ) ( x⁶ x x⁶ )]

E = 4 ( 4 x x² x y⁶ )

E = 16x²y⁶.

Therefore, the solution of the expression 4√(16x⁴y¹²) will be 16x²y⁶.

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[tex]f(x)=x^2-8\\\\g(x)=2x-5\\\\f(g(x))\to\text{instead of x write the equation of the function g(x)}\\\\f(g(x))=(2x-5)^2-8=(2x)^2-2(2x)(5)+5^2-8\\\\=4x^2-20x+25-8=4x^2-20x+17\\\\\text{used}\ (a-b)^2=a^2-2ab+b^2[/tex]

[tex]g(f(x))\to\text{instead of x write the equation of the function f(x)}\\\\g(f(x))=2(x^2-8)-5=(2)(x^2)+(2)(-8)-5=2x^2-16-5=2x^2-21[/tex]

Im not sure but i multiplied and got 1.134 for my answer

x + 5.39 > 4.48

   -5.39   -5.39

x            > -0.91

Answer: x > -0.91

The relationship between Kelvin and degrees Celsius is not proportional in any way.

The temperature is the degree of the hotness and the coldness.

We know that

1 Kelvin = -273.15 degree Celsius

Kelvin is a unit of absolute temperature used in measurements and it can also be associated with degrees Celsius.

0 Kelvin is equivalent to -273.15 degrees Celsius.

In order to solve for the unit of temperature, the equation is:

T(Kelvin)= T(degrees Celsius) + 273.15

T(degrees Celsius) = T(Kelvin) - 273.15

The relationship between Kelvin and degrees Celsius is not proportional in any way.

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Answer:

Answer is 225.

We have to find the sum of 15 terms of the series

sigma 1 to 15 (2n-1)

This can be split as per summation terms as

sigma 2n - sigma 1

sigma 2n can again be simplified by taking 2 outside

sigma 2n= 2 times sum of natural numbers of 1 to 15

= 2(15)(16)/2= 240

sigma 1= 1+1+...15 times= 15

Hence final answer is

= 2 times sigma n - (n) = 240-15 = 225.

Step-by-step explanation:

Step-by-step explanation:

Question 2) Answer

Use Arithmetic Series Formulas:

a) Nth term = F + (N - 1) x D, where F=First term, N=Number of terms, D=Common difference

6th row = 23 + (6 - 1) x -3

            = 23 + (5) x -3

            = 23 + (-15)

            = 8 - number of boxes in the top row.

b) Sum = N/2[2F + (N - 1) x D]

            = 6/2[2*23 + (6 - 1) x -3]

             = 3  [46  +    (5) x -3 ]

             = 3  [46  +      -15 ]

             = 3  [ 31 ]

             = 93 - total number of boxes in the entire display.

Question 3) Answer

Sum of the 8 first terms of the geometric progression with the first term 50 and the common ratio of 2:

=50 + 5*2 + 50*2^2 + . . . + 50*2^7

= 50*(1 + 2 + 2^2 + . . . + 2^7) = 50*(2^8-1)

= 50*(256-1) = 50*255

= 12750 Answer

I am also attached the solved question of this assignment please check and enjoy. Thanks

Hello,

This number is already in stranded form.

If you want it in scientific notation its : 5.4003*10^6

Hope this helps a bit.

Answer:

[tex]5.4x10^{6}[/tex]

Step-by-step explanation:

The standard form refers to the way of writing large numbers in a smaller expression using power of 10, this is also called scientific notation.

To write this number in standard form, we have to the decimal point to the position between the 5 and the 4, and all spaces jumped represent the exponent of the 10 power, as follows

[tex]5400300=5.4x10^{6}[/tex]

Therefore, the standard form would be

[tex]5.4x10^{6}[/tex]

Answer:

1400 dollars

Step-by-step explanation:

Let the original price = 100

Less: saving of 40%   =  40

Reduced price            = 60

Reduce price of 60 is equivalent to 840 dollars

Hence original price of 100 is equivalent to

100/60 = x/840

Or x = 1400 dollars.

Original price actual = 1400 dollars.

Verify: Original price = 1400

           Less: 40%      =    560

            Reduced price  = 1400-560 =840 (given)

Hence verified

y = - [tex]\frac{1}{4}[/tex] x + 3

the equation of a line in slope-intercept form is

y = mx +c ( where m is the slope and c the y-intercept )

rearrange x + 4y = 12 into this form

subtract x from both sides

4y = - x + 12 ( divide all terms by 4 )

y = - [tex]\frac{1}{4}[/tex] x + 3 ← in slope-intercept form

Answer:

A

Step-by-step explanation:

Hope this helps

Answer:

[tex]\left \{ {{x+y=745} \atop {23.50x+58.75y=29,668.75}} \right.[/tex]

Step-by-step explanation:

1. You must analize the information given in the problem.

2. The first equation:

- [tex]x[/tex] represents the number of copies of the home edition sold and [tex]y[/tex] represents the number of copies of the business edition sold.

- A total of 745 copies were sold last week.

- Therefore, if you add the number of copies of the home edition sold and the number of copies of the business edition sold, you will obtain a total of 745 copies, which you can express as below:

[tex]x+y=745[/tex]

3. The second equation:

-  The cost of each version is:

[tex]23.50x\\58.75y[/tex]

- If the company earned a total of $29,668.75, you have:

[tex]23.50x+58.75y=29,668.75[/tex]

Answer:

You should find the discounted price of the gear first.

The discount should be calculated on the original $100 price.

Step-by-step explanation:

Now let's check the answer options:

You can simplify the problem by calculating 33% of $100.

You should find the discounted price of the gear first.

The tax should be calculated on the original $100 price.

The discount should be calculated on the original $100 price.

Answer:

You should find the discounted price of the gear first.

The discount should be calculated on the original $100 price.

Step-by-step explanation:

Your Welcome;)

In the given equation (L = 1.25m), 1.25 means that the length of the Maya hair increased by 1.25 centimeters every month.

Given :

The following steps can be used in order to determine the meaning of 1.25:

Step 1 - According to the given data, Maya shaved her head and then began letting her hair grow.

Step 2 - It is also given that, L is the length of the hair in centimeters and m represents the month after she shaved her head.

Step 3 - The equation that represents the given situation is:

L = 1.25m

Step 4 - In the above equation 1.25 means that the length of the Maya hair increased by 1.25 centimeters every month.

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Answer:

When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen.          Here the card is chosen with replacement.  This implies probability for choosing a prime number remains the same as the previously drawn card is replaced.

The sample space= {1,2,3,4,5,6,7,8,9,10}

Prime numbers = {2,3,5,7}

Prob for drawing prime number = 4/10 = 0.4

is the same when replacement is done.

Also there are two outcomes either prime or non prime.  Hence in this case, X the no of times a prime number is chosen, is binomial with p =0.4 and q = 0.6 and n=5

When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.

Prob for an even number = 0.5

But after one card drawn say odd number next card has prob for even number as 5/9 hence each draw is not independent of the other.  Hence not binomial.

When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.

Here since every time replacement is done, probability of drawing a 3 remains constant = 1/10 = 0.3

i.e. each draw is independent of the other and there are only two outcomes , 3 or non 3. Hence here X is binomial.

When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen

Here X is the number of times a card is chosen with replacement till 5 is chosen.  This is not binomial.  Here probability for drawing nth time correct 5 is  P(non 5 in the first n-1 draws)*P(5 in nth draw) = 0.1^(n-1) (0.9)

Because nCr is not appearing i.e. 5 cannot appear in any order but only in the last draw, this is not binomial.

Step-by-step explanation:

Answer:

Step-by-step explanation:

hope this is helpful to anyone in the future!

For this problem, you don't need to know how much the pencils cost. You're only finding how much the 10 nickels are worth.

Start by knowing how much one nickel is worth. A nickel is worth five cents in US currency. Since you know the worth of one nickel, you can find the worth of ten nickels by multiplying ten nickels by five cents (0.05).

Multiply 10 by 0.05.

10 * 0.05 = 0.5

0.5 is equal to 50 cents in US currency, so this means that Ginger has 50 cents to spend to buy pencils at the school store.

Answer:

3.16 units

Step-by-step explanation:

It has been given that the triangles JKL and the triangle RST are congruent.

That implies that, the length of the side JK, KL, and JL is equivalent to the length of the sides RS, ST, and RT respectively.

Now, to find the length of JK we need to find the length of the side RS. The coordinates of the points R and S are [tex](-1,-2)[/tex] and [tex](2,-1)[/tex].

The length of the side RS is equal to the distance between point R and S.

RS [tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]= \sqrt{(2-(-1))^2+(-1-(-(-2))^2}[/tex]

[tex]=\sqrt{3^2+(-1+2)^2}[/tex]

[tex]=\sqrt{9+1}=\sqrt{10}=3.16[/tex]

Now that we have the length of the side RS, and the triangles JKL and RST are congruent therefore, the length of the side JK is 3.16 units.

Answer:

sq root of 10 over 2

Step-by-step explanation:

took it on edge