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Let cost of Emma's phone = x

Given that cost of Sophie's phone = 640

Then ratio of their phones cost will be x:640 or x/640

Given that ratio of their phones cost is 7:8 or 7/8

So both ratios will be equal.

[tex]\frac{x}{640}=\frac{7}{8}[/tex]

[tex]x=\frac{7}{8}*640[/tex]

x=560

So the new ratio of the cost of their phones will be 560:640

Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.

So let that decreased amount is k then we will get equation :

[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]

11(560-k)=9(640-k)

6160-11k=5760-9k

6160-5760=11k-9k

400=2k

200=k

Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.

Well, the opposite of an exponent is a square root. However, in this case, it is to the power of 3. So in order to find p, you must do the cube root on both sides in order to get your answer:

[tex]p^3=3[/tex]

[tex]\sqrt[3]{p^3} =\sqrt[3]{8}[/tex]

[tex]p=2[/tex]

The product of -2 1/2 and -3 1/3 is 8 1/3. This is calculated by converting mixed numbers into improper fractions and then multiplying. Multiplying two negative numbers gives a positive result.

To compute the product of -2 1/2 and -3 1/3, first convert these mixed numbers into improper fractions.  -2 1/2 can be converted to -5/2 and -3 1/3 is -10/3.  Then, simply multiply these two fractions:

(-5/2) x (-10/3) = 50/6 = 25/3 or 8 1/3 .So the product of -2 1/2 and -3 1/3 is positive 8 1/3. Remember, multiplying two negative numbers results in a positive product.

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Let the speed of the boat in still water = X

The current is 3 mph, so the speed of the boat going upstream would be x-3

Speed of the boat going down stream would be x +3

The trip upstream is 26 / x-3

The trip downstream is 38 / x+3

Set them to equal and solve for x:

26/x-3 = 38/x+3

Multiply both sides by (x+3)(x-3):

38(x-3) = 26(x+3)

Simplify:

38x - 114 = 26x+78

Subtract 26x from each side:

12x -114 = 78

Add 114 to each side:

12x = 192

Divide both sides by 12:

x = 192 / 12

x = 16

The speed is 16 miles per hour.

To determine the boat's speed in still water, an equation is set up that relates the upstream and downstream times, given that the current influences the boat's effective speed by 3 mph. Solving this equation yields a speed of 16 mph for the boat in still water.

To find the speed of the boat in still water, we need to account for the effect of the current on the boat's speed when going up and down the river. Let the speed of the boat in still water be v mph.

When the boat is going upstream (against the current), its effective speed is (v - 3) mph because the current slows the boat down by 3 mph. When the boat is going downstream (with the current), its effective speed is (v + 3) mph because the current speeds the boat up by 3 mph.

Since the boat covers 26 miles upstream and 38 miles downstream in the same time, we can set the time equal for both scenarios:

Time = Distance / Speed

By equating the two times, we get:

26 / (v - 3) = 38 / (v + 3)

To solve for v, cross-multiply and simplify:

26(v + 3) = 38(v - 3)

26v + 78 = 38v - 114

12v = 192

v = 192 / 12

v = 16 mph

Therefore, the speed of the boat in still water is 16 mph.

In f(x) = 2.20x + 50 the dependent function is the total cost of flooring the carpet.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, A flooring company sells stain-resistant carpets for $2.20 per square foot and will install the carpet for an additional fee of $50 which is represented by f(x) = 2.20x + 50.

Here dependent variable is f(x) which is the cost of the complete project depending on the square foot.

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The answer you are looking for would be 63.

63 is greater than 60, but less than 70, and the tens place (6) is double the ones place (3). Thus meaning 63 is the answer.

I hope this helps!

a=2

b=6

c=-6

You can use the substitution method to solve.

*(The first order pair)*

[tex]y=-9(0)+3[/tex]                   Substitute [tex]0[/tex] to [tex]y=-9(0)+3[/tex]

[tex]y=0+3[/tex]                        Multiply [tex]-9[/tex] to [tex]0[/tex]

[tex]y=3[/tex]                            Add [tex]3[/tex] to [tex]0[/tex]

*(Answer)*= [tex](0, 3)[/tex]

*(The second order pair)*

[tex]y=-9(3)+3[/tex]                   Substitute [tex]3[/tex] to [tex]y=-9(3)+3[/tex]

[tex]y=-27+3[/tex]                        Multiply [tex]-9[/tex] to [tex]3[/tex]

[tex]y=-24[/tex]                            Subtract [tex]3[/tex] to [tex]-27[/tex]

*(Answer)*= [tex](3, -24)[/tex]

*(The third order pair)*

[tex]30=-9x+3[/tex]                   Substitute [tex]30[/tex] to [tex]30=-9x+3[/tex]

[tex]27=-9x[/tex]                        Subtract [tex]3[/tex] to [tex]30[/tex]

[tex]x=-3[/tex]                           Divide [tex]-9[/tex] to [tex]27[/tex]

*(Answer)*= [tex](-3, 30)[/tex]

Hope this helps

The person who answer: BangtanBoyScouts

Answer : b) 13/16

Given : t varies as v

So t = k v  where k is the constant of proportionality.

t = 2 4/7 when v =13/14. Using these values we find out k

[tex]t = 2\frac{4}{7} =\frac{18}{7}[/tex]

[tex]v =\frac{13}{14}[/tex]

t = k * v

[tex]\frac{18}{7}= k *\frac{13}{14}[/tex]

Multiply by 14/13 on both sides

[tex]\frac{18}{7} *\frac{14}{13} = k *\frac{13}{14}*\frac{14}{13}[/tex]

So  [tex]k =\frac{36}{13}[/tex]

We got the value of k. Now we find v when t = 2 1/4

[tex]t = 2\frac{1}{4} =\frac{9}{4}[/tex]

t = k * v

We know the value of t and k

[tex]\frac{9}{4}= \frac{36}{13}* v[/tex]

Multiply by 13/36 on both sides

[tex]\frac{9}{4} *\frac{13}{36} =\frac{36}{13}*\frac{13}{36}* v[/tex]

So  [tex] \frac{13}{16}= v[/tex]

Option B is correct

The answer you are looking for is 2/3.

When adding or subtracting fractions, they must have the same denominator. To make 1/6 and 1/2 have the same denominator, you must multiply 1/2 by 3/3 straight across. This gives you 3/6 which you can now add 1/6 to to get 4/6. 4/6 can be simplified down to 2/3 by dividing by 2/2. Thus making 2/3 the answer.

I hope this helps!

To add one sixth and one half, convert them to have the same denominator, resulting in 1/6 plus 3/6 (or 4/6), which simplifies to two thirds.

When adding fractions such as one sixth and one half, it's essential to have a common denominator. To find a common denominator for 1/6 and 1/2, we need to think about the multiples of both 6 and 2. The smallest common multiple is 6, so we convert 1/2 into a fraction that has 6 as the denominator. The fraction 1/2 is equivalent to 3/6 since 2 multiplied by 3 equals 6. Now we can add the fractions:

Therefore, one sixth plus one half is equal to two thirds.

12/4=x/20

x=60

60 people are needed

4x3=12 right. Then 20x3=60.

If the speed in still air is s, and the wind speed is w,

580/(s+w) = 5

580/(s-w) = 10

s=87

w=29

Final answer:

To determine the speed of the plane in still air and the speed of the wind, we use the distances and times provided to create two equations. Solving this system reveals that the speed of the plane in still air is 87 mph and the speed of the wind is 29 mph.

Explanation:

To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations based on the given information. We'll let p represent the speed of the plane in still air and w represent the speed of the wind.

When the plane travels with the wind, its effective speed is p + w, and the time taken for the trip is 5 hours, covering 580 miles. So, our first equation is:

1) (p + w) * 5 = 580

When the plane returns against the wind, its effective speed is p - w, and the time taken for this trip is 10 hours, again covering 580 miles. Thus, our second equation is:

2) (p - w) * 10 = 580

Solving this system of equations, we'll start by simplifying both:

p + w = 116 (By dividing the first equation by 5)

p - w = 58 (By dividing the second equation by 10)

Now we can add both equations to eliminate w:

2p = 174

Divide by 2 to get the speed of the plane in still air:

p = 87 mph

To find the speed of the wind, substitute the value of p in one of the equations:

87 + w = 116

So, the speed of the wind is:

w = 116 - 87

w = 29 mph

The speed of the plane in still air is 87 mph, and the speed of the wind is 29 mph.

m + 3 = 7

m = 4

m + 3 = -7

m = -10

m = 4, -10

The given equation is |m + 3|= 7. The values of m are 4 and -10.

An equation represents the equality of two or more mathematical expressions.

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

The given equation is |m + 3|= 7.

m + 3 = 7

m = 4

m + 3 = -7

m = -10

Hence, m = 4, -10

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52 feet.

13 x 4 because its all the same length.

[tex]\{0,1,5,7\}\cap\{0,5,7,9\}=\{5,7\}[/tex]

This is an exponential decay because it decreases by 1/2 each time

Answer:

The answer is exponential decay.

Step-by-step explanation:

At a chess tournament the number of competitors in each round is 50% of the number of competitors in the previous round.

So, the relationship that most appropriately models this situation is exponential decay.

Exponential decay is the process of reducing any given amount by a fixed or gradual percentage rate over a period of time.

It can be written like [tex]y= a(1-b)^{x}[/tex]

Where, y is the final amount

a is the original amount

b is the decay factor

x is the amount of time that has passed.

Final answer:

The probability that neither of them suffer from myopia can be calculated by finding the probability that one individual does not suffer from myopia and then multiplying that probability by the probability that the second individual also does not suffer from myopia.

Explanation:

The probability that neither of them suffer from myopia can be calculated by finding the probability that one individual does not suffer from myopia and then multiplying that probability by the probability that the second individual also does not suffer from myopia.

The probability that one individual does not suffer from myopia is 1 - 0.381 = 0.619. Since the two individuals are chosen randomly and independently, the probability that the second individual does not suffer from myopia is also 0.619.

Therefore, the probability that neither of them suffer from myopia is 0.619 * 0.619 = 0.382161.

First open the bracket by multiplying with -2

-2x - 26 +9x = 4

Solving like terms

7x - 26 = 4

Adding 26 to both sides

7x - 26 +26 = 4+26

7x = 30

X = 30/7

[tex]-2(x+13)+9x=4\\\\-2x-26+9x=4\\\\7x=30\\\\x=\dfrac{30}{7}[/tex]

Step 1. Factor out the common term 2

n - 2 = 2(5n + 2)/2

Step 2. Cancel 2

n - 2 = 5n + 2

Step 3. Subtract n from both sides

-2 = 5n + 2 - n

Step 4. Simplify 5n + 2 - n to 4n + 2

-2 = 4n + 2

Step 5. Subtract 2 from both sides

-2 - 2 = 4n

Step 6. Simplify -2 - 2 to -4

-4 = 4n

Step 7. Divide both sides by 4

-1 = n

Step 8. Switch sides

n = -1

To find the value of n, rearrange the equation and simplify to solve for n.

To find the value of n, we need to solve the given equation. First, distribute the 2 on the right side:

n - 2 = 10n + 4

Next, subtract 10n from both sides:

n - 10n - 2 = 4

Combine like terms:

-9n - 2 = 4

Then, add 2 to both sides:

-9n = 6

Finally, divide both sides by -9 to solve for n:

n = -6/9 which simplifies to n = -2/3.

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The first integer (x) is equal to the consecutive even integers, x+2, x+4.

x = (x+2) + (x+4)

x = 2x + 6

x - 6 = 2x

x = -6 (First integer)

+2

-4 (Second integer)

+4

-2 (Third integer)

Integers: -6, -4, -2

Equation: x = (x+2) + (x+4)

Answer:

2x+2=x+4

Step-by-step explanation:

Answer:

The second gear will complete 75 complete revolutions

Step-by-step explanation:

- There are two connected gears

- One has 60 teeth and the other has 40 teeth

- The two gears have different revolutions depends on the number of

  their teethes

- They do the same job

- The relation between them is

   [tex]n_{1}*c_{1}=n_{2}*c_{2}[/tex], where n is the number of the complete

   revolutions and c is the number of the teeth

- The gear which has less teethes makes more complete revolutions

∵ [tex]n_{1}[/tex] = 50

∵ [tex]c_{1}[/tex] = 60

∵ [tex]c_{2}[/tex] = 40

- Substitute these values in the rule below

∵ [tex]n_{1}[/tex] × [tex]c_{1}[/tex] = [tex]n_{2}[/tex] × [tex]c_{2}[/tex]

∴ 50 × 60 = [tex]n_{2}[/tex] × 40

∴ 3000 = 40 [tex]n_{2}[/tex]

- Divide both sides by 40

∴ [tex]n_{2}[/tex] = 75 complete revolutions

The second gear will complete 75 complete revolutions

11

11.06

11.56

11.6

is what you are looking for

The order would go 11; 11:06; 11.56; 11.6

Answer:

5000 square feet of lawn would provide the daily supplies of oxygen for 8 organisms.

Explanation:

 The daily supply of oxygen for a particular multi cellular organism is provided by 625 square feet of lawn

Total area of lawn provided = 5,000 square feet

Number of organism for which provided lawn area supplies oxygen = Total area of lawn provided/ Daily requirement of lawn area for 1 organism.

Number of organism for which provided lawn area supplies oxygen = 5000/625 = 8 organisms.

So 5000 square feet of lawn would provide the daily supplies of oxygen for 8 organisms.

A total of 5,000 square feet of lawn would provide the daily supplies of oxygen for 8 organisms based on the ratio given.

The question can be solved using the concept of ratios. The ratio of lawn to organisms is 625 square feet to 1 multicellular organism. So, if we have 5,000 square feet lawn area, we can find how many organisms it can support by setting up a proportion and solving for the unknown number of organisms.

Let's denote the unknown number of organisms as X. The proportion would then be: 625/1 = 5000/X.

To solve this equation for X, we can cross-multiply and divide. So, X = 5000 / 625 = 8 multicellular organisms.

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The equation for this is x2-x1/y2-y1 and so you plug in the numbers and get -5/7, and that is your slope.

Answer: ⇒ =x-2

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Step-by-step explanation:

Compute [tex]\frac{x^3-3x^2+3x-2}{x-2}[/tex] to get the rest of the equation.

[tex]\frac{(x-2)(x^2-x+1)}{x^2-x+1}[/tex]

Then you had to cancel by the common factor of [tex]x^2-x+1[/tex]

[tex]=x-2[/tex]

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Have a great day!

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what is the expression

[tex]\dfrac{4}{9}-\left|\dfrac{5}{18}\right|=\dfrac{4}{9}-\dfrac{5}{18}=\dfrac{8}{18}-\dfrac{5}{18}=\dfrac{3}{18}=\dfrac{1}{6}[/tex]

Matthew traveled a total of 43 blocks.

To calculate the total blocks traveled by Matthew, we need to add up the distances he walked and the distances he rode on the bus. He walked 7 city blocks, rode 13 blocks on the bus, and then walked 1 and a half blocks to the store. To return home, he traveled the same route, so we can double the distance. Adding all these distances together, Matthew traveled a total of 7 + 13 + 1.5 + 7 + 13 + 1.5 = 43 blocks.

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The colors on the image should match the correct blank spots on the proof. Please let me know if you disagree or is confused by my choices.