y=-x+7 , y=x-1 and show your work Help !

Answer : The sixth term in the binomial expression is, [tex]^{10}C_5a^{5}b^{5}[/tex]

Step-by-step explanation :

The general formula to calculate the term of binomial expression is:

[tex]T_(r+1)=^nC_ra^{(n-r)}b^r[/tex]

where,

(r+1) = number of term

As we are given the binomial expression :

[tex](5y+3)^{10}[/tex]

For sixth term :

a = 5y

b = 3

n = 10

As, r + 1 = 6

So, r = 6 - 1

r = 5

Now put all the given values in the above formula, we get:

[tex]T_(r+1)=^nC_ra^{(n-r)}b^r[/tex]

[tex]T_(5)=^{10}C_5a^{10-5}b^5[/tex]

[tex]T_(5)=^{10}C_5a^{5}b^{5}[/tex]

Thus, the sixth term in the binomial expression is, [tex]^{10}C_5a^{5}b^{5}[/tex]

The location of point Q' after the dilation is (6, 0).

Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.

To dilate the trapezoid by a scale factor of 3 about the origin, we need to multiply the coordinates of each vertex by 3.

The coordinates of Q are (2, 0), so to find the coordinates of Q' after the dilation, we multiply both the x and y coordinates by 3:

Q' = (32, 30) = (6, 0)

Therefore, the location of point Q' after the dilation is (6, 0).

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The date set with the greater range is neither as the range is the same.

The median is not the same for both sets of data.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

Number of boys = 10

The number of hours from the 10 boys.

= 8, 10, 10, 10, 12, 13, 14, 15, 15, 20

Range = Highest value - Lowest value

= 20 - 8

= 12

Median = (12 + 13)/2 = 25/2 = 12.5

Number of girls = 10

The number of hours from the 10 girls.

= 3, 4, 4, 4, 6, 7, 8, 10, 10, 15

Range = Highest value - Lowest value

= 15 - 3

= 12

Median = (7 + 8)/2 = 15/2 = 7.5

Thus,

The range of both boys and girls is the same.

The median of boy's number of hours is 12.5.

The median of girl's number of hours is 7.5.

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Step-by-step explanation:

The expression for the pressure in terms of force is as follows;

[tex]P= \frac{F}{A}[/tex]

Here, F is the force, P is the pressure and A is the area.

It is given in the problem that an object exerts 140 N of force on a surface that has an area of 2.0 meter square.

Put F= 140 N and A= 2 meter square in the above expression.

[tex]P= \frac{140}{2}[/tex]

[tex]P= 70 N/m^2[/tex]

Therefore, the pressure exerts on the object is 70 N/m^2.

The motion of air particles inside an inflated balloons:

In the inflated balloons, the molecules of air are far apart. These molecules are in random motion. They collide each other inside the surface of the balloons. The pressure will be exerted by the air molecules on the surface of the balloons. The pressure caused by atmospheric molecules collides with the outside the surface is equal to the pressure caused by atmospheric molecules collides with inside the surface of the inflated balloons. Therefore, the volume of the balloons remains constant.

Answer:

400ft

Step-by-step explanation:

The elevation of Waikapu, Hawaii is 400 feet, and the elevation of Denver, Colorado is 5200 feet, derived from a simple algebraic equation based on their given relationship and sum of elevations.

We are given that the elevation of Denver, Colorado is 13 times greater than that of Waikapu, Hawaii, and the sum of their elevations is 5600 ft. To find the elevation of each city, we can set up a system of equations.

Let x represent the elevation of Waikapu, then the elevation of Denver is 13x. According to the problem, we can set up the equation as follows:

x + 13x = 5600

Combining like terms gives us:

14x = 5600

Dividing both sides by 14 to isolate x gives us:

x = 5600 / 14

x = 400

Now that we have the elevation of Waikapu, we can find Denver's elevation by multiplying 400 by 13:

Denver's elevation = 13 x 400 = 5200 ft

Therefore, the elevation of Waikapu, Hawaii is 400 feet, and the elevation of Denver, Colorado is 5200 feet.

Answer:

Balance = $367.5

Step-by-step explanation:

The 2.5% of $350 is,

→ (350/100) × 2.5

→ 3.5 × 2.5

→ $8.75

The balance after 2 years is,

→ $350 + (2.5%) × 2 years

→ 350 + 8.75 × 2

→ 350 + 17.5

→ $367.5

Hence, the answer is $367.5.

The balance after 2 years on principle amount of $350 at the rate of 2.5% will be $525.

The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money.

Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.

As per the information in the question,

Principle amount, p = $350

Rate, r = 2.5%

Time, t = 2 years.

Use the formula of simple interest,

[tex]S.I = (p*r*t)/100[/tex]

S.I = (350 × 2.5 × 2)/100

S.I = 17500/100

S.I = 175

Now, the total amount will be,

$350 + 175 = $525

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Answer:

0.7

Step-by-step explanation:

The probability that she will not spin a 4 will be 0.80 or 4/5.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Sandy spun a spinner with 5 equal parts labeled 1-5. Then the total number of events will be given as,

Total events = 5 {1, 2, 3, 4, 5}

Then the favorable events are given as,

Favorable events = 4 {1, 2, 3, 5}

Then the probability is given as,

P = 4 / 5

P = 0.80

The probability that she will not spin a 4 will be 0.80 or 4/5.

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Final answer:

The probability that Sandy will not spin a 4 on a spinner with 5 equal parts is 4/5 or 80%. There are 4 favorable outcomes and 5 possible outcomes in total.

Explanation:

The question asks for the probability that Sandy will not spin a 4 on a spinner that's divided into 5 equal parts, each labeled with the numbers 1-5. Since there are 5 outcomes and only one of them is the one we want to avoid, that leaves us with 4 favorable outcomes (spinning a 1, 2, 3, or 5). The probability of not spinning a 4 is therefore the number of favorable outcomes (not spinning a 4) divided by the total number of possible outcomes (spinning any number from 1 to 5).

To calculate this, we divide the favorable outcomes by the total number of outcomes. This gives us a probability of 4/5, or 80%. The calculation is as follows:

Therefore, P(not spinning a 4) = 4 favorable outcomes / 5 total outcomes = 4/5 or 0.8, which means there is an 80% chance that Sandy will not spin a 4.

The answer is C: systematic sampling

Answer:

The awnser is C

Step-by-step explanation:

Answer:

26.25

Step-by-step explanation:

I took the test.

Answer:

D) 256; 1,296 ^ 3/4; ^ 4square root of1,296 ^ 3

 Let's rewrite the expression step by step:

 1296 ^ 3/4

 (1296) ^ (3/4)

 (1296 ^ 3) ^ (1/4)

 (2176782336) ^ (1/4)

 216

 This result is different from 256.

 Answer:

 D) 256; 1,296 ^ 3/4; ^ 4square root of1,296 ^ 3

Step-by-step explanation:

The distance covered by a player on a rectangular football field will be 118.73 meters.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

A rectangular football field is 64 meters wide and 100 meters long. A player runs from one corner of the field in a diagonal line to the opposite corner.

Then the distance covered by a player on a rectangular football field will be given by the Pythagoras theorem.

H² = 100² + 64²

H² = 10000 + 4096

H² = 14096

H = 118.73 meters

The distance covered by a player on a rectangular football field will be 118.73 meters.

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