The __________________________________ property of addition states that the way addends are grouped does not affect their sum

The only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.

We can use substitution to find which value of x makes the inequality 2x < 18 true by trying each value in the set {7, 9, 36} one by one.

Let's start with x = 7:

2x = 2(7) = 14

14 < 18 is true, so x = 7 satisfies the inequality.

Next, let's try x = 9:

2x = 2(9) = 18

18 < 18 is not true, so x = 9 does not satisfy the inequality.

Finally, let's try x = 36:

2x = 2(36) = 72

72 < 18 is not true, so x = 36 does not satisfy the inequality.

Therefore, the only value of x from the set {7, 9, 36} that makes the inequality 2x < 18 true is x = 7.

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To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.

In mathematics, the Elimination method is about deleting one of the words containing any of the variables to make the calculations easier.
To solve the equations, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same.

The term is then eliminated or removed from the result by adding or subtracting from both equations.

Here we have

Equation 1: 2x - 5y = -8

Equation 2: 4x + 5y = 14  

We can multiply given equations as follows

To eliminate 'x' terms multiply the multiply equation 1 with -2

-2 × Equation 1 =>  - 4x + 10y = 16  ---- (Equation 3)  

Now add Equation (2) and Equation (3)

=> 4x + 5y - 4x + 10y = 14 + 16

=> 15y = 30

=> y = 2

Now substitute y = 2 in equation (2)

=> 2x - 5(2) = -8

=> 2x - 10 = -8

=> 2x = 2

=> x = 1  

Therefore,

To solve the given equations multiply equation 1 with - 2 and the solutions are x = 1 and y = 2.

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Answer as a mixed number =  1   1/8  mph

Answer as a decimal = 1.125 mph

Work Shown:

(3/4) of a mile : (2/3) of an hour

12*(3/4) of a mile : 12*(2/3) of an hour

9 miles : 8 hours

9/8 miles : 8/8 hours

1.125 miles : 1 hour

His speed is 1.125 miles per hour. This converts to the mixed number 1 1/8

The expected number of rolls is 12.The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2.

The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2. Therefore, the expected number of rolls can be calculated by multiplying the probability of rolling an even number (1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 12.

The expected number of rolls to get a specific result on a fair die can be calculated by multiplying the probability of achieving that result by the number of sides on the die. For example, if you wanted to know the expected number of rolls to get an odd number on a fair, 6-sided die, you would multiply the probability of rolling an odd number (3/6, or 1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 3. The same calculation could be applied to determine the expected number of rolls to get a specific number (e.g. a 4) on a fair, 6-sided die. The probability of rolling a 4 would be 1/6, and the expected number of rolls to get a 4 would be 1/6 x 6 = 6.

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The solution of the equation 16g + 3 = 4 - 13g is g = 1/29

An equation is a statement that two expressions are equal. In other words, it's a mathematical sentence that says that the value on the left side of the equation is equal to the value on the right side.

In your problem, you have the equation:

16g + 3 = 4 - 13g

To solve this equation, the goal is to isolate the variable "g" on one side of the equation, so we can find its value. To do that, we need to use some algebraic techniques.

First, we can simplify the equation by combining like terms. We can add 13g to both sides of the equation to get:

16g + 13g + 3 = 4

Now we can combine the like terms on the left side of the equation:

29g + 3 = 4

Next, we want to isolate the variable "g" on one side of the equation. To do that, we can subtract 3 from both sides of the equation:

29g = 1

Finally, we can solve for "g" by dividing both sides of the equation by 29:

g = 1/29

So the solution to the equation is g = 1/29.

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Complete Question:

I need help solving this assignment.

Solve the equations 16g+3=4–13g

Samantha drove 217 miles during the second day.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let D be the distance Samantha traveled during the second day. Then the total distance she drove is 468 miles. The equation will be:

D + 251 = 468

Solving for D:

D = 468 - 251

D = 217

Therefore, Samantha drove 217 miles during the second day.

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Answer:

Step-by-step explanation:

time take for 1 dough = 16kg/4hours= 4kg/hour

Dough in 5 hours = 4 x 5 = 20

She prepared 20kilograms of dough in 5 hours

The exponential equation in the form y= a[tex](b)^x[/tex] that can model is y= 500[tex](1.06)^x[/tex].

In mathematics, an exponential function is a relationship of the type

y = [tex]a^x[/tex], where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

Given:

Britney invested $500 in stocks.

After one year, the value of her stocks has increased to $530.

We know the Exponential Function y= a[tex](b)^x[/tex]

As, a= 500, y= 530, x= 1

So, y= a[tex](b)^x[/tex]

530 = 500 [tex](b)^1[/tex]

530 / 500 = b

b= 1.06

So, the exponential equation is y= 500[tex](1.06)^x[/tex]

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Answer:

s^2 + n^2 = 116

Step-by-step explanation:

s^2 + n^2 = ?

s^2 = 80

n = 6

n^2 = 36

s^2 +n^2 = 80 + 36

s^2 +n^2 = 116

The cost to ship a box of 250 grams, with 10 books of weight of 8.5kg by natalie is $ 29.75.

The total weight of the books and the box is:

10 books × 810 grams/book + 250 grams = 8,250 grams + 250 grams = 8,500 grams

To convert this to kilograms, we divide by 1000:

8,500 grams ÷ 1000 = 8.5 kg

The cost of shipping will be based on the weight, so we can multiply the weight in kilograms by the shipping cost per kilogram:

8.5 kg × $3.50/kg = $29.75

Therefore, it will cost Natalie $29.75 to ship the books of 8.5 kg

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Answer:

[tex]\boxed{\checkmark}\;\;52 = 8n + 4[/tex]

[tex]\boxed{\checkmark}\;\;4(2n + 1) = 52[/tex]

[tex]\boxed{\checkmark}\;\;4 = 52 - 8n[/tex]

[tex]\boxed{\phantom{\checkmark}}\;\;4n = 48[/tex]

[tex]\boxed{\checkmark}\;\;n = 6[/tex]

Step-by-step explanation:

To determine if the equations are equivalent, solve the equations for n.

Option 1

[tex]\begin{aligned}\implies 52&=8n+4\\52-4&=8n+4-4\\48&=8n\\48\div 8&=8n \div 8\\6&=n\\n&=6\end{aligned}[/tex]

Option 2

[tex]\begin{aligned}\implies 4(2n+1)&=52\\8n+4&=52\\8n+4-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]

Option 3

[tex]\begin{aligned}\implies 4&=52-8n\\4+8n&=52-8n+8n\\4+8n&=52\\4+8n-4&=52-4\\8n&=48\\8n \div 8&=48 \div 8\\n&=6\end{aligned}[/tex]

Option 4

[tex]\begin{aligned}\implies 4n&=48\\4n \div 4&=48 \div 4\\n&=12\end{aligned}[/tex]

Option 5

[tex]n=6[/tex]

Therefore, the equations that are equivalent are:

On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8

In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.

When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.

the line is y = -2/3x+1

so the slope, m = -2/3

since it parallel , new slope = 3/2

the slope intercept of line is

y +1 = 3/2(x+6)

y + 1= (3/2)x + 9

y = (3/2)x + 9 - 1

y = (3/2)x + 8

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The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

CLAIM: The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

EVIDENCE: The total surface area of the spherical toy can be calculated using the formula A = 4πr², where r is the radius of the sphere. Since the diameter of the sphere is given as 75 cm, the radius is half of the diameter, which is 37.5 cm. Therefore, the total surface area of the spherical toy is:

A = 4π(37.5)²

A = 4π(1406.25)

A ≈ 17593.29 cm²

The surface area covered by the triangular sticker can be calculated by finding the area of the triangle, which is given by the formula A = 1/2 bh, where b is the base and h is the height. Therefore, the surface area covered by the sticker is:

A = 1/2 (10)(12)

A = 60 cm²

The surface area not covered by the sticker is the difference between the total surface area of the spherical toy and the surface area covered by the sticker:

A_not_covered = A - A_sticker

A_not_covered ≈ 17593.29 - 60

A_not_covered ≈ 17533.29 cm²

Therefore, the surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

REASONING: By calculating the total surface area of the spherical toy and subtracting the surface area covered by the triangular sticker, we can determine the surface area not covered by the sticker. Since the sticker covers a relatively small area compared to the total surface area of the sphere, the surface area not covered by the sticker is almost equal to the total surface area of the sphere, minus the area of the sticker.

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We know that RS is parallel to PQ by comparing RS and PQ and both vector have the same value and hence prove to be parallel.

We know that R, S, Q and P are midpoints of OC, CB, BA and OA, and we are given that OR = a, CS = b and OP = c

we have to prove that RS is parallel to PQ,

therefore we need to find, PQ = PA + AQ,

= c - c + a + b = a + b,

since we get that  PA = OP = c

therefore when we compare RS and PQ ,we get,

RS  =  PQ = a + b

now that it is clear that both the vectors are same and have the same value we can conclude that they are parallel.

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Answer:

[tex]\mbox{\large a_n = 2 + 5n}[/tex]

Step-by-step explanation:

The sequence is 7  12  17  22

This is an arithmetic sequence where any two successive terms is a constant known as the common difference

The difference between any two successive terms is 5

The common difference is 5

The nth term can be found by the expression

[tex]a_n = a_1 + d(n-1)[/tex]

where

[tex]a_n \textrm{ is the $n^{th}$ term}[/tex]

[tex]\mathrm{a_1\;is\;the\;first\;term}[/tex]

[tex]\mathrm{d\;is\;the\;common\;difference}\\[/tex]

In this sequence

[tex]a_1 = 7\\d = 5\\[/tex]

[tex]a_n = 7 + 5(n-1)\\\\a_n = 7 + 5n - 5\\\\a_n = 2 + 5n[/tex]

We can verify that this is correct is to determine the 5th term of the sequence which should be 22 + 5 = 27

Applying the expression for 5th term

[tex]a_5 = 2 + 5(5)\\= 2 + 25\\= 27[/tex]

On solving the provided question, we can say that the linear equation 100(p + s) + 100(p + s)

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

salad costs s dollars per serving. he needs to order 100 lunches for seventh graders and 100 lunches for eighth graders

the linear equation

100(p + s) + 100(p + s)

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In the function rule p(t) - 700, the number 700 represents a constant value that is subtracted from the value of the function p(t).

Assuming that p(t) is a function of time t, it is possible that p(t) represents a physical quantity such as the population of a city, the price of a stock, or the number of customers in a store, among other things. If we know what p(t) represents, we can interpret the meaning of 700 in the context of the situation.

For example, if p(t) represents the population of a city, then p(t) - 700 would represent the difference between the population and a reference value of 700. This could mean that 700 is the estimated minimum viable population of the city, or it could represent a reference population for comparison with other cities.

If p(t) represents the price of a stock, then p(t) - 700 would represent the difference between the stock price and a target value of 700, such as a price floor or a strike price.

In general, the meaning of 700 in the function rule p(t) - 700 depends on the specific context of the situation and the physical quantity that p(t) represents.

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The hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

We can use the time it takes the hare to run 100 m to determine how long he can afford to nap.

First, let's find the time it takes the hare to run the 100 m:

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the hare.

t = 100 m / 15 m/s

t = 6.67 s

Next, let's find the time it takes the tortoise to run 1 km (1000 m):

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the tortoise.

t = 1000 m / 0.27 m/s

t = 3700 s

So, the time it takes the tortoise to run the race is 3700 s. The time it takes the hare to run the first 900 m is 7 s. Therefore, the time the hare has left to nap is:

3700 s - 7 s = 3693 s

And the time it takes the hare to run the last 100 m is 6.67 s. Therefore, the hare can afford to nap for:

3693 s - 6.67 s = 3686.33 s

So, the hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

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The width of standard television set is 16.8 inches.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

We can solve this by using the  Pythagorean theorem which is below:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Or we can say

[tex]w^{2} +h^{2} =d^{2}[/tex]

w = width

h = height

d = diagonal measure

With that said, we know the height is .75 times the width so .75w. We also know d = 21, which is our diagonal measure.

w = don't know yet but need to find

h = .75w

d = 21

[tex]w^{2} +h^{2} =d^{2}[/tex]

[tex]w^{2} +(0.75w)^{2} =21^{2}[/tex]

1.5625 w^2 = 441

w^2 = 441/1.5625

w ^2 = 282.24

w =16.8

The width of standard television set is 16.8 inches.

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Answer:

25 minutes

Explanation:

Subtract the two times to find the duration.

If Kashif and Ali invested equal sums in the two different banks at 9 % and 10% , then in 6 years Ali will have $0.0945 more than Kashif .

We use the formula for compound interest, to calculate the amount that each person will have after 6 years  ;

Amount after 6 years for Kashif is :

⇒ A = P(1 + r/n[tex])^{nt}[/tex]

where A = (amount after 6 years) ; P = (initial investment)

r = interest rate = 9%  ; n = 1 ; t = time period (6 years) ;

So, A = P(1 + 0.09/1)⁶  ⇒ P(1.09)⁶  ;

Amount after 6 years for Ali is :

⇒ A = P(1 + 0.10/1)⁶ = P(1.10)⁶  ;

So , difference in the amounts that Kashif has compared to Ali after 6 years is  ⇒ P(1.09)⁶ - P(1.10)⁶  ;

Simplifying this expression, we get:

⇒ P(1.09⁶ - 1.10⁶)  ;

≈ -$0.0945     ;

Since the value is negative, it means that after 6 years, Ali will have more money than Kashif and difference between their amounts is approximately $0.0945    .

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Answer:

In 287.9412, 9 is at the tenth place. So , the answer is 287.9.

Step-by-step explanation:

You did not make enough money to buy the television with a total earnings of $458

To write an expression for total earnings, we can use the given rates of pay and multiply them by the unit rates of the activites and then add them together.

So the expression for total earnings (E) is:

E = 10x + 8y + 20z

Where

Using the given parameters in the question, the total earnings (E) in the last 4 weeks is

E = ($10 x 9) + ($8 x 26) + ($20 x 8)

Evaluate

E = $90 + $208 + $160

E = $458

$458 is less than the cost of television ($540)

This means that you did not make enough money

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Complete Question

You earn $10 for each lawn you mow. You earn $8 per hour working part time at an ice cream shop. You earn $20 cach day you deliver newspapers.

In the last four weeks, you mowed 9 lawns, worked 26 hours at the ice cream shop, and delivered newspapers 8 days.

Did you make enough to buy the television? Explain...

The television price is $540

Answer: D and C

Step-by-step explanation:

To get the value of a market basket you would add up the cost of each year so

2019 market basket = 2.50 + 1.00 + 3.75 = 7.25

2020 market basket = 2.25 + 3.00 + 4.50 = 9.75

2021 market basket = 3.00 + 3.25 + 5.00 = 11.25

now CPI for 2020 would be 9.75 / 7.25 x 100 = 134.828 which is around 135

CPI 2021 would be 11.25 / 7.25 x 100 = 155.172 which is around 155

The angle of rotation that will bring Car 3 to the position of Car 18 is 11.25 degrees. The angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees. Car 3 needs to move 15 positions counterclockwise to reach Car 18.

a. We have to determine the angle of rotation that will bring Car 3 to the position of Car 18 on the London Eye, so we will first calculate the number of positions that Car 3 needs to move counterclockwise to reach Car 18.

We know that there are 32 observation cars on the London Eye, so the distance between two adjacent cars will be 360/32 = 11.25 degrees.

b. To find the angle of rotation that a car travels when it moves one position counterclockwise, we will divide the full rotation of the London Eye by the number of observation cars (i.e. 32).

360/32 = 11.25 degrees

Next, to determine the angle of rotation that would bring Car 3 to the position of Car 18, we will multiply the number of positions that Car 3 needs to move counterclockwise and the angle of rotation for each position as follows -

15 x 11.25 = 168.75 degrees

Therefore, the angle of rotation that a car travels when it moves one position counterclockwise is 168.75 degrees.

c. To find the number of positions that Car 3 needs to move counterclockwise to reach Car 18, we will subtract the position number of Car 18 from that of Car 3 and then take the absolute value, as it is a cyclical rotation.

|18 - 3| = 15

Hence, Car 3 needs to move 15 positions counterclockwise to reach Car 18.

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no

4x6=24

24x1=24

hence 24 is the lowest common multiple , i hope this helped xx

The function represented by the graph is:

f(x) = |x – 1| + 3

This function takes the absolute value of the difference between x and 1, and then adds 3 to the result. The graph of this function will have a "V" shape centered at x = 1 with the vertex at (1, 3). The left side of the vertex will have a slope of -1, and the right side of the vertex will have a slope of +1. The y-intercept will be 3 units above the x-axis.

Answer:  B

Step-by-step explanation: YES