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2 years ago

Problem Set 100 yd. =

Mathematics

1 answer:

Juli2301 [7.4K]2 years ago

8 0

Answer:

1 yard = 3 feet

We can re-write this by dividing both sides by yards or feet to get

1 = 3 feet / 1 yard

1 yard / 3 feet = 1

Since we're solving for feet we want yards to cancel, so use the top proportion

(3 feet / 1 yard)(100 yards) = 300 feet / 1 = 300 feet

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A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares,

svp [43]

Answer:

✅The table can be represented by the equation, $y = 4x + 4$

✅The relation is a function.

✅The graph of the function is linear.

Step-by-step explanation:

✍️The first statement: The table can be represented by the equation, $y = 4x + 4$ .

To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).

Using two pairs, (1, 8) and (2, 12),

Slope = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4$ .

Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.

Thus:

8 = (4)(1) + b

8 = 4 + b

Subtract 4 from each side

8 - 4 = b

4 = b

Plug in the values of b and m into y = mx + b.

Thus, the equation that represents the table would be:

$y = 4x + 4$ .

✅Therefore, the first statement is correct.

✍️The second statement: The graph of the function is non-linear.

This is NOT TRUE because the equation of the function, $y = 4x + 4$ , represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.

✍️The Third statement: The relation is a function.

This is TRUE because each input value (x-value) has exactly one output value (y-value).

✍️The Fourth statement: The rate of change is NOT constant.

This standby is NOT TRUE.

The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.

Therefore, this statement is not correct.

✍️The Fifth statement: The graph of the function is linear.

This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.

5 0

3 years ago

Every day your friend commutes to school on the subway at 9 AM. If the subway is on time, she will stop for a $3 coffee on the w

Shtirlitz [24]

Answer:

1.02% probability of spending 0 dollars on coffee over the course of a five day week

7.68% probability of spending 3 dollars on coffee over the course of a five day week

23.04% probability of spending 6 dollars on coffee over the course of a five day week

34.56% probability of spending 9 dollars on coffee over the course of a five day week

25.92% probability of spending 12 dollars on coffee over the course of a five day week

7.78% probability of spending 12 dollars on coffee over the course of a five day week

Step-by-step explanation:

For each day, there are only two possible outcomes. Either the subway is on time, or it is not. Each day, the probability of the train being on time is independent from other days. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

The probability that the subway is delayed is 40%. 100-40 = 60% of the train being on time, so $p = 0.6$

The week has 5 days, so $n = 5$

She spends 3 dollars on coffee each day the train is on time.

Probabability that she spends 0 dollars on coffee:

This is the probability of the train being late all 5 days, so it is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.6)^{0}.(0.4)^{5} = 0.0102$

1.02% probability of spending 0 dollars on coffee over the course of a five day week

Probabability that she spends 3 dollars on coffee:

This is the probability of the train being late for 4 days and on time for 1, so it is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{5,1}.(0.6)^{1}.(0.4)^{4} = 0.0768$

7.68% probability of spending 3 dollars on coffee over the course of a five day week

Probabability that she spends 6 dollars on coffee:

This is the probability of the train being late for 3 days and on time for 2, so it is P(X = 2).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{5,2}.(0.6)^{2}.(0.4)^{3} = 0.2304$

23.04% probability of spending 6 dollars on coffee over the course of a five day week

Probabability that she spends 9 dollars on coffee:

This is the probability of the train being late for 2 days and on time for 3, so it is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{5,3}.(0.6)^{3}.(0.4)^{2} = 0.3456$

34.56% probability of spending 9 dollars on coffee over the course of a five day week

Probabability that she spends 12 dollars on coffee:

This is the probability of the train being late for 1 day and on time for 4, so it is P(X = 4).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{5,4}.(0.6)^{4}.(0.4)^{1} = 0.2592$

25.92% probability of spending 12 dollars on coffee over the course of a five day week

Probabability that she spends 15 dollars on coffee:

Probability that the subway is on time all days of the week, so $P(X = 5)$ .

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.6)^{5}.(0.4)^{0} = 0.0778$

7.78% probability of spending 12 dollars on coffee over the course of a five day week

8 0

3 years ago

Please help me i really need help with this math

natima [27]

Answer:

y= 3/5x+ 6.2

Step-by-step explanation:

the slope is change in y over change in x.

-4-(-1) divided by 3-8 will be -3/-5 = 3/5

For the y-intercept, plug in x and y values. I will use (3,8).

8= 3/5(3)+b

8= 9/5+b

(subtract 9/5 from both sides)= 6 and 1/5 or 6.2 as a decimal.

6 0

3 years ago

Mrs.Henry hires a local moving company to help her move into her new apartment. The price includes a 15% tip. Mrs.Henry's total

tensa zangetsu [6.8K]

162.15 is the answer because you have to multiply 0.15•141 then add 21.15 to the 141 :)

6 0

2 years ago

Read 2 more answers

Urgent due for tommorow . will mark brainliest and get 50 pts<br>plz show workings

Vilka [71]

Answer:

Step-by-step explanation:

Sec B

1) 5p⁻³ = 8*5⁻²

p⁻³ = 2³*5⁻²/5

p⁻³ =2³*5⁻³ { 1/a^m = a^-m}

p⁻³ = 5⁻³ /2⁻³ {a^m = 1/a^-m}

p⁻³ = (5/2)⁻³

p= 5/2

2) 4x² = 81

x² = 81/4

x² = 9² /2²

x² =(9/2)²

x = 9/2

3) 9^x/3 =81

9^x/3 = 9^2

Comparing the powers, x/3 = 2

x = 2*3 =6

x = 6

6 0

3 years ago