Ask question

Ask question

All categories

1 year ago

3

A store receives a shipment of 320 skateboard wheels. After 3 days, 272 of the skateboard wheels are left. After 7 days, 208 ska

teboard wheels are left.
a. Write an equation that represents the number y of skateboard wheels remaining after x days.

b. Use the linear equation to predict how many skateboard wheels will be left after 11 days.

c. After how many days should the store plan to receive a new shipment of skateboard wheels so they do not run out?

d. What does the slope of the equation represent? What does the y-intercept represent?

1 answer:

Mariulka [41]1 year ago

6 0

Answer:

$y=-16x+320$

144

20 days

Change of the number of skateboards with respect to the change of days.

y intercept represents the total stock of the skateboard wheels.

Step-by-step explanation:

The points on the plane are $(3,272)$ and $(7,208)$ .

Slope is given by

$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{208-272}{7-3}\\\Rightarrow m=-16$

The equation of the line will be

$y-y_1=m(x-x_1)\\\Rightarrow y-272=-16(x-3)\\\Rightarrow y-272=-16x+48\\\Rightarrow y=-16x+320$

The equation that represents the situation is $y=-16x+320$

When the number of days is 11 we have $x=11$

$y=-16\times 11+320\\\Rightarrow y=144$

The number of wheels left after 11 day is 144.

When the shipment will run out $y=0$

$0=-16x+320\\\Rightarrow x=\dfrac{320}{16}\\\Rightarrow x=20$

So, after 20 days the shipment will run out.

The slope represents the change of the number of skateboards with respect to the change of days.

The y intercept represents the total stock of the skateboard wheels.

You might be interested in

The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars

stellarik [79]

Answer:

Revenue , Cost and Profit Function

Step-by-step explanation:

Here we are given the Price/Demand Function as

P(x) = 253-2x

which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.

Now let us revenue generated from this demand i.e. x units

Revenue = Demand * Price per unit

R(x) = x * (253-2x)

= $253x-2x^2$

Now let us Evaluate the Cost Function

Cost = Variable cost + Fixed Cost

Variable cost = cost per unit * number of units

= 3*x

= 3x

Fixed Cost = 6972 as given in the problem.

Hence

Cost Function C(x) = 3x+6972

Let us now find the Profit Function

Profit = Revenue - Cost

P(x) = R(x) - C(x)

= $253x-2x^2 - (3x + 6972)$

= $253x-3x-2x^2-6972\\= 250x-2x^2-6972\\=-2x^2+250x-6972\\$

Now we have to find the quantity at which we attain break even point.

We know that at break even point

Profit = 0

Hence P(x) = 0

$-2x^2+250x-6972=0\\$

now we have to solve the above equation for x

Dividing both sides by -2 we get

$x^2-125x+3486=0$

Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83

Hence we now solve the above quadratic equation using splitting the middle term method .

Hence

$x^2-42x-83x+3486=0\\x(x-42)-83(x-42)=0\\(x-42)(x-83)=0\\$

Either (x-42) = 0 or (x-83) = 0 therefore

if x-42= 0 ; x=42

if x-83=0 ; x=83

Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.

5 0

2 years ago

Ruby wants to start her own business taking photographs. She already has her own camera, but needs to purchase lights, a photo p

dangina [55]

Ruby wants to <u>start</u> her own <u>business</u> taking photographs. She has to <u>purchase</u>

photo printer for $251.99;
lights for $150.00;
photo paper for $30.98.

In total, she will use

$251.99 + $150.00 + $30.98 = $432.97.

If she has $840.32 in savings, then

$840.32 - $432.97 = $407.35 will remain.

Answer: she will use $432.97 - correct answer A

5 0

2 years ago

In a film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. He wittily

yanalaym [24]

Answer:the uncle is 54 years old.

The woman is 18 years old

Step-by-step explanation:

Let x represent the age of the uncle.

Let y represent the age of the woman that he married.

In the film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. This means that

x = 3y

He wittily replies, "Ah, but in 18 years time I shall only be twice her age. It means that

x + 18 = 2(y + 18)

x + 18 = 2y + 36 - - - - - - - - - - 1

Substituting x = 3y into equation 1, it becomes

3y + 18 = 2y + 36

3y - 2y = 36 - 18

y = 18

x = 3y = 3 × 18

x = 54

6 0

2 years ago

The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5.

Natasha_Volkova [10]

Answer:

Yes, it would be unusual.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If $Z \leq -2$ or $Z \geq 2$ , the outcome X is considered unusual.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1$

Would it be unusual for this sample mean to be less than 19 days?

We have to find Z when X = 19. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{19 - 22}{1}$

$Z = -3$

$Z = -3 \leq -2$ , so yes, the sample mean being less than 19 days would be considered an unusual outcome.

7 0

2 years ago

The number 8.64E9 appears on a calculator. In standard notation, this number is

Lunna [17]

Here are all of your answers:

1) 8,640,000,000
2) 864,000,000,000,000
3) 864,000,000,000
4) 86,400,000,000,000

I hope this helps! If it does, please rate as Brainliest :D

6 0

2 years ago

Read 2 more answers