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4 years ago

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a company bought 12 boxed lunches from a delli for $74.50 each boxed lunch costs the same amount which equation represents the p

roportional relationship between y the total cost of the boxed lunches and x the number of boxed lunches

1 answer:

Snowcat [4.5K]4 years ago

4 0

I they each cost 6.21$ caz if u do 6.21 you get 74.53 but if you do 6.20 you get74.40 what ever u prefer

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A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=

Romashka [77]

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after <em>t</em> seconds is modeled by the function:

$h(t)=-16t^2+104t+56$

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

$\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$

In this case, <em>a</em> = -16, <em>b</em> = 104, and <em>c</em> = 56.

Find the <em>x-</em> (or rather <em>t-</em>)<em> </em>coordinate of the vertex. So:

$\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}$

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

$\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}$

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for <em>t: </em>

$0=-16t^2+104t+56$

We can simplify a bit. Divide both sides by -8:

$0=2t^2-13t-7$

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

$\displaystyle 0=2t^2-14t+t-7$

Factor out a 2<em>t</em> from the first two terms and group the last two terms:

$0=2t(t-7)+(t-7)$

Factor by grouping:

$0=(2t+1)(t-7)$

Zero Product Property:

$2t+1=0\text{ or } t-7=0$

Solve for each case:

$\displaystyle t=-0.5\text{ or } t=7$

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

6 0

3 years ago

You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You g

noname [10]

Answer:

i believe it would be 15=3.75+2.50 <3

8 0

3 years ago

Read 2 more answers

a sociologist develops a test to measure attitudes towards public transportation and 27 randomly selected subjects are given the

horsena [70]

Answer:

The 95% confidence interval for the mean score is:

$\mu$ ∈ $(67.73,\ \ 84.67)$

Step-by-step explanation:

We want to estimate the population mean, that is, the average score of all the subjects.

An estimator for the population mean μ is ${\overline {x}}$

Since the sample size is $27$ then we use the statistic $t_{\frac{\alpha}{2}}$ with $27-1 = 26$ degrees of freedom

The confidence interval for the mean is:

$({\displaystyle {\overline {x}}} + t_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}},\ \ {\displaystyle {\overline {x}}} - t_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}})$

Where

${\displaystyle {\overline {x}}}=76.2$ is the average score of the sample

$S=21.4$ is the standard deviation of the sample

$n= 27$ is the sample size

$t_{\frac{\alpha}{2}} = 2.056$ for a confidence level of 95% and 26 degrees of freedom

Then confidence interval is

$(76.2 + 2.056\frac{21.4}{\sqrt{27}},\ \ {76.2 - 2.056\frac{21.4}{\sqrt{27}})$

$(76.2 + 8.467,\ \ 76.2 - 8.467)$

$\mu$ ∈ $(67.73,\ \ 84.67)$

7 0

3 years ago

I need help on this !!!!!

ikadub [295]

Answer: 5.4

Step-by-step explanation:

Use cosine to find the adjacent side.

cosine = adjacent/hypotenuse

Substitute these values in the cosine equation:

cos(39) = x/7

7*cos(39) = x

Use a calculator to find the value of x:

x = 5.4

4 0

3 years ago

Suppose you have a credit card debt of $4,000. Last month the bank charged you $40 interest on the debt. The solution to the equ

attashe74 [19]

Answer:

12%

Step-by-step explanation:

<u>As per the given formula:</u>

40= 4000/12r
r = 40*12/4000
r = 0.12
0.12*100% = 12%

Interest rate is 12%

7 0

3 years ago