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3 years ago

8

Nick borrowed $7150, to be repaired at an annual simple interest rate of 6.25%. How much interest will be due after 5 years? How

much will Nick have to repay?

1 answer:

Soloha48 [4]3 years ago

7 0

$2,234.38 after 5 years and he will have to repay $9,384.38.

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A game of basketball requires to players. at the park there are 5 games being played. how many total player are at the park

lara [203]

If one game needs two* players, and there are 5 games,
you multiply two by five to get ten players total.

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3 years ago

Math 7a using number sense to solve equations

Anika [276]

Simple...

you have: $\frac{n}{3} =12
$

and

$\frac{n}{3} =-12$

To solve for.... $\frac{n}{3} =12$

Multiply to remove the denominator-->>

$3* \frac{n}{3} =12*3$

n=12*3

n=36

Then-->>>

$\frac{n}{3} =-12$

Do the same thing-->>

$3* \frac{n}{3} =-12*3$

n=-12*3

n=-36

Thus, your answer.

6 0

3 years ago

An article presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new meth

Anna35 [415]

Answer:

With 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

Step-by-step explanation:

We are given that the effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 655.6 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.

A traffic engineer states that the mean improvement is between 583.1 and 728.1 vehicles per hour.

<em>Let </em> $\bar X$ <em> = sample mean improvement</em>

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = mean improvement = 655.6 vehicles per hour

$\sigma$ = standard deviation = 311.7 vehicles per hour

n = sample of simulations = 50

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the mean improvement is between 583.1 and 728.1 vehicles per hour is given by = P(583.1 < $\bar X$ < 728.1) = P( $\bar X$ < 728.1) - P( $\bar X$ $\leq$ 583.1)

P( $\bar X$ < 728.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{728.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z < 1.64) = 0.9495

P( $\bar X$ $\leq$ 583.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{583.1-655.6}{\frac{311.7}{\sqrt{50} } }$ ) = P(Z $\leq$ -1.64) = 1 - P(Z < 1.64)

= 1 - 0.9495 = 0.0505

<em />

<em>So, in the z table the P(Z </em> $\leq$ <em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.64 in the z table which has an area of 0.9495.</em>

Therefore, P(583.1 < $\bar X$ < 728.1) = 0.9495 - 0.0505 = 0.899 or 89.9%

Hence, with 89.9% we can say that the mean improvement is between 583.1 and 728.1 vehicles per hour.

6 0

3 years ago

Determine and describe the number and type of roots of the quadratic functions. Show any and all work necessary to determine

algol13

Answer:

See explanations below

Step-by-step explanation:

The root of a quadratic equation is determined by its discriminant

D = b²-4ac

If D > 0, the roots are real and unique

If D < 0, the roots are complex

If D= 0, the roots are real and equal

a) For the quadratic equation

y=3x^2+7x+8

Since the highest degree of the equation is 2, hence the equation will have 2 roots

From the equation, a = 3, b = 7 and c = 8

Get the discriminant

D = 7²-4(3)(8)

D = 49 - 96

D = -47

Since the discriminant value is less than 0, hence the roots are complex roots

b) For the quadratic equation

y=2x^2-7x-2

Since the highest degree of the equation is 2, hence the equation will have 2 roots

From the equation, a = 2, b = -3 and c = -2

Get the discriminant

D = (-3)²-4(2)(-2)

D = 9 + 16

D = 25

Since the discriminant value is greater than 0, hence the roots are real and unique.

c) For the quadratic equation

y=9x^2+30x+25

Since the highest degree of the equation is 2, hence the equation will have 2 roots

From the equation, a = 9, b = 30 and c = 25

Get the discriminant

D = 30²-4(9)(25)

D = 900 - 900

D = 0

Since the discriminant value is equal to 0, hence the roots are complex real and equal

7 0

2 years ago

What is the value of x?

katovenus [111]

Answer:

x = 15

Step-by-step explanation:

Using the Altitude on Hypotenuse theorem

( leg of large Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

Thus

x² = 9 × (9 + 16) = 9 × 25 = 225 ( take the square root of both sides )

x = $\sqrt{225}$ = 15

4 0

2 years ago