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2 years ago

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

Mathematics

2 answers:

OverLord2011 [107]2 years ago

8 0

D) Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem.

Anestetic [448]2 years ago

5 0

Answer:

D. Angles BAC and DCA are congruent by the Alternate interior angles theorem.

Step-by-step explanation:

Given ABCD is a parallelogram.

AB=CD and BC=AD

$AB\parallel CD \; and\; BC\parallel AD$

To prove that $AB\cong CD\; and\; BC\cong AD$ .

Proof: According to given information

$AB\parallel CD$ and segment $BC\parallel AD$ .

Construct diagonal AC with a straightedge.

In $\triangle ABC\; and\; \triangle ADC$

AC=AC

Reflexive property of equality.

$m\angle BCA\cong m\angle DAC$

By alternate interior angles theorem.

$m\angle BAC\cong m\angle DCA$

By alternate interior angles theorem.

$\triangle BCA\cong\triangle DAC$

By ASA( Angle-Side_Angle) theorem.

By CPCTC opposite sides AB and CD, as well as BC and DA are congruent.

Hence proved.

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How much money, as a one-time deposit, PV, would you need to deposit into an account that earns 1.5% compounded monthly to earn

Karolina [17]

Answer:

The amount needed as a one-time deposit to earn $7,500 in 3 years is $4388.17

Step-by-step explanation:

Basic Finance Formulas

One of the most-used formulas to compute present and future values is

$FV=PV(1+r)^{n}$

Where FV is the future value, PV is the present value, r is the interest rate and n is the number of periods. It's vital to keep in mind that r and n must be referred to the same compounded time, e.g. r is compounded monthly and n is expressed in months

The question requires to compute the PV needed as a one-time deposit to earn a future value of $7,500 in 3 years at a 1.5% rate compounded monthly.

FV=7,500

r=1.5%=0.015

n=3*12=36 months

We converted n to months because r is compounded monthly . The formula

$FV=PV(1+r)^{n}$

must be managed to make PV isolated

$PV=FV(1+r)^{-n}$

$PV=7,500(1+0.015)^{-36}$

$PV=\$4388.17$

Answer: The amount needed as a one-time deposit to earn $7,500 in 3 years is $4388.17

3 0

2 years ago

On average, the number of customers who had items to return for refunds or exchanges at a certain retail store's service desk is

spayn [35]

Answer:

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

Step-by-step explanation:

With the weekly average we can estimate the daily average for customers, assuming 7 days a week:

$M=756/7=108$

We can model this situation with a Poisson distribution, with parameter λ=108. But because the number of events is large, we use the normal aproximation:

$P(\lambda)\approx N(\lambda,\lambda)$

Then we can calculate the z value for x=100:

$z=\frac{x-\mu}{\sigma}=\frac{100-108}{\sqrt{108}}=\frac{-8}{10.4} =-0.77$

Now we calculate the probability of x>100 as:

$P(x>100)=P(z>-0.77)=0.78$

The probability that the service desk will have at least 100 customers with returns or exchanges on a randomly selected day is P=0.78.

5 0

2 years ago

For making a scatter plot of the data set, which would be the best scale and interval for the axis that represents the amount of

Serga [27]

I'd say the answer to the first question is D) 0 to 4 with intervals of 0.2.

Because, you can't just have 1 to 4, as some of the numbers are less than 1. Of course you can't have 2 to 5 either. And intervals of 2 would be too messy.

For the second question:

I believe the answer is A. Because it's obvious that there IS one outlier, and it looks like there are two clusters.

So, the answers are: A) and D).

8 0

2 years ago

Binks needs to raise at least $3600. He was given $200 and plans to save $50 a week. Select all of the inequalities that represe

kherson [118]

Answer:

I'm pretty sure it is 50n+200 < 3600

Step-by-step explanation:

Im to fully sure tho

5 0

1 year ago

You plan to rent a car from XYZ Car Rental Company for a flat rate of $35 a

vagabundo [1.1K]

Answer:

The piece-wise function is;

$f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}$

Step-by-step explanation:

The flat rate for renting the car = $35 per day

The amount charged as insurance fee per day for renting the car for 3 days or less = $10

The insurance fee charged per day when the car is rented for more than 3 days = $5

Let the number of days = x

Therefore, we have;

For x ≤ 3, f(x) = 35 × x + 10 × x = x × (35+10) = 45·x

For x > 3, f(x) = 35 × x + 5 × x = x × (35+5) = 40·x

Therefore;

The charge rate for renting the car for less than or equal to 3 days = 45·x

The charge rate for renting the car for more than 3 days = 40·x

The piece-wise function can be presented as follows;

$f\left (x \right ) = \begin{cases} \$ 45 \times x & \text{ if } x \leq 3 \ days \\ \$40 \times x & \text{ if } x > 3 \ days\end{cases}$

3 0

2 years ago