Which triangle has all three angle measuring less than 90°

PLEASE HELP

irina [24]

Using simple interest, it is found that:

The amount invested at 7% is $2,000.

The amount invested at 8% is $8,000.

<h3>Simple Interest</h3>

Simple interest is used when there is a single compounding per time period.

The interest after t years in is modeled by:

$I(t) = Prt$

In which:

P is the initial amount.

r is the interest rate, as a decimal.

In this problem:

A total of $10,000 was invested, hence $P_1 + P_2 = 10000$ .

Two accounts paying 7% and 8% annual interest, respectively, hence $r_1 = 0.07, r_2 = 0.08$ .

The total interest earned for the year was $780, hence $t = 1, I_1 + I_2 = 780$

Then:

$I_1 = 0.07P_1$

$I_2 = 0.08P_2$

Considering $P_1 + P_2 = 10000 \rightarrow P_2 = 10000 - P_1$ :

$I_2 = 0.08(10000 - P_1)$

Considering $I_1 + I_2 = 780 \rightarrow I_2 = 780 - I_1$ :

$780 - I_1 = 0.08(10000 - P_1)$

Considering $I_1 = 0.07P_1$ :

$780 - I_1 = 0.08(10000 - P_1)$

$780 - 0.07P_1 = 0.08(10000 - P_1)$

$0.01P_1 = 20$

$P_1 = \frac{20}{0.01}$

$P_1 = 2000$

And:

$P_1 + P_2 = 10000$

$2000 + P_2 = 10000$

$P_2 = 8000$

Then:

The amount invested at 7% is $2,000.

The amount invested at 8% is $8,000.

You can learn more about simple interest at brainly.com/question/25296782

8 0

2 years ago

In the data set below, what is the mean absolute deviation? 76, 67, 82, 25, 54, 15, 24

alina1380 [7]

Answer:

23.714285714286

Step-by-step

The mean absolute deviation of a set of data is the average distance between each data value and the mean.

1. Find the mean.

2. Find the distance between each data value and the mean. That is, find the absolute value of the difference between each data value and the mean.

3. Find the average of those differences.

4 0

2 years ago

Read 2 more answers

Simplify the expression by combining like terms. 2x + 4y + 6 + 2y - 5 + 3x

gtnhenbr [62]

I think the answer is 5x + 6y + 1

8 0

2 years ago

Find x options; a) 21√2/2 b) 21√2 c) 21√3/2 d) 7

pishuonlain [190]

The value of x is 21√2/2

The correct option is (A)

<h3>What is Trigonometry?</h3>

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles.

In triangle having angle 60.

sin 60 = P/ 7√3

√3/2= P/7√3

2P= 21

P= 21/2

Now again

cos 45= 21/2/x

1/√2 = 10.5/x

x= 21√2/2

Learn more about trigonometry here:

brainly.com/question/26719838

#SPJ1

6 0

1 year ago

A soup bowl is in the shape of a hemisphere with a diameter of 10 cm. What is the approximate maximum volume of soup that the bo

Oduvanchick [21]

Answer:

3.48cm³ (approximated)

Step-by-step explanation:

The maximum water that bowl can hold = The volume of the bowl

$\boxed{ \mathsf{volume \: of \: bowl = \frac{2}{3} \times \pi \: r {}^{3} }}$

Radius is half of diameter.

Given -

Diameter = 10cm .

From the given data we can derive that the radius of the hemispherical bowl is 5cm (10/2)

Putting the known values into the formula to get the value of the volume of bowl :

$\mathsf{volume = \frac{2}{3} \times \: 3.14 \: \times {5}^{3} }$

= 3.48888cm³

= 3.48cm³

5 0

2 years ago