If ray QS bisects angle PQR. Angle PQS=3x, angle SQR=5x-20. Find x

The two interior opposite Angel's of a triangle are 60° and 80°. Find the measure of the exterior angle.

Vadim26 [7]

let the exterior angle be x

x=60°+80°(being one exterior angle is equal to two interior angle)

x°=140°

5 0

2 years ago

Alex invests $2,000 in a company's stock. After a year, the value of Alex's stock has increased to $2,500. What rate of return h

Kay [80]

The rate of interest is 25%

<u>Explanation:</u>

Given:

Principal, P = $2,000

Amount, A = $2500

Time, t = 1 year

Rate of Interest, r = ?

We know:

$Amount = P(1+\frac{r}{100})^t$

On substituting the value we get:

$2500 = 2000 (1 + \frac{r}{100})^1\\ \\\frac{25}{20}= (1+\frac{r}{100})\\$

$\frac{5}{20} = \frac{r}{100}\\ \\r = \frac{100 X 5}{20} \\\\r = 25$

Therefore, the rate of interest is 25%

5 0

3 years ago

Read 2 more answers

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 1

BigorU [14]

Answer:

a: Sample mean: 20, Sample standard deviation: 1.732

b: 19.13 <µ < 20.87

c: 18.84< µ < 21.16

d: as the confidence level increases, the interval becomes wider

Step-by-step explanation:

a: Sample mean is found by adding up all the individual values of the sample, then dividing by the total number of values in the sample.

Sample standard deviation is the square root of the variance

See the first attached photo for the calculations of these values.

We need to create a 80% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.

Look for the column on the t-distribution chart that has "area in two tails" of 0.20 (80%), and row 7 (degree of freedom)

The t-value is 1.415

See the second attached photo for the construction of the confidence interval

We need to create a 90% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.

Look for the column on the t-distribution chart that has "area in two tails" of 0.10 (90%), and row 7 (degree of freedom)

The t-value is 1.895

See the third attached photo for the construction of the confidence interval

3 0

3 years ago

Examine the following system of inequalities.

lubasha [3.4K]

Answer:

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

Step-by-step explanation:

we have

$y > -x+4$ ----> inequality A

The solution of the inequality A is the shaded area above the dotted line $y=-x+4$

The dotted line passes through the points (0,4) and (4,0) (y and x-intercepts)

and

$y \leq -(1/2)^{x} +6$ -----> inequality B

The solution of the inequality B is the shaded area above the solid line $y=-(1/2)^{x} +6$

The solid line passes through the points (0,5) and (-2,2)

therefore

The solution of the system of inequalities is the shaded area between the dotted line and the solid line

see the attached figure

Dotted linear inequality shaded above passes through (0, 4) and (4, 0). Solid exponential inequality shaded below passes through (negative 2,2) & (0,5)

7 0

3 years ago

3x+5y = 15 find the slope of a line perpendicular to each given line

gladu [14]

Answer:

Slope = 5/3

Step-by-step explanation:

See attached image

5 0

1 year ago