Rt 9+ 10r - 5 - 4r.<br> Help me

In a right triangle, <A and <B are acute. Find the value of sin A, when tan A = 8/15

finlep [7]

Answer:sinA=8/17

Step-by-step explanation:

Using Pythagoras principle

x=√(15^2+8^2)

x=√(15x15+8x8)

x=√(225+64)

x=√(289)

x=17

SinA=opposite/hypothenus

SinA=8/17

3 0

3 years ago

Hannah wants to laminate the tabletop in her study room. The tabletop is the shape of an isosceles trapezoid shown here. If lami

kondaur [170]

Answer:

$16

Step-by-step explanation: I did the math in the comments.

5 0

2 years ago

Read 2 more answers

A log raft is moving downstream at a speed of 3 km/h. To insure that there are no river jams a supervisor travels along the raft

skad [1K]

Answer:

2000 meters

Step-by-step explanation:

When the motorboat is moving downstream, its speed relative to the ground is 18 km/h, so its speed relative to the raft is 15 km/h.

When the motorboat is moving upstream, its speed relative to the ground is 12 km/h, so its speed relative to the raft is again 15 km/h.

Converted to m/min, the relative speed is:

15 km/h × (1000 m/km) × (1 h / 60 min) = 250 m/min

It takes the motorboat 16 minutes to travel to the front of the raft and back. Since the speed is the same in both directions, the motorboat takes 8 minutes to travel the length of the raft.

So the length of the raft is 250×8 = 2000 meters.

8 0

3 years ago

Line XY was drawn on a plane. Using a compass and a straightedge the student wanted to construct an equilateral triangle. What w

Andrew [12]

1. Place your compass point on X and measure the distance to point Y. Swing an arc of this size above (or below) the segment.

2. Without changing the span on the compass, place the compass point on Y and swing the same arc, intersecting with the first arc.

3. Label the point of intersection as the third vertex of the equilateral triangle.

4. Use you straight edge and connect the points.

7 0

3 years ago

A survey collected data on annual credit card charges in seven different categories of expenditures: transportation, groceries,

Andru [333]

Answer:

A. Null and alternative hypothesis:

$H_0: \mu_d=0\\\\H_a:\mu_d\neq 0$

B. Yes. At a significance level of 0.05, there is enough evidence to support the claim that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

P-value = 0.00002

C. As the difference is calculated as (population 1 − population 2), being population 1: groceries and population 2: dinning out, and knowing there is evidence that the true mean difference is positive, we can say that the groceries annual credit card charge is higher than dinning out annual credit card charge.

The point estimate is the sample mean difference d=$840.

The 95% confidence interval for the mean difference between the population means is (490, 1190).

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

Then, the null and alternative hypothesis are:

$H_0: \mu_d=0\\\\H_a:\mu_d\neq 0$

The significance level is 0.05.

The sample has a size n=42.

The sample mean is M=840.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1123.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1123}{\sqrt{42}}=173.2827$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{840-0}{173.2827}=\dfrac{840}{173.2827}=4.848$

The degrees of freedom for this sample size are:

$df=n-1=42-1=41$

This test is a two-tailed test, with 41 degrees of freedom and t=4.848, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>4.848)=0.00002$

As the P-value (0.00002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

At a significance level of 0.05, there is enough evidence to support the claim that there is signficant difference between the population mean credit card charges for groceries and the population mean credit card charges for dining out.

We have to calculate a 95% confidence interval for the mean difference.

The t-value for a 95% confidence interval and 41 degrees of freedom is t=2.02.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.02 \cdot 173.283=350$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 840-350=490\\\\UL=M+t \cdot s_M = 840+350=1190$

The 95% confidence interval for the mean difference is (490, 1190).

7 0

3 years ago

Rt 9+ 10r - 5 - 4r. Help me