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2 years ago

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Qing attached a dog ramp to her bed, which allows her dog to easily climb onto the mattress. The ramp is 48 inches long. The bas

e of the ramp is 40 inches from the base of the bed. How high off the ground is the top of the mattress? Enter your answer, rounded to the nearest tenth, in the box.

1 answer:

geniusboy [140]2 years ago

4 0

Using the formula a^2+b^2=c^2you can fill in the numbers so that a=height of mattress in inches,b=40 inches or distance from base of the bed and c=48 or length of the ramp. a^2+40^2=48^2a^2+1600=2304
So then it becomes2304-1600=a^2704=a^2 26.5+=aSo, The top of the mattress(after rounding) is 26.5 inches off the ground.

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Mateus’s bank issued an advertisement saying that 90\%90%90, percent of its customers are satisfied with the bank’s services. Si

densk [106]

Answer:

The probability of getting a sample with 80% satisfied customers or less is 0.0125.

Step-by-step explanation:

We are given that the results of 1000 simulations, each simulating a sample of 80 customers, assuming there are 90 percent satisfied customers.

Let $\hat p$ = <u><em>sample proportion of satisfied customers</em></u>

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

Z = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, p = population proportion of satisfied customers = 90%

n = sample of customers = 80

Now, the probability of getting a sample with 80% satisfied customers or less is given by = P( $\hat p \leq$ 80%)

P( $\hat p \leq$ 80%) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ $\leq$ $\frac{0.80-0.90}{\sqrt{\frac{0.80(1-0.80)}{80} } }$ ) = P(Z $\leq$ -2.24) = 1 - P(Z < 2.24)

= 1 - 0.9875 = <u>0.0125</u>

The above probability is calculated by looking at the value of x = 2.24 in the z table which has an area of 0.9875.

8 0

2 years ago

A student wants to know how far above the ground the top of a leaning flagpole is. At high noon, when the sun is almost directl

MariettaO [177]

Answer:

15.43 ft

Step-by-step explanation:

To solve this question, one should use the concept of similar triangles.

The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem. Therefore, the distance of the top of the pole to the ground is:

$14 in = 1.1667 ft$

$1.1667x=6*3\\x = 15.43$

The distance of the top of the pole to the ground is 15.43 ft.

4 0

1 year ago

a number, n, is added to 15 less than 3 times itself.The result is 101.Which equation can be used to find the value of n? 3n-15+

Arturiano [62]

To solve for the system of equations, I will write the equation down as I rewrite the written form.
a number, n, (n) is added to 15 less than 3 times itself (+3n -15). The result is (=) 101. (101)
Now let's write only what's in the parenthesis.
n + 3n -15 = 101.
The correctly written form in your answers is:
3n - 15 + n = 101, your first answer.

4 0

1 year ago

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

3 0

2 years ago

Read 2 more answers

Side AB of square ABCD is parallel to the Y axis and the perimeter of ABCD is 36. If the coordinates of point B is (5,17) . What

Zarrin [17]

<h3>Answer: (C) (14,8)</h3>

============================================

Explanation:

The perimeter of the square is 36, so each side length is 36/4 = 9 units.

Point B is located at (5,17). We move down 9 units to get to (5,8), which is the location of point A. Then we move 9 units to the right to arrive at (14,8) which is point D's location.

Or we could go from B = (5,17) to C = (14,17) and then to D = (14,8). Each time we move 9 units.

8 0

1 year ago