Daisy has a pitcher that can hold 1000

Phantasy [73]

Answer:

$x=3\sqrt{7}$

Step-by-step explanation:

If a tangent and a secant connect to an exterior point of a circle, the tangent squared is equal to the product of the two segments the secant creates.

Therefore, we have:

$x^2=7 \cdot 9,\\x^2=63,\\x=\sqrt{63}=\boxed{3\sqrt{7}}$

8 0

3 years ago

The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

$\fbox {Pythagorean equation:}$ <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

$H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17$

H = 17

If we decrease the base and the height by 2 centimeters, we have

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

$H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3$

$H' \approx 14.3$

So, the hypotenuse decreases $H - H' \approx 17 - 14.3 = 2.7$

3 0

3 years ago

An analytical laboratory is asked to evaluate the claim that the concentration of the active ingredient in a specimen is 86%. Th

Olenka [21]

Answer:

Decision rule

Reject null hypothesis

Conclusion

There is significance evidence that the true mean is different from 0.86

Step-by-step explanation:

From the question we are told that

The population mean $\mu = 0.86$

The sample is mean is $\= x = 0.8708$

The standard deviation is $\sigma = 0.0068$

The level of significance is $\alpha = 0.01$

The sample size n = 3

The null hypothesis is $\mu = 0.86$

The alternative hypothesis is $\mu \ne 0.86$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{ 0.8708 - 0.86 }{ \frac{0.0068}{\sqrt{3} } }$

=> $z = 2.751$

Generally p- value is mathematically represented as

$p-value = 2 P(z >2.751 )$

From the z-table

$P(z >2.751 ) = 0.0029707$

So

$p-value = 2 * 0.0029707$

=> $p-value = 0.00594$

From the obtained question we see that $p-value < \alpha$

Hence we reject the null hypothesis

6 0

3 years ago

Can u show me the steps for answering this question

Oliga [24]

Answer: 6(2x+3)

Step-by-step explanation: its a factor

7 0

3 years ago

PLEASE HELP ME!!!! Nancie and Suresh are typing. The rate at which Nancie is typing is represented by the equation y = 35x, wher

Damm [24]

<span>answer 1
Nancie is typing is represented by the equation
y = 35x
Therefore, the rate at which Nancie is typing is given by the slope of the straight line that in this case is:
35 words per minute
answer 2
To find the rate at which Suresh is typing we have to find the equation of the line with the data in the table.
For this case, the equation of the line will be given by:
y = 56x
Therefore, the rate at which Suresh is typing is given by the slope of the straight line which in this case is:
56 words per minute
answer 3
Nancie's rate = 35
Suresh's rate = 56
56-35 = 21 words per minute
Nancie's rate is 21words per minute less than Suresh's rate.
</span>

6 0

4 years ago