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2 years ago

8

Leo drank 8 servings of iced tea and espresso beverages containing a total of 482 mg of caffeine. How many servings of espresso

did he drink?

2 answers:

amid [387]2 years ago

7 0

Leo drank 2 servings of it.

TEA [102]2 years ago

3 0

Answer:

Leo drand two servings of expresso. Hope it helps

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Hikers came across a part of a redwood stump. If the length of the chord is 8 feet, what was the diameter of the tree?

erastova [34]

So in the problem, the length of the chord there is the circumference of the tree. So in order to get the diameter of the tree, we must use the formula in getting the circumference of a circle that is stated as follows.

C = 2pi *Radius

so first we need the get the radius of the tree which represent by this formula:

Radius = C /2pi = 8/6.2832 = 1.2732 ft
Diameter = 2*radius = 2 * 1.27 32 = 2.5465 feet

In summary, the diameter of the tree is 2.565 feet.

7 0

2 years ago

Three trigonometric functions for a given angle are shown below. cosecant theta = thirteen-twelfths; secant theta = Negative thi

Kay [80]

Answer:

(–5, 12) is the correct answer.

Step-by-step explanation:

We are given the following values:

$cosec\theta = \dfrac{13}{12}\\sec\theta=-\dfrac{13}{5}\\cot\theta =-\dfrac{5}{12}$

Now, we know the following identities:

$sin \theta = \dfrac{1}{cosec\theta}\\cos \theta = \dfrac{1}{sec\theta}\\tan \theta = \dfrac{1}{cot\theta}$

Now, the values are:

$sin\theta = \dfrac{12}{13}\\cos\theta=-\dfrac{5}{13}\\tan\theta =-\dfrac{12}{5}$

Sine value is positive and cos, tan values are negative.

It can be clearly observed that $\theta$ is in 2nd quadrant.

2nd quadrant means, the value of $x$ will be negative and $y$ will be positive.

Let us have a look at the value of $tan\theta$ :

$tan\theta = \dfrac{Perpendicular}{Base}\\OR\\tan\theta = \dfrac{y-coordinate}{x-coordinate} = -\dfrac{12}{5}\\\therefore y = 12,\\x = -5$

Please refer to the attached image for clear understanding and detailed explanation.

Hence, the correct answer is coordinate (x,y) is (–5, 12)

8 0

2 years ago

Find the sum of the first 30 terms of the sequence below an=3n+2

Solnce55 [7]

First off, let's find the 1st term's value, and the 30th term's value,

$\bf a1=3(1)+2\implies a1=5\qquad \qquad \quad a30=3(30)+2\implies a30=92\\\\
-------------------------------\\\\
~~~~~~~\textit{ Sum of an arithmetic sequence}\\\\
S_n=\cfrac{n(a1+an)}{2}~ 
\begin{cases}
n=n^{th}\ term\\
a1=\textit{first term's value}\\
----------\\
a1=5\\
a30=92\\
n=30
\end{cases} \implies S_{30}=\cfrac{30(5+92)}{2}
\\\\\\
S_{30}=15(97)$

6 0

2 years ago

Read 2 more answers

A recent nationwide study investigated the value of the prostate-specific antigen (PSA) blood test for the detection of prostate

MaRussiya [10]

Answer:

Step-by-step explanation:

Remember:

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

You can arrange them in a contingency table as:

Probabilities Positive ; Negative

Sick + ∩ S ; - ∩ S S

Healthy + ∩ H ; - ∩ H H

+ - 1

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true positive rate).

⇒ P(+/S) = <u>P(+ ∩ S)</u>

P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly healthy (true negative rate)

⇒ P(-/H) = <u>P(- ∩ H)</u>

P(H)

1) You are studying the value of the prostate-specific antigen (PSA) blood test for the detection of prostate cancer on men of 50 years of age and older.

Total 100000 men

686 men tested positive

281 of the men that tested positive had cancer

45 men that tested negative had cancer

Total - positive cases: 100000 - 686 = 99314 tested negative

; Positive ; Negative ; Total

Sick ; 281 ; 45 ; 326

Healthy ; 405 ; 99269 ; 99674

Total ; 686 ; 99314 ; 100000

2)

Sensitivity of the test is

P(+/S) = <u>P(+ ∩ S) </u>= <u>0.00281 </u>= 0.86

P(S) 0.00326

Where:

P(+ ∩ S) = 281/100000 = 0.00281

P(S) = 326/100000 = 0.00326

The test has an 86% probability of detecting PSA in sick patients.

3)

Specificity of the test is

P(-/H) = <u>P(- ∩ H) </u>= <u>0.99269 </u>= 0.995

P(H) 0.99674

Where:

P(- ∩ H)= 99269/100000= 0.99269

P(H)= 99674/100000= 0.99674

The test has a 99.5% probability of not detecting PSA in healthy patients.

4)

Positive predictive value (PPV)

It's defined as the probability of being sick when the test is positive:

P(S/+)= <u>P(S ∩ +) </u>= <u>0.00281 </u>= 0.04

P(+) 0.0686

Where

P(+)= 686/100000= 0.0686

There is a 4% probability of having cancer if the test is positive.

5)

Negative predictive value (NPV)

P(H/-)= <u>P(H ∩ -) </u>= <u>0.99269 =</u> 0.999

P(-) 0.99314

Where:

P(-)= 99314/100000= 0.99314

There is a 99.9% probability of being healthy if the test is negative.

6 to 10 are all examples of medical tests.

I hope this helps!

7 0

2 years ago

The sum of an infinite geometric sequence is seven times the value of its first term.

Radda [10]

Answer:

a). r = $\frac{6}{7}$

b). At least 5 terms should be added.

Step-by-step explanation:

Formula representing sum of infinite geometric sequence is,

$S_{\inf}=\frac{a}{1-r}$

Where a = first term of the sequence

r = common ratio

a). If the sum is seven times the value of its first term.

$7a=\frac{a}{1-r}$

$7=\frac{1}{1-r}$

7(1 - r) = 1

7 - 7r = 1

7r = 7 - 1

7r = 6

r = $\frac{6}{7}$

b). Since sum of n terms of the geometric sequence is given by,

$S_{n}=\frac{a(1-r^{n})}{1-r}$

If the sum of n terms of this sequence is more than half the value of the infinite sum.

$\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}$ > $\frac{7a}{2}$

$\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}$

$\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}$

$1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}$

$1-(\frac{6}{7})^{n}> \frac{1}{2}$

$-(\frac{6}{7})^{n}> -\frac{1}{2}$

$(\frac{6}{7})^{n}< \frac{1}{2}$

$(0.85714)^{n}< (0.5)$

n[log(0.85714)] < log(0.5)

-n(0.06695) < -0.30102

n > $\frac{0.30102}{0.06695}$

n > 4.496

n > 4.5

Therefore, at least 5 terms of the sequence should be added.

8 0

2 years ago