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bearhunter [10]
2 years ago
13

What is the GCF of 16s3t, 40s5, and 68t2? 4 4s3t 8 8s3t

Mathematics
2 answers:
kumpel [21]2 years ago
9 0

Answer:  First option is correct.

Step-by-step explanation:

Since we have given that

16s^3t,40s^5\ and\ 68t^2

First we write the factors of all of these numbers:

Factors of 16s^3t is given by

4\times 4\times s\times s\times s\times t

Factors of 40s^5 is given by

2\times 2\times 2\times 5\times s\times s\times s\times s\times s

Factors of 68t^2 is given by

17\times 2\times 2\times t\times t

So, GCF ( Greatest common factor) will be

2\times 2=4

Hence, First option is correct.

Gemiola [76]2 years ago
3 0
4 is the only factor common among all terms
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If ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?
Alborosie

No, not possible to tell that the the two triangles, ΔBAC and ΔCED

are similar ⇒ answer D

Step-by-step explanation:

Let us revise the cases of similarity

1. AAA similarity : two triangles are similar if all three angles in the first

  triangle equal the corresponding angle in the second triangle  

2. AA similarity : If two angles of one triangle are equal to the

   corresponding angles of the other triangle, then the two triangles  

   are similar.

3. SSS similarity : If the corresponding sides of the two triangles are

   proportional, then the two triangles are similar.

4. SAS similarity : In two triangles, if two sets of corresponding sides  

   are proportional and the included angles are equal then the two  

   triangles are similar.

In the two triangles BAC and CED

∵ m∠BAC = 17°

∵ m∠CED = 17°

∴ m∠BAC = m∠CED

But we need another pair of angles to prove that the two triangles are

similar by AA similarity criterion

<em>OR </em>

The lengths of sides BA , CA and CE , DE to show that

\frac{BA}{CE}=\frac{CA}{DE} = constant ratio and prove that the

two triangles are similar by SAS similarity criterion

So it is not possible to prove that the two triangles are similar

No, not possible to tell that the the two triangles, ΔBAC and ΔCED

are similar

Learn more:

You can learn more about triangles in brainly.com/question/4354581

#LearnwithBrainly

5 0
2 years ago
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Mr. Jenkins deposited $1,250 into an account. He made no additional deposits or withdrawals. Mr. Jenkins earned 4.25% annual sim
monitta

Answer:

Step-by-step explanation:

1250(1 + .0425*4)

4 0
2 years ago
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Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If th
olchik [2.2K]

Let us assume number of nickels = n,

number of dimes = d and

number of quarters = q.

Total number of coins = 844.

We can setup a statement "number of nickels + number of dimes +number of quarters = Total coins.

And we can setup an equation for the above statement as

n+d+q = 844            ---------------------equation(1).

We also given: Emilia had as many quarters as dimes.

Therefore, number of quarters = number of dimes.

So, we can setup another equation as

q = d                          ------------------------equation(2).

Also given : "twice as many nickels as dimes".

We can setup another equation for this statement as

n = twice of number of dimes

or n= 2d                -------------------------- equation (3).

We got three equations.

Let us solve system of three equation by substitution method.

Substituting q = d and  n= 2d  in equation (1), we got

n+d+q = 844      => 2d +d + d = 844.

Adding d's, we get

4d =844.

Dividing both sides by 4, we get

\frac{4d}{4}=\frac{844}{4}

d = 211.

Therefore number of dimes = 211.

Let us find number of nickels and number of quarter coins now.

We know, number of quarters = number of dimes.

Therefore, number of qurters = 221.

Total number of coins = 844.

Therefore, number of nickels = 844 -  (number of quarters + number of dimes).

= 844 -(221+221) = 844 - 442

= 402.

So, the number of nickels =402.

Let us find the total values of all the coins.

A nickel = $0.05

A dime = $0.10

A quarter = $0.25.

Total value = 0.05 *(number of nickels) + 0.10*(number of dimes) + 0.25*(number of quarters).

= 0.05* 402 + 0.10 *221 + 0.25*221.

= 20.10 + 22.10 + 55.25.

= 97.45.

Therefore, total value of all 844 coins = $97.45.

Emilia had saved $97.45.


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The histogram shows a city’s daily high temperatures recorded for four weeks. A graph shows temperature (degrees Fahrenheit) the
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Answer:

b. left- skewed

Step-by-step explanation:

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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
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