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natulia [17]
3 years ago
7

Amanda is the owner of a small chain of dental offices. She sent out the yearly satisfaction survey to 600 randomly selected pat

ients and received 544 surveys back. When looking through the results, she noticed that the downtown dental office staff had 84% of clients reporting satisfaction with services, while the uptown dental office staff had 76% of clients reporting satisfaction with services. Which of the following sets shows Amanda's null hypothesis and alternative hypothesis?
Mathematics
1 answer:
Morgarella [4.7K]3 years ago
8 0

Answer:

Null Hypothesis: The proportion of clients satisfied at the uptown office is 76%.

Alternative Hypothesis: There is no difference in the satisfaction between the uptown and the downtown clients.

Null Hypothesis: The proportion of clients satisfied at the downtown office is greater than the proportion of clients satisfied at the uptown office.

Alternative Hypothesis: Downtown clients are less satisfied with the dental office staff than uptown clients.

Null Hypothesis: The proportion of clients satisfied at the downtown office is 84%.

Alternative Hypothesis: Uptown clients are more satisfied with the dental office staff than downtown clients.

Null Hypothesis: The proportion of clients satisfied at the downtown office is equal to the proportion of clients satisfied at the uptown office.  

Alternative Hypothesis: There is a difference in the satisfaction between the uptown and the downtown clients.

Step-by-step explanation:

pls mark as brainliest

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A total of $5000 is invested: part at 7% and the remainder at 12%. How much is invested at each rate if the annual interest is $
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The amount invested in the account that yields 7% interest is $4000.

The amount invested in the account that yields 12% interest is $1000.

<h3>What are the linear equations that represent the question?</h3>

a + b = 5000 equation 1

0.07a + 0.12b = 400 equation 2

Where:

a = amount invested in the account that yields 7% interest.

b =  amount invested in the account that yields 12% interest.

<h3>How much is invested at each rate?</h3>

Multiply equation 1 by 0.07

0.07a + 0.07b = 350 equation 3

Subtract equation 3 from equation 2

0.05b = 50

b = 50 / 0.05

b = 1000

Subtract 1000 from 5000: 5000 - 1000 = 4000

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Calculate the length of sides triangle pqr and determine weather or not triangle is a right angled. P(-4,6) q(6,1) r(2,9)
Tom [10]

\bold{\huge{\underline{ Solution }}}

<h3><u>Given </u><u>:</u><u>-</u></h3>

  • We have given the coordinates of the triangle PQR that is P(-4,6) , Q(6,1) and R(2,9)

<h3><u>To</u><u> </u><u>Find </u><u>:</u><u>-</u></h3>

  • <u>We </u><u>have </u><u>to </u><u>calculate </u><u>the </u><u>length </u><u>of </u><u>the </u><u>sides </u><u>of </u><u>given </u><u>triangle </u><u>and </u><u>also </u><u>we </u><u>have </u><u>to </u><u>determine </u><u>whether </u><u>it </u><u>is </u><u>right </u><u>angled </u><u>triangle </u><u>or </u><u>not </u>

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>Here</u><u>, </u><u> </u><u>we </u><u>have </u>

  • Coordinates of P =( x1 = -4 , y1 = 6)
  • Coordinates of Q = ( x2 = 6 , y2 = 1 )
  • Coordinates of R = ( x3 = 2 , y3 = 9 )

<u>By </u><u>using </u><u>distance </u><u>formula </u>

\pink{\bigstar}\boxed{\sf{Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}

<u>Subsitute </u><u>the </u><u>required </u><u>values </u><u>in </u><u>the </u><u>above </u><u>formula </u><u>:</u><u>-</u>

Length of side PQ

\sf{ = }{\sf\sqrt{ (6 - (-4))^{2} + (1 - 6)^{2}}}

\sf{ = }{\sf\sqrt{ (6 + 4 )^{2} + (- 5)^{2}}}

\sf{ = }{\sf\sqrt{ (10)^{2} + (- 5)^{2}}}

\sf{ = }{\sf\sqrt{ 100 + 25 }}

\sf{ = }{\sf\sqrt{ 125 }}

\sf{ = 5 }{\sf\sqrt{ 5 }}

Length of QR

\sf{ = }{\sf\sqrt{(2 - 6)^{2} + (9 - 1)^{2}}}

\sf{ = }{\sf\sqrt{(- 4 )^{2} + (8)^{2}}}

\sf{ = }{\sf\sqrt{16 + 64 }}

\sf{ = }{\sf\sqrt{80 }}

\sf{ = 4 }{\sf\sqrt{5 }}

Length of RP

\sf{ = }{\sf\sqrt{ (-4 - 2 )^{2} + (6 - 9)^{2}}}

\sf{ = }{\sf\sqrt{ (-6 )^{2} + (-3)^{2}}}

\sf{ = }{\sf\sqrt{ 36 + 9 }}

\sf{ = }{\sf\sqrt{ 45 }}

\sf{ = 3}{\sf\sqrt{ 5 }}

<h3><u>Now</u><u>, </u></h3>

We have to determine whether the triangle PQR is right angled triangle

<h3>Therefore, </h3>

<u>By </u><u>using </u><u>Pythagoras </u><u>theorem </u><u>:</u><u>-</u>

  • Pythagoras theorem states that the sum of squares of two sides that is sum of squares of 2 smaller sides of triangle is equal to the square of hypotenuse that is square of longest side of triangle

<u>That </u><u>is</u><u>, </u>

\bold{ PQ^{2} + QR^{2} = PR^{2}}

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>,</u>

\bold{  125 + 80 = 45 }

\bold{  205  = 45 }

<u>From </u><u>above </u><u>we </u><u>can </u><u>conclude </u><u>that</u><u>, </u>

  • The triangle PQR is not a right angled triangle because 205 ≠ 45 .
6 0
2 years ago
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