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Fittoniya [83]
2 years ago
12

Kevin asked his trainee, Anna, to help call some of his clients to sell a newly-issued municipal bond. If he had to call all of

the clients himself, it would take Kevin six hours to complete the job. If Anna alone were to call the clients, it would take her nine hours. Working together, how long will it take Kevin and Anna to call all of the clients?
Mathematics
1 answer:
weqwewe [10]2 years ago
7 0

Answer:

3.6 hours

Step-by-step explanation:

To solve, create a Rate, Time, Work chart:

Work is rate times time. For Kevin, his work is going to equal x over 6 job. For Anna, her expression for work will equal x over 9 job.

The work is 1 job of calling all clients, so their combined work is equal to 1.  

x over 6 plus x over 9 equals 1

In the rational equation, x is the amount of time it takes Kevin and Anna to call the clients together.  With rational equations, the terms can be added together once they have common denominators.  

x over 6 plus x over 9 equals 1

fraction numerator begin display style x left parenthesis 9 right parenthesis end style over denominator begin display style 6 left parenthesis 9 right parenthesis end style end fraction plus fraction numerator begin display style x left parenthesis 6 right parenthesis end style over denominator begin display style 9 left parenthesis 6 right parenthesis end style end fraction equals fraction numerator begin display style 1 left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end style over denominator left parenthesis 6 right parenthesis left parenthesis 9 right parenthesis end fraction

fraction numerator 9 x over denominator 54 end fraction plus fraction numerator 6 x over denominator 54 end fraction equals 54 over 54

9 x plus 6 x equals 54

15 x equals 54

x equals 3.6

If Kevin and Anna work together, they can call all the clients in 3.6 hours.

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For a button to fit through its button-hole the hole needs to be the size of the buttons diameter what size buttonhole is needed
Lena [83]

Answer:the size of the button hole is 2.35 cm

Step-by-step explanation:

For a button to fit through its button-hole, the hole needs to be the size of the buttons diameter.

The formula for determining the circumference of a circle is expressed as

Circumference = πd or 2πr

Where

d represents the diameter of the circle

π is a constant given as 3.14

From the information given, the circumference of the button is 7.38 cm. Therefore, the diameter of the button will be

d = circumference/π = 7.38/3.14

d = 2.35 cm

3 0
3 years ago
Identify the data set that could be quadratic. HELP ASAP!!
Ne4ueva [31]

Answer:

Option B can be quadratic.

Step-by-step explanation:

Take a look at the data.

A quadratic equation is of the form ,

y = ax^{2} +bx + c,

where, a,b,c are constants.

<em>To find an unknown equation of 3 variables,</em>

<em>we need 3 points lying on the equation.</em>

here they have given, 5 points, meaning all should lie on the curve.

<em>For first option,</em> inserting first 3 points to find equation, we get equation as,

y = x^{2} -4x +11, but the rest points don't satisfy the curve.

So first option is not quadratic.

Similarly, it can be shown that option C and D are also not quadratic.

While, in option B, it is clear that for every y, x is y squared,

x = y^{2}, thus quadratic in nature.

6 0
3 years ago
Answer choice <br> D) A worker with 15 years of service gets 5 weeks of vacation and each year.
otez555 [7]

Answer: it seems to be D, but the equation makes practically no sense!

The value of the factor changes for the different amounts of service years and vacation weeks.

Step-by-step explanation: The equation means that the employee is trying to figure out the value of the "v-factor" for how vacation time is earned.

If you substitute the number of service years into the left side of the "formula" and vacation weeks on the right side, then solve for "v", v(15)=5 you get v= 1/3 or 0.33

If you substitute other numbers, like v(2)=2, so v= 1 then v(30) = 8, v = 4/15 or 0.2667. You see the factor's value decreases. The company is much more generous to to employees with one or two years of service than with the older ones.

7 0
2 years ago
Rachel recorded the number of calls she made at work during the week:
Dmitry [639]

The chi-squared test statistic will be 3.11. The test statistic is contrasted with a predicted value based on the Chi-square distribution.

<h3>What is the chi-squared test statistic?</h3>

Finding the squared difference between the actual and anticipated data values, then dividing that difference by the expected data values, constitutes the test statistic.

The formula for the chi-squared test statistic is;

\sum \frac{(O_i-E_i)^2}{E_i } \\\\

Where,

\rm O_i is the observed value

\rm E_i is the expected value

The chi-square test statics is;

\rm( \frac{18-18}{18} )^2 +( \frac{14-18}{18} )^2 + (\frac{24-18}{18} )^2+( \frac{16-18}{18} )^2 \\\\ 0+ \frac{16}{18}+ \frac{36}{18} +\frac{4}{18}\\\\ \frac{56}{18} \\\\ 3.11

Hence, the chi-squared test statistic will be 3.11.

To learn more about the chi-squared test statistic refer;

brainly.com/question/14082240

#SPJ1

5 0
2 years ago
2 5/12 x 2 2/3<br><br> pls helpp
MA_775_DIABLO [31]

Answer: 58/9

Step-by-step explanation:

5 0
2 years ago
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