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timofeeve [1]
1 year ago
13

The construction of copying ∠"QPR" is started below. The next step is to set the width of the compass to the length of ("AB" ).

How does this step ensure that the new angle will be congruent to the original angle?

Mathematics
1 answer:
Roman55 [17]1 year ago
4 0

Answer:

Constant radius, AB = TU

Step-by-step explanation:

Construction: Copying of <QPR, so that;

         <QPR = <TSU

The compass is placed in such a way that its two pointed legs are place at points A and B respectively to copy distance AB.

Now, place the compass at T and describe an arc to locate point U. Draw a straight line through S and U.

Therefore,

             <QPR = <TSU

The step ensures that the angles are congruent by constant radius, AB = TU.

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1. Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 during
dolphi86 [110]

9514 1404 393

Answer:

  $3891.10

Step-by-step explanation:

This question is a bit unusual in that the interest is compounded annually, but payments and withdrawals are made monthly. The effective monthly rate is ...

  1.05^(1/12) -1 = 0.407412378% = i

We assume that payments to the annuity are made at the end of the month, and that withdrawals are made at the beginning of the month. (The last payment and the first withdrawal are made on the same day.)

The amount of money required in the fund is ...

  A = $4000(1 -(1.00407^-360))/(1 -1.00407^-1) = $757,712.88

The amount of money needed each month to be put into the fund is P, where ...

  $757,712.88 = P(1 -1.00407)^(-12(60-28))/(1 -1.00407^-1) = 194.7297P

  P = $757,712.88/194.7297 = $3891.10

Yejin needs to save $3891.10 each month to meet her retirement goal.

_____

<em>Sanity check</em>

Yejin wants payments for 30 years from the fund to which she has contributed for 32 years. The similarity of the time periods means that Yejin's monthly contribution will need to be very similar to the amount she plans to withdraw.

The only ways to reduce the required contribution are to earn a higher interest on deposits, or to adjust the relative time periods (retire later).

3 0
1 year ago
What is three decimals that have a sum of 10.806
White raven [17]

Answer:

  10 + 0.8 + 0.006 = 10.806

Step-by-step explanation:

Pick any two decimal numbers. The third one will be the difference between 10.806 and the sum of the two numbers you picked.

For example, choose 938.2 and 3.0055. Their sum is 941.2055. Then the third number that will make the sum be 10.806 is ...

  10.806 -941.2055 = -930.3995

So, your three numbers could be ...

  {938.2, 3.0055, -930.3995}

7 0
2 years ago
In order to estimate the average electricity usage per month, a sample of 125 residential customers were selected, and the month
mr_godi [17]

Answer:

[895.05; 940.81]kWh

Step-by-step explanation:

Hello!

Be X: monthly electricity usage by a residential customer

X~N

σ²: 12100KWh²

To estimate the population mean using a 98% CI you have to use the following formula

[X[bar]±Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }]

1-α: 0.98

α0.02

α/2: 0.01

1-α/2:0.99

Z_{1-\alpha /2}= Z_{0.99}= 2.326

n= 125

X[bar]= ∑X/n= 228565/125= 917.93

[917.93±2.326 * \frac{110}{\sqrt{125} }]

[895.05; 940.81]

Using a 98% confidence level you'd expect that the interval [895.05; 940.81]kWh will include the average monthly electricity usage of residential customers.

I hope this helps!

Raw data:

Electric Usage

765

1139

714

687

1027

1109

749

799

911

631

975

717

1232

806

637

894

856

896

1272

1224

621

606

898

723

817

746

933

595

851

1027

770

685

750

1198

975

678

1050

886

826

1176

583

841

1188

692

733

791

584

1163

593

1234

603

1044

1233

1178

598

904

778

693

590

845

893

1028

975

788

1240

1253

854

1185

1164

741

1058

1053

795

1198

1240

1140

959

938

1008

1035

1085

1100

680

1006

977

1042

1252

943

1165

1014

912

791

612

935

864

953

667

1005

1063

1095

1086

810

1032

970

1099

1229

892

1074

579

754

1007

1116

583

763

1231

966

962

1132

738

1033

697

891

840

725

1031

7 0
2 years ago
This Venn diagram shows the pizza topping preferences for 9 students
egoroff_w [7]

Answer:

D

Step-by-step explanation:

There are 6 students who like pepperoni or olives

joe katie noah maria zack or julia


there were 9 students serveyed

P (aor b) = 6/9 = 2/3

8 0
2 years ago
Read 2 more answers
Solve the inequality 6h−5(h−1)≤7h−11 and write the solution in interval notation. Use improper fractions if necessary.
Kobotan [32]

Answer:

h \geq 2\frac{2}[3}

Step-by-step explanation:

We solve the inequality similarly to how we would solve an equalitu.

6h - 5(h-1) \leq 7h - 11

6h - 5h + 5 \leq 7h - 11

h - 7h \leq -11 - 5/

-6h \leq -16

Multiplying everything by -1

6h \geq 16

Simplifying by 2

3h \geq 8

h \geq \frac{8}{3}

8 divided by 3 is 2 with rest two. So as a improper fraction, the answer is:

h \geq 2\frac{2}[3}

6 0
1 year ago
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