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AleksandrR [38]
3 years ago
6

The following table shows the length and width of two rectangles: Length Width Rectangle A 2x + 4 x − 1 Rectangle B 3x + 1 2x −

3 Which expression is the result of the perimeter of rectangle B minus the perimeter of rectangle A? 4x − 10 4x − 14 16x + 18 16x + 14
Mathematics
1 answer:
Anni [7]3 years ago
6 0

Answer:

4x − 10

Step-by-step explanation:

The width of rectangle A is 2x+4 and the length of rectangle A is x-1.  This makes the perimeter

2(2x+4)+2(x-1)

= 4x+8+2x-2

= 6x+6

The width of rectangle B is 3x+1 and the width of rectangle B is 2x-3.  This makes the perimeter

2(3x+1)+2(2x-3)

= 6x+2+4x-6

= 10x-4

Subtracting Perimeter B - Perimeter A, we ahve

(10x-4)-(6x+6)

= 10x-4-6x-6

= 4x-10

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1. Simplify -7 + (12 - 3[50 - 4(2+3)]) this expression step by step:

  • 2+3=5;
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  • 3\cdot [50-4(2+3)]=3\cdot 30=90;
  • 12-3\cdot[50-4(2+3)]=12-90=-78;
  • -7 + (12 - 3[50 - 4(2+3)])=-7+(-78)=-7-78=-85.

2. Simplify the expression \dfrac{1}{3} + 6\left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2 in the same way:

  • \dfrac{2}{3}-\dfrac{1}{6}=\dfrac{2\cdot 2-1}{6}=\dfrac{3}{6}=\dfrac{1}{2}
  • \left(\dfrac{2}{3} - \dfrac{1}{6}\right)^2=\left(\dfrac{1}{2} \right)^2=\dfrac{1}{4}
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Which of the following sentences could not be used to represent the equation x-5 = -10?
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What is 2 1\3 + 3 1\3
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Answer:

The Fraction 21/3+31/3=17 1/3

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Compound interest is the addition of interest on the interest of the principal amount.

<h3>What is compound interest?</h3>

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

A = P(1+ \dfrac{r}{n})^{nt}

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

A = Pe^{rt}

Substitute the values, we will get,

A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7

Learn more about Compound Interest:

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Answer: 0.6763 cm∧2

Step-by-step explanation: Variance is one of the measures of dispersion which is the the second central moment in probability. It is defined as a measure of by how much the values in a data set differs from the mean of the values. Thus it is the average of the squares of the deviations from the mean as this ensures that both the negative and positive deviations do not cancel each other out.

The sample variance would be calculated as follows:

Population size is 7 (5.6 4.9 6.0 5.1 5.5 5.1 7.5)

Mean: Sum of samples / population size ;

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Applying the formula for variance: [ Summation (x - mean) ] / population size =( |5.6 - 5.67| + |4.9 - 5.67| + |6.0 - 5.67| + (|5.1 - 5.67|) * 2 + | 5.5 - 5.67| + |7.5 - 5.67|) / 7 = 0.6763 cm^2

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4 years ago
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