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2 years ago

If PR = 4x – 2 and RS = 3x – 5, which expression represents PS? x – 7 x – 3 7x – 7 7x + 3

Mathematics

2 answers:

zubka84 [21]2 years ago

3 0

we have that

$PR = 4x - 2\\RS = 3x - 5$

we know that

$PS=PR+RS$

substitute the values of PR and RS in the formula above

$PS=(4x-2)+(3x-5)$

Combine like terms

$PS=(7x-7)$

therefore

<u>the answer is</u>

$PS=(7x-7)$

slavikrds [6]2 years ago

3 0

The right answer is 7x - 7.

4x - 2 + 3x - 5
Combine like terms.
7x - 7

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What value should going to the empty boxes to complete the calculation for finding the product of 0.98×0.73? both numbersare the

jeyben [28]

Answer:

Missing same value is 0.02

Step-by-step explanation:

Instead of multiplying big decimal numbers we put short cut by making 0.98 as a difference of near integer and one decimal.

i.e 0.98 =1-0.02

Since 0.02 is the same for other also other term

0.73 = 0.75-0.02

Now product can be done very easily.

Steps are shown below:

0.98x0.73

= (1-0.02) (0.75-0.02)

= 0.75 -0.02(1+0.75)+0.0004

= 0.7504-(0.035)

= 0.7154

=0.44

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2 years ago

A company produces precision 1 meter (1000 mm) rulers. the actual distribution of lengths of the rulers produced by this company

pogonyaev

Let X be the length of rulers. X follows Normal distribution with mean μ and standard deviation σ = 0.02. A sample of size n=4 is drawn from population and sample mean m=1000. We have to find 90% confidence interval for population mean μ.

Here population standard deviation is given to us so we will use z confidence interval for mean. It is given as

(Sample mean - Margin of error , Sample mean + Margin of error)

Where margin of error for z confidence interval is

ME = σ $\frac{z_{\alpha/2}}{\sqrt{n}}$

Where σ = population standard deviation = 0.02

n= sample size =4

$z_{\alpha/2}$ = Critical z score value for given confidence level

We have to find here 90% confidence interval so confidence level c= 0.9

α = 1 -c =1-0.9 = 0.1

$z_{\alpha/2}$ = $z_{0.1/2}$ = $z_{0.05}$

Here we have to find z score value such that area below it is -z is 0.05 and above z is 0.05

Using excel function to find z score value

=NORM.S.INV(0.05) = -1.645

For calculating confidence interval we consider positive z score value which is 1.645

So the margin of error is

ME = $\frac{0.02 * 1.645}{\sqrt{4}}$

ME = 0.01645

90% confidence interval for mean is

(Sample mean - ME, Sample mean+ME)

1000- 0.01645, 1000+0.01645

(1000.01645, 999.9836)

Rounding interval upto 3 decimal places

(1000.016, 999.984)

90% confidence interval for population mean is (1000.016, 999.984)

7 0

2 years ago

Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter. How

mixer [17]

To solve this, we are going to use the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the final amount after $t$ years
$P$ is the initial investment
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year

For the first 4 years we know that: $P=2350$ , $r= \frac{4.2}{100} =0.042$ , $t=4$ , and since the problem is not specifying how often the interest is communed, we are going to assume it is compounded annually; therefore, $n=1$ . Lest replace those values in our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2350(1+ \frac{0.042}{1} )^{(1)(4)}$
$A=2350(1+0.042)^{4}$
$A=2770.38$

Now, for the next 6 years the intial investment will be the final amount from our previous step, so $P=2770.38$ . We also know that: $r= \frac{4.9}{100} =0.049$ , $t=6$ , and $n=1$ . Lets replace those values in our formula one more time:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2770.38(1+ \frac{0.049}{1})^{(1)(6)$
$A=2770.38(1+0.049)^6$
$A=3691.41$

We can conclude that Collin will have <span>£3691.41 in his account after 10 years.</span>

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2 years ago

2. A drawing of a sailboat was made using a rectangle and two right triangles, as shown. What

Zarrin [17]

Answer:

45 square centimeters

Step-by-step explanation:

The area of the triangle is given by ...

A = (1/2)bh

where b is the base, 2 cm + 3 cm = 5 cm, and h is the height, 6 cm.

A = (1/2)(5 cm)(6 cm) = 15 cm^2

The area of the rectangle is given by ...

A = bh

where b is the base, 12 cm, and h is the height, 2.5 cm.

A = (12 cm)(2.5 cm) = 30 cm^2

The area of the whole figure is the area of the triangle added to the area of the rectangle:

drawing area = 15 cm^2 + 30 cm^2 = 45 cm^2

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2 years ago

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Ksju [112]

Answer:

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Step-by-step explanation:

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2 years ago