Let f(x)=3x .

What could be the Principal Amount, if rate if interest is 16% and $18 is earned as an interest after 3 months

liq [111]

The principal amount is $37.5

Step-by-step explanation:

Rate of interest= 16%

Rate of Interest = $18

Time = 3 months

Interest = (principal amount x rate of interest x time) /100

18 = (p x 16 x 3) /100

1800 = 48p

P = 1800/48

P = 37.5

The principal amount is $37.5

6 0

3 years ago

Someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi. We think the

denpristay [2]

Answer:

The sample size must be greater than 37 if we want to reject the null hypothesis.

Step-by-step explanation:

We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.

Also, we are given a level of significance of 5%.

Let $\mu$ = <u><em>mean breaking strength of their climbing rope</em></u>

SO, Null Hypothesis, $H_0$ : $\mu$ = 2,000 psi {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, $H_A$ : $\mu$ < 2,000 psi {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = ample mean strength = 1,997.2956 psi

$\sigma$ = population standard devaition = 10 psi

n = sample size

Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

SO, T.S. < -1.645 {then reject null hypothesis}

$\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645$

$\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645$

$(\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645$

$-0.27044 \times \sqrt{n}< -1.645$

$\sqrt{n}> \frac{-1.645}{-0.27044}$

$\sqrt{n}>6.083$

n > 36.99 ≈ 37.

SO, the sample size must be greater than 37 if we want to reject the null hypothesis.

7 0

4 years ago

1. Trapezoid KLMN has vertices K(1, 3) , L(3, 1) , M(3, 0) , and N(1, −2) .

chubhunter [2.5K]

Answer:

Step-by-step explanation:

(A) The vertices of the trapezoid KLMN are K(1, 3) , L(3, 1) , M(3, 0) , and N(1, −2)

Now, KL= $\sqrt{(3-1)^{2}+(1-3)^{2}}$ =\sqrt{8}[/tex]

LM= $\sqrt{(3-3)^{2}+(0-1)^{2}}=1$

MN= $\sqrt{(1-3)^{2}+(-2-0)^{2}}=\sqrt{8}$

NK= $\sqrt{(1-1)^{2}+(-2-3)^{2}}=5$

Now, as KL and MN are equal, therefore, KLMN is an isosceles trapezoid.

(B) Since m∠XWY=47°, therefore ∠XWZ=47+47=94° and ∠ZYW=18°, therefore ∠XYZ=36°( as diagonals bisect the angles)

In ΔXWO,

∠XWO+∠WXO+∠WOX=180°(Angle sum property)

∠WXO=43°

Also, from ΔXOY,

∠OXY=72° using the angle sum property.

Therefore, ∠WXY=43+72=115°

Now, sum of all the angles of a quadrilateral is equal to 360°, therefore

∠WXY+∠XYZ+∠YZW+∠ZWX=360°

115°+36°+∠YZW+94°=360°

∠YZW=115°

Therefore,∠WZY=115°

(C) Since, AB and CD are the two parallel lines as the slope of both the sides are equal.

LetM be the mid point of AB, therefore M= $(\frac{-2+4}{2}, \frac{4+3}{2})$

= $(1,\frac{7}{2})$

Also, let N be the mid point of DC, therefore,

N= $(\frac{4-2}{2},\frac{-2-5}{2})$

= $(1,\frac{-7}{2})$

Now, length of the mid segment MN= $\sqrt{(1-1)^{2}+(\frac{7}{2}+\frac{7}{2})^{2}}=\sqrt{0+49}=7 cm$

(D)Given: Kite PQRS, TS=6cm and TP=8cm

Then, From triangle TSP, we have

$(SP)^{2}=(TS)^{2}+(TP)^{2}$

$(SP)^{2}=36+64$

$SP=10cm$

8 0

3 years ago

Why can a problem with extra information be difficult to solve?

Semenov [28]

I think it is more difficult because it is more for your brain to have to process at once .

7 0

3 years ago

Why does -4i*i=4? what happens to the i when you multiply it

Alchen [17]

$▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪$

As we know that :

${i}^{2} = i \times i = - 1$

so, over here

$- 4i \times i$

$- 4 {i}^{2}$

plugging the value of i² as -1

$- 4 (- 1)$

$4$

8 0

3 years ago