Answer:
Original sum of money = $2246.51
Step-by-step explanation:
Interest = $96.60
Interest is compounded 6 times in a year ; n = 6
time = 1 year ; Rate of interest (r) = 4.2%
Interest = Future Value - Principal Value ...........(1)
![\text{Future Value = }Principal\cdot (1+\frac{r}{100\times n})^{n\cdot t}\\\\\text{Substituting this value in equation (1) , We get }\\\\Interest=Principal\cdot (1+\frac{r}{100\times n})^{n\cdot t}-Principal\\\\\implies 96.60=Principal[\cdot (1+\frac{4.2}{100\times 6})^{6\cdot 1}-1]\\\\\implies Principal=\$2246.51](https://tex.z-dn.net/?f=%5Ctext%7BFuture%20Value%20%3D%20%7DPrincipal%5Ccdot%20%281%2B%5Cfrac%7Br%7D%7B100%5Ctimes%20n%7D%29%5E%7Bn%5Ccdot%20t%7D%5C%5C%5C%5C%5Ctext%7BSubstituting%20this%20value%20in%20equation%20%281%29%20%2C%20We%20get%20%7D%5C%5C%5C%5CInterest%3DPrincipal%5Ccdot%20%281%2B%5Cfrac%7Br%7D%7B100%5Ctimes%20n%7D%29%5E%7Bn%5Ccdot%20t%7D-Principal%5C%5C%5C%5C%5Cimplies%2096.60%3DPrincipal%5B%5Ccdot%20%281%2B%5Cfrac%7B4.2%7D%7B100%5Ctimes%206%7D%29%5E%7B6%5Ccdot%201%7D-1%5D%5C%5C%5C%5C%5Cimplies%20Principal%3D%5C%242246.51)
Hence, the original sum of money borrowed = $2246.51
Answer:
The correct option is 4.
Step-by-step explanation:
If a figure it dilated by scale factor k, then the image and preimage are similar figures and their corresponding sides are proportional.
In triangle I, the base of the triangle is 1 unit and length of the perpendicular is 1 units.
In triangle II, the base of the triangle is 1 unit and length of the perpendicular is 2 units.
The corresponding sides are not proportional. It means both triangles are not similar. So, there is no dilation transforming triangle I into triangle II.
Therefore the correct option is 4.
Answer:
Here we have given two catogaries as degree holder and non degree holder.
So here we have to test the hypothesis that,
H0 : p1 = p2 Vs H1 : p1 not= p2
where p1 is population proportion of degree holder.
p2 is population proportion of non degree holder.
Assume alpha = level of significance = 5% = 0.05
The test is two tailed.
Here test statistic follows standard normal distribution.
The test statistic is,
Z = (p1^ - p2^) / SE
where SE = sqrt[(p^*q^)/n1 + (p^*q^)/n2]
p1^ = x1/n1
p2^ = x2/n2
p^ = (x1+x2) / (n1+n2)
This we can done in TI_83 calculator.
steps :
STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input all the values --> select alternative "not= P2" --> ENTER --> Calculate --> ENTER
Test statistic Z = 1.60
P-value = 0.1090
P-value > alpha
Fail to reject H0 or accept H0 at 5% level of significance.
Conclusion : There is not sufficient evidence to say that the percent of correct answers is significantly different between degree holders and non-degree holders.
Answer:
The width of the prism is 2 cm
Step-by-step explanation:
The given parameters are;
The volume of the prism = 170 cm³
The length of the prism = 5 cm
The height of the prism = 17 cm
The volume of the prism is given by the relationship v = Length, l × Height, h × Width, w
Therefore;
The volume of the prism = 5 cm × 17 cm × w = 170 cm³
Which gives;
w = 170 cm³/(5 cm × 17 cm) = 170 cm³/(85 cm) = 2 cm
∴ The width of the prism = 2 cm.
