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2 years ago

Find z. What is the length of the missing leg? b = _____ miles

Mathematics

2 answers:

ycow [4]2 years ago

6 0

Answer:

5√3

Step-by-step explanation:

tan30= 5/z

1/√3= 5/z

z= 5√3

ikadub [295]2 years ago

3 0

z = 5√3

...............

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You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that

step 1

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$r=10\%=10/100=0.10\\n=4$

substitute in the formula above

$A=P(1+\frac{0.10}{4})^{4t}$

$A=P(1.025)^{4t}$

Applying property of exponents

$A=P[(1.025)^{4}]^{t}$

$A=P(1.1038)^{t}$

step 2

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$r=10\%=10/100=0.10$

substitute in the formula above

$A=P(e)^{0.10t}$

Applying property of exponents

$A=P[(e)^{0.10}]^{t}$

$A=P(1.1052)^{t}$

step 3

Compare the final amount

$P(1.1052)^{t} > P(1.1038)^{t}$

therefore

Find the difference

$P(1.1052)^{t} - P(1.1038)^{t}$ ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0

3 years ago

Divide line segments

ser-zykov [4K]

tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,

$\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill$

$\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}$

6 0

3 years ago

A bench is 4 meter long. How long are 5 benches if they are placed from end to end?

sineoko [7]

Answer:

20m

Step-by-step explanation:

4 x 5 = 20

therefore the 5 benches are 20m long

3 0

3 years ago

Convert 50 feet per second to miles per hour.

AleksAgata [21]

FIrst we know that
1 second = 1/3600 hours
5280 ft = 1 miles

Which means that

50 Ft = 50/5280 miles

So the conversion
(5/5280 miles ) / (1/3600)

= 5/5280 miles x 3600

= 34.09 miles per hour

7 0

3 years ago

Read 2 more answers

Orders for a computer are summarized by the optional features that are requested. The proportion of orders with no optional feat

kap26 [50]

Answer: 0.28

Step-by-step explanation:

Let´s name the proportion of orders

with no optional features: "N"

with one optional feature: "O"

and the proportion of orders with more than one optional feature: "M"

<em>The sum of all of these proportions is equal to the total quantity of orders.</em>

Therefore,

N + O + M = 1

Then, substracting N and O on each side of that equation,

the proportion of orders with more than one optional feature (M) is:

M = 1 - N - O

M = 1 - 0.38 - 0,34

M = 0.28

6 0

3 years ago