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3 years ago

Work out the reciprocal of 3.5

Mathematics

1 answer:

horsena [70]3 years ago

3 0

Answer: 2/7

Step-by-step explanation: change the number into fraction form, reduce it and reverse the numerator and denominator.

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Nicole invested her savings in two investment funds. The amount she invested in Fund A was $3000 less than the amount she invest

victus00 [196]

Let us denote the amount of investment in the Fund B with x. We know that Fund B returned 8% and that in Fund A Nicole invested $3000 less than the amount she invested in Fund B, so we can write: x-3000Fund A returned 6%.
Interest = 2060
The percent has been converted by multiplying the equation by 100
8x+6(x-3000)= 2060*100
8x+6x-18000=206000
14x=206000+18000
14x=224000
x=16000
Nicole invested in Fund B $16000 and in Fund A $16000-3000=13000.

8 0

3 years ago

Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is i

Romashka-Z-Leto [24]

0.08 cm/min

Step-by-step explanation:

Given:

$\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}$

Find $\frac{dr}{dt}$ when diameter D = 20 cm.

We know that the volume of a sphere is given by

$V = \dfrac{4\pi}{3}r^3$

Taking the time derivative of V, we get

$\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}$

Solving for $\frac{dr}{dt}$ , we get

$\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})$

$\:\:\:\:\:\:\:= 0.08\:\text{cm/min}$

3 0

3 years ago

Is 10.2 x 10 written in scientific notation. EXPLAIN

Virty [35]

Answer:

Step-by-step explanation:

Scientific notation has to be a number between 1 and 10 times 10 to the something power. 10.2 is not between 1 and 10

7 0

3 years ago

Read 2 more answers

Consider the hypothesis test below.

Pavel [41]

Answer:

$Z_{H0} =1.79$

p-value: 0.0367

Decision: Reject H₀

Step-by-step explanation:

Hello!

Hypothesis to test:

H₀:ρ₁-ρ₂=0

H₁:ρ₁-ρ₂>0

The statistic to use to test the difference between two population proportions is the approximation of Z

Z= (^ρ₁-^ρ₂)-(ρ₁-ρ₂) ≈N(0;1)

√ (^ρ₁(1-^ρ₁))/n₁)+(^ρ₂(1-^ρ₂)/n₂))

Z= (0.28-0.15)-0 = 1.79

√ (0.28(1-0.28)/200)+(0.15(1-0.15)/300)

p-value

Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).

P(Z>1.79)= 0.0367

Conclusion:

Comparing the p-value against the significance level, you can decide to reject the null hypothesis.

I hope you have a SUPER day!

8 0

3 years ago

What is the volume of a hemisphere with a radius of 1.6 and height of 6.2?

qaws [65]

You can find the area of a hemisphere by using the following equation

V = (2/3) (pi)*r^3

so V = (2/3) (pi)*1.6^3

Which comes out as 8.5786423394 or 8.6

6 0

3 years ago