[y = x + 4][3x -2y =-7] substitution

Marcos has 3/5 of a pizza remaining and gives his friend 1/5 of the remaining pizza. How much pizza is left over?

LuckyWell [14K]

Answer

at first I said 1/2 but it's 2/5's.

Step-by-step explanation:

$\frac{3}{5} - \frac{1}{5 } = \frac{2}{5}$

3 0

3 years ago

A poll of 1,000 randomly selected registered voters was taken and 680 responded that they favor candidate X for mayor (p 1 = 0.6

Zielflug [23.3K]

Answer:

The interval (-0.0199, 0.0510) represents the region of values where the true difference (in population terms now) between the initial proportion of registered voters that favour candidate X and the proportion of registered voters that favour candidate X just before election can take on with a confidence level of 90%.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence. It is usually obtained from the sample.

p₁ represents the proportion of registered voters that favour candidate X in the initial poll, way before the election.

p₂ represents the proportion of registered voters that favour candidate X in the poll just before the election.

So, for this question the confidence interval for the true difference between the population proportion of registered voters that favour candidate X way before the elections and the population proportion that favour candidate X just before the election lies within (-0.0199, 0.0510) with a confidence interval of 90%.

Confidence interval is calculated mathematically as thus:

Confidence Interval = (Difference in Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the difference in the two sample proportions.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value = 1.645 (obtained from the z-tables because the sample size is large enough to ignore that information about the population standard deviation isn't given and t-critical value approximates z-critical value)

Hope this Helps!!!

4 0

3 years ago

You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, an

Mila [183]

This question can be approached using the present value of annuity formula. The present value of annuity is given by $PV=P\left( \frac{1-\left(1+ \frac{r}{t} \right)^{-nt}}{ \frac{r}{t} } \right)$ , where: PV is the present value/amount of the loan, P is the periodic (monthly in this case) payment, r is the APR, t is the number of payments in one year and n is the number of years.

Given that the<span> financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.

Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)

Thus,

</span> $2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\ \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\ \\ \Rightarrow P= \frac{2500}{20.9306} =119.44$
<span>
Therefore, his monthly payment is $119.44</span>

6 0

3 years ago

Use the spinner to identify the probability of the pointer landing on a shaded area to the nearest hundredth. HELP?!!

Pie

A full circle = 360 degrees.

The sum of the shaded portions is : 60 + 55 + 45 = 160.

The probability would be the shaded portion divided by the full circle:

160 / 360 = 0.44

4 0

3 years ago

Point G(−7, 4) is translated using the rule (x+10, y−6). What is the x-coordinate of G′ ?

den301095 [7]

Answer:

x = 3

Step-by-step explanation:

The translation rule (x + 10, y - 6) means add 10 to the original x- coordinate and subtract 6 from the original y- coordinate, that is

G(- 7, 4) → G'(- 7 + 10, 4 - 6) → G'(3, - 2)

6 0

3 years ago