Increase £16470.45 by 3.5% answer rounded to 2 DP.

Carlo used this number line to find the product of 2 and −3. A number line going from negative 7 to positive 3. An arrow goes fr

Vesnalui [34]

Answer:

The errors are;

a. negative 4 to negative 6

b. negative 2 to negative 4

Step-by-step explanation:

The number line is the mathematical representation of numbers in the horizontal line or the x-axis.

The result of the multiplication of a positive 2 and a negative 3 is;

2 x -3 = -6 , gives a negative 6.

So the number line should scale to accommodate the operands and the result, which is from negative 7 to positive 3, in the option given.

8 0

2 years ago

The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from th

bazaltina [42]

$\bf \qquad \textit{ inverse proportional variation}\\\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}

&&y=\cfrac{{{ k}}}{x}
\end{array}$

"The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth"

namely "w" varies inversely to $\bf d^2$ or $\bf w=\cfrac{k}{d^2}$

then
"A particular person weighs 192 pounds on the surface of the earth and the radius of the earth is 3900 miles. "
namely when w = 192, d = 3900

so $\bf w=\cfrac{k}{d^2}\qquad 
\begin{cases}
w=192\\
d=3900
\end{cases}\implies 192=\cfrac{k}{3900^2}
\\\\\\
\textit{solve for "k", to find the}\\
\textit{"constant of variation"}\\
\textit{once you've found it, plug it back in at }w=\cfrac{k}{d^2}$

7 0

2 years ago

G is the centroid of triangle ABC. What is the length of GF? ___ units

Ksenya-84 [330]

So the longer lines are 2x longer than the shorter lines
Look at line segment BD
40 is 2x as long as 9x+2
In order to make the equation true, multiple 9x+2 by 2
So, you should get:
40=18x+4
36=18x
x=2
Plug the 2 into 19X+14, and divide that answer by 2, because GF is 2x smaller than AG
19x+14
19(2)+14
52
52/2=26
Hope this helps!!

4 0

2 years ago

Read 2 more answers

Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her

Alex Ar [27]

Buying a reusable water bottle will save her money.
She drinks 50.7 ounces of water every day.
Each bottle of water costs around 15 cents
I would say the faucet filtered-mounted filter is the cheapest option

6 0

2 years ago

Searchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention a

VladimirAG [237]

Answer:

n=77

Step-by-step explanation:

Notation and definitions

$\hat p=0.025$ or 2.5%, estimated proportion for decline in crop yield when no-till is used with residue retention and crop rotation

$p$ true population proportion for decline in crop yield when no-till is used with residue retention and crop rotation

n (variable of interest) represent the sample size required

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.035$ or 3.5% and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

And replacing into equation (b) the values from part a we got:

$n=\frac{0.025(1-0.025)}{(\frac{0.035}{1.96})^2}=76.44$

And rounded up we have that n=77

5 0

2 years ago