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3 years ago

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A certain recipe requires 415 cups of flour and 237 cups of sugar. a) If 49 of the recipe is to be made, how much sugar is neede

d?

1 answer:

Bas_tet [7]3 years ago

7 0

49*237

11613

That's a lot of sugar, diabetes here we come :)

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An unmanned submarine ascends from the ocean floor at a rate of 2 meters per second. If the ocean floor is 4220 feet below sea l

KengaRu [80]

Answer:

a=4220-2t

This would be if we are finding the altitude of the submarine from the surface of the water(how many meters away from the surface it is). I don't know what it would be if you want to know from the bottom of the ocean.

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3 years ago

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A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at th

Valentin [98]

Answer:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12.8$

The sample deviation calculated $s=4.324 \approx 4.3$

$12.8-4.604\frac{4.324}{\sqrt{5}}=3.896$

$12.8+ 4.604\frac{4.324}{\sqrt{5}}=21.704$

So on this case the 99% confidence interval would be given by (3.896;21.704)

Step-by-step explanation:

Data: 10,9,20,13,12

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12.8$

The sample deviation calculated $s=4.324$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,4)".And we see that $t_{\alpha/2}=4.604$

Now we have everything in order to replace into formula (1):

$12.8-4.604\frac{4.324}{\sqrt{5}}=3.896$

$12.8+ 4.604\frac{4.324}{\sqrt{5}}=21.704$

So on this case the 99% confidence interval would be given by (3.896;21.704)

6 0

3 years ago

What is the equation of this circle in standard form?

creativ13 [48]

Answer:

Option C.

Step-by-step explanation:

Note : In the given points one point is (8,-2) instead of (-6,-2).

The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$

where, (h,k) is center of circle and r is radius.

It is given that center of the circle is (-1,-2). So,

$h=-1,k=-2$

$(x-(-1))^2+(y-(-2))^2=r^2$

$(x+1)^2+(y+2)^2=r^2$ ...(1)

It is given that the circle passing through the point (8,-2),(-1,5),(6,-2),(-1,-9).

Substitute x=6 and y=-2 in equation (1).

$(6+1)^2+(-2+2)^2=r^2$

$(7)^2+(0)^2=r^2$

$49=r^2$

Substitute $r^2=49$ in equation (1).

$(x+1)^2+(y+2)^2=49$

Therefore, the correct option is C.

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3 years ago

9=ln(x+7) | Solve for x

frez [133]

Remember that ln= $log_{e}$
and

$log_{a}x=y$ means $a^y=x$
convert
ln(x+7)=9 means
e^(9)=x+7
minus 7 from both sides
e^9-7=x
use calculator to evaluate
8096.08=x aprox

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3 years ago

Twice the sum of a number and 5 is equal to three times the difference of the number and 3. Find the number.

Volgvan

let x be the number

2(x+5)= ±3(x-3)

2x+10= 3x-9 or 2x+10= -3x+9

x=19 or x=0.2

8 0

3 years ago