Mary Catherine makes 2 gallons of punch how many cups of punch did she make

Liula [17]

Answer: if this is a triangle, then all triangles add up to 180 degrees. I dont know if this helps... sorry

Step-by-step explanation:

7 0

2 years ago

If $x$ and $y$ are positive real numbers for which $(x + y)^2 + (x - y)^2 = 10$ and $(x + y)^4 + (x - y)^4 = 98$, what is the va

slava [35]

$(x+y)^2+(x-y)^2=10$
$\implies 2x^2+2y^2=10$
$\implies x^2+y^2=5$
$\implies (x^2+y^2)^2=x^4+2x^2y^2+y^4=25$

$(x+y)^4+(x-y)^4=98$
$\implies 2x^4+12x^2y^2+2y^4=98$
$\implies x^4+6x^2y^2+y^4=49$
$\implies 25+4x^2y^2=49$

$4x^2y^2=24$
$\implies x^2y^2=6$
$\implies xy=\sqrt6$

6 0

4 years ago

A sailboat travels a distance of miles in of an hour. Which complex fraction represents the unit rate in miles per hour?

EastWind [94]

Answer:

A sailboat travels a distance of 2 1/2 miles in 1/6 of an hour.

Step-by-step explanation:

im built different

7 0

3 years ago

Suppose A and B are dependent events. If P(A) = 0.5 and P(BIA) = 0.6, what is

klasskru [66]

If the probability of independent event A is 0.5, then P(A|B) will be 0.5. Then the correct option is B.

<h3>Which pair of events are called independent events?</h3>

When one event's occurrence or non-occurrence doesn't affect occurrence or non-occurrence of other event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent iff we have:

P(A ∩ B) = P(A)P(B)

Comparing it with chain rule will give

P(A|B) = P(A)

P(B|A) = P(B)

Suppose A and B are dependent events.

If P(A) = 0.5

Then P(A|B) will be

P(A|B) = P(A)

P(A|B) = 0.5

Then the correct option is B.

Learn more about probability here:

brainly.com/question/1210781

#SPJ1

4 0

2 years ago

Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin a

IgorLugansk [536]

Answer: -8.16 to 15.84

Step-by-step explanation: <u>Confidence</u> <u>Interval</u> is an interval in which we are a percentage sure the true mean is in the interval.

A confidence interval for a difference between two means and since sample 1 and sample 2 are under 30, will be

$x_{1}-x_{2}$ ± $t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }$

where

x₁ and x₂ are sample means

t is t-score

$S_{p}$ is estimate of standard deviation

n₁ and n₂ are the sample numbers

The estimate of standard deviation is calculated as

$S_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2} }$

where

s₁ and s₂ are sample standard deviation of each sample

Degrees of freedom is:

$df=n_{1}+n_{2}-2$

df = 12 + 9 - 2

df = 19

Checking t-table, with 90% Confidence Interval and df = 19, t = 1.729.

The mean and standard deviation for 12 unlogged forest plots are 17.5 and 3.53, respectively.

The mean and standard deviation for 9 logged plots are 13.66 and 4.5, respectively.

Calculating estimate of standard deviaton:

$S_{p}=\sqrt{\frac{(12-1)(3.53)^{2}+(9-1)(4.5)^{2}}{12+9-2} }$

$S_{p}=\sqrt{\frac{299.07}{19} }$

$S_{p}=$ 15.74

The difference between means is

$x_{1}-x_{2}$ = 17.5 - 13.66 = 3.84

Calculating the interval:

$t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }$ = $1.729.15.74.\sqrt{\frac{1}{12} +\frac{1}{9} }$

$t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }$ = $27.21\sqrt{\frac{21}{108} }$

$t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }$ = $27.21\sqrt{0.194}$

$t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }$ = 12

Then, interval for the difference in mean is 3.84 ± 12, which means the interval is between:

lower limit: 3.84 - 12 = -8.16

upper limit: 3.84 + 12 = 15.84

The interval is from -8.16 to 15.84.

5 0

3 years ago