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RUDIKE [14]
3 years ago
10

The dairy goats on a farm give 2 gallons of milk each day. How much milk do they give in 5 days?

Mathematics
1 answer:
Dovator [93]3 years ago
4 0

Answer:

\huge\boxed{\sf 10\ gallons\ of\ milk}

Step-by-step explanation:

=> 2 gallons of milk each day.

<u>This means</u>

1 day = 2 gallon of milk

Multiply both sides by 5

5 (1 day) = 5 (2 gallons of milk)

<h3>5 days = 10 gallons of milk</h3>

\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
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Rewrite the quadratic y=3(x-2)^2-7 in standard form​
DochEvi [55]

Answer:

The answer is

y=3/(x-2)^5

8 0
2 years ago
1) The difference of twice a number and 14 is –37.
Ket [755]

Answer:

2x - 14 = -37

6 0
3 years ago
Hypothesis Testing for Means with Small Samples
Scorpion4ik [409]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: volume of root beer in a Windsor Bottling Company can.

A sample of n=24 cans was taken and their contents measured, resulting:

X[bar]= 11.4 oz

S= 0.62 oz

Assuming that the variable has a normal distribution X~N(μ;σ²), the parameter of interest is the average contents of the root beer cans of the Windsor Bottling Company (μ)

The claim is that the population mean content of the cans is different from 12 oz, symbolically: μ ≠ 12

The statistical hypothesis (Null and alternative) have to be complementary, exhaustive and mutually exclusive. The null hypothesis is the "no change" hypothesis and always carries the "=" sign.

If the claim is μ ≠ 12, its complement is μ = 12, the expression carrying the "=" sign will be the null hypothesis and its complement will be the alternative hypothesis:

H₀: μ = 12

H₁: μ ≠ 12

α: 0.05

To test the population mean of this normal population, you have to apply a one sample t-test, with statistic:

t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}

t_{H_0}= \frac{11.4-12}{\frac{0.62}{\sqrt{24} } } = -4.74

This test is two-tailed, using the critical value approach, you have to determine two rejection regions. Meaning, you'll reject the null hypothesis to small values of the statistic or to high values of the statistic.

t_{n-1;\alpha /2}= t_{23;0.025}= -2.069

t_{n-1;1-\alpha /2}= t_{23;0.975}= 2.069

The decision rule is:

If t_{H_0} ≤ -2.069 or if t_{H_0} ≥ 2.069, then you reject the null hypothesis.

If -2.069 < t_{H_0} < 2.069, then you do not reject the null hypothesis.

The value is less than the left critical value, the decision is to reject the null hypothesis.

Then you can say that with a 5% significance level, there is significant evidence to reject the null hypothesis, then the average amount of root beer of the Windsor Bottling Company is different from 12 oz, this means that the claim about the amount of root beer in the cans is correct.

I hope it helps!

6 0
3 years ago
si franco comió 8/3 de pizza y Fabián comió 5/6 de la misma pizza. ¿quien comió más ? si quedó 4/9 de pizza.​
devlian [24]

Answer:

Franco comió 8/3 de pizza.

Fabián comió 5/6 de pizza.

Queremos saber quien comió más.

Entonces básicamente queremos ver cuál número es más grande, 8/3 o 5/6,

Podemos reescribir el primero como:

8/3 = (2 + 3 + 3)/3 = 2/3 + 3/3 + 3/3 = 2/3 + 1 + 1

      = 2 + 2/3

En cambio, para el número 5/6, el numerador es menor que el denominador, entonces sabemos que:

5/6  < 1

Claramente podemos ver que 8/3 > 5/6

Entonces podemos concluir que Franco comió más.

8 0
3 years ago
You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us
Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that    

step 1

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

r=10\%=10/100=0.10\\n=4  

substitute in the formula above

A=P(1+\frac{0.10}{4})^{4t}  

A=P(1.025)^{4t}  

Applying property of exponents

A=P[(1.025)^{4}]^{t}  

A=P(1.1038)^{t}  

step 2

The formula to calculate continuously compounded interest is equal to

A=P(e)^{rt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

r=10\%=10/100=0.10  

substitute in the formula above

A=P(e)^{0.10t}  

Applying property of exponents

A=P[(e)^{0.10}]^{t}  

A=P(1.1052)^{t}  

step 3

Compare the final amount

P(1.1052)^{t} > P(1.1038)^{t}

therefore

Find the difference

P(1.1052)^{t} - P(1.1038)^{t} ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0
3 years ago
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