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2 years ago

You have $25 to spend on picking 21 pounds of three different types of apples in an orchard. The Empire apples cost $1.40 a

Mathematics

1 answer:

Semmy [17]2 years ago

3 0

Answer:

5 pounds of the Empire apples, 14 pounds of the Red Delicious apples, and 2 pounds of the Golden Delicious apples.

Step-by-step explanation:

Let's call the Empire apples weight at E, the Red Delicious at R, and the Golden Delicious at G. We know that the total weight must be 21 pounds so:

R + E + G = 21 (equation 1)

The total amount of spent must be $25, and the price given is per pound, so the priced paid is the cost multiplied by the weight:

1.40*E + 1.10*R + 1.30*G = 25 (equation 2)

And the weight of the Red Delicious must be equal to twice of the combined weight of the others:

R = 2*(E + G)

E + G = R/2 (equation 3)

Let's substitute equation 3 in equation 1

R + R/2 = 21

(2R + R)/2 = 21

3R = 42

R = 14 pounds.

So, E + G = 7

G = 7 - E (equation 4)

Let's substitute the result of R and the equation 4 in the equation 2:

1.40*E + 1.10*14 + 1.30*(7 - E) = 25

1.40E + 15.40 + 9.10 - 1.30E = 25

0.10E = 25 - 24.50

0.10E = 0.50

E = 5 pounds

G = 7 - E

G = 7 - 5

G = 2 pounds.

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Verify the continuity type C° and C1 between curve(l) and curve(2).

Damm [24]

Step-by-step explanation:

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2 years ago

Lauren is running in a marathon to raise money for her favorite charity. The total distance of the marathon is 12.5 miles. So fa

kirill [66]

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2 years ago

Solve for w when g=1/6(w+40)

sertanlavr [38]

The answer will be W=6g-40

4 0

2 years ago

Read 2 more answers

. En un concesionario de coches hay modelos de varios colores. Los rojos suponen 1 6 del total, los azules, 2 9 del total, y los

Sholpan [36]

Complete question :

En un concesionario de coches hay modelos de varios colores. Los rojos suponen 1/6 del total, los azules, 2/9 del total, y los blancos, 4/15 del total.

a)¿Cuál de esos colores es el más frecuente?

b) Si hay 40 coches azules, ¿cuántos hay en total?

Responder:

Coches blancos

180 coches

Explicación paso a paso:

Dado que:

Rojo = 1/6 del total

Azul = 2/9 del total

Blanco = 4/15 del total

Para determinar qué color es el más alto, convierta los valores en decimal:

1/6 = 0,166667

2/9 = 0,2222

15/4 = 0,26667

Por lo tanto;

4/15> 2/9> 1/6

Por tanto, los coches blancos son los que más

2.)

Sea Número total = x

Por lo tanto,

2/9 de x = 40

2x / 9 = 40

2x = 360

x = 180

Por tanto, hay 180 coches en total.

4 0

2 years ago

Suppose that the Department of Transportation would like to test the hypothesis that the average age of cars on the road is less

dimulka [17.4K]

Answer:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

$z_{critc}= -1.64$

Since our calculates values is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance. And the best conclusion for this case is:

B. Since the test statistic is less than the critical value, we can conclude that the average age of cars on the road is less than 12 years.

Step-by-step explanation:

Data given and notation

$\bar X=10.6$ represent the sample mean

$\sigma=4.1$ represent the population standard deviation

$n=45$ sample size

$\mu_o =12$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 12, the system of hypothesis would be:

Null hypothesis: $\mu \geq 12$

Alternative hypothesis: $\mu < 12$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29$

Critical value

For this case since w ehave a left tailed distribution we need to find a value who accumulates 0.05 of the area on th left in the normal standard distribution, and we can use the following excel code:

"=NORM.INV(0.05,0,1)"

$z_{critc}= -1.64$

Conclusion

Since our calculates values is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance. And the best conclusion for this case is:

B. Since the test statistic is less than the critical value, we can conclude that the average age of cars on the road is less than 12 years.

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2 years ago