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2 years ago

Grades 3, 4, and 5 have their annual field day together. Each grade level is given 16 gallons of water.

Mathematics

1 answer:

sineoko [7]2 years ago

6 0

Answer:

Their will be enough water for each student to consume 2 cups of water.

Step-by-step explanation:

Grade 3, 4 and 5 have their annual field day together . Each grade level is given 16 gallons of water. This means the three grades have 16 × 3 = 48 gallons of water.

The total students involved is 350 student. The total student is the sum of the student in all three grades.

Since the water will be distributed to the students in cups let us convert gallons to cups.

1 gallons = 16 cups

48 gallons = ? cups

cross multiply

48 × 16 = 768 cups.

768 cups of water is available to be shared among the 350 students.

1 student is entitled to 2 cups of water.

350 students will consume 350 × 2 = 700 cups of water.

Therefore, their will be enough water for each student to consume 2 cups of water.

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Which equation is the inverse of y = 2x2 – 8?

natita [175]

The inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

Explanation:

To find the inverse of the equation $y=2x^{2} -8$ , we need to interchange the variables x and y for the variables y and x.

Thus, the equation becomes

$x=2y^{2} -8$

Now, we shall find the value of y.

Now, adding 8 to both sides of the equation, we have,

$x+8=2y^{2}$

Interchanging the sides,

$2y^{2} =x+8$

Dividing by 2 on both sides,

$y^{2} =\frac{x+8}{2}$

Taking square root on both sides,

$y=\pm \sqrt{\frac{x+8}{2}}$

Thus, the inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

5 0

2 years ago

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by model

Ann [662]

Answer:

(1) The degrees of freedom for unequal variance test is (14, 11).

(2) The decision rule for the 0.01 significance level is;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The value of the test statistic is 0.3796.

Step-by-step explanation:

We are given that you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne's attire with those of Calvin Klein.

The following is the amount ($000) earned per month by a sample of 15 Claiborne models;

$3.5, $5.1, $5.2, $3.6, $5.0, $3.4, $5.3, $6.5, $4.8, $6.3, $5.8, $4.5, $6.3, $4.9, $4.2 .

The following is the amount ($000) earned by a sample of 12 Klein models;

$4.1, $2.5, $1.2, $3.5, $5.1, $2.3, $6.1, $1.2, $1.5, $1.3, $1.8, $2.1.

(1) As we know that for the unequal variance test, we use F-test. The degrees of freedom for the F-test is given by;

$\text{F}_(_n__1-1, n_2-1_)$

Here, $n_1$ = sample of 15 Claiborne models

$n_2$ = sample of 12 Klein models

So, the degrees of freedom = ( $n_1-1, n_2-1$ ) = (15 - 1, 12 - 1) = (14, 11)

(2) The decision rule for 0.01 significance level is given by;

If the value of our test statistics is less than the critical values of F at 0.01 level of significance, then we have insufficient evidence to reject our null hypothesis.

If the value of our test statistics is more than the critical values of F at 0.01 level of significance, then we have sufficient evidence to reject our null hypothesis.

(3) The test statistics that will be used here is F-test which is given by;

T.S. = $\frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }$ ~ $\text{F}_(_n__1-1, n_2-1_)$

where, $s_1^{2}$ = sample variance of the Claiborne models data = $\frac{\sum (X_i-\bar X)^{2} }{n_1-1}$ = 1.007

$s_2^{2}$ = sample variance of the Klein models data = $\frac{\sum (X_i-\bar X)^{2} }{n_2-1}$ = 2.653

So, the test statistics = $\frac{1.007}{2.653 } \times 1$ ~ $\text{F}_(_1_4,_1_1_)$

= 0.3796

Hence, the value of the test statistic is 0.3796.

3 0

2 years ago

Which model represents the factors of 4x2 – 9?

GREYUIT [131]

The factors of 4 x² - 9 :
4 x² - 9 = ( 2 x - 3 ) · ( 2 x + 3 )
We have to use the formula for the difference of squares:
a² - b² = ( a - b ) · ( a + b )

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2 years ago

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Which values are within the range of the piecewise-defined function? f(x) = StartLayout enlarged left-brace 1st Row 1st column 2

Otrada [13]

Answer:

the answer is below frum ed

Step-by-step explanation:

y= -6

Y= -4

Y= -3

Y= 0

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2 years ago

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3) George walks away from his house. He walks 25 km west and then

Romashka-Z-Leto [24]

Answer:

29.15 km

Step-by-step explanation:

Given;

George walks; 25km west and then 15 km south

Resolving the directions to x and y axis;

North and South represent positive and negative y axis.

East and West represent positive and negative x axis respectively.

25km west

Rx = -25 km

15 km south

Ry = -15 km

The resultant displacement from the house is;

R = √(Rx^2 + Ry^2)

Substituting the values;

R = √((-15)^2 + (-25)^2)

R = √(225+625)

R = √(850)

R = 29.15 km

Therefore, he is 29.15 km from house

8 0

2 years ago