Solve the system using elimination.

Answer:

171

Step-by-step explanation:

6x6x4.75 is 171

a) The GCD of 27,720 and 58,212 is 1.

b) Integers r = 3 and s = -1 satisfy the equation 27720r + 58212s = GCD(27720, 58212).

(a) To find the greatest common divisor (GCD) of 27,720 and 58,212, we can use the Euclidean Algorithm.

Divide 58,212 by 27,720.

58,212 ÷ 27,720 = 2 remainder 2

Divide the previous divisor (27,720) by the remainder (2).

27,720 ÷ 2 = 13,860

Divide the previous remainder (2) by the new remainder (2).

2 ÷ 2 = 1

Since the remainder is now 1, the GCD is found.

Therefore,  the greatest common divisor (GCD) of 27,720 and 58,212 is 1.

(b) To find integers r and s such that 27720r + 58212s = GCD(27720, 58212), we can use the Extended Euclidean Algorithm.

Using the Euclidean Algorithm from part (a), we can backtrack to find the coefficients r and s:

2 = 27,720 - 13,860

Substituting the values:

2 = 27,720 - (58,212 - 2 * 27,720)

Simplifying:

2 = 3 * 27,720 - 58,212

Comparing with the form 27720r + 58212s = GCD(27720, 58212):

r = 3

s = -1

Therefore, we substitute r = 3 and s = -1 into the equation 27720r + 58212s, it will result in the greatest common divisor (GCD) of 27720 and 58212.

Learn more about  Euclidean Algorithm

brainly.com/question/32265260

#SPJ11

Answer:

25 tickets

Step-by-step explanation:

If the answer is wrong, I don't know what to say because the answer I got is 25

The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets

An equation is an expression that shows the relationship between two or more numbers and variables.

The shopping spree raffle tickets is 35% while the gift card tickets is 40%. Hence for 500 tickets:

Difference = (40% - 35%) * 500 = 25 tickets

The would be 25 more gift card raffle ticket than shopping spree raffle tickets if there are 500 total raffle tickets

Find out more on equation at: https://brainly.com/question/2972832

3.14 x 11 = 34.54

Pi = 3.14 so times by 11 = 34.54

The concentration of sugar in the solution in the tank after 33 minutes is approximately 0.00734 kg/L or 7.34 g/L.

(a) Initially, the tank contains pure water, so there is no sugar in the tank. Therefore, the amount of sugar in the tank initially is 0 kg.

(b) The amount of sugar in the tank after t minutes can be calculated using the formula:

amount = 166.6(1 - [tex]e^{-t/340}[/tex])

Here, t is the time in minutes. This formula is derived from the exponential decay model, where the rate of sugar leaving the tank is proportional to the amount of sugar present. The constant 166.6 represents the equilibrium amount of sugar in the tank.

As time passes, the term [tex]e^{-t/340}[/tex] approaches 1, and the amount of sugar in the tank approaches the equilibrium amount of 166.6 kg.

(c) To find the concentration of sugar in the solution in the tank after 33 minutes, we need to divide the amount of sugar by the volume of the tank. The volume of the tank is given as 2380 L.

First, let's calculate the amount of sugar in the tank after 33 minutes using the formula from part (b):

amount = 166.6(1 - [tex]e^{-33/340}[/tex])

amount ≈ 166.6(1 - 0.895)

amount ≈ 166.6(0.105)

amount ≈ 17.493 kg

Now, we can calculate the concentration:

concentration = amount / volume

concentration = 17.493 kg / 2380 L

concentration ≈ 0.00734 kg/L

Therefore, the concentration of sugar in the solution in the tank after 33 minutes is approximately 0.00734 kg/L or 7.34 g/L.

Learn more about exponential decay model here:

https://brainly.com/question/30165205

#SPJ11

The statement |A ∪ B ∪ C| = |A| + |B| + |C| is true, which means the statement is proven.

Let A, B, and C be sets with finite cardinalities that satisfy A ∩ B ∩ C = ∅.

We have to prove that |A ∪ B ∪ C| = |A| + |B| + |C|.

The addition law of sets states that the cardinality of a union of two finite sets is equal to the sum of the cardinalities of the sets minus the cardinality of their intersection.

Thus, we get: |A ∪ B ∪ C| = |A ∪ B| + |C| − |(A ∩ B) ∪ C| = (|A| + |B| − |A ∩ B|) + |C| − |(A ∩ B) ∩ C| = |A| + |B| + |C| − |A ∩ B ∩ C|.Since A ∩ B ∩ C = ∅, we get |A ∪ B ∪ C| = |A| + |B| + |C|.

Thus, the statement is proven.

To learn more about sets

https://brainly.com/question/30096176

#SPJ11

If we fail to reject the null hypothesis, we cannot conclude that the means are significantly different.

To check whether the means of the samples from different states are significantly different or if the difference is just by chance, we can use the one-way analysis of variance (ANOVA).

The premise is that the ANOVA assumption of normality and homogeneity of variance has been satisfied.

Here, the null hypothesis is that the means of all the samples are equal while the alternative hypothesis is that at least one mean is different.

The significance level is 5%.

To perform the ANOVA test, we can follow these steps:

Step 1: State the null and alternative hypotheses

H0: μ1 = μ2 = μ3 = ... = μk (where k is the number of groups)

Ha: At least one mean is different

Step 2: Set the significance level (α)α = 0.05

Step 3: Calculate the test statistic

The test statistic used in ANOVA is the F-statistic, which is the ratio of the between-group variance to the within-group variance.

If the F-statistic is large and the p-value is less than the significance level, we can reject the null hypothesis and conclude that at least one mean is different. If the F-statistic is small and the p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the means are not significantly different.

Step 4: Calculate the p-value

Using the F-statistic and the degrees of freedom for the between-group and within-group variance, we can calculate the p-value. If the p-value is less than the significance level, we can reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.

Step 5: State the conclusion

Based on the p-value, we can either reject or fail to reject the null hypothesis. If we reject the null hypothesis, we can conclude that at least one mean is different. If we fail to reject the null hypothesis, we cannot conclude that the means are significantly different.

To learn more about ANOVA

https://brainly.com/question/15084465

#SPJ11

Answer:

32

Step-by-step explanation:

Answer:

heres the answer I think

Step-by-step explanation:

-3 < x < 1/2

Answer:

pi, and square root of 2

I don't think you're ACTUALLY going to give me brainliest

Answer:

B

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² = 4² + ([tex]\sqrt{5}[/tex] )² = 16 + 5 = 21 ( take the square root of both sides )

x = [tex]\sqrt{21}[/tex] → B

The absolute maximum and minimum of the function z = f(x, y) = 3x² - 12x + 3y² - 12y on the domain x² + y² < 4 are not provided.

To find the absolute maximum and minimum of the function z = f(x, y) = 3x² - 12x + 3y² - 12y on the domain D: x² + y² < 4, we need to locate the critical points and examine the boundaries of the domain.

Since the absolute maximum and minimum values are not provided, further calculations are needed to determine these values for the given function on the given domain.

To learn more about “Lagrange multipliers” refer to the https://brainly.com/question/4609414

#SPJ11

Answer:

If the triangle is similar then their ratio is also same

x = 8

6 4.8

X =8×6

4.8

x = 10 cm

hope this helps

good day mate

Answer:

24 IN.

Sorry for all caps

Step-by-step explanation:

Answer: i think its 10

Step-by-step explanation:

Answer:

56 oz or 3 1/2 lbs

Step-by-step explanation:

1 1/4 + 1 1/2 = 2 3/4lbs = 44 oz

44 oz + 12 oz = 56 oz

Answer:

81/4

Step-by-step explanation:

the answer is not sure

Answer:

A small box of the same cereal has 19 ounces and costs 4.19.

Step-by-step explanation:

In the first case, you have $3.37 per 15.3 ounces

Thus take 3.37 / 15.3 and you get $0.2203 per ounce or 22 cents per ounce

In the second case, you have $4.59 per 20 ounces

Thus take 4.59 / 20 and you get $0.2295 per ounce or almost 23 cents per ounce

So the smaller box actually has a slightly cheaper cost per ounce associated with it.

Answer:

a complementary angle adds up to 90 degrees.So 90 minus 64 and the measure of the other angle is 26

Step-by-step explanation:

Hope it helped ;)

This is the answer

I hope if you get it correct or right

Good luck everyone

The total vertical change from the start of the ride for the roller coaster after the 20 seconds 76 m.

The rise is the vertical difference between two points called vertical change.

Thus, the total vertical rise will be,

100 (upward) - 72 (downward) = 28(upward)

So, the total rise will become,

28(upward) + 48(upward) = 76(upward)

Therefore, the total vertical rise of the roller is 76 meter during the time of 20 seconds.

To know more about the vertical line test, here

https://brainly.com/question/2257047

#SPJ2

y = -2/5 x + 22/5 is the required equation of the line passing the coordinates

The equation of a line in slope intercept form is expressed as y = mx +b

where;

m is the slope

b is the y-intercept

Given the coordinate points (-4, 6) and (6, 2), the slope of the line is expressed as:

Slope = 2-6/6+4

Slope = -4/10
Slope = -2/5

For the y-intercept

2 = -2/5(6) + b

2 + 12/5 = b
b = 22/5

Hence the equation of the line passing the coordinate is y = -2/5 x + 22/5

Learn more on equation of a line here: https://brainly.com/question/18831322

#SPJ1

Answer:

Top:(4r⁹+3r³-5)

Bottom: r⁵

Step-by-step explanation:

Answer:

The answer to this question is $14,916

Step-by-step explanation:

18,469 - 3,553 = 14916

As he already has money for the car.

A bar model is shown in the linked picture.

Answer:

1047.12in³

Step-by-step explanation:

The volume of the sphere is:

V= 4/3 πr³

Where r is radius

Therefore the volume of each pinata is:

V= 4/3 x π x 5³

V= 523.6in³

The total:

V = 523.6 + 523.6 = 1047.12in³

Answer:

$5934

Step-by-step explanation:

Answer:

x = 138

Step-by-step explanation:

Exterior angle thm:

68 + 70 = x

x = 138

Answer:

[tex]1\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{10}{12} +\frac{11}{12} \\\\\frac{21}{12} \\\\1\frac{9}{12} \\\\1\frac{3}{4}[/tex]

The p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.

Null hypothesis (H0): The population means are equal, μ1 = μ2.

Alternative hypothesis (Ha): The population means are different, μ1 ≠ μ2.

Select the significance level (α): In this case, α = 0.05.

Now, The test statistic for a two-sample t-test is given by:

  t = (sample mean 1 - sample mean 2) / √((s1² / n1) + (s2² / n2))

  where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Here X₁ = 10, X₂ = 14, s= 3, n₁ =12, n₂ = 18

So, t= (10-14) / √(3²/12) + (3²/18) et:

t= (-4)/ √(3/4 + 1/2)

t= -4 / (5/4)

t= -2.7931

Now, degrees of freedom (df):

= (9/12 + 9/18)² / (((9/12)² / 11) + ((9/18)² / 17))

= 25.164

So, the p value will be 0.0208.

As, p-value is less than α (0.0208 < 0.05), we reject the null hypothesis.

Since the p-value (0.0208) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to suggest the case.

Learn more about Hypothesis test here:

https://brainly.com/question/17099835

#SPJ4