2. The two figures are similar. Write the similarity statement. Consider Triangle 1 to be the pre-image and Triangle 2 to be the image (Hint: What scale factor would you multiply the side lengths of Triangle 1 by to obtain the side lengths in Triangle 2)?

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.

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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

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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.

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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: i think its 10

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.

The 90% confidence interval is approximately 2,400 and 3,400.

The 90% confidence interval of the true population mean can be calculated using the formula: sample mean ± (critical value * standard error). Since the sample size is small (n=27), we need to use the t-distribution and its corresponding critical value. For a 90% confidence level with 26 degrees of freedom (n-1), the critical value is approximately 1.706.

Using the given values, the standard error is calculated as the sample standard deviation divided by the square root of the sample size: 900 / sqrt(27) ≈ 171.97.

Substituting the values into the formula, the 90% confidence interval is approximately 3,000 ± (1.706 * 171.97), which yields a range of approximately 2,424.5 to 3,575.5.

Therefore, the closest option to the 90% confidence interval is 2,400 and 3,400.

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Answer:

$5934

Step-by-step explanation:

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:

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 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.

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T-value is not always greater than Z-value. Therefore, the statement is false

False. The relationship between a T critical value and a Z critical value is not that a T value is always greater than a Z value. The choice between using a T critical value or a Z critical value depends on the specific context and assumptions of the statistical analysis.

In general, when the sample size is small (typically below 30) and the population standard deviation is unknown, a T critical value is used. The T distribution accounts for the additional uncertainty introduced by the smaller sample size, resulting in wider confidence intervals and more conservative hypothesis tests compared to the Z distribution.

On the other hand, when the sample size is large (typically above 30) or the population standard deviation is known, a Z critical value is used. The Z distribution assumes a large sample size, and it is based on the known population standard deviation or the approximation of the sample standard deviation to the population standard deviation.

Therefore, it is incorrect to state that a T-value is always greater than a Z-value. The choice between T and Z critical values depends on the specific conditions and assumptions of the statistical analysis being performed.

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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 ;)

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

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

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Answer:

32

Step-by-step explanation:

Answer:

Top:(4r⁹+3r³-5)

Bottom: r⁵

Step-by-step explanation:

Answer:

24 IN.

Sorry for all caps

Step-by-step explanation:

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.

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Answer:

5.86

Step-by-step explanation: its right on delta math

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.

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Answer:

heres the answer I think

Step-by-step explanation:

-3 < x < 1/2

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.

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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.

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Answer:

pi, and square root of 2

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

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]