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7 days ago

The given equation has been solved in the table. In which step was the subtraction property of equality applied?

Mathematics

1 answer:

tester [10.8K]7 days ago

5 0

The correct answer is Option (D). The subtraction property of equality asserts that whatever is subtracted from one side of an equation must also be subtracted from the other side. In the instance where x + 2 = 2, applying this property leads to: x + 2 - 2 = 2 - 2, simplifying to x = 0. However, the provided question displays the addition property of equality utilized in step 2, indicating that the subtraction property was not applied there. Consequently, Option (D) is the correct response.

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Kennedy has a gross income of $95,000. What is her total tax due?

AnnZ [10993]

Answer:

This brings her total gross income to $140,000 ($3,000 + $500 + $41,500 + $90,000 + $5,000), with her farm gross income being $95,000 ($90,000 + $5,000). Since 67.9% (which is at least two-thirds) of her gross income derives from farming ($95,000 ÷ $140,000 = .679), she qualifies for the special estimated tax rules designed for qualified farmers.

Step-by-step explanation:

3 0

1 month ago

Isaac is purchasing two pairs of shoes—one pair for $37.00 and the second pair for $42.00. The state sales tax applied to Isaac’

tester [10823]

Respuesta:

El total de la factura de Isaac es $84.53

Explicación detallada:

$37.00 + $42.00 = $79.00 < b (factura)

b + t (impuesto sobre ventas) = c (costo total)

(7%/100 = 0.07)

(0.07 * 79 = 5.53)

(t = $5.53)

$79.00 + $5.53 = $84.53

¡Buena suerte!

6 0

1 month ago

Read 2 more answers

A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich

babunello [10317]

A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)

b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells

d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour

e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours

8 0

28 days ago

Read 2 more answers

1. Darnell reads at a constant rate

Svet_ta [11397]

Answer:

Darnell reads 1,715 words in 7 minutes.

Step by step Explanation:

1. First, determine how many words he can read in a minute by dividing 735 words by 3. The result is 245.

245

______

3)735

6 drop the 3 to form 13

-_____

1 3

12 drop the 5 to make 15

-______

1 5

___________

2. Next, since he reads 735 words over 3 minutes, multiply that by 2 to find words read in 7 minutes: 3×2=6, thus, 735+735 (735×2) equals 1,470 words.

3. Finally, add 245 to account for the last minute we calculated. Therefore, the total is 1,715 words in 7 minutes.

8 0

1 month ago

Two random samples are taken from private and public universities

babunello [10317]

Response:

Detailed explanation:

For private institutions,

n = 20

Average, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(sum of (x - mean)²/n

Sum of (x - mean)² = (43120 - 34623.05)^2 + (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public institutions,

n = 20

Average, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Sum of (x - mean)² = (25469 - 25063.15)^2 + (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This involves two independent samples. Define μ1 as the mean out-of-state tuition for private institutions and μ2 as the mean out-of-state tuition for public institutions.

The random variable represents μ1 - μ2 = the difference between the mean out-of-state tuition for private vs. public institutions.

The hypothesis is established as follows. The correct choice is

-B. H0: μ1 = μ2; H1: μ1 > μ2

As the sample standard deviation is known, the test statistic is calculated using the t test formula:

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The method for finding degrees of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

The probability value is obtained from the t test calculator. It is

p value = 0.000065

Given that alpha, 0.01 > the p value, 0.000065, we will reject the null hypothesis. Hence, at a significance level of 1%, the mean out-of-state tuition for private institutions is statistically significantly greater than that of public institutions.

4 0

1 month ago