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The Columbian Exchange is the name given to the items shared between the New World and the Old World. Once European exploration began, items passed both ways. Which of the following explains the result this exchange had on many Native Americans living in North and South America?
A.
Native Americans began using tobacco.
B.
Native Americans died because of diseases.
C.
Native Americans gave livestock to Europe.
D.
Native Americans started growing corn.

Answer:

○ \(\displaystyle Perpendicular\)

Step-by-step explanation:

Convert each equation to Slope-Intercept Form:

\(\displaystyle 3y - 6x - 7 = 0 → 3y - 6x = 7 → 3y = 6x + 7 → y = 2x + 2\frac{1}{3} \\ \\ 2y + x = 3 → 2y = -x + 3 → y = -\frac{1}{2}x + 1\frac{1}{2}\)

Take a look at \(\displaystyle 2\) and \(\displaystyle -\frac{1}{2}.\) Their rate of changes [slopes] have a '2' in common, they are not similar. This tells you that these linear equations are not parallel, but perpendicular, because perpendicular equations have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES].

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Answer:

She will practice 2.5 for week four

Step-by-step explanation:

The table is going by 0.5 so I added 0.5 +2 =2.5

on solving the provided question, we can say that by equation we Consequently, he will sell 16 automobiles at this price.

A number, a variable, or a mix of both, combined with certain operation symbols, make up an expression. An equal sign is used to denote the separation of two expressions in an equation.

Here,

Given: Number of cars sell in a day = 12

Price of a car =\($23,000\)

For each $300 price reduction dealer can sell two more cars per day.

Solution: Let there be x unit 300 price reduction

2x unit increase in sale of car

\(|R(x)=(15000-300x)(12+2x)\)

Cost

\(|C(x)=1000+12000 (12+2x)\)

Profit

\(|P(x)=(15000-300x)(12+2x)-1000+12000 (12+2x)\\15000(12+2x)–12000 (12+2x)-300x(12+2x)-1000\\=180000-144000+30000x-24000x -3600x -600-1000\\=36000+2400x-600 = P'(x)=-1200x +2400 = P"(x)=-1200\)

For critical points

\(P'(x)=0= -1200x + 2400=0= x=2\)

Since P"(x) <0at x = 2it is max profit 12+2x=12+2(2)=16

16cars per day he will sell

\(Price = 15000-300*16 = $10200\)

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Answer:

Step-by-step explanation:

Therefore, the height of the tower is approximately 121.4 meters.

The ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

The median weekly earnings on the graphs are

Represent as a ratio

Ratio = $750 : $1250

Divide by 250

Ratio = 3 : 5

Hence, the ratio of the median weekly earnings is 3 : 5

In (a), we have:

Ratio = 3 : 5

The horizontal scale is given as:

Ratio = 1 unit : 1 grid mark

The rectangles in graph A have a width of 1 unit.

So, we have:

Ratio = 3 * 1: 5 * 1

Ratio = 3 : 5

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

Recall that:

Ratio = 3 : 5

Ratio = 1 unit : 1 grid mark

From the graph, we have the following widths:

Red = 3 units

Blue = 5 units

So, we have:

Ratio = 3 * 3 : 5 * 5

Simplify

Ratio = 9 : 25

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25

Recall that:

Ratio = 3 : 5

Ratio = 1 unit : 1 grid mark

From the graph, we have the following widths:

Red = 3 units

Blue = 5 units

Since the base are squares, we have:

Ratio = 3 * 3  * 3 : 5 * 5 * 5

Simplify

Ratio = 27 : 125

Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125

The most misleading graph is graph B.

This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

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Looking at the image, the angles BCF and GHF are in the same position considering the transversal line and a parallel line (that is, they are in the same side of the transversal line and above both parallel lines).

Since these angles are in the same relative position regarding the transversal line and the parallel lines, they are called corresponding angles.

Therefore the correct option is the first one (A).

With a monthly repayment of $809.49, the total interest on the car loan will be $5,569.67.

We assume that there are monthly repayments and compounding interest on the car loan.

With periodic repayments and compounding interest, the total interest paid on the car loan will be as shown by the car loan calculator.

Car loan = $43,000

Down payment = $0

Fixed Annual Percentage Rate (APR) = 4.9%

Loan term = 5 years

Car Loan Calculator with monthly Repayment:

Payment = $809.49/month

Interest Paid =$5,569.67

Total Paid = $48,569.67

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Answer:

(6,11)

I can confirm that this question is right.

12/2      22/2

(6   ,        11)

Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

The probability about an occurrence in an experiment is the likelihood that the event will occur. Any event's probability is a number between (including all) "0" and "1".

If an event's probability is represented by P(E), then we get

Given data:

Total pennies = 50

number of 1977 dated pennies = 12

probability = favourable outcome / total outcome

probability(1977 dated pennies) = number of 1977 dated pennies/ Total pennies

probability(1977 dated pennies) = 12/50

Divide numerator and denominator by 2.

probability(1977 dated pennies) = 6/25

Thus, probability that the one drawn penny is from 1977 dated pennies is 6/25.

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Answer:

Options D, E, F

Step-by-step explanation:

Given the following system of linear inequalities in two variables:

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

We can substitute the given ordered pairs to see whether they satisfy both linear inequalities.

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(8) < 2

 ⇒  16 < 2  (False statement).  

y > 7

 ⇒  2 > 7 (False statement).  

 ⇒  (8, 2) is not a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(0) < 2

 ⇒  0 < 2  (True statement).  

y > 7

 ⇒  0 > 7 (False statement).  

 ⇒  (0, 0) is not a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(5) < 5

 ⇒  10 < 2  (False statement).  

y > 7

 ⇒  5 > 7 (False statement).  

 ⇒  (5, 5) is not a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(1) < 9

 ⇒  2 < 9  (True statement).  

y > 7

 ⇒  9 > 7 (True statement).  

 ⇒  (1, 9) is a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(17) < 50

 ⇒  34 < 50  (True statement).  

y > 7

 ⇒  50 > 7 (True statement).  

 ⇒  (17, 50) is also a solution to the system.  

\(\displaystyle\sf\ System\:of\:Linear\:Inequalities = \begin{cases}\displaystyle\sf\ 2x < y} \\\displaystyle\sf\ y > 7}\end{cases}\)

2x < y

 ⇒  2(-1) < 10

 ⇒ -2 < 10  (True statement).  

y > 7

 ⇒  10 > 7 (True statement).  

 ⇒  (-1, 10) is also a solution to the system.  

Therefore, Options D, E, and F are the solutions to the given system of linear inequalities.  

Linear Inequalities in two variables

System of linear inequalities  

________________________________

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Solution:

The substitution method is best used when one of the equations is in terms of one of the variables.

From the system of equations given, the one where substitution is the best method is;

This is because the first equation is already in terms of the variable y.

Answer:

144

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

108/4 = 27

224/4 = 56

The other ones don't work if you distribute the outside numbers.

The solution of the expression after factoring is,

⇒ 4 (27 + 56)

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The expression is,

⇒ 108 + 224

Now, We can factor as;

⇒ 108 + 224

⇒ 4 × 27 + 4 × 56

⇒ 4 (27 + 56)

Thus, The solution of the expression after factoring is,

⇒ 4 (27 + 56)

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I can so just follow me and I will explain

Answer:650 people were surveyed

The length of the side of his garden can be16.6 ft

From the question, we have the following parameters that can be used in our computation:

He has enough compost to cover an area of 276 square feet.

This means that

Area = 276 276 square feet.

The area of a square is calculated as

Area = Length^2

Substitute the known values in the above equation, so, we have the following representation

Length^2 = 276

Take the square root of both sides

Length = 16.6

Hence, the length is 16.6 ft

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Answer:

\(H_0:\) less than or equal to 600

\(H_a:\)  greater than 600

Step-by-step explanation:

The null hypothesis will maintain the manager's claim, since the null hypothesis always suggests that their is no difference in the general population.

Therefore if the mean guest bill is represented by \(\mu_g\), the null hypothesis will be that the mean guest bill is less than or equal to 600.

Since the alternative hypothesis is the opposite of the null hypothesis which indicates a difference in the general population, the alternative hypothesis will be that the guest meal is greater than 600

\(H_0: \mu_g \leq 600\\H_a: \mu_g > 600\)

The computation of the factors shows that the greatest number of bags that Lucia can make will be 16.

From the information given, Lucia has 48 markers and 64 stickers that she wants to give as favors for a party.

The computation of the factors shows that the greatest number of bags that Lucia can make will be calculated through then factors. This goes thus:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48

Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.

Therefore, the highest common factor is 16.

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Answer:

16

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Answer: s + 30 ≥ 50; s ≥ 20

Step-by-step explanation:

let s be the amount you have yet to spend in order to reach $50 or more

you already have $30.

This means you need to spend at least $20 more ($50 - $30 = $20)

S can be greater than or equal to $20 because your total will be 50 or more, therefore qualifying for the discount.

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

The solution is any point in the common part of red and blue

The two lines intersect each other at (4 , 7)

Step-by-step explanation:

∵ y > 1/4 x + 6 ⇒ y = 1/4 x + 6

∵ y > 2x - 1 ⇒ y = 2x - 1

∴ 2x - 1 = 1/4 x + 6

∴ 2x - 1/4 x = 6 + 1

∴ 7/4 x = 7 ⇒ x = 7 ÷ 7/4

∴ x = 4

∴ y = 2(4) - 1 = 7

∴ The two lines intersect each other at (4 , 7)

∴ The solution is any point in the common part of red and blue

The equation of line AB using the coordinates of point A(-2,2) and B(1.4) with the help of formula for equation of line in two point form is 3y=2x+10

or 3y-2x=10 or 3y-2x-10=0

What are coordinates?

The two-dimensional cartesian coordinates are (x, y), while the three-dimensional cartesian coordinates are (x, y, z). The abscissa and ordinate are the terms used to describe ordered pairs in the form of (x,y). Abscissa: The first number in the ordered pair is termed the abscissa.  The abscissa is the value of x in the ordered pair & ordinate is value of y.

We know that equation of line in slope-intercept form is given by:y=mx+b where m denotes slope & b denotes intercept. Also the equation of line can be given in the form of \(\frac{Y-Y1}{X-X1} =\frac{Y2-Y1}{X2-X1}\), where (X₁,Y₁) and (X₂,Y₂) are two points through which the line passes.

From the graph it can be seen that the line passes through two points A(-2,2) and B(1,4)

Equation of line  through two points A(-2,2) and B(1,4):

\(\frac{Y-Y1}{X-X1} =\frac{Y2-Y1}{X2-X1}\)

Consider point A as  (X1,Y1) and point B as (X2,Y2)

\(\frac{Y-2}{X-(-2)}\) = \(\frac{4-2}{1-(-2)}\)

\(\frac{Y-2}{X+2}\)      =\(\frac{4-2}{1+2}\)

\(\frac{Y-2}{X+2}\)      =\(\frac{2}{3}\)

Y-2       =\(\frac{2}{3}\) (X+2)

3(Y-2)    =2(X+2)

3Y-6      =2X + 4

3Y          = 2X + 4 + 6

3Y          = 2X +10

Equation of line  through two points A(-2,2) and B(1,4): 3y=2x+10

or 3y-2x=10 or 3y-2x-10=0

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Answer:

Amadi: 20 years old

Chima : 4 years old

The sampling distribution of the difference between the two-sample means, X1 - X2, can be characterized by the following properties:

1. Expected value (mean):

  E(X1 - X2) = E(X1) - E(X2) = mu1 - mu2

  The expected value of the difference is equal to the difference of the means of the two populations.

2. Variance:

  V(X1 - X2) = V(X1) + V(X2)

  Since X1 and X2 are independent, the variance of their difference is equal to the sum of their individual variances.

(b) Given the information provided:

For X1:

Mean (mu1) = 29.8

Standard deviation (sigma1) = 4

For X2:

Mean (mu2) = 34.7

Standard deviation (sigma2) = 5

Sample size for X1 (n1) = 20

Sample size for X2 (n2) = 20

To find the sampling distribution of X1 - X2:

Expected value (mean):

E(X1 - X2) = mu1 - mu2 = 29.8 - 34.7 = -4.9

Variance:

V(X1 - X2) = V(X1) + V(X2) = (sigma1^2 / n1) + (sigma2^2 / n2)

          = (4^2 / 20) + (5^2 / 20)

          = 16/20 + 25/20

          = 41/20

          = 2.05

Therefore, the sampling distribution of X1 - X2 has an expected value (mean) of -4.9 and a variance of 2.05.

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The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

102 donuts

Step-by-step explanation:

12% of 850 is 102, so since 12% more donuts are sold this week, we sold 102 more donuts this week compared to last week.

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:Asa

Step-by-step explanation:because I know

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)