By creating a General Court made up of delegates from each town in the colony, this document reflects the principle of:


federalism


individual rights


checks and balances


republicanism

Given the inequality:

Let's select the graph which represents the solution.

Let's solve the inequality.

Add 5 to both sides of the inequality:

Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.

Therefore, the graph of the solution is:

ANSWER:

A

To simplify the given expression we will use the following property of exponents:

Using the above property we get:

Answer:

Answer

Explanation

The 750 percent as a fraction or mixed number in simplest form is calculated as follows:

Answer:

C. The graph of f(x) is shifted 17 units up.

Step-by-step explanation:

When + is outside the equation, it means up.

Answer:

320 red bell peppers

Step-by-step explanation:

First, let's calculate how many green and red bell peppers the farmer harvest in the first time:

Green peppers: 600*70/100 = 420

Red peppers: 600*30/100 = 180

If the farmer wants that half (50%) of the pepper harvest are red:

The total number of red peppers harvest have to be:

100*50/100 = 500

For this reason, the amount of remaining red peppers that have to be harvest are:

500 - 180 = 320

Answer: The farmer has to harvest more 320 red bell peppers

50 X 5 X 3

answer divide

by 36

We need to find the probability of the card chosen at random is yellow or brown.

So, since there are 3 yellow cards and 7 brown cards, the total numbers of cards that are yellow or brown is:

Now, the probability that the chosen card is yellow or brown can be found by dividing the above value by the total number of cards in the box.

The total number of cards in the box is:

Thus, that probability is given by:

Therefore, the answer is:

Answer

3(1/2) or (7/2) or 3.5

Step-by-step Explanation

The question wants us to divide (7/8) by (1/4).

The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.

That is, in changing ÷ into ×, (1/4) changes to (4/1)

So,

Hope this Help!!!

We need to find the area of Shape C.

Please have a look at the diagram below:

To find x, we can use the Pythagorean Theorem on the right triangle.

Now, let's solve for x. The steps are shown below:

So, the top part (dotted line) is

Now, we have a trapezoid. Let's find the area of the trapezoid:

Now, we need to subtract the area labeled (K) from the area of the trapezoid found.

--------------------------------------------------------------------------------

Area k is a triangle with side lengths 117, 117, and 176.14. Let's find the area of the triangle. The diagram is shown below:

Now, we will find h, the height of the triangle using Pythagorean Theorem.

The area of the triangle (region K) is,

The area of region C is the area of trapezoid - area of region k (triangle). So, the area is >>>>

Solution:

Given:

The right triangle can be sketched as shown below;

To get the distance between the building and the base of the ladder, we use the Pythagoras theorem since it is a right triangle.

Hence,

Therefore, the distance between the building and the base of the ladder in feet is 6 feet.

In order to find the interval of values where 95% of the shoe sizes lie, let's find the values of z-score that represents 2.5% to the left and 2.5% to the right of the standard distribution curve:

Looking at the z-table for the probabilities of 0.025 and 0.975, we have z1 = -1.96 and z2 = 1.96.

Now, we can calculate the values that define the interval using the formula below:

Therefore the correct option is the second one. (It's the only option with very close values to the ones calculated)

To answer this question we will use the z-score.

Recall that the z-score is given as follows:

The z-score of 54 is:

The z-score of 56 is:

Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:

Therefore:

The most appropriate choice for equation of line in slope intercept form will be given by

x + 2y = -16 is the required equation of line

What is equation of line in slope intercept form?

Equation of line in slope intercept form is given by y = mx + c

Where, m is the slope of the line and c is the y intercept of the line

The distance from the origin to the point where the line cuts the x axis is called x intercept

The distance from the origin to the point where the line cuts the y axis is called y intercept

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

[tex]m=tan\theta[/tex]

If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

The line passes through (0, -8) and (-2, -7)

Slope =

[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]

The line passes through (0, -8)

Equation of line

[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]

To learn more about equation of line in slope intercept form, refer to the link-

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Given a function f(x) = x(9 - x).

We need to find the value of f(2) and f(2.1) and use them to approximate the value of f'(2).

The value of f(2) is calculated below:

The value of the f(2.1) is calculated as follows:

Now, by the definition of f'(x), we know that

For the given condition, x = 2, and delta x = 0.1. So, the value of f'(2) is

Thus, the approximate value of f'(2) is 4.9.

The rule to show the number of dots in the pattern is

A pattern is a repetition of items, when the repetition is in ordered then the pattern can be forecasted.

The given pattern is ordered by the rule at which it was formed. The rule helps to forecast the number of dots in the next row

The information given in the question include:

row 1 = 2 dots

row 2 = 4 dots

row 3 = 6 dots

it can be seen that

2 * number of rows  = number of dots

Hence:

d = 2 * a

d = 2a

checking the rule for the 4th row

d = 2 * 4

d = 8

counting the dots confirms the rule is okay

Learn more about pattern at: https://brainly.com/question/27033681

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Solution

First, we need to convert the dimensions in feet to inches

Hence, the volume is;

A Nickel is 5 cents = 5/100 = $0.05

A dime is 10 cents = 10/100 = $0.1

A quarter is 25 cents = 25/100 = $0.25

Let N represent the number of nickels

Let D represent the number of dimes

Let Q represent the number of quarters

Jacob opened his piggy bank and found Nickels, Dimes, and Quarters totaling 81 coins. It means that

N + D + Q = 81

The total value of the coins was $7.90. It means that

0.05N + 0.1D + 0.25Q = 7.9

The number of Dimes was 7 less than triple the number of Quarters. It means that

D = 3Q - 7

The system of equations is

N + D + Q = 81

0.05N + 0.1D + 0.25Q = 7.9

D = 3Q - 7

SOLUTION:

Case: Z-scores and probabilities

Given: z-score of standard normal distribution, z= 1.65

Required: To get the percentage of observation

Method: We will be reading it off the z-score table

Step 1: First we see what the table looks like

Step 2: From the table, we trace 1.65 by looking at 1.6 on the column title and 0.05 on the row title

Step 3: We observe the value is 0.4505

This translates to 45.05%.

However, we are interested in the values above the 45.05%. So everything from the left of that line to the 50th percentile is 45.05% of the populations. In addition to that you have another 50% of the people below the 50th percentile. That's a total of 95.05% below this z score

To get the z-score above this, we do:

1 - 0.9505

P(> z) = 0.0495 or 4.95%

Final answer:

A) The answer is 4.95%

Given:

Step 1: To identify the quadratic form of the given equation.

So, t = x²

Step 2: Factor the quadratic equation in step 1.

Thus, the factors of the equation is

Step3: solve for x.

Answer: x = 1

A linear equation in slope-point form looks like this:

y -y0= m(x-x0)

Where m is the slope of the line and (x0,y0) is a point of the line.

In this case, we know that the slope of the line equals 4 and that the line goes through the point (1, -3), then, we can substitute these values into the general form to get:

y-(-3) = 4(x-(1))

Answer: 12

Explanation:

Given:

Total number of students in a classroom = 73

Ratio of students to computers = 6:1

To find the number of computers needed to achieve the desired ration, we use the ratio:

Therefore, the number of computers needed is 12.

Let the number of apple pies x

Let the number of blue pies y

Since they sold 38 pies on Saturday, then

Add x and y, then equate the sum by 38

Since they sold each apple pie for $11 and each blueberry pie for $13

Since they collected $460 on Saturday, then

Multiply x by 11 and y by 13, then add the products and equate the sum by 460

Now, we have a system of equations to solve it

Multiply equation (1) by -13 to equate the coefficients of y in values and opposite them in signs to eliminate them

Add equations (2) and (3)

Divide both sides by -2

Substitute the value of x in equation (1) to find y

Subtract 17 from both sides

The y sold 17 apple pies and 21 blueberry pies

The answer is the last choice

if 1ml = 0.00011 then 9ml=

Apply proportion

0.00011/1=x/9

solve for x

x=9*0.00011

x=0.00099

answer is

Answer: 15cm

Step-by-step explanation:

Your welcome

To find the new amount, substract the percent of the original amount to the original amount, this way:

The new amount is 91.

from the question;

we are to construct 99% confidence interval. this can be done using

where,

inserting values

therefore the 99% confident inter vale is between 98.041 to 98.359

we can change a fraction to a percentage multiplying the fraction by 100

also, we can change a decimal number to a percentage multiplying by 100

for example

1. 1/5

In this case, 1/5 represent 20%

4. .625

In this case, 0.625 represent 62.5%

If we do the same process to all the next numbers we will obtain the next solutions.

1. 1/5 ------ a. 20%

2. 8/10 ------ f. 80%

3. 0.08 ------ d. 8%

4. .625 ---- g. 62.5%

5. 32/100 ---- b. 32%

6. 1/2 ------ c. 50%

7. 1.25 ---- e. 125%

From the question,

Age 18 - 22 has 177 people, 48 of whom smoke.

Age 23-30 has 146 people, 31 of whom smoke.

Age 31-40 has 81 people, 28 of whom smoke.

People who do not smoke = (177- 48)+(146-31)+(81-28) = 129 + 115 +53 = 297 people.

People within age 18-22 who do not smoke = 129

Total number of events = 404

Hence, option B is the answer.

SOLUTION

Exterior property of a triangle

An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.

Hence,

Simplify and evaluate for x

Therefore,