Determine which is the better buy. 7 kilograms of wood for $13.65 or 5 kilograms of wood for $7.50. What is the unit price for each? Explain how you determined which one is the better buy. Get right, I'll give you brainliest

x ≤ 2  but must be greater than 0 .  triangles are the possible lengths of the remaining side.

How is an isosceles triangle defined?

The length of one of the congruent side is 5

The total length of two congruent sides is 10

Perimeter at the most is 12 (meaning the maximum length of perimeter is 12)

The third side of the triangle must be 12-10 = 2 at the most

Writing this requirement as inequality we have

x ≤ 2  but must be greater than 0

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This value of x doesn't satisfy the Equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.

Let's start with the given information: we have two arc measures and an angle measure. We know that the sum of the arc measures is equal to the total circumference of the circle, which is 360 degrees. So, we can set up an equation:

59 + 2x = 360

Solving for x, we get:

2x = 301

x = 150.5

So, the value of x that makes one arc measure 2x and the other arc measure 59, and the angle measure 15, is 150.5.

Now, let's think about why this makes sense. The sum of the arc measures is equal to the total circumference of the circle, which means that the angle formed by those two arcs must be half of the central angle that intercepts them. In other words, the angle formed by the 59-degree arc and the 2x-degree arc is (59 + 2x)/2. We also know that the angle formed by the 15-degree angle and the same arc is equal to half of the angle formed by the two arcs. So:

(59 + 2x)/2 = (180 - 15)/2

59 + 2x = 165

2x = 106

x = 53

However, this value of x doesn't satisfy the equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.

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The probability that a t random variable with 7 degrees of freedom is greater than 1.895 is 0.05

We have to solve this by using the t distribution table that has the degree of freedom as 7.

Under this table we have to search for the value 1.895 and the probability value that it falls under.

Hence we would have 1.895 (1-0.95) = 0.05

Hence we have to conclude that the  the probability that a random variable with 7 degrees of freedom is greater than 1.895 is 0.05

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(1,2,4)

Range describes the y-values of a graph.

Range

Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.

Finding Range

In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).

Answer:

12x+6y+2

Step-by-step explanation:

Multiply -2 by every number

Answer:

150 lemon jellybeans

Step-by-step explanation:

Add the ratios up to get 12 lemon jelly beans out of 64 jellybeans.

\(\frac{12}{64} =\frac{x}{800}\)

Cross multiply:

9600 = 64x

---> x = 150 lemon jellybeans

Answer: a piecewise function is a function that is defined on a sequence of intervals.

Step-by-step explanation:

A piecewise function is a function that is "different" at different intervals.

The function may behave linearly between x = 0 and x = 10, and after that point, the function may be constant for a while, then change again.

This type of functions can be written as:

f(x) = g(x) if x1 ≤ x ≤ x2

f(x) = h(x) if x2 ≤ x ≤ x3

f(x) = k(x) if x3 ≤ x ≤ x4

and so on, where g(x), h(x) and k(x) are different functions, and those functions only act on the givenintervals: (x1, x2), (x2, x3) and (x3, x4)

Thomas finished 2.4 seconds faster than Mikah which has higher speed than Mikah.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

200-meter race finished by Thomas =  25.7 sec

200-meter race finished by Mikah = 28.1 sec

The difference between their time shows How much faster did Thomas run the race than Mikah.

=28.1 - 25.7

=2.4 seconds

Hence, Thomas finished 2.4 seconds faster than Mikah which has higher speed than Mikah.

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The difference in mass between the bananas and the apples is 4 times the difference between the mass of one banana and the mass of one apple, which is represented by (b - a).

Let's say the mass of one banana is 'b' grams and the mass of one apple is 'a' grams. Since we have four bananas and four apples, the total mass of the bananas would be 4b grams, and the total mass of the apples would be 4a grams.

To find the difference in mass between the bananas and the apples, we need to subtract the mass of the apples from the mass of the bananas:

Difference in mass = Mass of bananas - Mass of apples

Mathematically, this can be represented as:

Difference in mass = (4b) - (4a)

We can simplify this further by factoring out the common factor of 4:

Difference in mass = 4(b - a)

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1. x/(x - 5) = 4/(x - 4)

x (x - 4) / ((x - 5) (x - 4)) = 4 (x - 5) / ((x - 5) (x - 4))

x (x - 4) = 4 (x - 5)

x² - 4x = 4x - 20

x² - 8x = -20

Solving for x by completing the square gives

x² - 8x + 16 = -4

(x - 4)² = -4

x - 4 = ± 2i

x = 4 + 2i   or   x = 4 - 2i

2. Since -7 + 2i and -7 - 2i are roots of the given quadratic, we have

z² + bz + c = (z - (-7 + 2i)) (z - (-7 - 2i))

z² + bz + c = (z + (7 - 2i)) (z + (7 + 2i))

z² + bz + c = z² + ((7 - 2i) + (7 + 2i)) z + (7 - 2i) (7 + 2i)

z² + bz + c = z² + 14z + 53

so that b = 14 and c = 53, which makes b + c = 67.

3. If x + y = 4, then

x³ + y³ = 100

x³ + (4 - x)³ = 100

x³ + (64 - 48x + 12x² - x³) = 100

12x² - 48x + 64 = 100

12x² - 48x = 36

x² - 4x = 3

and by completing the square,

x² - 4x + 4 = 7

(x - 2)² = 7

x - 2 = ± 7

x = 2 + 7   or   x = 2 - 7

x = 9   or   x = -5

If x = 9, then y = -5, so one pair of solutions would be (x, y) = (9, -5).

transfer of questionnumber 12 is B-112

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

Therefore, \(8\sqrt{2}\) number of inches in the perimeter of new square if the perimeter of the original  square is 16 inches.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeters, meters, inches, and feet.

Given: The midpoints of the adjacent sides of a square are connected to form a new square. The perimeter of the original square is 16 inches.

As perimeter is 16 in, so the side is 4 in.

Each side of the new square is the hypotenuse of an isosceles right triangle with legs of length 2 inches.

\((2 in)^2 + (2 in)^2 = s^2\\s^2 = 8 in^2\\s = 2\sqrt{2} in\)

Therefore,

Perimeter = 4s

\(P = 4(2\sqrt{2}) = 8\sqrt{2} in\)

Therefore, \(8\sqrt{2}\) number of inches in the perimeter of new square if the perimeter of the original  square is 16 inches.

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Answer:

B) 5

Circle is 360 degr. So (21x+9) +(23x-5) +(26x+6)=360

Combine like terms 70x+10=360

Additive inverse -10 from both sides, 70x= 350

Divide both side by 70 division Property of Equality x=5.

Check your answer by substituting 5 back into original solution!

Step-by-step explanation:

Northside Christian Academy has 528 students enrolled this year. That is an in- crease of 10% over last year's enrollment. How many students were enrolled last year?

Let

x ------> students enrolled last year

we have that

100%+10%=110%=110/100=1.10

so

528=1.10x

solve for x

x=528/1.10

x=480

The mean is 172, the variance is 34.4, and the standard deviation is 5.86.

The United States has a system of bicameralism, which means that each state has two chambers in its legislature: a lower chamber (such as the Assembly or House of Representatives) and an upper chamber (such as the Senate).

The number of constituents per district in each chamber varies from state to state, and it is usually determined by the state's constitution or by a state redistricting commission.

As of the 2010 census, Texas had about 811,147 constituents per state senate district.

However, this is not the highest number of constituents per senator among all the states.

In fact, the state with the highest number of constituents per senator is California.

According to the U.S. Census Bureau, as of the 2010 census, California had a population of approximately 37.3 million people.

The state's constitution provides for 40 state senators, which means that each senator represents approximately 933,000 constituents.

This is significantly higher than the number of constituents per senator in Texas.

The high number of constituents per senator in California can be attributed to the state's large population and the fact that the number of state senators has not kept up with population growth.

The last time the number of state senators in California was increased was in 1973, when the state's population was around 20 million people.

In conclusion, while Texas has a high number of constituents per state senate district, it is not the only state with a high number of constituents per senator.

California has a significantly higher number of constituents per senator, due to its large population and the fact that the number of state senators has not kept up with population growth.

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Answer:

third side is 4

Step-by-step explanation:

using Pythagoras theorem,

(√33)² + l² = 7²

33 + l² = 49

l² = 49 - 33

l² = 16

l = √16

l = 4

Answer:

Step-by-step explanation:

f(x)=x²

f(-2)=(-2)²=4

f(f(-2))=f(4)=4²=16

Answer:

algebraically" whether a function is even or odd. To do this, you take the function and plug −x in for x, and then simplify. If you end up with the exact same function that you started with (that is, if f (−x) = f (x), so all of the signs are the same), then the function is even

Step-by-step explanation:

Even functions are symmetrical about the y-axis: f(x)=f(-x). Odd functions are symmetrical about the x- and y-axis: f(x)=-f(-x)

The picture has the dimension of a rectangle and will have the area of 66.166 in square feet.

We have to convert the length and width to be in same unit, before calculating for the area by multiplying the length by the width, and then convert the result to be in square feet.

1 cm = 0.394 inches

126 cm = 126 × 0.394 inches

126 cm = 49.644 inches

So the picture has length 16 inches and width 49.644 inches

area of picture = 16 inches × 49.644 inches

area of picture = 794.304 square inches

1 inch = 0.0833 feet

794.304 square inches = 794.304 × 0.0833 square feet

794.304 square inches = 66.166 square feet.

In conclusion, the picture has an area of 66.166 square feet.

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Using the formula for area of a circle the value for area is obtained as option D: 196 (π) ft².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The formula for the area of a circle is -

A = π × r², where r is the radius.

Substituting r = 14 ft into the equation -

A = π × (14 ft)²

A = π × 196

A = 196 π  ft²

Therefore, the area of circle V is 196 π ft².

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the correct translation is ((∃x)E(x) → ((A(g) & ¬W(g)) ∨ (¬A(g) & W(g))))

The correct translation of the third premise "Evil can exist only if God is either able but unwilling or unable yet willing to prevent it" is:

((∃x)E(x) → ((A(g) & ¬W(g)) ∨ (¬A(g) & W(g))))

Explanation:

(∃x)E(x): There exists an x such that x is evil. This represents the existence of evil.

A(g): God is able to prevent evil.

¬W(g): God is unwilling to prevent evil.

¬A(g): God is unable to prevent evil.

W(g): God is willing to prevent evil.

The premise states that evil can exist only if one of two conditions is met:

God is able to prevent evil but unwilling to do so (A(g) & ¬W(g)).

God is unable to prevent evil yet willing to do so (¬A(g) & W(g)).

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There are 9438 different committees possible without Tarzan and Jane together.

a) To find the total number of possible committees, we need to choose 7 people out of 16 people, regardless of their gender. We can do this using the combination formula:

\(${{16}\choose{7}} = \frac{16!}{7!(16-7)!} = 11440$\)

Therefore, there are 11440 different 7-person committees possible.

b) If the committee must be made up of women only, we need to choose 7 women out of the 10 women available. We can do this using the combination formula again:

\(${{10}\choose{7}} = \frac{10!}{7!(10-7)!} = 120$\)

Therefore, there are 120 different 7-woman committees possible.

c) If the committee must be made up of 5 men and 2 women, we need to choose 5 men out of 6 men available, and 2 women out of 10 women available. We can do this using the combination formula:

\(${{6}\choose{5}} \times {{10}\choose{2}} = \frac{6!}{5!(6-5)!} \times \frac{10!}{2!(10-2)!} = 6 \times 45 \times 9 = 2430$\)

Therefore, there are 2430 different committees possible with 5 men and 2 women.

d)

i) If Tarzan and Jane must be together on the committee, we can treat them as a single entity and then choose 6 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{6}} = \frac{14!}{6!(14-6)!} = 3003$\)

Therefore, there are 3003 different committees possible with Tarzan and Jane together.

ii) If Tarzan and Jane refuse to serve on the committee, we need to choose 7 people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{7}} = \frac{14!}{7!(14-7)!} = 3432$\)

Therefore, there are 3432 different committees possible without Tarzan and Jane.

iii) If Tarzan and Jane are not on the committee together, we can count the number of committees that include both of them and subtract it from the total number of committees. The number of committees that include both Tarzan and Jane can be found by treating them as a single entity and choosing 5 more people out of the remaining 14 people. We can do this using the combination formula:

\(${{14}\choose{5}} = \frac{14!}{5!(14-5)!} = 2002$\)

Therefore, the number of committees that do not include both Tarzan and Jane is:

\($11440 - 2002 = 9438$\)

Therefore, there are 9438 different committees possible without Tarzan and Jane together.

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If Henry has a plot of land that is 3km by 4.3km, he will require fencing supply of 14.6km.

Henry has a plot of land that is 3km by 4.3km, so his plot of land is rectangle shaped with length, l = 4.3km and breadth, b = 3km. To determine km of fencing supply needed, we have to calculate the perimeter of the plot.

P = 2×(l + b)

= 2×(4.3 + 3)

= 2×7.3

= 14.6 km

Joanna has a an equilateral triangle shaped plot of side a = 4.5m. An equilateral triangle has all sides equal. Fencing material required for fencing can be determined by calculating perimeter of the plot.

P = 3a

= 3×4.5

= 13.5m

So Joanna will require 13.5m of fencing material.

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The part of the coordinate plane that is equidistant from the points A(-3, 2) and B(3, 2) is the horizontal line with a y-coordinate of 2.

The points A(-3, 2) and B(3, 2) have the same y-coordinate, which means they lie on a horizontal line. The midpoint of the line segment AB will also lie on this line.

To find the midpoint, we can average the x-coordinates and the y-coordinates of the two points.

The x-coordinate of the midpoint is (-3 + 3) / 2 = 0 / 2 = 0.

The y-coordinate of the midpoint is (2 + 2) / 2 = 4 / 2 = 2.

Therefore, the midpoint of AB is (0, 2).

Since the midpoint lies on the same horizontal line as the points A and B, any point on this line will be equidistant from A and B. This line is parallel to the x-axis and has a y-coordinate of 2.

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Answer:

4071.5 in^2

Step-by-step explanation:

The surface area of a sphere of radius r is A = 4πr²

In this case, with r = 18 in, A = 4π(18 in)² = 4071.5 in²

The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

What is the null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Here,

We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.

We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

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Answer:

g=20

Step-by-step explanation:

3g−10+10=50+10

3g=60

3g / 3 = 60/3

g=20