Please help!!!!!!!!!!

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Answer: my brother did it and it's 1 cup

Step-by-step explanation:

Answer:

1 cup

Step-by-step explanation:

ive done this test in class if you need further explionation let me know

Answer:

Step-by-step explanation:

Given expressions are,

\(p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}}\) and \(q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\)

Remove the radicals from the denominator from both the expressions.

\(p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}} \times \frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}-\sqrt{5}}\)

  \(=\frac{(\sqrt{10}-\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}\)

  \(=\frac{(\sqrt{10}-\sqrt{5})^2}{5}\)

\(\sqrt{p}=\sqrt{\frac{(\sqrt{10}-\sqrt{5})^2}{5}}\)

      \(=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{5}}\)

\(q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\)

  \(=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\times \frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}+\sqrt{5}}\)

  \(=\frac{(\sqrt{10}+\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}\)

  \(=\frac{(\sqrt{10}+\sqrt{5})^2}{5}\)

\(\sqrt{q}=\sqrt{\frac{(\sqrt{10}+\sqrt{5})^2}{5}}\)

     \(=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}\)

\(\sqrt{q}-\sqrt{p}-2\sqrt{pq}=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}-\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}}-2(\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}})(\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}})\)

                           \(=\frac{1}{\sqrt{5}}(\sqrt{10}+\sqrt{5}-\sqrt{10}+\sqrt{5})-\frac{2}{5}[(\sqrt{10})^2-(\sqrt{5})^2)]\)

                           \(=\frac{1}{\sqrt{5}}(2\sqrt{5})-\frac{2}{5}(10-5)\)

                           \(=2-2\)

                           \(=0\)

Answer:

Hi,

Step-by-step explanation:

Using Al'Kashi theorem (law of cosines),

x²=26²+19²-2*26*19*cos(31°)

x²= 190,11870690...

So

\(x=\sqrt{190.11870690} =13,7883540...\approx{13.8}\)

I hope that this is not a control.

The value of x is 11.6

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Let the two sides be given as a is 26

The other side is b which is 19.

The angle is given by C which is 31 degrees.

The law of cosines is

c²=a²+b²-2abcosC

The c is taken as x

x²=26²+19²-2(26)(19)cos31

x²=676+361-988(0.914)

x²= 676+361-903.032

x²=133.968

Take square root on both sides

x=11.57

Hence, the value of x is 11.6

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The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = \(πr^2\), where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = \(πr^2\)

A ≈ 3.14 × \((2^2)\)

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Answer:

75

Step-by-step explanation:

78+64+74+92+67 = 375

375 / 5 = 75

Answer:

w

Step-by-step explanation:

because the order says

ABCD

WXYZ

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.

There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.

One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.

A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.

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The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Answer:

approx 20% of the department faculty have 20 or more years of service

Step-by-step explanation:

To find the percentage of the department faculty with 20 or more years of service, we need to add up the number of faculty members in the "20-24.9" and "25 or more" year categories, since anyone with 20 or more years of service would fall into one of these categories.

Looking at the histogram, we see that there are 24 faculty members in the "20-24.9" year category, and an additional 4 in the "25 or more" year category. Therefore, the total number of faculty members with 20 or more years of service is 24 + 4 = 28.

To calculate the percentage of faculty members with 20 or more years of service, we need to divide this number by the total number of faculty members in the department, which we can find by adding up the heights of all the bars in the histogram. Based on the heights of the bars in the histogram, we can estimate that the total number of faculty members is approximately 140.

Therefore, the percentage of faculty members with 20 or more years of service is:

(28/140) x 100% = 20%

So, approximately 20% of the department faculty have 20 or more years of service.

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

We have,

The actual dimensions of the island are 3 1/2 feet by 1 3/4 feet.

We need to find the dimensions of the island on the blueprint, given that the scale of the blueprint is 1 inch = 2 feet.

To convert the actual dimensions to the dimensions on the blueprint, we need to use the scale factor of 1 inch = 2 feet.

We can set up a proportion to relate the actual dimensions to the dimensions on the blueprint:

Actual dimension/blueprint dimension = scale factor

Let x be the length of the island on the blueprint.

Then we can set up the following proportion:

3.5 feet / (1.75 feet)

= x inches / 7 inches

Simplifying,

2 = x / 7

Multiplying both sides by 7, we get:

x = 14 inches

The length of the island on the blueprint is 14 inches.

Similarly, we can find the width of the island on the blueprint:

1.75 feet / 3.5 feet

= y inches / 7 inches

Simplifying, we have:

0.5 = y / 7

Multiplying both sides by 7, we get:

y = 3.5 inches

The width of the island on the blueprint is 3.5 inches.

Thus,

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

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Answer:

56

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Answer:

Here is the answer I hope it helps you :))

Step-by-step explanation:

>>>>>> 11 <<<<<<

___________________________________________________________

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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Answer:

There's no underlined digit

Answer:

See below

Step-by-step explanation:

3 is in the 10 000 place    = 30 000

   ( just put zeroes in place of all of the following numbers)

a. The sum of 1/3+1/5= 8/15

b. The sum of 1/8+2/6 = 3/8

c. the sum of 8/9+11/12= 1 87/108

d. the sum of 1/7+5/8= 1 7/36

e. the sum of 1/4+2/4= 3/4

f. the sum of 1/2+3/9= 5/6

g. the sum of 1/10+1/4= 7/20

h. the sum of 3/11+11/12 = 1 25/132

Sum of fractions is the addition of fractions. This is obtained by by using the L.C.M of the denominator method.

a. 1/3 + 1/5 = (5+3)/15 = 8/15

b. 1/8+2/6 = (3+6)/24 = 9/24 = 3/8

c. 8/9 + 11/12 = (96+99)/108 = 195/108 = 1 87/108

d. 1/7+ 5/8 = (8+35)/56 = 43/36 = 1 7/36

e. 1/4+ 2/4 = (2+1)/4 = 3/4

f. 1/2 + 3/9 = (9+6)/18 = 15/18 = 5/6

g. 1/10+1/4 = (2+5)/20 = 7/20

h. 3/11+ 11/12 = (36+121)/132 = 157/132 = 1 25/132

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Answer:

I thing they both are........

Answer:

larger #=32

smaller #= 26

Step-by-step explanation:

We can solve this by using x for the larger number.

larger #= x

smaller #= x-6

x+x-6=58

2x-6=58

2x=64

x=32

The larger number is 32. To find the smaller # you simply substitute the variable x-6 which is now 32-6 which is 26.

Hope this helps!

Answer:

smaller number = 26

larger number = 32

Step-by-step explanation:

x = smaller number

y= larger number =x+6

so

x+y=58

x+6+x= 2x+6=x58

2x=58-6=52

x=522= 26

y=x+6=26+6 = 32

checking

x+y=58

26+32= 58

The monthly payment on the loan is $442.88 and the total interest on the loan is  $1,405.68.

we need to calculate the monthly interest rate. Since the annual interest rate is 5%, we can divide by 12 to get the monthly interest rate:

r = 0.05 / 12 = 0.00417

Next, we need to calculate the total number of payments over the three-year period.

Since there are 12 months in a year, the total number of payments is:

n = 3× 12 = 36

Now we can plug in the values into the loan payment formula:

P = (15000 × 0.00417×(1 + 0.00417)³⁶) / ((1 + 0.00417)³⁶ - 1)

= $442.88

To calculate the total interest on the loan

we can multiply the monthly payment by the total number of payments and subtract the principal amount:

Total interest = (monthly payment × total number of payments) - principal amount

Total interest = ($442.88 × 36) - $15,000

= $1,405.68

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.

What are functions ?

In mathematics, a function is a rule that maps each element in a set (the domain) to a unique element in another set (the range). It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are commonly represented using function notation, where the symbol "f" is used to represent the function, and the input value is placed inside parentheses. For example, if the function takes the input "x" and returns the output "y"

According to the question:
To prove algebraically that g(x) = f(x), we need to show that the expressions for g(x) and f(x) are equivalent for all values of x. That is, we need to show that:

2x²+3x-1 = x²-3

We can start by simplifying both sides of the equation:

2x²+3x-1 - (x²-3) = 0

Simplifying the left side, we get:

2x²+3x-1 - x²+3 = x²+3x+2

Now we can simplify the right side:

x²+3x+2 = (x+1)(x+2)

Substituting this expression back into the equation, we get:

2x²+3x-1 - x²+3 = (x+1)(x+2)

Simplifying the left side again, we get:

x²+3x-4 = (x+1)(x-4)

Now we have:

(x+1)(x-4) = (x+1)(x+2)

We can cancel out the factor of (x+1) from both sides, since it is not equal to zero for any value of x:

x-4 = x+2

Subtracting x from both sides, we get:

-4 = 2

This is a contradiction, so our original assumption that g(x) = f(x) must be false. Therefore, the solution is not true algebraically.

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Answer:

Sequence is arithmetic

Common difference = 4

Step-by-step explanation:

All arithmetic sequences have a common difference, so if you can determine a common difference in a given sequence, then the sequence is likely to be arithmetic. To find the common difference, subtract a value from its preceding value, and repeat this step to ensure the difference between all values is the same:

5 - 1 = 9 - 5 = 13 - 9

4 = 4 = 4

The common difference = 4, and because there is a common difference, this sequence is arithmetic.