O LINEAR EQUATIONS AND INEQUALITIES
Graphing a compound inequality o...
Graph the compound inequality on the number line.
x>-8 and x≤-3

The interest rate on the principal that yield an interest of $43.75, in 5 years is 3.5% per annum.

Simple interest is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data;

Plug the given values into the above formula and solve for interest rate r.

I = P × r × t

r = I / Pt

r = 43.75 / ( 250 × 5 )

r = 43.75 / 1250

r = 0.035

Rate = r × 100%

Rate = 0.035 × 100%

Rate = 3.5%

Therefore, the interest rate per annum is 3.5%.

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Answer:

1) 894

or

2) 43

Step-by-step explanation:

The way this question is worded is unclear.

1) If you mean 37.25x24, it's simple multiplication and the answer is 894.

2) If you mean 37 and 1/4 x 24, then the question becomes a multiplication problem in which you add 37 to the product.

43

Step-by-step explanation:

first we have to add 37 with 1/4×24 and the product of 1/4×24 is 6.then we have to add 6 with 37 and the final answer is 43.and sorry if it's wrong

The statement that illustrates symmetric property is that If angle A=angle B, then angle B=angle A.That is option D.

Symmetric property is defined as the property that shows that when one number is equal to another number, the other number should also be equal to the former number.

An angle is defined as that structure that is formed when two lines meet at a plane.

For example: Using the number 4 and 6, if 4 = 6 then 6 should also be = 4.

Therefore, the statement that illustrates symmetric property is that If angle A=angle B, then angle B=angle.

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The set {1, 3, 5, 9, 11, 13} with multiplication modulo 14 forms a group. Additionally, the set 〈nZ, +〉, where n is a positive integer, is also a group. Moreover, 〈nZ, +〉 is isomorphic (or equivalent) to the group 〈Z, +〉.

In the first case, to determine whether the set {1, 3, 5, 9, 11, 13} forms a group under multiplication modulo 14, we construct a table by multiplying each element with every other element modulo 14. If every product is in the set and satisfies the group properties (closure, associativity, identity element, and inverses), then it is a group. The table would look as follows:

| * | 1 | 3 | 5 | 9 | 11 | 13 |

|---|---|---|---|---|----|----|

| 1 | 1 | 3 | 5 | 9 | 11 | 13 |

| 3 | 3 | 9 | 1 | 13 | 5  | 11 |

| 5 | 5 | 1 | 11 | 3 | 13 | 9  |

| 9 | 9 | 13 | 3 | 5 | 1 | 11 |

| 11 | 11 | 5 | 13 | 1 | 9 | 3 |

| 13 | 13 | 11 | 9 | 11 | 3 | 1 |

As every element appears exactly once in each row and column, and the group properties hold, this set forms a group under multiplication modulo 14.

In the second case, we consider the set 〈nZ, +〉, where n is a positive integer. This set represents the multiples of n, i.e., n times any integer. To show that it is a group, we need to verify the group properties. Closure is satisfied since adding any two multiples of n gives another multiple of n. Associativity holds for addition. The identity element is 0 since adding 0 to any multiple of n yields the same multiple. Inverses exist for every element since adding the additive inverse of any multiple of n results in 0. Therefore, 〈nZ, +〉 is a group.

Furthermore, we can establish an isomorphism between 〈nZ, +〉 and 〈Z, +〉. An isomorphism is a mapping that preserves the group structure. In this case, we can define a function f: 〈Z, +〉 → 〈nZ, +〉 such that f(m) = nm. This function is a homomorphism, as f(m₁ + m₂) = nm₁ + nm₂ = n(m₁ + m₂), which satisfies the group operation. It is also bijective since every element in 〈nZ, +〉 can be mapped back to an element in 〈Z, +〉. Therefore, 〈nZ, +〉 is isomorphic to 〈Z, +〉, indicating their equivalence as groups.

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The graph of the given order pairs is attached below.

What is graph of a function?

In mathematics, the set of ordered pairs where f(x) = y exists is known as the graph of a function. These pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane in the typical case where x and f(x) are real numbers.

Given:

The table below shows the number of dog licenses issued in the town of Palmer over a 5-year period.

We have to plot the graph for the given order pairs.

The graph of the given order pairs is attached below.

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The corss-product of the two ratios is 159.03

You should know that two ratios are proportional if they are equal. Using cross-product to determine proportionality of two ratios entails multiplying the numerator of the firs with the denominator of the second ratio vice versa

The two ratios are

9.3 : 5.7 and  27.9 : 17.1

To know if they are proportional we express them as follows

9.3/5.7 = 27.9/17.1

= 9.3*17.1 = 27.9*5.3

⇒159.03 = 159.03

Therefore the two ratios are proportional

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The coordinates of the vertices of the new triangle are A'(8,-12), B'(-16,20), C'(-20,0). The area of the new triangle will be 4 times the original triangle.

The scale factor is defined as the ratio of the new image's size to the old image's size. The dilation center is a fixed point in the plane. The dilation transformation is defined based on the scale factor and the center of dilation. If the scale factor is greater than one, the image will stretch.

Given that ABC is a triangle. The vertices of the triangle are A(2,-3), B(-4,5), C(-5,0).

The triangle is dilated by a scale factor of 4.

To find the coordinate of the new triangle multiply 4 with x-coordiante and y-coordiante of the vertices of the triangle ABC.

The new coordinate of A is (2×4,-3×4) → A'(8,-12).

The new coordinate of B is (-4×4,5×4) → B'(-16,20).

The new coordinate of C is (-5×4,0×4) → B'(-20,0).

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The ratio of 20:19 for the number of floor seats and the number of balcony seats means that for each 20 floor seats in the theater, there are 19 balcony seats. Hence, the theater has more floor seats.

The ratio between two amounts a and b is calculated applying the proportion of these two amounts, that is, the division of a by b, as follows:

r = a : b.

The ratio is not commutative, meaning that the ratio between b and a is given as follows:

r = b : a.

(which is different of r = a : b).

The ratio for the number of floor seats to balcony seats in this problem is given as follows:

20:19.

(20 floor seats for each 19 balcony seats).

Hence there are more floor seats in the theater.

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The answer choice which represents a solution to the given equation as required to be determined is; x = -51

It follows from the task content that the solution to the given equation is to be determined.

Since the given equation is; 1/5 × ( x + 21 ) = -6

The equation above can be solved as follows;

Multiply both sides of the equation by 5 so that we have;

x + 21 = -6 × 5

x + 21 = -30

x = -30 - 21

x = -51.

On this note, the solution to the given equation is; x = -51.

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84percent of Senate incumbents win reelection in the United States.

In the United States, Senate incumbents have a high rate of re-election. This is due to a number of factors, such as name recognition, access to resources, and the advantages of incumbency. According to the Center for Responsive Politics, 84% of Senate incumbents have won re-election since 1982, with an average of 84.5% over that period. This figure is higher than the rate of re-election for House incumbents, which stands at around 90%. This indicates that while incumbency is an advantage in Senate races, it is not as strong as it is in House races.84% of Senate incumbents win reelection in the United States.

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The Approximate percent of senate incumbents that have win the reelection is (d) 84% .

In the united States Of America , The Incumbents  have a very high rate of Re-election because of various factors which are access to resources , the name recognition and advantage of incumbency .

So , by the Center of Responsive Politics , the 84% of  senate incumbents have won the reelection since the year 1982 where the average percent of win is 84.5% .

Whereas , the rate of reelection in the house of incumbents is 90% which is higher that the Senate Incumbents .

Therefore , approximately 84% of the senate incumbents win the re-election .

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Answer:

length = 20 meters

width = 66 meters

Step-by-step explanation:

P = perimeter. l = length. w=width

P = 2l + 2w  ==> perimeter formula

Consecutive integers have a difference of 2 ( 4 - 2 = 2 )

Hence, the width(w) in terms of length(l) is:

w = 3 * (l + 2)

w = 3l + 3*2  ==> distribute 3 to l and 2

w = 3l + 6  ==> simplify

P = 2l + 2(3l + 6) ==> substitute w=3l + 6 into the equation P = 2l + 2w

P = 2l + 2*3l + 2*6  ==> distribute 2 to 3l and 6

P = 2l + 6l + 12

P = 8l + 12

172 = 8l + 12  ==> substitute 172 for P since the perimeter is 172 meters

160 = 8l  ==> subtract 12 on both sides

l = 20 ==> divide both sides by 8

length = 20 meters

Now solve for the width:

w = 3(20) + 6  ==> substitute l=20 in w = 3l + 6

w = 60 + 6  ==> simplify

w = 66

width = 66 meters

The sum of the perimeters of the squares formed through geometric sequence is; 80 + 40√2.

We want to find the sum of the perimeters of the squares formed;

From the diagram attached, we see that;

In ∆PCQ;

<PCQ = 90°,

Then PQ² = PC² + QC²

Since, P and Q are mid - points of square ABCD, then it means that;

PC = BP = 5

QC = DQ = 5

Thus , PQ = √(25 + 25) =

PQ = √50 = 5√2

Since; E,F,G and H are mid-points of square PQRS, then it means that;

EP = PF = (5√2)/2

FQ = QG = (5√2)/2

Now , In ∆ FQG

∠FQG = 90°

Then ,FG²= FQ²+GQ²

FG² = 5

Similarly , The process the continued indefinitely .

Sum of the perimeters of the squares formed = perimeter of square ABCD+ Perimeter of square PQRS + Perimeter of square PQRS+....+∞

= (4 × 10) + (4 × 5√2) + (4 × 5) +......+∞

= 40 + 20√2 + 20 + ...... + ∞

In this Infinite geometric series, we see that;

First term; a = 40

Common ratio; r = (√2)/2

Sum of infinite GP is given by the formula;

Sₙ = a/(1 - r)

Thus;

Sₙ = 40/(1 - ((√2)/2)

This can be simplified by rationalizing the denominator to get 80 + 40√2.

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Therefore , the solution to the given problem of equation comes out to be there were 264 cans were initially stocked.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A statistical statement that shows the equality of two mathematical terms is known as an equation in algebra. For instance, the elements 6x + 6 and 12 are separated by an equal sign with in equations 6x + 6 = 12. The relationship between the two phrases on either side of either a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 4x – 4 = 0.

Here,

Given :

where c is total numbers of cans

=> c/2 + 68 = 200

=>  c + 136 = 400

=> c = 264

Therefore , the solution to the given problem of equation comes out to be there were 264 cans were initially stocked.

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The value of h(-3) given that h(x)=-x+5 is 8.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign. It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, h(x) =-x+5

There h(-3) will be gotten by substituting -3 into x. This will be:

h(x)=-x+5

h(-3) = -(-3) + 5

h(-3) = 3 + 5

h(-3) = 8

Therefore, the value is 8.

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a. y = 22,500x + 4,600,000

b. 5,050,000

y = mx + b

4,600,000 is our b intercept because it is the population we start out with (since 2010).

y = mx + 4,600,000

Half of 45,000, 22,500 acts as the rate per year (the m). This is because the problem had stated that South Carolina gained 45,000 people in 2 years.

This gives us: y = 22,500x + 4,600,000

For b, just input 20 years in the equation just made. The 20 is from the difference of 2030 and 2010.

y = 22,500(20)+4,600,000 Multiply 22,500 & 20

y = 450,000 + 4,600,000 Add 450,000 & 4,600,000

Then you get

y = 5,050,000

Answer:

8

Step-by-step explanation:

Since the smaller shape's side is 5, and on the bigger side its 10, that means you multiply 4 time 2.

There are several ways to prove that two triangles are similar, but the most common method is using the concept of corresponding angles and corresponding sides.

What is an example of congruence?

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.

If two triangles have corresponding angles congruent (equal in measure), and the ratios of their corresponding sides are equal, then the triangles are similar. This is known as the Angle-Angle (AA) Similarity criterion.

Another way is when two triangles have corresponding sides in proportion and no angles are congruent, then the triangles are similar, it is known as the Side-Side-Side (SSS) Similarity criterion.

Another way is when two triangles have a pair of corresponding angles congruent and their corresponding sides are in proportion, the triangles are similar. This is known as the Side-Angle-Side (SAS) Similarity criterion.

So, In order to prove that two triangles are similar, you have to show that either the angles are congruent and the sides are proportional using (AA), (SSS), (SAS) or (ASA) Similarity criteria.

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On the number line the point that is closest to pie is 3, between 3.1 and 3.2.

You should be aware that a number line is the representation of numbers on a straight line.  

The number line compares numbers that are placed on equal intervals on an infinite line that extends to both sides vertically and horrizontally.

On the number line, Zero (0) is considered to be the origin of a number line. The numbers to the left of 0 are negative numbers and the numbers to the right of 0 are all positive numbers.

In conclusion from the attached graph, the number that is closest to pie is 3

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Answer:

if u free can u come please...

Answer:

D

Step-by-step explanation:

It is Dilation because image b is bigger than image a

Answer:

180 inch.

Step-by-step explanation:

Multiply the length value by 36

5 yd = 180 in.

We know the relation between yards and inches:

1 yard = 36 inches

So, 5 yds = 5×36 inches

5 yds = 180 inches

Therefore, the answer is 5 yd = 180 in.

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Answer:

There is no variable.

Step-by-step explanation:

In math, a variable is a letter that represents a value. There are no letters in this equation, so there are no variables.

Answer:

Draw 6 black and leave 4 blank

Step-by-step explanation:

6+4=10

Answer: I feel like your too young to not to know this. Besides you say you are in college?

Step-by-step explanation:

Just put anything that sums up to 10. There are many I'll give you 2 examples: 7+3 or 5+5. You can use either one of those.

The reason and calculation on why why 81 ^ 3/4 equals 27 is given below.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

The reason and calculation on why why 81 ^ 3/4 equals 27 is;

= (4✓81)³

= 3³

= 3 × 3 × 3

= 27

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The complete statement is: The probability of A given B is not the same as the probability of A, so A and B are not independent events.

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

P(A) = 12%

P(B) = 3%

P(A|B)= 20%

P(B|A)= 25%

The expressions P(A|B) and P(B|A) are the conditional probabilities

This means that the probability of A given B is 20%

For independent events, we have

P(A) = P(A|B)

From the question, we have

P(A) = 12%

P(A|B)= 20%

They are not equal

Hence, the events are not independent events

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1) The conditional probabilities of the two events are:

P (A|B) = 0.2; and P(B|A) = 0.25.

2) Note that A and B are independent events.

3) The probability of A given B is not the same as the probability of A, so A and B are note independent events.

The possibility of an event or consequence occurring dependent on the occurrence of a preceding event or outcome is described as conditional probability. Conditional probability is derived by multiplying the preceding event's probability by the updated likelihood of the next, or conditional, occurrence.

The expression for conditional probability is given as:

P (A|B) = P(A and B)/(P(B)

P (B|A) = P(A and B)/(P(A)

Note that the events A and B are independent if:

P (A|B) = P(A) or P(B|A) = P(B)

Since

P (A) = 12% = 0.12

P (B) = 15% = 0.15

P (A and B) = 3% = 0.03

i) P (A|B) = P(A and B)/(P(B)

P (A|B)  = 0.03/0.15

P (A|B)  = 0.2

ii) P (B|A) = P(A and B)/(P(A)

P (B|A) = 0.03/0.12

P (B|A)  = 0.25

From the above, we can see that  P (A|B) ≠ P (B|A). Hence, it is correct to state that; "the probability of A given B is not the same as the probability of A, so A and B are not independent.  

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Answer:

6n+2.5

Step-by-step explanation:

Right of the bat you would combine like terms

2n + 1.75n + 2.25n +2.5

= (2n+1.75n+2.25n) + (2.5)

Once you add up the numbers with the variable next to it your final answer should be ---> 6n+2.5

*The reason why we can't add these is because the 6 has an (n) next to it and 2.5 is a decimal number (in other words they are NOT like terms)

Hope this helps!

Answer:

185 teenagers

Step-by-step explanation:

0.05 x 3700 = 185

Answer:

x = [tex]\frac{9}{2a}[/tex]

Step-by-step explanation:

ax + [tex]\frac{3}{2}[/tex] = 6 ( multiply through by 2 to clear the fraction )

2ax + 3 = 12 ( subtract 3 from both sides )

2ax = 9 ( isolate x by dividing both sides by 2a )

x = [tex]\frac{9}{2a}[/tex]

Factor 2 is 4x greater, Factor 3 is 9x greater and Factor 5 is 25x greater and  the pattern in part A is Factor square.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

A₁= 2πrh

If multiply both dimensions by a factor of 2:

A₂= 8πrh

Comparing A₁ to A₂ :

A₁/A₂=4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

A₃=18πrh

Comparing areas:

A₃/A₁=9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

A₅=50πrh

Comparing A₅ to A₁

A₅/A₁=25

The new area is 25 times greater.

We can notice the increase in area is factor².

For example, when multiplied by a factor of 3, the new area is 9 times greater.

Hence, Factor 2 is 4x greater, Factor 3 is 9x greater and Factor 5 is 25x greater and  the pattern in part A is Factor square.

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There is one long cable that extends from the centre of each neuron in your brain.

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