Find the 52nd term of the arithmetic sequence -24, -7, 10, ...

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

x      y

0     0

3      2

6      4

9      6

The variable 'y' is directly proportional to the variable 'x'. Then we have

y ∝ x

y = k x

At (9, 6), the value of the constant 'k' is given as,

6 = 9k

k = 6 / 9

k = 2/3

The proportionality is given as,

y = (2/3) x

The constant of proportionality in the box to match the table will be 2/3. Then the last option is correct.

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The number of years it will take the national debt of Bovinia to exceed -- that is, be greater than -- the national debt of Porcini is x > 8.75 years

let

Number of years = x

Bovinia:

2 + 0.65x

Porcini:

5.5 + 0.25x

Number of years national debt of Bovinia exceed the national debt of Porcini;

2 + 0.65x > 5.5 + 0.25x

0.65x - 0.25x > 5.5 - 2

0.4x > 3.5

divide both sides by 0.4

x > 3.5/0.4

x > 8.75

In conclusion, the number of years it will take Bovinia debt to exceed Porcini debt is x > 8.75 years.

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Answer:

4 and 16

Step-by-step explanation:

difference betwen 22 and 10 is 12 divide that by two and get 6 then add 6 to 10 to get 16 and subtract 6 from 10 to get 4

The speed of the larger pulley is 20 radian

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

The speed of two connected pulleys given their diameters is given as:

d₁n₁ = d₂n₂

Where d₁, d₂ are their diameters and n₁, n₂ are their speeds

A belt connects a pulley of 2-inch radius with a pulley of 5-inch radius. If the smaller pulley turns through 50 radians, hence:

d₁ = 2 in, n₁ = 50 rad, d₂ = 5 in:

d₁n₁ = d₂n₂

2(50) = 5(n₂)

n₂ = 20 rads

The larger pulley turn with 20 radian

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The number of movie tickets Mai can buy is 8 movie tickets.

Amount Mai will spend on movie ticket = $36

cost of each movie ticket = $4.50

Division equation:

Number of tickets Mai can buy = Amount Mai will spend on movie ticket / cost of each movie ticket

= $36 / $4.50

= 8 tickets

Multiplication equation:

Amount Mai will spend on movie ticket = Number of tickets Mai can buy × cost of each movie ticket

= 8 × 4.50

= $36

Hence, Mai can buy 8 movie tickets

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An inequality that represents elevations (p) below -8 meters is p < -8.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Let the variable p represent the elevation of a passage in meters. Therefore, translating the word problem into an inequality, we have the following:

p < -8.

In conclusion, the elevation of a passage (p) in meters is less than negative eight (-8) meters.

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Complete Question:

Let p be the elevation of a passage in meters. Write an inequality that represents elevations below -8 meters

1,072 feet for Tower A and 326 feet for Tower B.

Height is a measurement of distance from the base of an object to its highest point. It is usually measured in feet and inches (Imperial system) or in meters and centimeters (Metric system). Height is an important factor in many scientific, medical and engineering applications. For example, height is used to calculate the weight and body mass index of a person, to determine the capacity of a container, and to measure the size of a room. Height also plays a role in determining one's social standing, as taller people tend to be seen as more attractive and powerful.

Tower A's height is 1,072 feet and Tower B's height is 326 feet. To solve this problem, the equation 746 + B = 1818 was used, where B is the height of Tower B. Solving the equation yielded a value of 1,072 feet for Tower A and 326 feet for Tower B.

The height of Tower A being more than Tower B can be explained by their respective purposes. Tower A likely serves a higher purpose than Tower B, such as providing a view or providing a broadcasting signal, and therefore requires more height. Tower B, on the other hand, might be used for a less demanding purpose, such as providing a cellular signal, and thus requires less height.

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The height (in inches) of a visitor able to ride is h ≥ 52.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

A visitor must be taller than 52 inches.

let h be the height (in inches) of a visitor able to ride.

So, h must be greater than or equal to 52.

Then, the mathematical expression as

h ≥ 52.

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Looks like you're not in a test.  :) I can answer your question!

So of course you probably know that anything lower than 0 is a negative number.  So the variable (or unknown number in this case) is "k".  K is less than or equal to -1.  So, -2, -3, -4, -5, -6, and so on, would all fit this inequality.

Hope that helps!  I don't want to give you the answer directly, but hope this helps you solve it.. If it doesn't, just go ahead and click "see solution" or "show example".  ;)

Answer:

p=8

Step-by-step explanation:

-132 = 12p -36

0 = 12p + 96

12p = 96

p = 8

The graph for the inequality -12x-4y<5 is option C.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

The given inequality expression is -12x-4y<5.

First plot the graph for 12x-4y=5.

The expression has a < symbol which means the graph will have dotted lines.

Now, check does the origin (0,0) satisfy -12x-4y<5.

Substituting the values of x and y -

-12(0) - 4(0) < 5

0 - 0 < 5

0 < 5

Since, the condition is satisfied the region including the origin (0,0) is shaded.

Therefore, the graph is plotted for the expression.

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The line segment with new endpoints would be (-2, 0) and (3.4, 0).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

Given that the line segment with endpoints (0,0) and (5.4) units

To translate a line segment to the left by 2 units, we subtract 2 from the x-coordinate of each endpoint.

So the new endpoints would be :

(0-2, 0) = (-2, 0)

(5.4-2) = (3.4, 0).

Thus, the new endpoints would be (-2, 0) and (3.4, 0).

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The average speed of the athlete is 225 m/s.

Given is that an athlete runs 400m to the East and then 500m to the West. If the total time of his trip was 4 minutes.

We can write the average speed as -

{s} = (400 + 500)/4 = 900/4 = 225 m/s

Therefore, the average speed of the athlete is 225 m/s.

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{An athlete runs 400 m to the East and then 500 m to the West. If the total time of his trip was 4 minutes, consider the direction to the East as positive, calculate his average speed in m/s.}

The prove that triangle ABC is congruent to triangle CDA as shown is done using the SSS congruence theorem.

The given figure is a square hence all the sides are equal as rightly given.

Considering that the figure is a square means that

AB = BC = CD = DA

Using the reflexive property theorem  side AC is shared by the two triangles. Because of this the 3 sides of the triangle are equal to t=each other

This completes the side side side sss congruence theorem

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Answer:

18m-20

Step-by-step explanation:

4(3m-2)+3(2m-4)=

12m-8+6m-12=

collect like terms

12m+6m-8-12=

18m-20

Answer:

Step-by-step explanation:

5 (days) x 2 (people) = 10

Total must add to 10

3(Mary)+4(Ana)=7

10-7=3

therefore Nata works 3 days

The area of a circle is found by using the formula A = πr2, where r is the radius.

Area is a measure of the two-dimensional size of a shape or surface. It is commonly measured in square units, such as square meters or square feet. To calculate the area of a shape, you need to know the length and width of the shape. Area can also refer to the amount of space within a three-dimensional shape, such as a cube or sphere. In this case, the area is measured in cubic units, such as cubic meters or cubic feet.

This means that the area of a circle with a radius of 6 yards is A = π(6)2 = 113.04 yd2. Therefore, the area of the circle with a radius of 6 yards is 113.04 yd2.

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After 4 weeks they will have studied the same number of hours.

What is algebra?

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

Here, we have

Given: Maria and Curtis both study a second language. Maria studies German 3 hours per week, and Curtis studies French 2 hours per week. Curtis has already studied 4 hours when Maria begins her studying.

We have to find out how many weeks will they have studied the same number of hours.

Suppose x weeks they will have studied the same number of hours.

Then,

4 + 2x = 3x

x = 4

Hence,  after 4 weeks they will have studied the same number of hours.

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The x and the y values of the equation are x = 3 and y = 1

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

y= -2/3x + 3 and y= 2x - 5

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

-2/3x + 3 = 2x - 5

Evaluate the like terms

8/3x = 8

so, we have

x = 3

Also, we have

y = -2/3x + 3

This gives

y = -2/3 * 3 + 3

Evaluate

y = 1

Hence, the solution is x  3 and y = 1

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Answer:

True

Step-by-step explanation:

Slope:

The slope of an equation represents how the y value changes as the x values changes, defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex], so the slope of 60 can be represented as: [tex]\frac{60}{1}[/tex], which tells us the amount of water (y-axis) increases by 60 units each hour (x-axis), or in other words, the rate at which the amount of water changes each hour.

The best definition of a sample is a part of the population that represents the entire population.

Option B is the correct answer.

It is a small part of a larger group to determine some attributes of the large group.

We have,

The entire population of the group.

This is not a sample.

A part of the population that represents the entire population.

This is a sample.

The difference between the maximum and minimum values observed.

This is range.

A measure of how much the values within a population vary.

This is variance.

Thus,

A part of the population that represents the entire population is a sample.

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Here we must see in which way we would save more money, we will see that the better option is the online store.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Online store:

Here we have a $20.00 off coupon that can be used. The price of the item is $75, and there is a flat rate of $8.99

Then the total price is:

$75 + $8.99 - $20 = $63.99

Physical store:

The price of the object is the same, $75, but here we have a sales tax of 7.5% and a coupon for 20% off.

Then the total price is:

$75*(1 - 0.2)*(1 + 0.075)

Where

(1 - 0.2) represents the discount of 20%

(1 + 0.075) represents the tax of 7.5%

Notice that these are the percentages in decimal form, you just need to divide them by 100%.

So the price in the physical store is:

$75*(1 - 0.2)*(1 + 0.075) = $64.5

Comparing the prices, you can see that the online store is the cheaper option.

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The length of side x expressed in the simplest radical form with a radical denominator is √36 / √1

The value of length x is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

Information from the question

The direction of movements describes a right angle triangle of

opposite = x

adjacent = √12

The value of x is solved using tan, TOA

tan 60 = Opposite / Adjacent

tan 60 = x / √12

x = √12 tan 60

x = √12 * √3

x = √36

x = 6

the value of x = 6/1 = 6

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Answer:

Try It 1

Option C: 14

Try It 2
Option B: 6

Step-by-step explanation:

Definition GCF

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder

Try It 1:
GCF of 14 and 28 is 14

This is the largest number that can divide both 14 and 28 evenly

So, Option C

Try It 2:

This problem is nothing but asking to find the GCF of 12, 24 and 30

The smallest number is 12

But 30 cannot be divided evenly by 12

Take 12/2 = 6

Yes, all 3 numbers can be divided evenly by 6

So the correct answer is 6 packs and is Option B

The usual approach to solving bigger problems of this type is to find the factors of each of the numbers and then proceed to find the number which is common to all and the highest value is taken which divides each number evenly

For 12, 24, 30:

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

As you can see 6 is common to all three numbers; so it is the GCF of 12, 24 and 30

Answer:

612

Step-by-step explanation:

567 + ((543 / 543) * 45)

= 612

With the use of the percentage concept, it is found that:

a. 18.54% of the survey respondents do not like both hamburgers and burritos. (b). The marginal relative frequency of all customers that like hamburgers is of 0.6049. (c.) The data that has the strongest association of its two factors is liking hamburgers and not liking burritos.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

p=a/b * 100%

Item a:

Out of 205 people, 38 like neither, hence:

This implies that 38/205 * 100 = 18.54%

18.54% of the survey respondents do not like both hamburgers and burritos.

Item b:

The relative frequency is the percentage as a decimal, hence a divided by b.

Out of the 205 participants, 205 - 81 = 124 like hamburgers, hence:

124/205 * 100 = 0.6049

The marginal relative frequency of all customers that like hamburgers is of 0.6049.

Item c:

The table is, considering the totals:

49 - 43

75 - 38

Due to the higher total, the data that has the strongest association of its two factors is liking hamburgers and not liking burritos.

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An inequality which models the scenario correctly is 4x + 7y ≤ 55.

In order to write an inequality that represents or models this scenario, we would assign variables to the number of green bows and number of yellow bows respectively, and then translate the word problem into algebraic equation as follows:

Since Inda is purchasing hair bows, and she has a total of $55 to spend with Green bows costing $4 each, and yellow bows costing $7 each, an inequality that represents this situation can be written as follows;

4x + 7y ≤ 55.

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GCF of 22 and 32:

=

2 .

They are not alike in anyway

The correct order of the steps is CEABD ⇒ B

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

Let us arrange the figures:-

To construct a bisector of an angle

First: Draw angle AOB

The first step is figure C

Second: Place the pin of the compass on point O and draw an arc that intersects the two sides of the angle OA and OB at points D and E

The second step is figure E

Third: Place the compass on point D and draw an arc in the interior of the angle

The third step is figure A

Fourth: without change, the opening of the compass places its pin on point E and draws an arc that intersects the arc drawn from point D at point C

The fourth step is figure B

Fifth: Draw a line from point A to point C, this line AC is the bisector of angle AOB

The image is attached with the answer below.

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