If 6 times the 6th term of an A.P., is equal to 9 times the 9th term, find its 15th term

As the firm develops a specific sort of sensor and ships them in boxes of four, each sensor weighed 10 grams at first.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

Let's call the original weight of each sensor "w". The total weight of 4 sensors would be 4w.

With the new design, each sensor weighs 9 grams more, so each sensor weighs w + 9 grams. The total weight of 4 sensors is 76 grams, so we can write an equation:

4(w + 9) = 76

Expanding the left-hand side and solving for w, we have:

4w + 36 = 76

4w = 40

w = 10

So each sensor originally weighed 10 grams as company manufactures a special type of sensor, and packs them in boxes of 4 for shipment.

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The probability that the student chooses both math and Spanish is 0.5.  

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that professor is deciding which classes to teach in the fall.

The chooses math 341 with probability 3/7 and math 340 with probability 1/4 and neither class with probability 1/2.

P(M) = 3/7

P(S) = 1/4

P (M' ∩ S') = 1/2

According to De-Morgans law

P (M ∩ S) = P(M) + P(S) - P (M' ∩ S')

P (M ∩ S) =1/2

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Answer:

3.75

Step-by-step explanation:

Answer:

3.75

Step-by-step explanation:

Let's call the number of players on Team A as "A" and the number of players on Team B as "B".

We know that 1/5 of the players on Team A score a goal, so:

5 players / (1/5) = A players

5 * (1/5) = A

A = 25

We also know that 1/11 of the players on Team B score a goal, so:

2 players / (1/11) = B players

2 * (1/11) = B

B = 22

So there are 25 players on Team A and 22 players on Team B.

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A graph of the linear function with its points is shown in the image attached below.

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = 0, the linear function is given by;

y - x = 4

y = x + 4

y = 0 + 4

y = 4

(x, y) = (0, 4).

When the value of x = 1, the linear function is given by;

y = x + 4

y = 1 + 4

y = 5

(x, y) = (1, 5).

When the value of x = 2, the linear function is given by;

y = x + 4

y = 2 + 4

y = 6

(x, y) = (2, 6).

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For the given nonlinear equation for population growth ax where a>0,  a0 the equation exhibits exact compensation  whereas b) it has a non-trivial steady state.

The equation describes a population that grows at a rate that is proportional to its size. Specifically, the equation states that the population growth rate is equal to the product of a constant multiplier, a, and the size of the population, x. This means that when the population size increases, the rate of growth increases in proportion, causing the population to grow at a steady rate. the equation expresses a population growth rate that is proportional to the population size.

This means that when the population size is large enough, any further increases in the population size will be met with an equal increase in the population growth rate. This causes the population growth rate to remain constant, which is the definition of a non-trivial steady state

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Answer:

5 1/20

Step-by-step explanation:

5.05 = 5 + 0.05 = 5 + 1/20 = 5 1/20

Answer: 5 1/20

Step-by-step explanation:

Split it into 2 parts:

5+0.05

0.05=5/100

Simplify:

1/20

Overall, the answer is 5 1/20

Brainliest please! I would apperciate it.

Check the picture below.

[tex]\sin(35^o )=\cfrac{\stackrel{opposite}{ST}}{\underset{hypotenuse}{34}}\implies 34\sin(35^o)=ST[/tex]

Answer:

Step-by-step explanation:

bc=12.605

The horizontal distance between the base of the ladder and the wall is  8.9 feet.

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

If we draw a right triangle with the ladder being the hypotenuse, the angle between the ladder and the ground is given as 69 degrees.

We can use trigonometric functions to solve for the horizontal distance between the base of the ladder and the wall.

Let x be the horizontal distance between the base of the ladder and the wall.

cos(69°) = x/26

Solving for x, we get:

x = 26 cos(69°)

Using a calculator, we find that cos(69°) ≈ 0.342, so:

x ≈ 26 × 0.342 ≈ 8.892

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.9 feet.

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As per unitary method, the amount it will cost to fill the pool is $2.68

The Unitary Method is a mathematical concept which encourages students to use one single rule or principle to solve a problem. It can be used to solve a variety of mathematical problems in algebra, geometry, and other areas.

In this case, the pool is 10 ft wide. To calculate the capacity of a pool with a rectangular shape, you need to multiply its width by its length and then multiply that result by its depth.

If we assume that the length and depth of the pool are both equal to 10 ft, then the capacity of the pool can be calculated as follows:

=> 10 ft x 10 ft x 10 ft = 1,000 cubic feet.

To convert the capacity to gallons, you need to divide

=> 1,000  / 7.48 = 133.89

gallons of water required to fill the pool.

Finally, to calculate the cost of filling the pool, you just need to multiply the number of gallons by the cost per gallon of water ($0.02).

=> 133.89 x 0.02 = 2.68

This gives us a total cost of $2.68 to fill the pool with water.

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A day on the moon (from sunrise to sunrise) is approximately 29.5 Earth days or about 23 hours and 56 minutes.

A day on the moon, known as a "lunar day," lasts approximately 29.5 Earth days.

This means that it takes 29.5 Earth days for the moon to rotate once on its axis and complete one full rotation.

This is due to the fact that the moon rotates very slowly and takes a long time to complete one full rotation. It is also worth noting that a lunar day is also referred to as a "synodic month" and that a lunar day is longer than a solar day,

which is the time it takes for the sun to return to its highest point in the sky. The length of a solar day on the moon is about 23 hours and 56 minutes.

Thus, a day on moon  (i.e., from sunrise to sunrise) is 3 hours and 56 minutes.

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Based on the U.S. Dollars to British Pounds exchange rate, when John changes these dollar notes to pounds, the amount he will get in total is £186.05.

The exchange rate is the unit rate at which two or more currencies are exchanged or transacted.

The exchange rate is the ratio that shows the value of one country's currency compared to another country's currency.

Notes    $50    $20     $10     $5      Total

Number     1         7         3       4

Total     $50    $140   $30   $20     $240

The exchange rate from British Pounds to U.S. Dollars is given as £1 = $1. 29.

Therefore, $240 = £186.05 ($240/$1.29)

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Answer:

21

Step-by-step explanation:

Using unit value, Kelly earned a total of $87.55 this week.

In most cases, the unit value is obtained by dividing the cost or value of a group of objects by the total number of items.

The appraisal of a single item or component within a group is known as unit value. The concept of unit value is applicable in a variety of contexts, including building, inventory control, sales, and stock trading. The unit value is typically the result of dividing the price or worth of a set of things by the total number of items.

Kelly delivered three packages on Monday, five on Wednesday, and nine on Saturday in light of this.

There have been 17 shipments delivered in all.

Additionally, she earns $5.15 for every shipment she delivers.

Kelly made a total of $5.15 × 17.

= $87.55

Kelly consequently made $87.55 in total for the week.

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You would need a sample size of 384 in order to create a population proportion with a margin of error of no more than 0.025 and a 95% confidence interval.

In order to calculate the sample size needed for a 95% confidence interval with a margin of error of no more than 0.025, the formula to use is the following:

[tex]n = (z-score)^2 * p * (1-p) / (margin of error)^2[/tex]

Where n = sample size, z-score = 1.96 (for 95% confidence interval), p = 0.5 (the expected population proportion) and margin of error = 0.025.

Substituting these values into the equation, we get:

[tex]n = (1.96)^2 * 0.5 * (1 - 0.5) / (0.025)^2\\n = 384[/tex]

Therefore, you would need a sample size of 384 in order to create a population proportion with a margin of error of no more than 0.025 and a 95 %  confidence interval.

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Therefore , the solution of the given problem of quadrilateral comes out to be x value is  8.13 .

A rectangle is a four-sided, four-cornered object in mathematics. Either the Latin quartet or creative portfolio are the terms' sources (meaning "side"). Four states, corners, and provincial assemblies make up the three divisions of a rectangle. Convex and curved surfaces can be broadly divided into two categories. Convex quadrilaterals also include parallelograms, triangles, rhombuses, rectangles, and trapezoids as subcategories.

Here,

Given :

=> 11x + 4 , 18x - 2 and 114 degree ,

Let m∠B is x:

So ,

According to angle sum property :

=> 11x + 4 + 18x - 2 + 114 + x = 360

=> 116 + 30x = 360

=> 30x = 360 - 116

=> 30x = 244

=> x = 244/30

=> x = 8.13

Therefore , the solution of the given problem of quadrilateral comes out to be x value is  8.13 .

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The answer is 25. 25 is the heaviest possible weight for pack i.e. for d among pack of a, b, c, and d.

let (a, b, c, d) be the packs sorted from lightest to heaviest.

The following four equations must hold:

a + b = 34

a + c = 37

b + d = 43

c + d = 46

we then have a pair of equations which can be satisfied in two ways:

b + c = 39 and a + d = 41

or

b + c= 41 and a + d = 39

Solving the first set of 6 equations gets:

(a, b, c, d) = (16, 18, 21, 25)

Solving the second set gets:

(a, b, c, d) = (15, 19, 22, 24)

Therefore, 25 is the heaviest possible weight for pack d.

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Step-by-step explanation:

Probability works in fractions. The first part says a cube was tossed 60 times. That confirms that 60 is the denominator. So let's start that fraction.

[tex] \frac{x}{60} [/tex]

Next, what numbers are less than 4? 1, 2, and 3. So let's add the results of 1, 2, and 3

1 was 12

2 was 13

3 was 11

12 + 13 + 11 = 36. 36 is our other number, making the answer

[tex] \frac{36}{60} = 36 \: over \: 60[/tex]

Answer:

The result of 8 minus 3 is 5. Then, if you subtract u from 5, the result is 5 - u.

Answer: 5-u

Step-by-step explanation: Subtracting 3 from 8 is 5. Subtracting u from the result is 5-u.

The answer is True. Finding a parametric description of the solution set of a linear system is the same as solving the system.

Finding a parametric description of the solution set of a linear system is equivalent to solving the system. A parametric description of the solution set of a linear system is a way of representing all solutions to the system in terms of a set of parameters. Solving a linear system involves finding the specific values of the variables that satisfy the constraints specified by the system. By finding a parametric description of the solution set, we are effectively solving the system and finding all possible solutions. In this sense, finding a parametric description of the solution set and solving the system are equivalent.

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Answer: 3.65

Step-by-step explanation:

j=20

Substitute: 20-16.35

20.00-16.35=

3.65

Answer:

3.65

Step-by-step explanation:

Looking at the equation j - 16.35, if we substitute j for 20, the new equation will look like this:

Therefore, the value of the expression is 3.65 if we were to substitute j for 20.

The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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By the figure of a circle, 70% of the figure is shaded.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A circle divided into ten equal parts. Seven of the parts are shaded.

Now, Number of total parts = 10

And, Shaded parts of a circle = 7

Hence, The percent of shaded part is,

⇒ Shaded part / Total parts × 100

⇒ 7/10 × 100

⇒ 70%

Thus, There are 70% of the figure is shaded.

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Answer:

x = -4, y = 7

Step-by-step explanation:

The two equations are:

5x + y = -13  ... (1)

-5x - 6y = -22 ...(2)

Isolate for x in (1)

5x + y = -13

5x = -13 -y

x = (-13-y)/5

Substitute this value of x into equation (1) -5x - 6y = -22

-5 · (-13-y)/5 -6y = -22

-1(-13-y) - 6y = -22

13 + y -6y = -22

y - 6y = -22 - 13

-5y = - 35

y = -35/-5 = 7

Substitute y = 7 in equation 1
5x + 7 = -13

5x = -13 - 7

5x = -20

x = 20/-5 = -4

Ans:

x = -4, y = 7

Answer:

Step-by-step explanation:

Cos0 = adj/hyp

cos0 = 40/41

find the inverse cos of that.

0 = cos^-1(40/41)

0 = 12.68

Answer:

Therefore, there is 8 children that is 9 years old and 6 children that is 11 years old.

Step-by-step explanation:

Let x be the no. of 9 years old and y be the no. of 11 years old.

x+y= 14 (1)

9x+11y= 138 (2)

From (1) :

x=-y+14 (3)

sub (3) into (2) :

9(-y+14)+11y= 138

-9y+126+11y=138

2y= 138-126

y= 6 (4)

sub (4) into (1) :

x+6= 14

x= 8

By applying the properties of a parallelogram, it can be concluded that the quadrilateral would be a parallelogram since the opposite sides EF and GH are congruent and parallel.

Parallelogram is a 2-D shape formed by two pairs of sides, each of which is the same length (congruent) and parallel to its pair, and has two pairs of angles, each of which is equal to the angle opposite it.

Distance between two points is the length of the line segment that connects the two points in a plane.

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Slope of a line is its vertical change divided by its horizontal change.

m = (y₂ - y₁) / (x₂ - x₁)

We have these points E (-7,-4), F (2,-3), G (0,-7), and H(-9,-8), and we want to prove that they formed a parallelogram.

To do so, we have to prove that EF and GH are congruent by calculating the distance between EF and GH:

EF = √((x₂ – x₁)² + (y₂ – y₁)²)

    = √((2 + 7)² + (-3 + 4)²)

    = √(9² + 1²)

    = √82

GH = √((x₂ – x₁)² + (y₂ – y₁)²)

     = √((-9 – 0)² + (-8 + 7)²)

     = √((-9)² + (-1)²)

     = √82

Because EF = GH = √82, they are congruent.

In the second step, we have to prove that EF and GH are parallel by calculating their slope:

slope of EF = (y₂ - y₁) / (x₂ - x₁)

                   = (-3 + 4) / (2 + 7)

                   = 1/9

slope of GH = (y₂ - y₁) / (x₂ - x₁)

                    = (-8 + 7) / (-9 – 0)

                    = 1/9

Because EF and GH have the same slope, they are parallel.

Thus, since the opposite sides EF and GH are congruent and parallel, so the quadrilateral would be a parallelogram.

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The probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.

The probability of a card being black given it is a queen can be determined using the formula P(A|B) = P(A ∩ B) / P(B). Where P(A) is the probability of a card being black and P(B) is the probability of a card being a queen.

To calculate this, we first need to calculate the probability of a card being a queen, which is 4/52 (there are 4 queens in a standard deck of 52 cards). The probability of a card being black is 26/52 (there are 26 black cards in a standard deck of 52 cards).

Using the formula, the probability of a card being black given it is a queen is P(A|B) = P(A ∩ B) / P(B) = (4/52) / (4/52) = 1. This means that if you draw a queen from a standard deck of 52 cards, it will be black with a probability of 100%.

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The amount of Mark-up of crystal sculpture is $ 244.18.

The purchased price for crystal sculpture that store pays is $842.00. 

The store increase the percentage of price is by 29%.

So to find the amount of mark up price on crystal sculpture we have to find the value of increased percentage on purchased price ($842.00) of sculpture.

The 29% of $842.00 is = $ 842.00  *  29%

= $ 842.00 * 29/100

= $ 244.18                                

so the Mark-up amount of crystal sculpture is = $ 244.18.

The store has a make-up amount of $244.18 on the purchased amount of crystal sculpture which cost them $842.00.

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3349/1260 is the amount, according to the provided document.

The outcome of an addition is a total. For instance, adding 1, 2, 3, and 4 results in the printed number 10. (1) Addends—also known as summands—are the integers that are being added together.

(a)

[tex]\begin{aligned}& \text { D) } \sum_{j=1}^7 \frac{2}{j+2} \\& j=1 ; \frac{2}{1+2}=\frac{2}{3} \\& j=2 ; \frac{2}{2+2}=\frac{2}{4}=\frac{1}{2} \\& j=3 ; \frac{2}{3+2}=\frac{2}{5} \\& j=4 ; \frac{2}{4+2}=\frac{2}{6}=\frac{1}{3} \\& j=5 ; \frac{2}{5+2}=\frac{2}{7} \\& j=6 ; \frac{2}{6+2}=\frac{2}{8}=\frac{1}{4} . \\& j=7 ; \frac{2}{7+2}=\frac{2}{9} \\& \sum_{j=1}^7 \frac{2}{j+2}=\frac{2}{3}+\frac{1}{2}+\frac{2}{5}+\frac{1}{3}+\frac{2}{7}+\frac{1}{4}+\frac{2}{9} \\& =\frac{3349}{1260}\end{aligned}[/tex]

(b)

[tex]\begin{aligned}\frac{7}{2} \frac{8+0}{2} & =\frac{840}{1}+\frac{840}{2}+\frac{840}{3}+\frac{840}{4}+\frac{840}{5}+\frac{840}{6}+\frac{840}{7} \\& =840+420+280+210+168+140+120\end{aligned}[/tex]

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