Seven more than the quotient of a number and 3 is 10? What is the number?

The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.

Given the following definition of functions

a₁ = 5

aₙ = 2aₙ₋₁ + 3

To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:

a₂ = 2a₁ + 3 = 2(5) + 3 = 13

a₃ = 2a₂ + 3 = 2(13) + 3 = 29

a₄ = 2a₃ + 3 = 2(29) + 3 = 61

Therefore, the fourth term of the sequence is 61.

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After solving the given expression, the value of x is 5.

What exactly are expressions?

An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be simple or complicated, with one or more variables involved.

Now,

To solve the equation 6x+14x+5=5(4x+1), we first need to simplify both sides of the equation using the distributive property of multiplication:

6x + 14x + 5 = 20x + 5

Now we can simplify further by subtracting 20x and 5 from both sides of the equation:

6x + 14x - 20x = 0 - 5

Simplifying again:

x = -5

Finally, we can solve for x by multiplying both sides by -1:

x = 5

Therefore, the solution to the equation 6x+14x+5=5(4x+1) is x=5.

Word problem:

A clothing store sells two types of shirts: T-shirts and polo shirts. The store makes a profit of $6 on each T-shirt sold and a profit of $14 on each polo shirt sold. Last week, the store sold a total of 5 shirts and made a total profit of $25. If x represents the number of T-shirts sold, write an equation to represent the situation.

Solution:

Let x be the number of T-shirts sold, then the number of polo shirts sold is 5 - x (since a total of 5 shirts were sold). The total profit from selling x T-shirts and (5-x) polo shirts can be calculated as:

Profit = (profit per T-shirt x number of T-shirts) + (profit per polo shirt x number of polo shirts)

Profit = (6x) + (14(5-x))

Profit = 6x + 70 - 14x

Profit = -8x + 70

Since the total profit is given as $25, we can write the equation:

-8x + 70 = 25

Simplifying:

-8x = -45

x = 5.625

Since we can't sell a fraction of a shirt, we need to round down to the nearest integer. Therefore, the store sold 5 T-shirts.

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Answer$81

Step-by-step explanation:

The distance between Sam from the top of the temple is 56. 6 feet

To determine the distance, we need to know that trigonometric identities are mathematical identities that is mostly used to prove that all the values of the functions of trigonometry are true.

The types of trigonometric identities are;

From the information given, we can deduce that;

The angle of elevation, θ = 62 degrees

The opposite side of the angle that is the height of the temple is 50 feet

The distance is the hypotenuse side

Then, using sine identity, we have;

sin 62 = 50/d

d = 50/0. 8829

d = 56. 6 feet

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The radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC

Since the line AB is tangent to the circle at point B, then the triangle ABC is a right triangle and the Pythagoras rule can be applied as follows:

(50 + r)² = r² + 80²

r² = (50 + r)² - 80²

r² = (50 + r - 80)(50 + r + 80) {difference of two square}

r² = (r - 30)(r + 130)

r² = r² + 130r - 30r - 3900 {expansion of brackets}

r² - r² + 130r - 30r = 3900 {collect like terms}

100r = 3900

r = 3900/100 {divide through by 100}

r = 39

Therefore, the radius r for the circle C is equal to 39 using the Pythagoras rule for the right triangle ABC.

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In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.

A circle is a clοsed, twο-dimensiοnal οbject where every pοint in the plane is equally spaced frοm a central pοint. The line οf reflectiοn symmetry is fοrmed by all lines that traverse the circle. Additiοnally, every angle has rοtatiοnal symmetry arοund the centre.

A circle is given with centre marked as O.

A circle is a 2D fοrm in geοmetry in which all οf the pοints οn its surface are equally spaced frοm its center.

The radius is the length frοm any pοint οn the surface tο the center.

A diameter is a chοrd that is equidistance frοm centre οf the circle.

Here οnly the straight line is equidistance frοm centre οf the circle.

That line is BQ.

Thus, In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.

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Answer:

The correct answer is option B.

To find the function with an average rate of change of -4 over the interval [-2,2], we need to calculate the slope of the function between the two points -2 and 2.

Average rate of change = (f(2) - f(-2))/(2 - (-2)) = (-4)

Option B has the function qx with values {-4, 0, 0, -4, -12} at x values {-2, -1, 0, 1, 2}. The average rate of change of this function over the interval [-2,2] is indeed -4.

Answer: x= 6241/2

Step-by-step explanation:

Answer: 82y

Step-by-step explanation:

147y - 65y = 82y

Just perform simple subtraction

Explanation:

She scored 92 points in 4 games. The unit rate is 92/4 = 23 points per game.

Over the course of 17 games, Maria would have a total of 17*23 = 391 points assuming her scoring rate is kept the same.

Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Answer:

Step-by-step explanation: it is -2x + 430298= -9n79000.

Answer:

a_2 = 16

a_3 = -32

a_4 = 64

Step-by-step explanation:

Multiply each term by r to get the next term.

a_1 = -8

a_2 = -8 × (-2) = 16

a_3 = 16 × (-2) = -32

a_4 = -32 × (-2) = 64

Therefore , the solution of the given problem of unitary method comes out to be P = 1/72.

The objective can be accomplished by utilizing what has been expression learned thus far, making use of this global availability, and incorporating all essential components from earlier changeable study that utilized a particular method. If the anticipated claim result actually occurs, it will be feasible to contact the entity once more; otherwise, both important processes will undoubtedly miss the statement.

Here,

There are two situations to take into consideration because there are seven courses in Group A and six courses in Group B:

The student in Case 1 selects two classes from Group A. The student has seven choices for the first course in this situation, and six options for the second course.

Case 2: The student has a total of 5 choices for courses, as follows:

=>2 × (42 + 30) = 144

As a result, the student has 144 choices for 5-course sequences.

b. There are two choices for the fifth course because the student can select one more course from either Group A or Group B.

There are a total of three methods to select this set of courses:

=> 1 × 1 × 1 × 1 × 2 = 2

the likelihood of selecting Introduction

=>  P = 2/144 = 1/72

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Answer:

Step-by-step explanation:

We can solve the equation m + 9 = 27 by subtracting 9 from both sides to isolate m:

m + 9 - 9 = 27 - 9

m = 18

Therefore, Ibrain biked 18 miles last week.

Answer:

Step-by-step explanation: 1

The demand equation for commodity A is Xa = (4/10)Xb.

A demand equation is a mathematical representation of the relationship between the quantity of a good or service that consumers are willing to buy and the various factors that influence that demand, such as price, income, and preferences.

In the given question,

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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The demand equation for commodity A is Xa = (4/10)Xb.

What is demand equation?

A demand equation is a mathematical formula that expresses the relationship between the quantity of a good or service that consumers are willing and able to purchase and various factors that affect that quantity, such as price, income, and the prices of other goods.

To find the consumer's demand equation for A, we need to use the utility maximization rule, which states that a consumer will allocate their budget in such a way as to maximize their total utility subject to their budget constraint.

Let Xa be the quantity of commodity A and Xb be the quantity of commodity B. We know that the consumer has $30 to spend, so the budget constraint is:

3Xb + pXa = 30

where p is the price of commodity A. We also know the utility function:

U = 4XgXb

To maximize U subject to the budget constraint, we can use the Lagrangian method:

L = 4XgXb + λ(30 - 3Xb - pXa)

where λ is the Lagrange multiplier.

To find the demand equation for A, we need to take the partial derivative of L with respect to Xa and set it equal to zero:

∂L/∂Xa = -λp = 0

This gives us λ = 0, which we can substitute back into the Lagrangian equation to get:

L = 4XgXb + 0(30 - 3Xb - pXa)

L = 4XgXb

To find the demand equation for A, we need to take the partial derivative of L with respect to p and solve for Xa:

∂L/∂p = -4XgXb/Xa = -30/3

Xa = (4/10)Xb

So the demand equation for commodity A is Xa = (4/10)Xb.

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13

First, we divide to figure out how much Jane makes an hour

143 ÷ 11 = 13

Second, we multiply multiply by 13 until we get 169

13 × 13 = 169

So Jane will make 169 dollars in 13 hours

Answer:

13 Hours

Step-by-step explanation:

$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169

$169 ÷ $13 = 13 hours

Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.

The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.

Here,

=>  A = L x W,

where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.

Inputting the numbers provided yields:

=>  A = (7/4) x (1/3)

These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.

The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:

=>  A = (7 x 1) / (4 x 3)

When we multiply the numerator by the remainder, we obtain:

=> A = 7/12

The rectangle's size is 7/12 square inches as a result.

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The correct statement about the diagonals of a non-square rectangle is "The diagonals bisect a pair of opposite angles"

A rectangle is a four-sided flat shape with opposite sides of equal length and opposite sides that are parallel.

A non-square rectangle is simply a rectangle whose opposite sides are not equal in length. In other words, a non-square rectangle is a rectangle that has two pairs of sides, each of which has a different length.

If a rectangle has sides that are equal in length, it is called a square. However, if the sides are not equal, then it is a non-square rectangle. Non-square rectangles are commonly encountered in everyday life, such as in the shape of paper, books, windows, doors, and many other objects.

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hi :) i sense that it's the rhombus again, but please let me know if i'm wrong.

assuming this is about the rhombus, which i've attached below, here is your answer:

the diagonals of a rhombus bisect each other at right angles. this means that the angles created by the intersection of AC and BD are all equal to 90 degrees, including CEB.

hope this helps!

Answer:

93 million

Step-by-step explanation:

93 Million

A 90 degree clockwise rotation about the point (0,0), the new coordinates of Point B are (3, -1) and the new coordinates of Point C are (1, -2).

A quadrilateral can be proven to be a rectangle in a number different ways. Here are the three simplest methods: 1. Establish that all angles are 90 degrees; 2. Establish that two opposed angles are 90 degrees; and 3. Establish that the diagonals are equally long and intersect one another.

The following transformation matrix can be used to rotate a point (x,y) 90 degrees clockwise with respect to the origin (0,0):

|0 1|\s|-1 0|

This transformation matrix can be applied to each point to determine its new coordinates upon rotation.

Point B is the first point, and its initial coordinates are (-1, 3). The transformation matrix in use:

|0 1| |-1| |3|

|-1 0| x |3| = |-1|

After rotating Point B 90 degrees clockwise, the new coordinates are: (3, -1).

The transformation matrix is then applied to Point C, whose initial coordinates are (2, 1):

|0 1| |2| |1|

|-1 0| x |1| = |-2|

After rotating in a clockwise direction by 90 degrees, Point C's new coordinates are (1, -2).

As a result, after rotating 90 degrees in a clockwise direction around Point 0, Point B's new coordinates are (3, -1), while Point C's new coordinates are (1, -2).

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Answer:

Answer:

50313.28

Step-by-step explanation:

A = total amount  

P = principal or amount of money deposited,

r = annual interest rate  

n = number of times compounded per year

t = time in years

For the formula:

A=P(1+r/n)n⋅t

P=$5000 , r=8% , n=1 and t=30 years

Solution:

A= 5000(1+0.08/1) to the power 1.30

 = 5000*1.08 to the power 30

 = 5000*10.062657

 = 50313.28

The probability of losing is [tex]\frac{999}{1000}[/tex] (since there are 999 ways to lose and 1 way to win), so the odds against winning are [tex](\frac{\frac{999}{1000} }{\frac{1}{1000} })[/tex] = 999:1.

To understand the concept of odds against winning, we can use the analogy of flipping a coin. There are only two outcomes that can occur when we flip a fair coin: heads or tails. The probability of getting heads is 1/2 and the probability of getting tails is also [tex]\frac{1}{2}[/tex] . The odds against getting heads are the ratio of the probability of getting tails to the probability of getting heads, which is 1:1 or even odds. In the case of the Florida Pick 3 lottery, there are 1000 possible outcomes, but only one is a winning outcome. Therefore, the actual odds against winning the Florida Pick 3 lottery with a straight bet are 999 to 1.

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The complete question is:

In the Florida Pick 3 lottery, you can place a “straight” bet of $1 by selecting the exact order of three digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/1000. If the same three numbers are drawn in the same order, you collect $500, so your net profit is $499.

Find the actual odds against winning

The height of the trapezoid is approximately 7 feet.

What is the area of a trapezoid?

To find the height of the trapezoid, we can use the formula for the area of a trapezoid: A = ((b1 + b2) / 2) * h

where A is the area, b1 and b2 are the lengths of the two parallel bases, and h is the height.

We are given that the area is 24.5 ft², and the lengths of the bases are 3 ft and 4 ft. Substituting these values into the formula, we get:

24.5 = ((3 + 4) / 2) * h

Simplifying:

24.5 = 3.5 * h

h = 24.5 / 3.5

h ≈ 7

Therefore, the height of the trapezoid is approximately 7 feet.

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To find the area of the total figure, we need to first find the areas of the rectangle and triangle, and then add them together.Therefore, the area of the total figure is 200 square feet.

Area is the measurement of the size of a two-dimensional surface enclosed by a closed figure

Area of rectangle = length x width

= 20 ft x 8 ft

= 160 sq. ft

Area of triangle = 1/2 xbase xheight

= 1/2 x 8 ft x 10 ft

= 40 sq. ft

To find the base of the triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse (slope) of a right triangle is equal to the sum of the squares of its two sides. In this case, the hypotenuse is 12 ft, one of the other sides is the height of the triangle (10 ft), and the other side is the base of the triangle (b).

Using the Pythagorean theorem, we have:

12² = 10² + b²

144 = 100 + b²

44 = b²

b = √44

b ≈ 6.63 ft

Now that we know the base of the triangle, we can find the area of the total figure by adding the area of the rectangle and the area of the triangle:

Area of total figure = area of rectangle + area of triangle

= 160 sq. ft + 40 sq. ft

= 200 sq. ft

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The circle E with diameter CD and radius EA having the length of AC is approximately 4.2 units.

What is Pythagoras' Theorem?

In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.

Since EA is a radius of circle E, and AB is tangent to E at A, we know that AB is perpendicular to EA. Thus, triangle EAB is a right triangle.

Let x be the length of AC. Then, by the Pythagorean Theorem in triangle EAC, we have:

[tex]AC^{2} = EA^{2} +EC^{2}[/tex]

[tex]AC^{2} = 3^{2} + 3^{2}[/tex]

[tex]AC^{2} = 18[/tex]

AC ≈ 4.2 (rounded to the nearest tenth)

Therefore, the length of AC is approximately 4.2 units.

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(a) The p-value = 0.017 (b)  the conditions are met to conduct the test. (c) the correct conclusion is: Reject the null hypothesis

(a) Using the given data, we can calculate the test statistic z-score as:

z = (xbar - μ) / (σ / sqrt(n))

= (1138 - 1000) / (605 / sqrt(42))

= 2.378

Using StatCrunch, the p-value for a two-tailed test with a test statistic of 2.378 and degrees of freedom of 41 (n - 1) is 0.017.

Therefore, the p-value = 0.017 (to 3 decimal places).

(b) To conduct a hypothesis test for a population mean, we need to check if the following conditions are met:

The population is approximately normal or the sample size is large (n ≥ 30).

The population standard deviation (σ) is unknown.

Here, n = 42 which is greater than 30, so we can assume that the population is approximately normal. The standard deviation of the population is unknown.

Therefore, the conditions are met to conduct the test.

(c) The null and alternative hypotheses are:

Null hypothesis (H0): The mean wastewater discharged by the industrial plant is 1000 gallons per hour (μ = 1000).

Alternative hypothesis (Ha): The mean wastewater discharged by the industrial plant exceeds 1000 gallons per hour (μ > 1000).

At alpha = 0.05 (5% level of significance), the critical z-value for a one-tailed test is 1.645.

Since the calculated z-score (2.378) is greater than the critical value (1.645), we reject the null hypothesis.

Therefore, the correct conclusion is: Reject the null hypothesis. There is sufficient evidence that the wastewater discharged by the industrial plant exceeds 1000 gallons per hour.

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