A package of 6 pairs of insulated socks costs ​$41.34 What is the unit price of the pairs of socks​?

For any positive integer n, 1 × 1! + 2 × 2! + . . . + n × n! = (n + 1)! - 1

We use mathematical indution technique to prove  1 × 1! + 2 × 2! + . . . + n × n! = (n+1)! - 1, for  a positive integer n.

Let T(n) be the given expression  1 × 1! + 2 × 2! + . . . + n × n! = (n+1)! - 1

For n = 1,

1 × 1! = 1

and (1 + 1)! - 1 = 1

This means T(1) is true.

Assume that T(k) is true.

So, 1 × 1! + 2 × 2! + . . . + k × k! = (k + 1)! - 1

We need to prove T(k + 1) is also true.

i.e., to prove: 1 × 1! + 2 × 2! + . . . + (k + 1) × (k + 1)! = ((k + 1) + 1)! - 1

Consider,

1 × 1! + 2 × 2! + . . . + (k + 1) × (k + 1)!

= 1 × 1! + 2 × 2! + . . . + k × k! + (k + 1) × (k + 1)!

= (k + 1 )! - 1 + (k + 1) × (k + 1)!

= (1 + k + 1)(k + 1)! - 1

= (k + 2)(k + 1)! - 1

= (k + 2)! - 1

= ((k + 1) + 1)! - 1

This means, T(k+1) is also true.

So, ​T(n) is true for all positive integers n .

Hence proved.

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Answer:

B is true

Step-by-step explanation:

Square root of 32 comes out to be around 5.7 which is greater than 4.8. Rest are false.

The value of variable x that makes -4x-(-10 - 8x) = -(12x-14) true is 1/4. thus, option c is correct.

In algebra, a symbol known as a variable (typically a letter) is used to represent an equation's undetermined numerical value. Frequently used variables include t, r, and s, as well as X and Y, which are real-number unknowns, as well as z, which is a complex-number unknown (arc length).

Given

-4x-(-10 - 8x) = -(12x-14)

-4x + 10 + 8x = -12x + 14

4x + 10 = 14 - 12x

4x + 12x = 14 - 10

16x = 4

x = 4/16

x = 1/4

Thus, Option C is correct, x = 1/4

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Answer:

Step-by-step explanation:

4x - 16 = 2x + 6

4x - 2x = 6 + 16

2x = 22

x = 11

-------------------------------

check

4 × 11 - 16 = 2 × 11 + 6

44 - 16 = 22 + 6

28 = 28

Answer: x=11

Step-by-step explanation:

4x-16=2x+6

Start by combining like terms cancelling out the smaller one.

4x(-2x)-16=2x(-2x)+6

Then cancel out -16 so you get the variable x by itself.

2x-16(+16)=6(+16)

Then divide both sides by 2 to get x value.

2x/2=22/2

x=11

Answer:

Angles of the triangle are 90°, 50.77° and 39.23°.

Step-by-step explanation:

The complete table would be such that the corresponding x and y - values would be:

The values of x are given as x is the independent variable. Those values are 3, 6, and 9.

The values of y can be found as x . 8 which means that the values of y would be the corresponding value of x, multiplied by y.

The values of y would then be:

= x . 8

= 3 x 8

= 24

X - value of 6 :

= 6 x  8

= 48

x - value of 9 in the table :

= 9 x 8

= 72

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Answer:

190m is 623.39ft

189m is 620.109

the probability possible amounts of time for which they could rent the meeting room  for a maximum of six hours

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

[tex]t = time\\44 + 7.30t < 87.80\\7.30t < 43.80\\t < 6[/tex]

They may reserve the room for a maximum of six hours.

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Answer:

320in

Step-by-step explanation:

Brainliest?

Answer:

surface area of the box = l×w×h

surface area = 10× 8 × 4 = 320in

the total number of hats and scarves he can make cannot exceed 13.

x ≤ 5

y ≤ 8

x + y ≤ 13

x ≤ 5 represents the most hats Ronald can make, which is 5. y ≤ 8 represents the most scarves Ronald can make, which is 8.

x + y ≤ 13 represents the total number of hats and scarves Ronald can make, which is 13.

The inequalities among the constraints for this situation are x ≤ 5, y ≤ 8, and x + y ≤ 13.

The given situation is that Ronald has enough yarn to make 5 hats and 8 scarves, and it takes him 12 hours to knit a hat and 6 hours to knit a scarf; he has 20 hours to knit. The inequalities among the constraints for this situation are x ≤ 5, y ≤ 8, and x + y ≤ 13. This means that Ronald can make a maximum of 5 hats, 8 scarves, or a combination of the two that is no more than 13 in total. x stands for the number of hats made, and y stands for the number of scarves made. In order for Ronald to meet the constraints, he must make at least one hat and one scarf, and the maximum number of hats he can make is 5 and the maximum number of scarves he can make is 8. Additionally, the total number of hats and scarves he can make cannot exceed 13.

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Inequality representing the constraints for the given situation of making hats and scarves is given by :

x ≤ 5

y ≤ 8

12x + 6y ≤ 20

As given in the question,

Let 'x' represents the number of hats made by Ronald.

And 'y' represents the number of scarves made by Ronald.

As per given condition for hat and scarves , the inequality of constraints to represents the given situation is written as :

Enough yarn represents the quantity:

x ≤ 5

y ≤ 8

Knitting represent the inequality of time,

Time to knit hats is 12 hours

Time to knit scarves is 6 hours

Total time to knit is 20 hours

12x + 6y ≤ 20

Therefore, the inequality to represents the constraints of the given situation is given by :

x ≤ 5

y ≤ 8

12x + 6y ≤ 20

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The area of the trapezium is 21cm²

You should know that a trapezium is a quadrilateral with two parallel opposite sides while thw other two are not parallel.

The area of the trapezium is denoted by the formular

Area= 1/2(a+b)*h

Where

We are told that the trapezium occupies centimeter grid

a= = 5, b=9 and h=3

This implies that Area = 1/2*(5+9)*3

Area= 1/2*14*3

=7*3 =21 cm²

In conclusion the trapezium has an area of  21cm²

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In Analysis of variance,  X (bar) is not affected by whether or not the population means are equal.

Analysis of variance  is a statistical method for examining differences in means. It consists of a number of statistical models and the accompanying estimating techniques (such as the "variation" within and between groups). Ronald Fisher, a statistician, created Analysis of variance. The rule of total variance, on which the Analysis of variance is based, divides the observed variance in a given variable into components owing to various causes of variation.

ANOVA generalizes the t-test beyond two means by offering a statistical test to determine if two or more population means are equal. In other words, the Analysis of variance is employed to determine whether two or more means differ from one another.

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The domain and range of a ln function can be found out easily from their graphical representation.

Consider a function y = f(x) , where x here is the input and y is the output of this function.

So we can define the domain of a function as all possible set of inputs and range as all the outputs that domain will give. The spread of all the y values from minimum to maximum is the range of the function here. Coming to the logarithmic functions domain and range can be found in following ways :

Set the argument in ln(x) greater than 0 to find where the expression is defined. The domain is all values of x that make the expression defined. The range is the set of all valid y values. Use the graph to find the range.

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Answer:

scale factor

Step-by-step explanation:

The dilation of a line segment is longer or shorter based on the ratio given by the scale factor.

Answer: True

Step-by-step explanation: Because all your doing is flipping it

Answer:

[tex]9x^{2} -33x+30[/tex]

Step-by-step explanation:

The opposite of being short $4.28 would be having $4.28 or more. That is a surplus or extra of $4.28.

Surplus refers to an amount or quantity that is left over or in excess of what is needed or used. It can refer to various things, such as:

In finance, a surplus refers to an excess of revenue over expenses, or an excess of assets over liabilities. It means having more of something than is necessary or expected.

Therefore, the opposite of being short $4.28 would be having $4.28 or more. This is often referred to as having a surplus or extra of $4.28.

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The solution of the equation p = √2 - p is as follows: p = 1 and p = -2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. Therefore, let's solve the equation as follows;

let's solve for the variable p in the equation

p = √2 - p

square both sides

p² = (√2 - p)²

p² = 2 - p

p² + p - 2 = 0

The equation forms a quadratic equation.

Therefore,

p² + p - 2 = 0

p² - p + 2p - 2 = 0

p(p - 1) +2(p - 1) = 0

(p - 1)(p + 2) = 0

Hence,

p = 1 and p = -2

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Integrate (ax)2 − b2 3/2 with respect to x. The result is (2/5)ax5/2 − (b2/5)x3/2 + c, where c is the constant of integration.

Integrate (ax)2 − b2 3/2 with respect to x.

First, use the power rule to rewrite the integrand as

(2/5)ax5/2 − (b2/5)x3/2.

Next, use the integration by parts formula to integrate the expression:

∫(2/5)ax5/2 − (b2/5)x3/2 dx

= (2/5)ax5/2 − (b2/5)x3/2 + c,

where c is the constant of integration.

Integrating (ax)2 − b2 3/2 with respect to x involves using the power rule and the integration by parts formula. The power rule states that when integrating a function to the nth power, the exponent is reduced by one and the coefficient is multiplied by the original exponent divided by the reduced exponent. Therefore, the integrand is rewritten as (2/5)ax5/2 − (b2/5)x3/2. The integration by parts formula is then used to integrate the expression, resulting in (2/5)ax5/2 − (b2/5)x3/2 + c, where c is the constant of integration.

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Answer:

14t + 38 feet

Step-by-step explanation:

Let L be the Length and W the width.  The perimeter of a rectangle is given by 2L + 2W.

Perimeter = 2(9.5+t) + 2(6T+9.5)

Perimeter = 19+2t + 12T+19

Perimeter = 14t + 38 feet

Answer:

Step-by-step explanation:

6x [tex]\geq[/tex]15

x= $2.5

since it deals with money make it $2.50

_made my kharis:)

Carson expects to spend at least $15 on the popsicles, so the cost of each popsicle multiplied by the number of popsicles he is buying (6) must be greater than or equal to $15. Therefore, the inequality 15 ≤ 6x describes the problem.

Step 1: Let x represent the cost of each popsicle.

Step 2: Multiply 6 (the number of popsicles) by x (the cost of each popsicle): 6x

Step 3: Set the equation equal to 15 (the amount of money Carson expects to spend on the popsicles):

6x = 15

Step 4: Divide both sides of the equation by 6:

6x/6

= 15/6

Step 5: Simplify to get the answer:

x = $2.50

Carson wants to buy 6 popsicles from the ice cream truck and expects to spend at least $15. To figure out how much each popsicle should cost, I used an inequality. I let x represent the cost of each popsicle, multiplied it by 6 (the number of popsicles Carson is buying), and set the equation equal to 15 (the amount of money Carson expects to spend). After dividing both sides of the equation by 6 and simplifying, I got the answer that each popsicle should cost $2.50. Therefore, Carson should expect to spend at least $15 on the 6 popsicles.

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Emma could use the expression 300(1.15)^t to calculate her amount using a compound interest rate every year.

We know that Compound interest, also known as interest on principal and interest, is the process of adding interest to the principal amount of a loan or deposit.

The interest one earns on  the previous interest is known as compound interest.

For eg - if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

We will have $110.25 at the end of the second year.

Now, here we know that:

Interest rate = 15%

Now, compound interest formula is given by

A = P(1 + r/n)^nt

Upon putting the values, we get 300(1.15)^t.

Therefore, Emma could use the expression 300(1.15)^t, to calculate the amount using a compound interest rate every year.

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Answer:

B. One

Step-by-step explanation:

The system has one solution because when graphed, the lines intersect.

Answer:

64

Step-by-step explanation:

using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](2^{3}) ^{2}[/tex]

= [tex]2^{3(2)}[/tex]

= [tex]2^{6}[/tex]

= 64

Amazon has a better price, their rate is more cheaper.

Amazon sells the slime as 15packs for $45.15

The price of one pack can be calculated as follows

15= 45.15

1= x

Cross multiply both sides

15x= 45.15 × 1

15x= 45.15

divide both sides by the coefficient of x which is 15

15x/15= 45.15/15

x= 3.01

one pack of slime at Amazon is $3.01

The girls sell 5 packs of slime for $20.35

The price of one pack can be calculated as follows

5= 20.35

1= y

cross multiply both sides

5y= 20.35

y= 20.35/5

y= 4.07

The girls sell 1 pack of slime for $4.07

Therefore the person with the best deal is Amazon because their price is much more cheaper

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The first step in constructing a segment congruent to a given segment is to draw a vertex and a ray.

Step 1: draw a vertex and a ray

Step 2: Draw a line segment that is longer than the specified line segment if we are not given the line segment on which we are to create the congruent section. The portion we just sketched will be known as the second line segment.

Step 3: Place the needle of the compass at an endpoint of the second line segment.

Step 4: Draw an arc of the circle so that it intersects the line segment.

Step 5: Label the point where we placed the needle and the point of intersection using two letters. The congruent line segment we want is the line segment formed by these two endpoints.

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Answer:

[tex]x = \frac{-20}{7}\\\\y = \frac{4}{7}[/tex]

The graph of the function [tex]G(x) = 2^x + 2 -3[/tex] is obtained from the transformation of the parent function [tex]F(x) = 2^x[/tex].

The transformation of graph either translates, dilates or reflects the parent or the original graph according to the given instructions.

Vertical translation is the movement of the graph up or down on the y-axis depending on the units and its sign.

In the given graph when we add the value 2 the original graph shifts upwards on the y-axis by 2 units.

When 3 is subtracted from the translated graph the graph then shifts downwards on the y-axis by 3 units.

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