Explain how the successive values of a geometric sequence could become infinitesimally small but never be equal to 0. Include an example.

Answer:

b = 10

Step-by-step explanation:

substitute x = 10 into the equation

b = [tex]\frac{2(10)^2(10-5)}{10(10)}[/tex]

  = [tex]\frac{2(100)(5)}{100}[/tex] ← cancel 100 on numerator/ denominator

 = 2(5)

 = 10

The profit in dollars cent that the store makes per sweater is $23.

In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product. It is the gain amount from any kind of business activity. In short, if the selling price (SP) of the product is more than the cost price (CP) of a product, then it is considered as a gain or profit. It describes the financial benefit obtained if the revenue from the business activity exceeds the taxes, expenses, and so on, which are involved in sustaining business activities.

Through this information, we can calculate.

[tex]\because p=23 \mathrm{~s} \text {. }[/tex]

when S=1, we could get:

[tex]\therefore P=23 \times 1=23$ \{Operation\}.[/tex]

Therefore, the profit in dollars cent that the store makes per sweater is $23.

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The expression equivalent to given expression is -1/(4x²+9x+5).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 4/(4x+5) -1/(x+1)

Here, 4(x+1)-(4x+5)/(4x+5)(x+1)

= (4x+4-4x-5)/(4x²+5x+4x+5)

= -1/(4x²+9x+5)

Therefore, the expression equivalent to given expression is -1/(4x²+9x+5).

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Lee estimated he would need a total number of ten bags of sand, which is 25% more than the eight bags he actually used.

Lee estimated he would need 10 bags of sand.

To calculate how many number of bags of sand Lee estimated he would need, we must first find 25% of 8 bags.

25% of 8 is 2, so Lee estimated he would need 8 + 2 = 10 bags of sand.

Lee estimated he would need a total of ten bags of sand, which is 25% more than the eight bags he actually used.

Lee was filling a new sandbox and he used his best judgement to estimate how many bags of sand he would need. He thought that he would need 25% more than the amount of sand he actually used, which was 8 bags. To calculate the amount of sand he estimated he would need, we must first find 25% of 8 bags. 25% of 8 is 2, so Lee estimated he would need 8 + 2 = 10 bags of sand to fill the sandbox. Thus, Lee estimated he would need a total of ten bags of sand, which is 25% more than the eight bags he actually used.

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Answer:

x = 1/10

Step-by-step explanation:

3x - 4/5 = -1/2

-1/2 + 4/5 =

-5/10 + 8/10 =

3/10

3x = 3/10

x = 1/10

The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.

An arithmetic progression whenever there is a steady difference amongst terms that follows to each other in a series. For instance, following new number 5, 7, 9, 11, 13, and 15 is an example of an exponential function with a limitation of two. A progress with a set tolerance among any two consecutive numbers generally referred to as a "arithmetic progression" (A.P.). Two types of mathematical progress are possible: series in arithmetic with a finite length A finite mathematical progression is a progression with a finite number of terms. The soon, late, allowance, and quantity of terms may all be calculated using the entries in the series.

given

The geometric sequence 8,12,18,27,81/2's 

first five partial sums, S1,S2,S3,S4, and S5, must be found in order.

S1=8

S2=8+12=20

S3=8+12+18=38

S4=8+12+18+27=65

S5=8+12+18+27+81/2=105.5 as a result.

The total of all S5 terms, the first five terms, and the two different types of mathematical advancement equal 105.5.

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Answer:

gradient= -1 1/5

Step-by-step explanation:

1st point : (3,-3)

2nd point : (-2,3)

gradient= rise/run

= -3-3/3-(-2)

=-6/5

=-1 1/5

Answer:

degree is 2

standard form is

-x^2+2x-8

classification is trinomial

leading coeff is -1

hope i helped

Step-by-step explanation:

The solution of the inequality will be x ≥ -1/4.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that inequality is one-fourth time the absolute value of the quantity x plus 1 end quantity.

The given inequality can be solved as below:-

4x ≥ −1

4x ≥ −1

x ≥ -1 / 4

Therefore, the value of x for the inequality is - 1 / 4.

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Answer:

The answer Is B)  x ≤ −17 or x ≥ 15

Step-by-step explanation:

The correct statement regarding the solution to the system of equations is given as follows:

A. There are no solutions.

The system of equations for this problem is defined as follows:

Multiplying the first equation by 3, we have that:

1.5x - y = 5.

Substituting the second equation into the first, the solution for y is obtained as follows:

3/2(2y/3 + 10) - y = 5.

y + 15 - y = 5

0y = -10

y = -10/0.

Division by zero is not possible, hence the system of equations has zero solutions.

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Jara has 2 alternatives: -2 and -1 A number line is a diagram that depicts numbers,

As we walk along the line from left to right, the numbers rise. Positive numbers are often to the right and negative numbers to the left of zero, which is typically in the middle of the line.

Jara wants to choose a negative number that, in this instance, is closer to zero than -3. This suggests that instead of choosing -3, she should choose a negative integer that is situated nearer to zero on the number line.

-2 and -1 are the two negative numbers that are nearer to zero than -3. On the number line, these values are to the right of -3 and are nearer to zero than -3.

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Therefore , the solution of the given problem of angle comes out to be  x value is 3.

An angle in Euclidean space is a shape made up of two poles that divide at the centre, or apex, of the structure. These beams are referred to as the sides or loops. When two rays are combined, there may be an inclination inside this surface where they are situated. Angles can also be created by combining two surfaces. Dihedral angles are what these are known as. Two-dimensional designs can be created by arranging two line beams at their ends in a variety of ways.

Here,

Give :

=> GH is tangent to ⨀F.

According to angle sum property of triangle :

=> ∠HGJ+ ∠JHG + ∠HJG= 180

=> 8x + 9 + 58 + 90 = 180

=> 8x = 24

=> x = 24/8 = 3

Thus , x value is 3.

Therefore , the solution of the given problem of angle comes out to be  x value is 3.

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The significance level is an factor in hypothesis testing and helps us determine the likelihood of making a Type I error.

A significance level is a critical value in hypothesis testing that determines the probability of making a Type I error, which is rejecting a null hypothesis when it is actually true.

To test whether a specific slope coefficient is equal to one, we can perform a t-test to see if the estimated slope coefficient is significantly different from one at a certain significance level.

The null hypothesis for this test is that the slope coefficient is equal to one, and the alternative hypothesis is that it is not equal to one.

We can use the t-statistic to determine the level of significance for the estimated slope coefficient. The t-statistic is calculated by dividing the estimated slope coefficient minus one by the standard error of the slope coefficient.

The resulting t-value is then compared to the critical t-value from a t-distribution table with the appropriate degrees of freedom.

If the t-value is less than the critical t-value, we fail to reject the null hypothesis and conclude that the estimated slope coefficient is not significantly different from one at the 5% significance level.

On the other hand, if the t-value is greater than the critical t-value, we reject the null hypothesis and conclude that the estimated slope coefficient is significantly different from one at the 5% significance level.

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Answer:

The expression 7/8 + x = 3/8 for x = 3/8 can be solved as follows:

7/8 + 3/8 = 10/8

Therefore, the value of the expression 7/8 + x = 3/8 for x = 3/8 is 10/8, which is equal to 1 1/8 or 1.125 when expressed as a whole or mixed number.

Step-by-step explanation:

The expression 7/8 + x = 3/8 can be solved as follows:

7/8 + x = 3/8

Replace x with 3/8

7/8 + 3/8 = 10/8

Therefore, the value of the expression 7/8 + x = 3/8 for x = 3/8 is 10/8, which is equal to 1 1/8 or 1.125 when expressed as a whole or mixed number.

The value of the given factorial expression is 10! - 6! will be 3,628,800.

The factor of n is given as the production of the number n, (n - 1), (n - 2)... and 1. Then the factorial of n is given as

n! = n x (n - 1) x (n - 2) x ... 3 x 2 x 1

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 10! - 6!

Simplify the expression, then we have

⇒ 10! - 6!

⇒ 10 x 9 x 8 x 7 x 6! - 6!

⇒ 6! (10 x 9 x 8 x 7 - 1 )

⇒ 6 x 5 x 4 x 3 x 2 x 1 x (5040 - 1 )

⇒ 6 x 5 x 4 x 3 x 2 x 1 x 5039

⇒ 3,628,800

The value of the given factorial expression is 10! - 6! will be 3,628,800.

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Solving a system of equations we will see that they sold 184 adult tickets.

We know that the theater sells two types of tickets:

adult tickets for $8 and child tickets for $4.

The variables that we will use are:

x = number of adult tickets sold.

y = number of child tickets sold.

Then we can write the cost revenue equation as:

8x + 4y = 1900

And the total number of tickets sold is 291, then:

x + y = 291

Then we have a system of equations:

8x + 4y = 1900

x + y = 291

We can isolate y on the second equation to get:

y = 291 - x

Replacing that on the other equation we will get:

8x + 4*(291 - x) =1900

4x + 1164 = 1900

4x = 1900 - 1164 =736

x = 736/4 = 184

They sold 184 adult tickets.

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Answer: im not sure how but i hope you can get ut

Step-by-step explanation:

5 : 3  is the ratio of cooking times for the rice to pasta .

What does a math ratio mean?

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.

                                    You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Rice takes 20 minutes to cook

pasta takes 12

the ratio of cooking times for the rice to pasta = 20  :  12

                                                                            = 5 : 3

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Answer:

7%

Step-by-step explanation:

To find the percentage of grape tomatoes among all plants, we can multiply the percentage of tomato plants by the percentage of grape tomatoes among tomato plants:

(35%) * (20%) = 7%

So, 7% of the plants in the greenhouse are grape tomato plants.

Answer: 1: -8x+6

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The plane's distance is the hypotenuse of a right triangle with legs of

(50 -20)mi = 30 miles     and     30500 - 18000 = 12500 ft

                             for consistent units  12500ft/5280ft/mile = 2.36742 miles

Now just use Pythagorean theorem

Hypotenuse^2 = leg1^2 + leg2^2

               h^2    = 30^2 + 2.36742^2

                   h = ~ miles 30.093 miles  ( note that the vertical descent distance does not matter much)

    (this is 158 892 feet)

(a) To find the product of 1/2x-1/4 and 5x^2-2x+6, we can use the distributive property of multiplication:

(1/2x - 1/4)(5x^2 - 2x + 6)

= (1/2x)(5x^2) + (1/2x)(-2x) + (1/2x)(6) - (1/4)(5x^2) + (1/4)(2x) - (1/4)(6)

= (5/2)x^2 - x + 3 - (5/4)x + (1/2)x - (3/2)

= (5/2)x^2 - (3/4)x + 3/2

Therefore, the product of 1/2x-1/4 and 5x^2-2x+6 is (5/2)x^2 - (3/4)x + 3/2.

(b) No, the product of 1/2x-1/4 and 5x^2-2x+6 is not equal to the product of 1/4x-1/2 and 5x^2-2x+6. This is because when we expand both products using the distributive property, we get different expressions:

(1/2x - 1/4)(5x^2 - 2x + 6) = (5/2)x^2 - (3/4)x + 3/2

(1/4x - 1/2)(5x^2 - 2x + 6) = (5/4)x^2 - (7/4)x + 3

So the coefficients of the x^2 and x terms in the two products are different. Therefore, the two products are not equal.

There are 252 different ways that the combination of 5 heads and 5 tails can occur. The coefficient for this term in the binomial equation is [tex]\mathrm{10C_x}[/tex]

The binomial theorem is a mathematical result that describes the expansion of the power of a binomial expression. A binomial expression is an expression that consists of two terms, such as (x + y) or (a + b). The binomial theorem states that for any positive integer n, the expansion of the expression (x + y)^n will contain exactly n+1 terms, each of which is a power of x multiplied by a coefficient.

If we want 5H and 5T,hence there are 10 trials.

Hence it is similar to choosing 5 out of 10 or choosing 2 similar sets of 5 each out of 10 in 10C5 ways:

[tex]$\mathrm{10C_5=\frac{10!}{5!(10-5)!}=252}[/tex]

The coefficient is actually the number of ways of choosing the 5 out of 10.

So similarly the coefficient of:

[tex]$\mathrm{coeff(p^xq^{10-x})=10C_x=\frac{10!}{x!(10-x)!}}[/tex]

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Lastly, the 7 does not need to be multiplied so it remains at 7. After expanding and grouping like terms, we are left with 8h^3 - 32h^2 + 73h - 27.To solve the given equation, we first need to expand the terms in the parentheses and group like terms together.

= 8h^3 - 32h^2 + 73h - 27

To solve the given equation, we first need to expand the terms in the parentheses and group like terms together. We start by expanding the first term (8h - 4) which gives us 8h + -4. Then, we move on to the second term (4h^3 - 8h^2 + 9h + 7). We start by multiplying the 4h to the third power, which gives us 4h^3. Then, we multiply the 8h squared, which gives us -8h^2. Then, we multiply the 9h, which gives us 9h. Lastly, the 7 does not need to be multiplied so it remains at 7. After expanding and grouping like terms, we are left with 8h^3 - 32h^2 + 73h - 27.

The complete question is :

Simplify the expression : 8h - 4 + (4h to the third power - 8h squared + 9h + 7)

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Set up as a system of equations,

Let x represent the number of 4 credit courses and y represent the 3 credit courses.

The total number of courses the student took was 15. So we can say[tex]x+y=15[/tex]

The total credits earned was 54. So we can say, [tex]4x+3y=54[/tex]

Now we have the following system of equations, solve for the value of x.

[tex]\left \{ {{x+y=15} \atop {4x+3y=54}} \right.[/tex]

Take the top equation and solving for y. We get,

=> [tex]x+y=15[/tex]

=>[tex]y=15-x[/tex]

Take the value of y above and plug it into the second equation.

=> [tex]4x+3y=54[/tex]

=> [tex]4x+3(15-x)=54[/tex]

=> [tex]4x+45-3x=54[/tex]

=> [tex]x+45=54[/tex]

=> [tex]x=54-45[/tex]

=> [tex]x=9[/tex]

Thus, the student took 9, 4 credit classes.

The side length of quadrilateral WXYZ are

|WX| = 4.47

|XY| = 2

|YZ| = 4

|ZW| = 4

The perimeter of quadrilateral WXYZ is 14.47 units.

The four points W, X, Y, and Z are located at ponts (3,1), (7,-1), (7,-3), and (3,-3) respectively.

To find the distance between two points, A and B, with coordinates (x1, y1) and (x2, y2) respectively, we use the formula:

|AB|=√(x2 – x1)² + (y2 – y1)²

The side lengths of the quadrilateral are calculated using this formula.

|WX| = √(– 1 – 1)² + (7 – 3)² = 4.47

|XY| = √(– 3 – (– 1))² + (7 – 7)² = 2

|YZ| = √(– 3 – (– 3))² + (3– 7)² = 4

|ZW| = √(– 3 – 1)² + (3 – 3)² = 4

Hence, the Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units

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Answer:

(1) 17 (2) +3 every new term (5+3) or 8+3) or 5+x*3

we can use this as to find 2nd number (1) as its first one to be found 5+3(1) 5+3=8

(3) 5+9*3=5+27 , 32

(4) 5+9*3 ,

we can test this out by counting

starter: 5

1 -> 8

2-> 11

3-> 14

4 -> 17

5 -> 20

6 -> 23

7 -> 26

8 -> 29

9 -> 32 (realisticly it is still the 10th but it's the 9th after the 1st.)

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Equivalent interest rate in decimal form will be   ( 1+i)^n - 1    

   where i = periodic interest in decimal = .05/4     n = periods = 4  per year  

(1+ .05/4)^4 -1 = 5.09 % equivalent interest per year

.05 / 4 = .0125    or    1.25%   16 times   ( 4 times per year x 4 years)