Here are the first 5 terms of a quadratic sequence.
2
10
24
44
Find an expression, in terms of n, for the nth term of this sequence.
70

Answer:

Step-by-step explanation:

Firstly, I presume that the question talks about a rectangle and there is consistency in units i.e.Area is in units^2 and perimeter is in units (else there is no possible solution).

Now, perimeter = 2(L+B) = 40

OR (L+B) = 20.

Also, area = LxB = 100.

Now, LxB = 100 will give you the following values for LxB (Note in a rectangle, L>B or L=B):- (100×1),(50×20),(25x4),(20×5),(10×10).

Only one value gives L+B = 20 viz.L=10 & B=10.

Hope this helps! :)

(This was by another user you can search it up and see.)

The length of the side DE, that is parallel to the side AC is 6.3 units

Here the line DE is parallel to the side AC of the triangle

In the given triangle

The length of the side BD = The length of the side AD

The length of the side BE = The length of the side EC

That mean the parallel line AC is equally dividing the two side of the triangle

Therefore, the length of the line DE will be be exactly half of the line AC

The length of the side AC = 12.6 units

The length of the side DE = The length of the side AC / 2

Substitute the values in the equation

= 12.6 / 2

= 6.3 unit

Therefore, the length of DE is 6.3 units

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After changing  the denominators to rename these fractions  the sum is 5/6 .

Given :

If necessary, use / for the fraction bar(s).

We still need to find a way to add these fractions. Now you try.

Change the denominators to rename these fractions and find their sum.

To find sum we need to find LCM of denominators .

Least common multiple :

Least Common Multiple ( LCM ) is a method to find the smallest common multiple between any two or more numbers.

so = 1 / 2 + 1 / 3

LCM of 2 and 3 is 6

= 1 * 3 + 1 * 2 / 6

= 3 + 1 * 2 / 6

= 3 + 2 / 6

= 5 / 6

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Using theory about stereotypes and different associated thoughts, we have to:

A stereotype, basically, can be defined as an idea that is already pre-established and accepted, it is applied to different individuals.

¡Hope this helped!

The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle.

Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is 7 ⁷/₈ cm² and the base length of the triangle is 5 ¹/₄ cm.

Convert the mixed fraction number into a fraction number. Then we have

7 ⁷/₈ = 63/8

5 ¹/₄ = 21/4

The height of the triangle is given as,

63/8 = (1/2) x h x (21/4)

Simplify the equation, then we have

63/8 = (1/2) x h x (21/4)

63/8 = (21/8)h

21h = 63

h = 3 cm

The height of the triangle that has an area of 7 ⁷/₈ square cm will be 3 cm.

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Answer:

14772

Step-by-step explanation:

As a result, the likelihood of a flush (five cards of the same suit) is.198% while the likelihood of getting three cards of the same rank and two cards from any other rank is 0.07612%.

Probability is the study of numerical representations of the likelihood that an event will happen or that a statement is true. An event's probability is a number between 0 and 1, where 0 generally denotes the event's impossibility and 1 typically denotes its certainty.

Here,

a) It is irrelevant what suit the opening card is. Any of the suits may be drawn first, provided that the subsequent four cards are dealt from the same deck and are of the same suit.

After the initial card is drawn, there are only 12 of a given suit left in the deck, which has 13 of each suit in total. The third card, which has 11, the fourth card, which has 10, and the fifth and final card, which has nine, are then the cards that are still available. Each time, one fewer card will be present in the deck as a whole.

(ℎ) = (2 ) ∙ (3 ) ∙ (4ℎ )\s∙ (5ℎ )

(ℎ) = [tex]\frac{12}{51} *\frac{11}{50} *\frac{10}{49} *\frac{9}{48}[/tex]

(ℎ) =11880 / 5997600

(ℎ)= 33/16660 = .00198 .198%

c) The likelihood of three identical cards and two cards from one other rank.

Considering that the cards have 13 ranks

So, P =  [tex]\frac{13}{52} *\frac{12}{51} *\frac{11}{50} *\frac{10}{49}[/tex]

P = 267696/351655200

P=0 .0007612 or 0.07612 %

As a result, the likelihood of a flush (five cards of the same suit) is.198% while the likelihood of getting three cards of the same rank and two cards from any other rank is 0.07612%.

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In the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.

In the given question, linear function k has a zero at 3 and a y-intercept of 9.

We have to choose which graph best represents k.

As we know that;

The link between the two unknown variables is represented by a linear equation. The linear equation have one degree.

The most basic linear equation demonstrates the relationship between (x,y), which can be used to create a table, a graph on the coordinate plane, or to perform an assessment at a particular x or y value.

We represent linear function in the form of y=mx+c.

where m is the slope of the line, c is the y intercept of the line, x is independent variable and y is the dependent variable.

As we see the y intercept in the graph crosses the y axis.

Here y intercept is 9.

The zeros of the linear function is that where y value is zero.

As in the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.

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The correct order of the given statements is- 1, 2, 3, 4, 5, 6, followed by 7.

Here, we are given the following statement-

For all sets A, B and C if A ≤ B and B∩C = Φ

then A∩C = Ф

We can use the proof-by-contradiction method to prove the given statement as shown below-

Suppose that there exist 3 sets, that are- A, B, and C

Such that A ≤ B, B∩C = Φ

and A∩C ≠ Φ

Then, there must exist an element x such that x ∈ A∩C

Now, by the definition of intersection, we have- x ∈ A and x ∈ C

Then x ∈ B because A ≤ B. Additionally, we know that x ∈ C

Hence, by the definition of intersection, x ∈ B∩C

Thus, B∩C ≠ Φ by definition of null set (Φ)

But this contradicts the supposition. Hence, our assumption is false and so A∩C = Ф.

The correct order of the given statements is- 1, 2, 3, 4, 5, 6, followed by 7.

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Answer:

-4 im pretty sure

Step-by-step explanation:

= -4

= -4

The linear equation parallel to the line that passes through (-6, 1) and (10,0) and that passes through (-7, -2) is:

y = (-1/16)*x - 39/16

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept

If a linear equation crosses through two known points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:

a = (y₂ - y₁)/(x₂ - x₁)

And two lines are parallel if and only the two lines have the same slope and different y-intercept.

Here we want to find a line that passes through (-6, 1) and (10, 0), the slope of that line is:

a = (0 - 1)/(10 + 6) = -1/16

And we want to find a line with this slope that passes through the point (-7, -2), so we need to have:

-2 = (-1/16)*-7 + b

-2 = 7/16 + b

-2 - 7/16 = b

-32/16 - 7/16 = b

-39/16 = b

So the linear equation is:

y = (-1/16)*x - 39/16

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Answer:

$18

Step-by-step explanation:

15 : 100 = x : 15

x =  15 · 15 / 100

x = 225 / 100

x = $ 2.25 (tips)

5 : 100 = x : 15

x = 15 · 5 / 100

x = 75 / 100

x = $ 0.75 (tax)

15 + 0.75 + 2.25 = $18

The total expected waiting time including the morning and the evening time is 41/3

given that your waiting time for a bus in the morning is uniformly distributed on [0, 8], whereas waiting time in the evening is uniformly distributed on [0, 10] independent of morning waiting time.

Sum of both waiting times = X+Y

Where X = morning wait time is U(0.8) and

Y = evening wait time is U(0,10)

Since X and Y are independent

Var(x+y) = Var(x)+Var(y)

Var(x) = (8^2 - 0^2)/12 = 16/3

Var(Y) = (10^2 - 0^2)/12 = 25/3

Var(x+y) = 16/3 + 25/3

= (16 + 25)/3

= 41/3

Therefore, the total expected value of waiting time including the morning and the evening time is 41/3.

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On solving the provided question, P = 0.037 reject H o,P-value < 0.05 ( level of significance )

If there is no statistical significance between two variables, the null hypothesis is that there isn't any. The researcher or experimenter generally aims to refute or undermine the theory. An alternate explanation is that the two variables have a statistically significant association.

based on P value -

P = 0.037 reject H o

P-value < 0.05 ( level of signifance )

we are 95% y confidence that the average age of divorced man is how different than it was in 1989.

we would have concluded that the average age is not different wher, it really was different.

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Answer:

Step-by-step explanation: Raúl should put a turn of -30° in the walkway after the tree in order to continue in the same direction as before. This is because the negative angle will cancel out the positive angle and the walkway will continue in the same direction as before.

The t statistic used to determine whether the slope is significant is 6.709 when applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).

Given that,

The following information was discovered after applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).

y=12+1.8x

n=17

SSR=225

SSE=75

S₀₁=0.2683

We have to find what is the t statistic used to determine whether the slope is significant.

We know that,

Given by, the t test is used to determine whether the slope is significant.

t= b1/s.e

Where b1= slope of the given regression line

s.e= standard error of the line ( Sb1)= 0.2683

The regression line is given by

Y=12+1.8X

X is the independent variable here, and Y is the dependent variable.

Intercept = 12

Slope = 1.8

The t test is used to determine whether the slope is significant.

t= b1/s.e=1.8/0.2683= 6.7089=6.709

Therefore, The t statistic used to determine whether the slope is significant is 6.709 when applying regression analysis to sales data (in $1,000s) and advertising data (in $100s).

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Answer:

OD=Vertex: (1, -25); intercepts: x= 6,-4

Step-by-step explanation:

y=x²-2x-24

where a = 1,b = –2 and c = –24

to find the vertex we will use this formula

Step 1

(h,k) = (-b/2a, -D/4a), where D = b²–4ac.

(h,k) = (–(–2)/2×1) , –((–2)² – 4 × 1 × –24/4×1)

(h,k)= (2/2) , –(4 + 96)

(h,k) = (1 , –100/4)

(h,k) = (1,–25)

STEP 2

To find x intercept make y = 0

y=x²-2x-24

x² – 2x – 24 = 0

x² –6x + 4x – 24 = 0

x(x –6) +4(x –6) = 0

(x+4)(x–6)=0

x+4 = 0; x = –4

x–6 = 0; x = 6

x = (–4,6)

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Answer:

small car: 2

medium car: 2

luxury car: 2

Small van: 2

Large van: 3

Step-by-step explanation:

just multiply the amount per day by numbers increasing from 1 till you get a number that is larger than the week.  I swear whoever made this car rental will not be in business much longer lol.

For 2 days, vehicle can be given to rent before it would be less expensive to rent.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

Given that,

Rent for small car,

For 1 day = $100.

For 1 week = $250

The maximum days in which small car could be given to rent,

= 250 / 100 = 2.5 ≅ 2 days.

Similarly, for medium car = 290 / 110 = 2.7 ≅ 2 days.

For luxury car = 325 / 120 = 2.54  ≅ 2 days.

For small van = 350 / 150 = 2.3  ≅ 2 days.

And for large can = 390 / 170 = 2.28  ≅ 2 days.

Each car can be rented for 2 days before it would be less expensive for the week.

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Answer: 2

Step-by-step explanation:

Answer:

t ≥ 5

Step-by-step explanation:

In the tank now: 19

Fill rate per minute: 6

Number of minutes: t

Amount filled in t minutes: 6t

Total amount in tank after t minutes: 6t + 19

Amount desired: at least 49 liters

At least 49 liters means "greater than or equal to 49"

Inequality:

6t + 19 ≥ 49

Subtract 19 from both sides.

6t ≥ 30

Divide both sides by 6.

t ≥ 5

The null hypothesis in the given question is 'the mean annual consumption of high fructose corn syrup by a person in the United States is 48.8 pounds' and the alternative hypothesis in the given question is 'the population standard deviation is 3.6 pounds.'

Population mean = 48.8 pounds

Sample size = 120

Sample mean = 49.5 pounds

Population standard deviation = 3.6

α = 0.05

The standardized statistic z is:

z = (Sample mean - Population mean) x (√n / standard deviation)

z = (49.5 - 48.8) x (√120/3.6)

z = 2.13

The standardized statistic P is:

P = 2 - 2 x Φ(z)

P = 2 - 2 x 0.983

P = 0.034

Since, the result we get is statistically significant. We reject the null hypothesis.

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For the given circle the value of cotθ is -√30/√19.

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

The terminal side of an angle θ.  

The standard position intersects the unit circle at (√30/7, -√19/7).

We need to find the value of cotθ.

Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)

cotθ=x/y

=-√30/7/√19/7

=-√30/7×7/√19

=-√30/√19

Hence, the value of cotθ is -√30/√19 for the given circle.

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The Florida health insurance company can use a variety of predictive methods to predict the annual claims for the sample of 50 customers. These methods include machine learning algorithms such as linear regression and decision trees, as well as statistical methods such as regression analysis and logistic regression.

The company can also use qualitative methods such as interviews and surveys to gain insight into customer needs and preferences. By combining quantitative and qualitative methods, the company can create a more accurate prediction of the annual claims for its sample of 50 customers.The company can calculate its predictions by first gathering data on each of the 50 customers, such as age, gender, health history, lifestyle, and other factors. It can then use this data to create a predictive model that can be used to estimate the annual claims of each customer. These methods include machine learning algorithms such as linear regression and decision trees, as well as statistical methods such as regression analysis and logistic regression. The model can be tested and refined as necessary to ensure it is accurate and reliable. Finally, the company can use the model to make its predictions for the 50 customers.

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The profit earned per day is $6674.695 at point (449.93,500.02).

Let the number of pair of super-fit jeans = x

Let the number of pair of super-hug jeans = y

We know that x,y≥0.

Total time provided for cutting per day = 18,999 minutes

Total time provided for sewing and finishing per day = 40,999 minutes

Therefore, the inequalities are:

20x+20y ≤ 18,999

30x+55y ≤ 40,999

The shaded region is the feasible region and the point of intersection is (449.93,500.02).

The profit on Super-fit jeans = $6.50

The profit on super-hug jeans = $7.50

To maximise the profit in a day, we maximize z = (6.50 x x) + (7.50 x y)

The maximum profit is obtained at (449.93,500.02).

Therefore, z = (6.50 x 449.93) + (7.50 x 500.02)

z = 2924.545 + 3750.15

z = 6674.695

The profit earned per day is $6674.695.

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The probability of both people being Democrats is 0.243, and the probability of one person being a Republican and one person being a Democrat is 0.486.

To find the probability of each of the following, we can use the formula for the probability of selecting a group of items from a larger group with replacement:

P(A and B) = P(A) * P(B)

Where P(A) is the probability of selecting the first item, and P(B) is the probability of selecting the second item.

Both people are Democrats:

There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting two Democrats is (16/31) * (16/31) = 0.243.

One person is a Republican and one person is a Democrat:

There are 15 Republicans and 31 total people, so the probability of selecting a Republican is 15/31. There are 16 Democrats and 31 total people, so the probability of selecting a Democrat is 16/31. Therefore, the probability of selecting one Republican and one Democrat is (15/31) * (16/31) = 0.486.

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Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50. We can infer that he has 60 nickels and 35 dimes.

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given,

Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50.

Set d and n to the appropriate numbers.

Timmy has 95 coins in total, all of which are dimes and nickels, as far as we know.

Equation,

So d + n = 95

His bank is worth a total of $6.50.

A nickel is worth $0.05, while a dime is worth $0.10.

So

0.10d + 0.05n = $6.50

Take note that we have just produced an equation system that we can solve.

The two equations exist.

D + n = 95

and

0.10d + 0.05n = 6.50.

The replacement approach is probably going to be the simplest way to solve this problem out of all the options available to us.

First, we'll want to change the second equation's terms so that one of the variables is defined.

d+ n = 95

Take d off on both sides.

n = 95 - d

Now, let's define "n."

After defining one of the variables, we can now enter (or replace) its value in the other equation. After replacing it, we can find a solution for the other variable.

0.10d + 0.05n = 6.50

n = 95 - d

0.10d + 0.05(95 - d) = 6.50

We now determine d.

0.10d + 0.05(95 - d) = 6.50

distribution of the 0.05 in step 1

0.05 × 95 = 4.75

and

0.05 × -d = -0.05d

0.10d + 4.75 - 0.05d = 6.50

Step 2: Add like terms together (0.10 - 0.05) to get 0.05

0.05d + 4.75 = 6.50

step 3: Take 4.75 off of each side.

0.05d = 1.75

step 4: Subtract 0.05 from both sides.

0.05d / 0.05 = d and 1.75 / 0.05 = 35

d = 35

Now that we know the value of one variable, we can use it to solve for the second variable by plugging it into one of the equations ( note that the equation that we use does not matter, we will acquire the same answer )

d + n = 95

d = 35

35 + n = 95

Take 35 off both sides.

n = 60

We can infer that he has 60 nickels and 35 dimes.

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(a) The probability that X, = 1 will be =1/2

(b) The probability that X, = 1 given X,= 1 will be =2/3

(c) The probability that in the first 4 trials you get (at least) three white balls in a row will be=2/5

(d) The expected value of the number of white balls in 4 trials will be=2

(e) The variance of the number of white balls in 4 trials will be=2

A box starts with 2 balls; [ black and 1 white, x draw on these balls are supposed to be uniformly at random then we will replace it with 2 of the same colour. The Process repeats for Each i=1,2,3..........

Let x_1=1, if we draw a white ball on trial 1

The Property of the x_1 is

The Event where The drawn fall is white =A

Let the number of white balls in 4 trials is denoted by 'x'.

[tex]P(x=0) P\left(A^c A^c A^c A^c\right) . \\=1 / 2 \times 3 / 3 \times 3 / 4 \times 4 / 5=1 / 5 . \\P(x-1)=P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right) \\=1 / 2 \times 1 / 3 \times 1 / 4 \times 3 / 5+1 / 4 \times 1 / 3 \times 2 / 3 \times 3 / 5+1 / 2 \times 2 / 3 \times 1 / 4 \times 3 / 5+1 / 2 \times 2 / 3^2 \times 3 / 4 \times 1 / 5 . \\=\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20} . \\=4 \times \frac{1}{20}=1 / 5 . \\[/tex]

[tex]\therefore P(x=2)=1 / 2 \times 2 / 3 \times 1 / 4 \times 2 / 5 \times 4 / 2=6 \times 1 / 3=1 / 5 .[/tex]

[tex]$\begin{aligned} \therefore P(x=2) & =1 / 2 \times 2 / 3 \times 1 / 4 \times 2 / 5 \times 4 / 2=6 \times 1 / 3=1 / 5 . \\ P(x=3) & =1 / 2 \times 2 / 3 \times 3 / 4 \times 1 / 5 \times 4 / 3 . \\ & =1 / 20 \times 4=1 / 5 . \\ P(x=4) & =1 / 2 \times 2 / 3 \times 2 / 4 \times 4 / 5=P(\text { AAAA })=1 / 5 .\end{aligned}$[/tex]

(a)

[tex]P\left(X_2=1\right) & =P(A A)+P\left(A^C A\right) . \\& =1 / 2 \times 2 / 3 \times 1 / 2 \times 1 / 3 . \\& =2 / 6+1 / 6=3 / 6=1 / 2 . \\P\left(X_4=1\right)= & P(A A A)+P\left(A A A A^{\prime} A\right)+P\left(A^C A A\right)+P\left(A^{\prime} A^{\prime} A\right)+P \\& \left.\quad\left(A^{\prime} A A A\right)+P\left(A^{\prime} A^{\prime} A\right)+P\left(A^A A A\right)\right) \\[/tex]

[tex]= & 1 / 5+1 / 20+1 / 20+1 / 20+1 / 20+1 / 30+1 / 30+1 / 20 . \\= & 1 / 5+4 / 20+3 / 20 .=2 / 5+1 / 10 . \\= & \frac{4+1}{10}=5 / 10=1 / 2 .[/tex]

[tex]$\therefore$[/tex] Probability that x_2=1 is equal with probability that x_4 >1

(b) Probability that x_2=1 given x_4=1

[tex]$$\begin{aligned}& =P\left(x_2=1 / x_{4=1}\right)=\frac{P\left(x_2=1 \& x_4=1\right)}{P\left(x_4=1\right) .} \\& =\frac{P(A A A A)+P\left(A A A^{\prime} A\right)+P(A A A A)+P\left(A^C A A^C A\right)}{1 / 2} \\& =2 \times(1 / 5+1 / 20+1 / 20+1 / 30] \\& =2 \times[1 / 5+1 / 10 \times 1 / 30] \\& =2 \lambda\left[\frac{6+30+1}{30}\right] \\& =2 \times \frac{10}{30} .=2 / \mathrm{3} .\end{aligned}$$[/tex]

(c) Probability that in that the nuts is 3 which is P(x=3)+P(x=4) is [tex]=1 / 5+1 / 5=2 / 5[/tex]

(d) Expected volume of number of white ball is 4 trial is,

[tex]$$\begin{gathered}{[0 \times 1 / 5+1 \times 1 / 5+2 \times 1 / 5+3 \times 1 / 5+3 \times 1 / 5+4 \times 1 / 5]} \\=\frac{1+2+3+4}{5}=10 / 5=2 .\end{gathered}$$[/tex]

(e)

[tex]E\left(x^2\right) & =0^2 \times 1 / 5+1^2 \times 1 / 5+2^2 \times 1 / 5+3^2 \times 1 / 5 .+4^2+1 / 5 . \\& =\frac{1+4+9+16}{5 .} \\& =30 / 51=6 . \\\therefore var/x =E\left(x^2\right)-E[(x)]^2 . \\& =6-2^2 =6-4=2[/tex]

[tex]$\therefore$[/tex] The variance of the number of white balls in 4 trails =2

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Answer: D & C

Step-by-step explanation:

The net Income of the business is represented as

Net profits or income = Net sales revenue (gross income) – Cost of goods and services sold – Administration, operating, marketing, and advertising costs, taxes, interests, and other expenses.

Here C is an option because we need to take operating expenses into consideration but if you consider cost of goods brought into store as operating then option changes to D.

D represents the sales which helps us determine the net income of the business.