Please help me with this!​

(1) The missing term in the sequence, a₁₂  = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6)  The missing term in the sequence, a₆ = 40.

(7)  The missing term in the sequence, a₃₆ = -52.

(8)  The missing term in the sequence, a₂₁ = -58.

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

T₄ = a + 3d

18.4 = a + 3d  ---(1)

T₅ = a + 4d

16.2 = a + 4d  ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂  = a + 11d

a₁₂  = 25 + 11(-2.2)

a₁₂  = 0.8

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d  --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ =  a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

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Answer:

Normally,in calculating the amount of space an object occupies...the volume method is require due to 3 dimensional rule,vice versa an area

The probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

Let A represent Female and B represents civil engineering.

The above representation means that the given parameters are:

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

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Answer: 0.5 or - 0.834

Step-by-step explanation: Here is the explanation!

Answer:

Adults = 448

Students = 888

Step-by-step explanation:

Write equations with info given

A = Adult tickets

S = Student tickets

5A+1S=3,128

A+S=1336

Subtract equations from each other

4A=1792

Solve for A

A=448

Plug A into second equitation

448+S=1336

Solve for S

S=888

Answer:

y = 2/3

Step-by-step explanation:

Assuming you are looking for "y":

15 * ( y - 4 ) - 2 * (y - 9 ) + 5 * (y + 6) = 0

15y - 60 - 2y + 18 + 5y + 30 = 0

15y - 2y + 5y -60 + 18 + 30 = 0

18y = 60 - 18 - 30

18y = 12

y = 12/18

y = 2/3

The answers to the question are

The median of the data set is gotten by arranging the values in order

3, 4, 5, 5, 7, 8

The median can be gotten by

5 + 5 / 2

= 10/2

Median = 5

This is the value under which 25 percent of the data are found in the group of data. The lower quartile is 4.

This is the point from which 75 percent of the data is found when it is in ascending order. The upper quartile is 7.

The lowest value in the data set is 3

The highest value in the data set is 8

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The computation of the index shows that the value of 9 × 10² will be 900.

From the information given, we are told to calculate the value of 9 × 10². This will be calculated thus:

= 9 × 10²

Note that 10² simply means that you've to multiply 10 twice. This will be:

= 10 × 10 = 100

Therefore, 9 × 10² will be:

= 9 × 100

= 900

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Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

So for 13th n

#c

attached

#d

Already given in c

Answer:

67m²

Step-by-step explanation:

12m + 6m + 4m + 36 m 8m = 67m²

Answer:

175 ft^2

Step-by-step explanation:

split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2

then the pentagon has an area 35*5 = 175 ft^2

Answer:

[tex]31.8\%[/tex]

Step-by-step explanation:

The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]

The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]

Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]

Answer:

Multiply:

[tex](x+y)by (x+y)[/tex]

[tex] : \implies(x + y)(x + y)[/tex]

[tex] : \implies \: x(x + y) + y(x + y)[/tex]

[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]

[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]

Multiply:

[tex]a+b \: by \: a^2-b^2[/tex]

[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]

[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]

[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]

Multiply:

[tex](a+5) by (a^2-2a-3)[/tex]

[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]

[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]

[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]

[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]

[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]

Multiply:

[tex](a^2-ab+b^3) by (a+b)[/tex]

[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]

[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]

[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]

[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]

Step-by-step explanation:

[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]

Answer:

tiookvgvc. jbjvth kivtcth jjvf h. bkbgv

Answer:

The IQR of the given distribution is

Step-by-step explanation:

The given distribution has the five-number

28, 34, 43, 59, 62

Divide these numbers in two equal parts.

(28, 34), 43,( 59, 62)

Now divide each parenthesis in two equal parts.

(28), (34), 43,( 59), (62)

It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.

The interquartile range (IQR) of this distribution is

Therefore the IQR of the given distribution is 29.5.

Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

where:

Rewrite both equations into slope-intercept form:

a) 2x + 4y = 15

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

b) 6x + 12y = 45

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

New equations:

[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

No Solution: the same slope (both lines will be parallel)

One Solution: different slopes and different y-intercepts

Infinitely Many Solutions: the same slope and y-intercept

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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

Equation #1

Subtract 2x from both sides

Divide both sides by 4

Equation #2

Subtract 6x from both sides

Divide both sides by 12

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

Answer: Yes it is possible

Example: Yeast is a single-celled fungus.

There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.

Answer:

2

Step-by-step explanation:

the same as...

(2) is the answer

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

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Answer:

[tex]x=\frac{3}{4},\:x=-1[/tex]

Keys:

For this problem, you need the quadratic formula(listed below).

When you see ± in a quadratic equation, you must know there is going to be at least 2 solutions.

Step-by-step explanation:

solving for x₁ and x₂

[tex]4x^2+x=3\\4x^2+x-3=3-3\\4x^2+x-3=0\\x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot 4\left(-3\right)}}{2\cdot 4}\\[/tex]

[tex]1^2=1\\=\sqrt{1-4\cdot \:4\left(-3\right)}\\=\sqrt{1+4\cdot \:4\cdot \:3}\\=\sqrt{1+48}\\=\sqrt{49}\\=\sqrt{7^2}\\\sqrt{7^2}=7\\=7[/tex]

[tex]x_{1,\:2}=\frac{-1\pm \:7}{2\cdot \:4}\\x_1=\frac{-1+7}{2\cdot \:4},\:x_2=\frac{-1-7}{2\cdot \:4}\\[/tex]

solve for x₁

[tex]\frac{-1+7}{2\cdot \:4}[/tex]

[tex]=\frac{6}{2\cdot \:4}[/tex]

[tex]=\frac{6}{8}[/tex]

[tex]= \frac{6\div2}{8\div2}[/tex]

[tex]=\frac{3}{4}[/tex]

solve for x₂

[tex]\frac{-1-7}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{2\cdot \:4}[/tex]

[tex]=\frac{-8}{8}[/tex]

[tex]=-\frac{8}{8}[/tex]

[tex]=-1[/tex]

Hope this helps!

[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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9880 different possibilities are there in Sally's new combination option second 9880 is correct.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

We have:

Total unique numbers consists in a Sally locker = 3

From the digits 0 to 39

Total numbers = 40

Apply combination formula:

= C(40, 3)

= 40!/(3!37!)

= 9880

Thus, 9880 different possibilities are there in Sally's new combination option second 9880 is correct.

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Answer:

B

Step-by-step explanation: