If the 1st and 10th terms of geometric sequence are 4 and 100, fin the nth term of the sequence.

Answer:

180°

cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°

The profit margin required to achieve 15% targeted ROE is 9.0%

The ROE means return on equity, it is the return earned on shareholders fund or shareholders equity.

Based on the three-way DuPont approach to computing the ROE, the below formula is very relevant to this analysis:

ROE=net profit margin*assets turnover*equity multiplier

ROE=15%

net profit margin=the unknown now(assume it is X)

assets turnover=sales/total assets

assets turnover=$778,500/$468,500

assets turnover=1.6616862326574200

equity multiplier=total assets/total equity

Note the company is entirely financed by equity(zero debt) which means that total assets is the same as total equity

equity multiplier=$468,500 /$468,500

equity multiplier=1.00

15%=X*1.6616862326574200*1.00

15%=X*1.6616862326574200

X=15%/1.6616862326574200

X=9.0%

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Answer:

960 feet

Step-by-step explanation:

30×6=180

180×2=360

50×6=300

300×2=600

360+600=960

The energy is compared based on the information given below.

Energy released by burning 1 kilogram of element A = EA = 5.1 * (10)8

Energy released by fission of hydrogen in 1 kilogram of element B = EB = 1.3 * (10)10

Therefore,

Ratio = EB / EA = 1.3 * (10)10 / 5.1 * (10)8 = 25

Thus, the fission of 1 kg of element B releases 25 times as much energy as burning 1 kilogram of element A.

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The other part of the question:

Energy released by burning 1 kilogram of element A = 5.1 times 10 Superscript 8

Energy released by the fission of hydrogen in 1 kilogram of element B = 1.3 times 10 Superscript 10

Answer:

t + 3

Step-by-step explanation:

adding 3 years onto t amount of years

Answer:

[tex]\implies y=(x-2)^2-6[/tex]

Step-by-step explanation:

Vertex form of a quadratic equation:

[tex]y=a(x-h)^2+k[/tex]

where:

Given vertex:  (2, -6)

⇒ h = 2 and k = -6

Substitute the values of h and k into the formula:

[tex]\implies y=a(x-2)^2+(-6)[/tex]

[tex]\implies y=a(x-2)^2-6[/tex]

As we have not been given a value for the constant [tex]a[/tex], assume this is 1.

Therefore, the vertex form of the quadratic function with vertex (2, -6) is:

[tex]y=(x-2)^2-6[/tex]

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Vertex form

a=1

Put values

Answer: -5

Step-by-step explanation:

-3x+9y=-57                x=4

-3(4)+9y=-57

-12+9y=-57

             +12

9y=-45

    9y

y=-5

Answer:

Step-by-step explanation:

First find the percentage of the ones that pass that study

.93 *(88)=88.84%

next find the ones that pass that did not study

.09*(100-88)=1.08

sum these to get the total passing percentage

88.84+1.08=82.92%

The probability is 82.9 per 100 or .8292 for student

E is the answer

The area between the two functions is 0

The functions are given as:

f₁(x)= 1

f₂(x) = |x - 2|

x ∈ [0, 4]

The area between the functions is

A = ∫[f₂(x) - f₁(x) ] dx

The above integral becomes

A = ∫|x - 2| - 1 dx (0 to 4)

When the above is integrated, we have:

A = [(|x - 2|(x - 2))/2 - x] (0 to 4)

Expand the above integral

A = [(|4 - 2|(4 - 2))/2 - 4] - [(|0 - 2|(0 - 2))/2 - 0]

This gives

A = [2 - 4] - [-2- 0]

Evaluate the expression

A = 0

Hence, the area between the two functions is 0

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The equation of the median in standard form is; 9y - 38x = 179.

It follows from the task content that the point D is the midpoint of segment BC; Hence, the coordinates of point D given the coordinates of B and C above are given as; D(-13, -35).

The equation of the median which is the line joining points A and D is therefore determined as follows;

Slope = (-35-3)/(-13-(-4)) = 38/9

38/9 = (y-3)/(x+4)

9y -27 = 38x + 152

9y - 38x = 179.

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Answer:

Step-by-step explanation:

A) The median number is just the middle number so it should be 2.8

B) Bottom 30% are the six lowest amounts. The highest of the bottom six numbers is 2.3. Not sure what it means by calculating them. 1.8, 1.9, 1.9, 2.0, 2.1, and 2.3 are the lowest six. If you need to add them up the answer is 12.
C) I don’t know what your Q1 is.

Answer:

b

Step-by-step explanation:

(-4(-1)-8)(3(2)^2+2=4-8×12+2

-4×14=-56

Answer:

80 square units

Step-by-step explanation:

These are rectangles and triangles.

The formula to get the area of a rectangle is its length multiplied by its width.

The formula to get the area triangle is its base multiplied by its height, then divided by 2.

The 3 rectangles all share the width of 6 units, so we can combine the 3 rectangles and consider it as 1 large rectangle.

The lengths of the rectangles are 2, 8, and 2 units.

We can add them together to get a total height of 12 units.

So, the formula to get the area of this rectangle is:
[tex]6\times12= A[/tex]

By solving this, we get:
A = 72 square units

There are 4 triangles remaining.

The base and height of all the triangles are 2 units.

So, by plugging these values into the triangle area formula, as mentioned from the beginning, we get:

[tex](2\times2)\div2=A[/tex]

So, the area of 1 triangle is 2 square units.

But since there are 4 triangles with the same bases and heights, we will multiply the area of 1 triangle by 4.

So, [tex]4 \times 2 = A[/tex]

This means the area of all the triangles together is 8 square units.

By adding the area of the triangles and rectangles together, we will get the answer.

[tex]72+8 = A[/tex]

So, the total area of this box is 80 square units.

Answer:

16.7 degrees

Step-by-step explanation:

The measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two lines that are parallel to each other or p ll q

The angle made by transversal t is 136 degrees

The measure of the other angle = 180 - 136 = 44 degrees

Draw a line parallel to p and q and passes through the intersection point of line t and v

The angle made by the transversal and the line drawn is the same as 44 degrees.

The measure of the other angle = 121 - 44 = 77 degrees

Thus, the measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

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The expanded form of the given exponential equation is 6718464

Exponential equations are inverse of logarithmic equations. The standard exponential equation is expressed as. y = ab^x

where

a is the base

x is the exponent

Given the expression below;

a = 4(6)^8​

Expand to have:

a = 4 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6

a = 4 * 1679616
a = 6718464

Hence the expanded form of the given exponential equation is 6718464

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The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

In this case, we know two angles (A = 25°, C = 90°) and a side of a triangle (b = 16) and Euclidean properties and the law of the sines must be used to find the rest of variables:

B = 180° - A - C

B = 180° - 25° - 90°

B = 65°

a = 16 × (sin 25°/sin 65°)

a ≈ 7.461

c = 16 × (sin 25°/sin 90°)

c ≈ 6.762

The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

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The values of x after the statement are:

This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.

Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false

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Adding the difference between [tex]$\frac{9}{16}[/tex] and [tex]$\frac{5}{4}[/tex] we get [tex]$1 \frac{13}{16}[/tex].

Find the least common denominator or LCM of the two denominators:

LCM of 4 and 16 exist 16.

Subsequently, estimate the equivalent fraction of both fractional numbers with denominator 16.

For the 1st fraction, since 16 × 1 = 16,

9/16 = (9 × 1) / (16 × 1) = 9/16

For the 2nd fraction, since 4 × 4 = 16,

5/4 = (5 × 4) / (4 × 4) = 20/16

Add the two like fractions, then we get

(20/16) + (9/16) = (20 + 9)/16 = 29/16

So, [tex]$\frac{5}{4}+\frac{9}{16} =\frac{29}{16}[/tex]

In mixed form: [tex]$1 \frac{13}{16}[/tex].

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The solution to the system of inequalities is (-3.375, 1.75)

The system of inequalities is given as:

3y > 2x+12

2x+y < -5

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-3.375, 1.75)

Hence, the solution to the system of inequalities is (-3.375, 1.75)

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The cost of one ounce of peanuts is $0.20

The cost of one ounce of cashew is $0.35

15p + 5c = 4.75 equation 1

5p + 15c = 6.25 equation 2

Where:

Multiply equation 2 by 3

15p + 45c = 18.75 equation 3

Subtract equation 1 from equation 3

40c = 14

c = 14/40

c = $0.35

Substitute for c in equation 1

15p + (5 x 0.35) = $4.75

15p + 1.75 = 4.75

15p = 4.75 - 1.75

15p = 3

p = 3/15

p = $0.20

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By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.

From statement we have two lines in space, whose vector forms are described below:

(x, y, z) = (1, - 9, 1) + t · (4, 1, 2)     (1)

(x, y, z) = (1, 0, - 9) + s · (5, - 1, 5)     (2)

The point of intersection satisfies the following condition:

(1, - 9, 1) + t · (4, 1, 2) = (1, 0, - 9) + s · (5, - 1, 5)

(1, - 9, 1) - (1, 0, - 9) = s · (5, - 1, 5) + t · (- 4, - 1, - 2)

s · (5, - 1, 5) + t · (- 4, - 1, - 2) = (0, - 9, - 8)

There is a point of intersection if the resulting system of linear equations has at least a solution:

5 · s - 4 · t = 0      (2)

- s - t = - 9      (3)

5 · s - 2 · t = - 8     (4)

By (2):

s = 4 · t/5

(2) in (3):

- 4 · t/5 - t = - 9

- 9 · t/5 = - 9

t/5 = 1

t = 5

(2) in (4):

5 · (4 · t/5) - 2 · t = - 8

4 · t - 2 · t = - 8

2 · t = - 8

t = - 4

By reduction to the absurd, the two lines do not intercept each other because of the following absurd: 5 = - 4.

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The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. then the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be 15.1kg or less is 0.121 and 15.1kg or more is 0.879.

Given Information:

Population mean, μ = 15.8 kg

Population standard deviation, σ = 4.2 kg

For finding the probability for the sample mean, we first need to find the standard score.

(a) For sample mean to be 15.1kg or less,

z = (x - μ) / (σ/√n)

Here, x = 15.1

⇒ z = (15.1 - 15.8) / (4.2/√49

z =-0.7 / (4.2/7)

z = -1.17

Now, we can use the z-table to find the probability of the sample mean to be 15.1kg or less.

∴ P(x ≤ 15.1) = 0.121

(b) Now, to find the probability of sample mean to be 15.1kg or more, we can simply subtract P(x ≤ 15.1) from 1.

⇒ P(x ≥ 15.1) = 1 - P(x ≤ 15.1)

P(x ≥ 15.1) = 1 - 0.121

P(x ≥ 15.1) = 0.879

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The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.

Total number of people for a trip to a baseball game = 15

Number of people planning to go on Saturday = 10

Number of people planning to go Sunday = 12

Let x be the number of people who can go on both Saturday and Sunday.

Then, the number of people who can go only on Saturday is 10 - x.

And the number of people who can go only on Sunday is 12 - x.

Total of 15 people are going to the baseball game.

Using set theory we have,

Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15

Substitute the value we have,

⇒(10 - x) + (12 - x) + x = 15

Simplifying the above equation, we get,

⇒22 - x = 15

⇒ x = 7

The number of people who can only go to the game on Sunday is

= 12 - x

= 12 - 7

= 5

Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .

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Answer:3/7

Step-by-step explanation:There are total 7 days in a week. 3 days were dry so the fraction is 3/7 . The dry days over the total days of the week

After rounding to the nearest tenth, we get:

[tex]\frac{2.1}{1.488} = 1.5[/tex]

We have the quotient:

[tex]\frac{2.1}{1.488}[/tex]

If you multiply the numerator and denominator by 1000, you will get the simpler quotient:

[tex]\frac{2100}{1488}[/tex]

It gives:

[tex]\frac{2100}{1488} = 1.45[/tex]

Now we want to round it to the nearest tenth, which is the first digit after the decimal point.

To do so, we need to look at the number at the right of it.

In this case, we can see a 5, so we should round up, then we have:

[tex]\frac{2100}{1488} = 1.5[/tex]

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Possible Dimensions of one prism are; 2cm, 3 cm and 4cm

Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm

We are told that volume of both rectangular prisms is; V = 24 cm³

Now, formula for Volume of a rectangular prism is;

V = lwh

where;

l is length

w is width

h is height

Thus, to solve this, we have to look for multiples of 24 which are;

1, 2, 3, 4, 6, 8, 12, 24.

Now, we must pick 3 numbers from the above in which their products will be equal to 24.

Thus;

Possible Dimensions of one prism are; 2cm, 3 cm and 4cm

Possible Dimensions of second prism are; 1 cm, 4 cm, 6 cm

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The first three statements are not a negation. Only the last statement is a negation.

The opposite of the given mathematical statement is the negation of a statement in mathematics. If "P" is a statement, then "P" is the statement's negation. The words negation is used to denote a statement's denial.

It's vital to know the opposite of a given mathematical statement from time to time in mathematics. This practice is known as "negating" a statement. Remember that if a statement is true, then its negation must be false (and if a statement is false, then its negation is true).

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