When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 4?
A. 1:3
B. 3:1
C. 1:4
D. 4:1

The total area of the regular pentagon prism is 485 square units

The given parameters are:

Base area = 50

Height = 11

Base = 7

Start by calculating the total area of the 5 sides using

Sides = n * Height * Base

Sides = 5 * 11 * 7

Sides = 385

The total surface area is

Total = 2 * Base area + Sides

This gives

Total = 2 * 50 + 385

Evaluate

Total = 485

Hence, the total area of the regular pentagon prism is 485 square units

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The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

In this problem we have the following relationship bewteen the two quadratic equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):

[tex]k = \frac{x_{g}}{x_{f}}[/tex]

Let suppose that y = 3, then [tex]x_{f} = - 5.5[/tex] and [tex]x_{g} = - 1.8[/tex], then the value k is:

k = (- 5.5)/(- 1.8)

k = 3.056

The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.

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The value of the probability P(A∪B) is 39/50

The given parameters are:

P(A)= 9/20

P(B) = 3/5

P(A∩B) = 27/100

To calculate the probability P(A∪B), we make use of the following equation

P(A∪B) = P(A) + P(B) - P(A∩B)

So, we have:

P(A∪B) = 9/20 + 3/5 - 27/100

Evaluate the expression

P(A∪B) = 78/100

Simplify

P(A∪B) = 39/50

Hence, the value of the probability P(A∪B) is 39/50

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One sample Z Test is used by cate.

According to the statement

The average tuition in Illinois is $28,950 with a standard deviation of $3,470.

Assuming we have a large enough sample, since we are testing one group's mean relative to a hypothesized value, this would be a one-sample z-test.

So, One sample Z Test is used by cate.

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The geometric series which result in a sum of -69,905 is: D. [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]

Mathematically, the standard form of a geometric series can be represented by the following expression:

[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]

Where:

Also, the sum of a geometric series is given by:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

For option A, we have:

r = -5, n = 8, a₁ = 1/4 = 0.25

[tex]S=\frac{0.25(1-(-5)^8)}{1-(-5)}[/tex]

S = -24,414.

For option B, we have:

r = 5, n = 12, a₁ = -1/4 = -0.25

[tex]S=\frac{-0.25(1- 5)^{12})}{1-5}[/tex]

S = -15,258789.

For option C, we have:

r = -4, n = 11, a₁ = 1/5 = 0.2

[tex]S=\frac{0.2(1-(-4)^{11})}{1-(-4)}[/tex]

S = -279,620.

For option D, we have:

r = 4, n = 10, a₁ = -1/5 = -0.2

[tex]S=\frac{-0.2(1-4^{10})}{1-4}[/tex]

S = -69,905.

In conclusion, the geometric series which result in a sum of -69,905 is [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]

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a. The continuous growth rate of the bacteria is 21%

b. The initial population of bacteria is 715

c. The culture will contain 2043 bacteria after 6 × 10⁻⁴ years

Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture.

This function is similar to an exponential function of the form  [tex]y(t) = Ae^{\lambda t}[/tex] where λ = growth rate

Comparing n(t) and y(t), we see that λ = 0.21

So, the continuous growth rate of the bacteria is 0.21 = 0.21 × 100 %

= 21%

So, the continuous growth rate of the bacteria is 21%

Since [tex]n(t) = 715e^{0.21t}[/tex] represents the number of bacteria in the culture, the initial population of bacteria is obtained when t = 0.

So, [tex]n(t) = 715e^{0.21t}[/tex]

[tex]n(0) = 715e^{0.21(0)} \\= 715e^{0} \\= 715 X 1\\= 715[/tex]

So, the initial population of bacteria is 715

To find the time when the number of bacteria will be 2043, this means n(t) = 2043.

Since  [tex]n(t) = 715e^{0.21t}[/tex]

Making t subject of the formula, we have

t = ㏑[n(t)/715]/0.21

So, substituting n(t) = 2043 into the equation, we have

t = ㏑[n(t)/715]/0.21

t = ㏑[2043/715]/0.21

t = ㏑[2.8573]/0.21

t = 1.05/0.21

t = 4.99

t ≅ 5 hours

Converting this to years, we have t = 5 h × 1 day/24h × 1 year/365 days

= 5/8760

= 5.7 × 10⁻⁴ years

≅ 6 × 10⁻⁴ years

So, the culture will contain 2043 bacteria after 6 × 10⁻⁴ years

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1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3,    h = 7) {where x = 8}. This can be obtained by forming equations for the given figures.

Given that,

dimensions (l = 3x, b = 3x, h = x) and there is one door (b =3, h = 7)

expression of square feet of wallpaper for family room,

⇒ area of four walls - area of one door= [(3x)(x)+(3x)(x)+(3x)(x)+(3x)(x)] - [3×7]

                                                               =[3x²+3x²+3x²+3x²] - 21

                                                               =12x² - 21 square feet

Given that,

height and width are same as of the family room but length is 5 times more than height [length = 5(height) ⇒ l = 5x]

dimensions (l = 5x, b = 3x, h = x) and there is two doors (b =3, h = 7)

expression of square feet of wallpaper for family room,

area of four walls - area of two doors= [(3x)(x)+(5x)(x)+(3x)(x)+(5x)(x)] - 2[3×7]

                                                               =[3x²+5x²+3x²+5x²] - 2(21)

                                                               =16x² - 42 square feet

total amount of wallpaper needed

⇒wallpaper for family room + wallpaper for living room = 12x²-21 + 16x²-42

                                                                                        =28x²-63 square feet

Area of wallpaper of living room - area of wallpaper of family room

= 1750 - 747

= 1003 square feet

Hence 1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3,    h = 7) {where x = 8}.

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Henry was 40 feet away from his original starting point. Using Pythagorean's theorem it is calculated.

The theorem says that,

In a right-angled triangle, the sum of squares of the lengths of two arms (opposite and adjacent sides) is equal to the square of the hypotenuse.

I.e, Consider a right-angled triangle ΔABC, where AC is the hypotenuse side of the triangle. So, according to the theory,

AC² = AB² + BC²

It is given that,

Henry walked on a flat field,

9 meters - towards the north

24 feet - towards the east

9 meters + 32 feet - towards the south

This can be shown in the diagram below.

In the diagram, the distance from the starting point is X, and the last point is  S.

To find the distance between these two points, a line is joined as shown in the diagram. Thus, it is formed as a right-angled triangle.

So, according to the Pythagorean theorem,

XS² = (24)² + (32)²

(here 32 feet is the only distance from the assumed point to the endpoint)

⇒ XS² = 1600 = 40²

∴ XS = 40 feet

So, Henry is 40 feet away from the original starting point.

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Answer:

Option C more peaked and more widely spread.

Step-by-step explanation:

15 + 35 + 18 + 30 + 25 + 21 + 32 + 16

80 + 78 + 34

192/8 = 24

24 + 22 + 27 + 28

46 + 55 = 101/4 = 25.2

Using the Pythagorean theorem and the law of sines, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are: A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°

The theorem states that the square of the longest side of a right triangle equals the sum of the squares of the lengths of the other two smaller sides of the right triangle.

The points, M(3,2), E(3,−3), and R(9,−3) has been plotted on the graph which shows that angle E  is a right triangle, therefore:

m∠E = 90 degrees.

Find ME and ER:

ME = 5 units

ER = 6 units.

Using the Pythagorean theorem, find MR:

MR = √(ME² + ER²)

MR = √(5² + 6²)

MR = √(25 + 36)

MR = 7.81 units

Using the law of sines, find m∠M:

sin M/ER = sin E/MR

sin M/6 = sin 90/7.81

sin M = (sin 90 × 6)/7.81

sin M = 0.7682

M = sin^(-1)(0.7682)

m∠M ≈ 50°

m∠R = 180 - 50 - 90

m∠R = 40°

Thus, the correct lengths to the nearest hundredth and the angle measures to the nearest degree are:

A) ME = 5; ER = 6, MR ≈ 7.81 m∠E = 90°, m∠M ≈ 50°, m∠R ≈ 40°

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The percentage of population has a resting heart rate is 15.7%.

Given that the mean of the data is 70 beats per minute and standard deviation is 4 beats per minute.

A probability distribution is a mathematical function that describes the probability of several possible values ​​of a variable.

Mean, μ=70

Standard deviation, σ=4

Given that the heart rate is resting between 74 and 82.

Now, we will use the standard normal formula

P(x₁<x<x₂)=P((x₁-μ)/σ<x<(x₂-μ)/σ)

Here x₁=74 and x₂=82.

Substitute these values in the formula, we get

P(74<x<82)=P((74-70)/4<x<(82-70)/4)

P(74<x<82)=P(4/4<x<12/4)

P(74<x<82)=P(1<x<3)

P(74<x<82)=P(x<3)-P(x<1)

Now, we will find the values by using the z-table, we get

P(74<x<82)=0.998-0.841

P(74<x<82)=0.157

P(74<x<82)=15.7%

Hence, the percentage of the population has a resting rate between 74 and 82 with the mean data is 70 beats per minute and the standard deviation data is 4 beats per minute is 15.7%.

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There are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

Given a word of 4 letters of the word "SOLVE".

We are required to find the number of ways the four letters of the word SOLVE if no letter can be used more than once.

Permutation is an arrangement of objects in a definite order of things.

Factorial of a number is the product of it and its lesser numbers upto 1.

Number of letters=4

Number of ways=4!

=4*3*2*1

=24 ways

Hence there are 24 ways in which we can arrange 4 letters of the word "SOLVE" if no letter can be used more than once.

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The value of the expression 6/5 * 240 is 288

The expression is given as:

6/5 * 240

Divide 240 by 5

6 * 48

Multiply 6 and 48

288

Hence, the value of the expression 6/5 * 240 is 288

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Answer:

Step-by-step explanation:

5*10*2=100

8*10/2=40

12*4*2=96

12*5=60

4*5*2=40

100+40+40+96+60=336cm²

The surface area for the given composite figure is 442 cm²

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is a composite figure, composed of a triangular prism and rectangular prism, attached to each other.

We will find the surface area of the composite figure by adding surface areas of both the solids and subtracting the common base area from it.

We know that, surface area of a triangular prism and rectangular prism, are S = bh+(b1+b2+b3)l and 2(lh+wh+lw) respectively.

Therefore, SA = 12(8)+(12+10+8)5 +2(12×5+4×5+12×4) - lw

= 96+150+2(60+20+48) - 12×5

= 246+256-60

= 442

Hence, The surface area for the given composite figure is 442 cm²

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One can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

It should be noted that an extraneous equation means a root of a transformed equation that isn't the root of the original equation due to the fact that it's excluded from the domain of the original equation.

In this case, one can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

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The x values to make a suitable ordered pair must be a multiple of 5

The function is given as:

y = -2/5x + 2

The slope of the above equation is:

m = -2/5

The above is a fraction with a denominator of 5.

So, the x values to make a suitable ordered pair must also be a multiple of 5

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By critically observing the graph shown in the image attached below, we can logically deduce that the slope of the graph of this function is equal to 0 for x, between x = -3 and x = -2.

Similarly, the slope of the graph of this function is also equal to 0 for x, between x = 3 and x = 4.

Based on the graph (see attachment), the greatest value of y is 4 while the smallest value of y is -3.

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The volume of the given composite figure is: 375 m³.

Volume of the composite figure = volume of triangular prism at the bottom + volume of rectangular prism at the top.

Volume of the composite figure = 0.5 * b * h * length + (l)(h)(w)

= 0.5 * 5 * 4 * 5 + (13)(5)(5)

= 50 + 325

Volume of the composite figure = 375 m³

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[tex]f(x) = 3(x + 2)(x - 5)[/tex]

[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]

[tex]ac {}^{2} = cb {}^{2} + ba {}^{2} - 2(cb)( ba)(cos \alpha ) \\ ac {}^{2} = 21 {}^{2} + 26 {}^{2} - 2(21)(26)(cos112) \\ ac {}^{2} = 441 + 676 - 1092(cos112) \\ ac {}^{2} = 1526.07 \\ ac = 39.065[/tex]

Answer:

Step-by-step explanation:

Step-by-step explanation:

Part A: [tex]u^6[/tex] can be written as the square of u³, or [tex](u^3)^2[/tex]. Similarly, [tex]v^6=(v^3)^2[/tex]. Hence, we can write this as a difference of two squares by writing it as

[tex](u^3)^2-(v^3)^2[/tex]

Part B:

We can first factor a difference of two squares a² - b² into (a+b)(a-b). Here, a would be u³ and b would be v³.

[tex](u^3+v^3)(u^3-v^3)[/tex]

We can factor this further by the use of two special formulas to factor a sum of two cubes and a difference of two cubes. These formulas are as follows:

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

Since u³ + v³ is a sum of two cubes, let's rewrite it.

[tex]u^3+v^3=(u+v)(u^2-uv+v^2)[/tex]

Since u³ - v³ is a difference of two cubes, we can rewrite it as well.

[tex]u^3-v^3=(u-v)(u^2+uv+v^2)[/tex]

Now, let's multiply them together again to get the final factored form.

[tex]u^6-v^6=(u+v)(u^2-uv+v^2)(u-v)(u^2+uv+v^2)[/tex]

Part C:

If we want to factor [tex]x^6-1[/tex] completely, we can just see that x to the sixth power is just [tex]x^6[/tex] and 1 to the sixth power is just 1. Hence, x can substitute for u and 1 can substitute for v.

[tex]x^6-1=(x+1)(x^2-x(1)+1^2)(x-1)(x^2+x(1)+1^2)\\x^6-1=(x+1)(x^2-x+1)(x-1)(x^2+x+1)[/tex]

We can repeat this for [tex]x^6-64[/tex], as 64 is just 2 to the sixth power.

[tex]x^6-64=(x+2)(x^2-x(2)+2^2)(x-2)(x^2+x(2)+2^2)\\x^6-64=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)[/tex]

Answer: [tex]\frac{2}{25} +\frac{11}{25}i[/tex]

Step-by-step explanation:

To get the following you have multiply the conjugate. [tex]\frac{(2-i)(3-4i)}{(3+4i)(3-4i)}[/tex]

Answer:

x = 75/4

Step-by-step explanation:

5/8 + 1 1/4 = x/10

5/8 + 5/4 = x/10

15/8 = x/10

8x = 15 × 10

8x/8 = 150/8

x = 150/8

x = 75/4

The 95th percentile for the average number of residents within five miles of each store is 20219.86.

Given mean of 19000 , sample size of 75 stores and standard deviation of 7600.

We have to find the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores.

We have to first find the margin of error to calculate the upper level of confidence interval.

Margin of error is the difference between the real values and calculated values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the critical value of z at given confidence level.

σ is standard deviation

n is the sample size.

z value at 95% confidence level is 1.39. (one tailed)

Put the values in the formula to get margin of error.

Margin of error=1.39*7600/[tex]\sqrt{75}[/tex]

=10564/8.66

=1219.86

Upper level=19000+1219.86

=20219.86

Hence the 95th percentile is 20219.86 for the average number of residents within five miles of each store in a sample of 75 stores.

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Based on the given inequality; x < 9 or x ≥ 14, the possible values of x are $8 and $14

x < 9 or x ≥ 14

From the options

All values less than 9 are

$8

All values greater than or equal to 14 are

$14

Therefore, based on the options given, the possible values of x are $8 and $14

Complete question:

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15

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The total sale of the bedding set including 5% sale tax is $69.66

An equation is an expression that shows the relationship between two or more variables and numbers.

Discount = 20% of 86 = 0.2 * 86 = 17.2

Selling price of bed = 5% of 17.2 = 0.05 * 17.2 = 0.86

Total sale = 86 - 17.2 + 0.86 = 69.66

The total sale of the bedding set including 5% sale tax is $69.66

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Percent of the original volume that is removed is; 18%

Formula for volume of a box is;

V = lbh

where;

l is length

b is breadth

h is height

Thus;

V_original = 15 * 10 * 8

V_original = 1200 cm³

Volume for each cube removed = 3 * 3 * 3 = 27 cm³

Since there are 8 corners on the box, then 8 cubes are removed.

So the total volume removed is; 8 * 27 = 216

Thus;

Percent of the original volume that is removed is;

216/1200 * 100% = 18%

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Answer:

[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

- 6 ÷ 3 = 12 ÷ - 6 = - 24 ÷ 12 = 48 ÷ - 24 = - 2

this indicates the sequence is arithmetic with explicit rule

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 3 and r = - 2 , then

[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]

Answer:

[tex]\sf \dfrac{-3}{2}(-2)^n[/tex]

Step-by-step explanation:

Explicit formulas are used to represent all the terms of the geometric sequence with a single formula.

  [tex]\sf \boxed{\bf t_n = ar^{n-1}}[/tex]

a is the first term.

r is the common ratio.

r = second term ÷ first term.

   3 , - 6 , 12, - 24, 48 ,........

a = 3

r = -6 ÷ 3 = -2

         [tex]\sf t_n = 3*(-2)^{(n-1)}\\\\[/tex]

             [tex]\sf = 3*(-2)^{n}*(-2)^{-1}\\\\ =3*(-2)^n*\dfrac{-1}{2}\\\\= \dfrac{-3}{2}(-2)^n[/tex]

Check:

[tex]\sf t_1 =\dfrac{-3}{2}*(-2)^1=\dfrac{-3}{2}*(-2) = 3\\\\\\t-2 = \dfrac{-3}{2}*(-2)^2 = \dfrac{-3}{2}*4=-6\\\\\\t_3=\dfrac{-3}{2}*(-2)^3=\dfrac{-3}{2}*(-8)=12[/tex]

Answer:

Hope it helps u, any questions u may ask me

x=70 [alternate interior angles]

y=60 [alternate interior angles]

a=110 [By linear pair]

b=120 [By linear pair]

The value of z-score for a score that is three standard deviations above the mean is 3.

In this question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Let x be the score

let μ be the mean and

let σ be the standard deviations

Now, x =  μ + 3σ

The formula of z-score is

[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]

⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]

⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]

⇒ [tex]z_{score} = 3[/tex]

Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.

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