3.) Solve 5y +1 <36

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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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:

Step-by-step explanation:

Day 1 = 2 birds

day 2 = 3 birds

day 3 = 9 birds

day 4 = 8 birds

day 5 = 1 bird

On day 1 the points are (1,2)

On day 5 the points are (5,1)

(I am picking these for the points because I don't know your options for the selecting area.)

we use this formula y2-y1/x2-x1

2-5/1-1

3/0

our answer is infinite which is the relation and this is an infinite function

Answer:

◘ (1, 2)

◘ (2, 3)

◘ 3

◘ is

◘ each value of Day corresponds to exactly one value of Number of birds

Explanation:

◘◘ In the graph, Days represents the x-axis, and Number of birds represents the y-axis. Therefore each marked point on the graph can be thought of as a Cartesian coordinate. This means that the answers for the first and second question could be any of (1, 2), (2, 3), (3, 9), (4, 8), or (5, 1).

◘ In the graph, we can see that the point above Day 2 corresponds to 3 on the Number of birds axis, which means on day 2, 3 birds visited the feeder.

◘ The relation shown is a function because each value of Day corresponds to exactly one value of Number of birds. A function is a relationship that provides one output for each input, and this graph follows that.

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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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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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]

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

[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:

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 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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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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Answer:

g and f are inverse functions because g(f(x)) = f(g(x)) = x

Step-by-step explanation:

Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):

[tex]f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x[/tex]

Now, let's find g(f(x)):

[tex]g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x[/tex]

There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:

[tex]f(x)=y=7x-6[/tex]

Swap x and y:

[tex]x=7y-6[/tex]

Solve for y:

[tex]x+6=7y\\y=\frac{x+6}{7}[/tex]

Notice that we got g, which means f and g are inverse.

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:

[tex] y = \frac{4}{3} x + 5[/tex]

Step-by-step explanation:

The slope is

[tex] \frac{ - 3 - 1}{ - 6 - ( - 3)} = \frac{4}{3} [/tex]

Substituting into point-slope form,

[tex]y - 1 = \frac{4}{3} (x + 3) \\ \\ y - 1 = \frac{4}{3} x + 4 \\ \\ y = \frac{4}{3} x + 5[/tex]

The percentage of tardiness among the 102 pupils is 2.94.

According to the query,

Course A: Total number of students = 102

                   Number of tardy students = 3

Percent of students tardy in course A = (number of tardy students/total  

                                                                   number of students) * 100

  =(3/102)*100

  = 2.941

  ≈2.94

In case of course B: Total number of students = 85 & tardy student = 5

So, the percent of tardy student = (5/85)*100 = 5.88 %

Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.

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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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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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Answer: (2, 18)

Step-by-step explanation:

When x=2, [tex]f(2)=2(3)^{2}=18[/tex].

So, it should pass through (2, 18).

Answer:

(2, 18)

Step-by-step explanation:

i posted this at 1:19 in the morning, good day

The value of sample size n in this statement according to a confidence interval is 350.

According to the statement

we have a given that the value of error and population proportion and we have to find the value of sample size.

So, we know that the

confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Here

p represent the real population proportion of interest

ρ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

z represent the critical value for the margin of error

So, The population proportion have the following distribution  

P≈n ( p, ([p (1-p)]/n)^1/2)

Here In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by  α = 1 - 0.95 = 0.05

and α/2 = 0.025 And the critical value would be given by:  

z = 1.96

And on this case we have that ME = ±0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got the value

n = 0.35(1-0.35) / (0.05/1.96)^2

so, the value becomes

n = 350.

So, The value of sample size n in this statement is 350.

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Question:

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95% confidence interval with a margin of error of 0.05?

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Calculating the circumference of a circle based on the circle's diameter.

What kind of problems can a quantum computer solve?

10 Difficult Problems Quantum Computers can Solve Easily-

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The complete question is -

Which type of mathematical problem is too complex for a classical computer to solve efficiently?

a. converting an irregular fraction to an approximate decimal value

b. multiplying two numbers that both have a large number of digits

c. finding two prime factors that result in a specific value when multiplied

d. calculating the circumference of a circle based on the circle's diameter

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 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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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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Step-by-step explanation:

[tex]f(x) = ln( \frac{1}{x} ) [/tex]

To find the derivative, notice we have a function 1/x inside of another function, ln(x)

We use what we call the chain rule,

It states that

derivative of a '

[tex] \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)[/tex]

Here f is ln(x)

f is 1/x

So first, we know that

[tex] \frac{d}{dx} ( ln(x) = \frac{1}{x} [/tex]

so

[tex]f'(g(x)) = \frac{1}{ \frac{1}{x} } [/tex]

We know that

[tex]g'(x) = - \frac{1}{ {x}^{2} } [/tex]

So we have

[tex]x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} [/tex]

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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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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[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]

The value of n is 99

Integers are the set of numbers including all natural numbers and 0. They are part of the real numbers that do not include fractions, decimals, or negative numbers. Counting numbers are also considered whole numbers.

Natural numbers together with zero (0) are referred to as whole numbers. We know that natural numbers refer to the set of counting numbers starting from 1, 2, 3, 4 and so on. Simply put, integers are a set of numbers without fractions, decimals, or even negative integers. It is a collection of positive integers and zero. Or we can say that integers are the set of non-negative integers.

Integers are the set of natural numbers togethe with the number 0. In mathematics, the set of integers is given as {0, 1, 2, 3, ...}, denoted by the symbol W.

W = {0, 1, 2, 3, 4, …}

All natural numbers are integers.

All integers are real numbers.

It is given that If n a whole number, and 0.01 is between 1/n and 1/n+2, then we need to find the value of n.

1/n+2 < 0.01 < 1/n

1/n+2 < 1/100 < 1/n

n< 100 < n +2

Put n = 99, then we get

99 < 100 < 101

Hence the value of n is 99.

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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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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