Graph the function f(x)=(1/4)^x

a) Probability of exactly three boys is 0.3185

b) Probability of at least one boy is 0.9717

c) Probability of at least one girl is 0.9655

d) Probability of all of same sex is 0.06275

What is probability?

a) Probability of exactly three boys

Choose 3 out of 5 in C(5,3)=10 ways

So probability is:10*0.51^3*0.49^2

~0.3185

(b) Probability of at least one boy

p(at least one boy)=1-p( all girls)

=1-0.49^5

=0.9717

c) Probability of at least one girl

p(at least one girl)=1-p( all boys)

=1-0.51^5

=0.9655

d) Probability of all of same sex

p(all of same sex)=p(all boys)+p(all girls)=

0.51^5+0.49^5

=0.06275

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Answer: 21:38 on a 24 hour clock and 9:38 on a 12 hour clock

Step-by-step explanation:

So if Theo started the movie at 7:30 and the movie was 1 hour 56 minutes, and he paused half way for 12 minutes, we can conclude that the total time taken to watch the movie/break was 2 hours and 8 minutes.

Now we just add that time

7:30 + 2 hours and 8 minutes = 9:38

On a 24 hour clock the answer would be 21:38

The areas of each of Reuben's fields are given as follows:

Hence the total area of all of Reuben's fields is given as follows:

204,000 square feet.

The areas of the fields is given by the multiplication of each of the dimensions of the field, as the fields have a rectangular format.

Then the total area is obtained as the sum of the areas of each field.

The dimensions of each field are given as follows, from the table given by the image at the end of the answer:

Hence the areas of each of the fields are given as follows:

Then the total area is given as follows:

24,000 + 140,000 + 40,000 = 204,000 square feet.

The problem asks for the areas of each field and the total area.

The dimensions are given by the image shown at the end of the answer.

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The rate of change of the perimeter is  4 in/sec .

In the question ,

it is given that ,

the length of the rectangle is [tex]=[/tex] 1 inch

the width of the rectangle is = 6 inch

the rate of increasing length is (dL/dt) = 4 in/sec

rate of shrinking width is (dW/dt) = -22 in/sec ,

We know that the perimeter of the rectangle is = 2(L + W) ,

that is , P = 2L + 2W ,

Differentiating perimeter with respect to time "t" ,

we get ,

dP/dt = 2 × ( dL/dt) + 2 × (dW/dt )

Substituting the values from above ,

we get ,

= 2 × (4) + 2 × (-2)

= 8 - 4

= 4

Therefore , the required rate of change is = 4 in/sec .

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The congruence of the angles and triangles are proven as follows;

a. The composition angles of FGH are alternate interior angles to the composition angles of angle AHEF

b. The three sides of triangle ∆EHG are congruent to the three sides of triangle ∆GFE, therefore, triangles ∆EHG and ∆GFE are congruent by SSS congruency rule

The lengths of the three sides of triangles that are congruent.

a. The shape of quadrilateral EFGH = A parallelogram

The measure of angle HEF = 90°

Angle HEF = 90°

Angle HEF = Angle HED + Angle DEF

Angle HED is congruent to angle FGD (Alternate interior angles theorem)

Angle HED = angle FGD

Angle DEF is congruent to angle DGH (Alternate interior angles theorem)

Angle DEF = angle DGH

Angle FGH = Angle FGD + Angle DGH

Angle FGH = Angle HED + Angle DEF (Substitution property)

Angle FGH = Angle HEF (Transitive property)

Angle FGH = Angle HEF = 90°

Therefore, the statement that will help prove angle FGH is also a right is that angle FGH is the sum of angles FGD and angle DGH which are alternate interior angles to angles HED and DEF which makes up angle HEF, which is a right angle.

b. The two-column method can be used to prove that triangle EHG and triangle GFE are congruent as follows;

Statement. Reason

EF is congruent to HG. Opposite sides of a parallelogram are congruent

EH is congruent FG Opposite sides of a parallelogram are congruent

EG is congruent to EG Reflexive property of congruency

∆EHG is cong. to ∆GFE SSS, Side-Side-Side, congruency rule

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Answer: We write J raised to the 9th power as J9 (which means J multiplied by J a total of nine times). "Sum" means "add them" so J9 + K

Step-by-step explanation:

Answer:

753

Step-by-step explanation:

Arithmetic sequences are sequences that change by a constant factor.

Explicit Rule

The formula that describes an arithmetic sequence is called the "explicit rule". This formula is f(x) = f(1) + d(x-1). Sometimes the rule will be written with [tex]a_{n}[/tex] instead of f(x) but the equations are still the same.

In this equation, f(1) is the first term of the sequence, d is the common difference, and x is the term. The common difference is the factor that the sequence changes by.

Setting Up the Equation

To set up the equation, we need to find f(1) and d.

The first term, f(1), is directly given to us in the equation. The first term written is -6, so f(1)=-6.

It is slightly more difficult to find d. But, one easy way to find d is by subtracting terms. Take the second term, 5, and subtract the first term, -6.

So, d = 11. Each term in the sequence increases by 11.

The final equation is f(x) = -6 + 11(x-1).

Finding the 70th Term

Now, all we have to do is plug 70 in for x. To find any term in the sequence, all you have to do is plug the term number in for x.

The 70th term in the sequence is 753.

This question is based on the probability. Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.

Given:

There are 5 marbles in a bag. Each marble is a different color. The colors are: red, orange, green, blue, purple. Two marbles are randomly drawn from the bag without replacement.

We need to determined the probability that the red marble is drawn first and the white marble is drawn second.

According to the question,

It is given that, there are 5 different marbles. In the first draw, you have a one out of 5 chance of getting the red is 1/5 .

In the second draw, there are 4 marbles remaining, so a one out of 4 chance of drawing a white marble i.e. 1/4.

Now, calculating the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.

⇒ 1/5 × 1/4 = 1/20

Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.

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If the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. The statement: This set is closed under scalar multiplications This set is a subspace .This set is closed under vector addition The set contains the zero vector is False.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.

Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a Scalar . Examples of scalars include speed, mass, electrical resistance, and hard-drive storage capacity.

Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).

For quaternion scalars and matrices:

λ = 2     A = [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

2A = 2[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]

     = [tex]\left[\begin{array}{ccc}2a&2b\\2c&2d\\\end{array}\right][/tex]  = [tex]\left[\begin{array}{ccc}a.2&b.2\\c.2&d.2\\\end{array}\right][/tex]

     = [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] × 2 = A2

In mathematics, and more specifically in linear algebra, a linear subspace, also known as a vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.

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a. sample mean = 7.1838

b. sample variance = 0.0004 and standard deviation = 0.0207

c. coefficient of variation = 0.29%

What is sample variance?

The expectation of a random variable's squared deviation from its population mean or sample mean is known as variance in probability theory and statistics. Dispersion is a measure of how far apart a group of numbers is from their mean value, and variance is a measure of dispersion.

A probability distribution's variance is defined as the mean of the squared deviation from the distribution's mean. The expected value, commonly known as the mean, is the value you will obtain on average if you take several samples of a probability distribution.

Solution Explained:

a) Mean x=∑x/n

=7.15+7.2+7.18+7.19+7.21+7.2+7.16+7.18/8

=57.47/8

=7.1838

b) Sample Variance S2=∑x2-((∑x)^2/n)/n-1

=(412.8531-(57.47)^2/8)/7
=412.8531-412.8501/7

=0.003/7

=0.0004

Sample Standard deviation S=√∑x^2-((∑x)^2)/n)/n-1

=√(412.8531-((57.47)^2/8))/7

=√412.8531-412.8501/ 7

=√0.003/7

=√0.0004 =0.0207

c) Coefficient of Variation (Sample) =

S/x X100%

=(0.0207/7.1838) X 100%

=0.29%

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The probability that both will experience allergies to pollen is 0.0484, and the probability that at least one will is 0.9516.

The following information is provided in the question:

A large country has a pollen allergy rate of about 22%.

As a result, the probability of people has a chance of having an allergy is  0.22.

P(allergic) = 0.22

P(Not allergic) = 1 - 0.22 = 0.78

If A and B are independent even, then,

P(A∩B) = P(A) × P(B)

Two people are randomly selected.

a) P( both will be allergic to pollen)

Since these are independent events,

P(both will be allergic to pollen)= P(allergic)*P(allergic)

= 0.22*0.22 =  0.0484

b) P(at least one person is allergic to pollen)

= 1 - P(both are not allergic to pollen)

= 1 - P(P(not allergic)*P(not allergic))

= 1 - (0.22*0.22)

= 0.9516

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If the bond angle between two adjacent hybrid orbitals is 120° the hybridization is Sp2 hybridization .

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

sp2 hybridization

There are other ways to combine the orbitals than sp3 hybridization when an excited state carbon atom is produced. As opposed to the three p orbitals in the sp3 hybridization, the s orbital only interacts with two p orbitals in the sp2 hybridization. As a result, three orbitals are combined to create three hybrid orbitals, also known as sp2 hybrid orbitals.

The sp2 hybridization occurs when the s orbital is mixed with only two p orbitals as opposed to the three p orbitals in the sp3 hybridization

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The lower limit for the 95%confidence interval for the given mean and standard deviation is equal to 39.03.

As given in the question,

Sample size 'n' = 60

Mean 'μ' = $40.80

Standard deviation 'σ' = $7.00

Using z-score table of normal distribution

z-value for 95%confidence interval = 1.96

Formula used

Confidence interval

= μ ± ( z-value × σ ) /√n

= 40.80 ±  (1.96 × 7)/√60

= 40.80 ± (13.72 /7.75)

= 40.80 ±1.770

Lower limit of the confidence interval is equal to :

40.80 - 1.770 = 39.03

Upper limit of the confidence interval is equal to :

40.80 + 1.770 = 42.57

Therefore, the lower limit for the 95% confidence interval is equal to 39.03.

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Yes, it would be unusual for a  500 adult Americans to result in 210 or more who believe marriage is obsolete. The probability value is 0.39 for adult Americans.  

We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.

We have given that 39% american adults women believes that marriage is now obsolete.

So,39% of 500 adult American women is =[(39/100)×500]

                                                                     =39×5=195

So,probability of adult women who believes marriage is obsolete is =(195/500)=0.39

Now, we need to check that whether 210 women believes marriage is obsolete or not.

So, number of favorable outcome is 210 and total number of outcomes=500.

Therefore, probability of adult women who believes marriage is obsolete is=(210/500)=0.42

Now,we can see that 195 women probability is lower than 210 women probability. It means that more number of women considered marriage is obsolete.

Hence, yes it is unusual and the  probability value of adult Americans is 0.39

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(Complete question) is:

would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?If so determine the probability, otherwise type 0 for this result NOT to be unusual

with the help of Advanced Placement statistics correct answer is option B.

what is Advanced Placement statistics?

In the United States, the College Board's Advanced Placement programme offers a college-level high school statistics course known as Advanced Placement Statistics.

explanation:

The data are paired where the pairing involves the volunteers who use the new chair and the volunteers who use their old chair.

hence the correct option is B by Advanced Placement statistics

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The total cost of the ingredient is $0.84 for 6 ounces.

Define fixed cost.

The cost or expense known as fixed cost is unaffected by a short-term horizon's growth or reduction in the number of units produced or sold. To put it another way, it refers to a cost that is linked to a time period rather than a specific economic activity.

It can be viewed as costs that a business must pay regardless of the volume of business activity, such as the number of units produced or sales made. One of the two main parts of the overall manufacturing cost is the fixed cost.

Solution Explained:
Given,

1 pound = $2.25

Since 1 pound = 16 ounces

So, 16 ounces = 2.25

      1 ounce = 2.25/16 = 0.14

Therefore, 6 ounces = 0.14 X 6 = 0.84

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The expression 20 m−60 n+20 can be written as 20(m−3 n +1).

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given expression,

20 m−60 n+20

can be factorized as

20(m−3 n +1).

A) John’s reasoning is incorrect because he has not included the constant term in the expression.

B) 20 m−60 n+20 can be factorized as 20(m−3n +1).

C) The expression can be factorized by taking common from each and every term of the expression.

Therefore,The expression 20 m−60 n+20 can be written as 20(m−3 n +1).

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By solving a system of equations we will see that she sold 80 phones and 240 accessories.

Let's define the variables:

x = number of phones.

y = number of accessories.

We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:

y = 3x

x*$8 + y*$4 = $160

To solve the system, we can replace the first equation into the second one.

x*$8 + (3x)*$4 = $160

x*$8 + x*$12 = $160

x*$20 =  $160

x  = $160/$20 = 80

She sold 80 phones, and the number of accessories is:

y = 3x

y = 3*80 = 240

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The constant of proportionality is 1/3 and the equation is y = 1/3x

The table of values represents the given parameter

From the table of values, we have the following ordered pair

(x, y) = (3, 1)

The constant of proportionality (k) is then calculated as

k = y/x

So, we have

k = 1/3

Recall that, we have

k = y/x

Substitute k = 1/3

y/x = 1/3

So, we have

y = 1/3x

Hence, the equation is

y = 1/3x

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Answer:

Step-by-step explanation:

B becuase the way the angle is

The kiwi as per the given relation of ostrich and kiwi's height is equal to 22inches tall.

As given in the question,

Ostrich height is equal to 108 inches

Let us consider 'x' inches be the height of the kiwi.

Ostrich is 20inches more than four times of x.

Ostrich height  = 20 + 4x

⇒ 108 = 20 + 4x

Subtract 20 from both the sides we get,

108 - 20 = 20 + 4x -20

⇒ 88 = 4x

Divide by 4 on both the sides we get,

88/ 4 = 4x / 4

⇒ x = 22 inches

Therefore, as per the given relation of ostrich and kiwi's height , kiwi is 22inches tall.

The complete question is :

The height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?

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The equation for of graph of  g(x) = 3x-4  

y = afb(x +c) + d

where a represent the vertical stretch

b represent the horizontal stretch

c represent the horizontal translation

d represent the vertical translation

from the equation we are given g(x) has a vertical stretch and a vertical translation ( y-axis represent up and down therefore its a vertical translation)

The equation of g(x) is:

g (x) = 1/2(6x) - 4

g(x) = 3x-4  

Therefore, the equation for of g(x) = 3x-4  

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The Value of r(2) is -6 and x-2 is not a factor of r(x).

What is the value of a function on a Variable?

A real-valued function of a real variable is a function that takes as input a real number, commonly represented by the variable x, for producing another real number, the value of the function, commonly denoted f(x).

What is Factor?

A factor of polynomial P(x) is any polynomial that divides evenly into P(x).

How to find out the value of r(x)?

Given  r(x)=x^3-4x^2+4x-6,

Put x = 2 ,

r(2)=2^3-4(2)^2+4(2)-6

r(2)=8-16+8-6

r(2)=-6

As we see that x=2 is not equal to zero,

implies x-2 does not divide r(x) evenly.

thus x-2 is not a factor of given r(x).

The quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3) is; y = 0.2x² - 2.2x + 2

The standard form of a quadratic equation is;

y = ax² + bx + c

where a, b and c are constants

Thus, for the coordinate (10,0), we have;

0 = a(10)² + b(10) + c

100a + 10b + c = 0  -----(1)

For the coordinate (1,0), we have;

0 = a(1)² + b(1) + c

a + b + c = 0   -----(2)

For the coordinate (4,3), we have;

3 = a(4)² + b(1) + c

16a + b + c = 3  ------(3)

Using online simultaneous equation, we have;

a = 0.2 and b = -2.2 and c = 2

The quadratic function is;

y = 0.2x² - 2.2x + 2

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The total cost of the set and the tax is 2653.6 dollars.

The Myer family purchased a bedroom set for $2,480.  The sales tax rate is  7 percent.

Therefore, the total cost of the set and the tax can be calculated as follows:

tax = 7% of 2480

tax = 7 / 100 × 2480

tax = 17360 / 100

tax = $173.6

Therefore, let's find the total cost of the set and tax.

total cost = 173.6 + 2480

total cost = 2653.6 dollars

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It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.

If the average student age is not substantially different from 24 years, then the null hypothesis is tested, which is:

[tex]H_{0}[/tex] : μ = 24

If it differs from 24 years, the alternative premise is tested, so:

[tex]H_{1}[/tex] :  μ ≠ 24

The z-distribution is utilized because we have the population's standard deviation. The test statistic comes from:

z = x -  μ÷ σ/[tex]\sqrt{n}[/tex]

The parameters in this issue have the following values:

x(mean) = 25

μ = 24

σ = 2

n=16

As a result, the test statistic's value is:

z = 25-24÷ 2/[tex]\sqrt{16}[/tex]

z = 2

The probability of a sample mean older than 25 years determines the test's p-value, which is 1 less than the p-value of z = 2.

The p-value for z = 2 in the z-table is 0.9772; 1 - 0.9772 = 0.0228.

Given that the test's p-value is 0.0228 0.05, we may say that:

It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.

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Answer: Neither (5/2, 0)

Step-by-step explanation:

-4x + 7 = 2y - 3

+3 +3

2y = -4x + 10

(Divide both sides by 2)

y = -2x +5

—————————————————

-4x + 7 = 2(-4x + 10) - 3

-4x + 7 = -8x + 20 - 3

-4x + 7 = -8x + 17

+8x -7 +8x -7

8x - 4x = 17 - 7

4x = 10

(Divide both sides by 4)

x = 5/2

—————————————

y = -2(5/2) + 5

y = -5 + 5

y = 0

——————————

Check Work:

-4x + 7 = 2y - 3

-4(5/2) + 7 = 2(0) -3

-10 + 7 = 0 - 3

-3 = -3 ✔️

The boundary value and initial value statement are,

T surrounding = 100°c

IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].

What is Initial Value Problem?

In multivariable calculus, an initial value problem is an ordinary differential equation that also includes an initial condition that identifies the value of the unknown function at a specific location in the domain. An initial value problem is frequently solved when modelling a system in physics or another scientific field.

Consider a cylindrical potato, sliced into thin slices with thickness L = 1 cm, much smaller than the diameter slices.

Initial temperature [tex]T_i = 20^o[/tex]

Final temperature = [tex]T_f = 75^o[/tex]

Now we have to solve the given cases.

Consider the heat equation,

q = k(∂T / ∂x)                   ..(1)

(a) Now we have to find the boundary value

Boundary Value:

[tex]T_i = 20^oc, T_f = 75^oc\\[/tex]

⇒ ΔT = [75 - 20]

⇒ΔT = 55°c

T surrounding = 100°c

IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex]

Hence, the boundary value and initial value statement are,

T surrounding = 100°c

IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].

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Complete question:

Complete question is attached below,

Using technology, the correlation coefficient is 0.997

We should know that correlation coefficient is a statistical model which is used to determine or measure the relationship between two variables.

The table is

                            x               y              x²            y²             xy

                          8              22             64          484            176

                         12              23            144          529            276

                         18             26             324         676           468

                         24             30            567         900         720

                          30           32              900        1024         960

                        32              33              1024     1089         1056

                         35             35             1225       1225         1225

                          37             36            1369        1369         1332

                          40             38           1600         1444         1520

    Total          236           275          7226         8740        7733

[tex]r= \frac{nExy)-(Ex)(Ey)}{\sqrt{[n(EX^{2}][nEy^{2}(Ey)^{2} } }[/tex]

applying the figures from the table we have

r=[tex]\frac{9*7733-(236)(275)}{\sqrt{[9*7226-55696][9*8740-75625]} }[/tex]

Simplifying the expression we have

r=[tex]\frac{4697}{\sqrt{28340830} }[/tex]

r=0.88

r=0.9 approximately

Therefore the correct answer is 0.997 which is the correlation coefficient.

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