Apply Math Models You have 20 quarters. You
find 40% more quarters in your room. Then you go
shopping and spend 50% of the total number of
quarters.
a. Write an expression that represents the
total number of quarters you take with
you when you go shopping.
b. How much money do you have left?
18. H
F
S
F
t

The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

The population propose will match the pattern mean's proposal. The population trendy deviation divided by the rectangle root of the sample length yields the same results as the standard deviation of the distribution of the sample means, also known as the same old mistakes of the proposed (n).

The general sample recommends factors to be included in the pattern mean calculation.

The population suggest is calculated using the sum of all values within the population denoted with the aid of the summation of X divided by the number of values in the population that is denoted with the aid of N. The population suggest is the mean or average of all values within the given population.

Therefore,

The mean of the sample means from all feasible samples is less than the population means for random samples of size 100 from a population.

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According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.

A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.

The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.

Given that John paid $485 to build a deck.

And he will pay $25 per hour to his brother for building the deck.

one hour of work costs John $25 + $485 .

Total cost of building deck = $25 × h number of hours + $485

3 hour of work costs $25 × 3 = $75 + $485 = $560

8 hour of work costs = $25 × 8 = $200 + $485 = $685

12 hour of work costs = $25 × 12 = $300 + $485 = $785

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The complete question is-

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?

h c

0 485

3 510

8 535

12 560

h c

0 510

3 535

8 560

12 585

h c

0 485

3 560

8 685

12 785

h c

0 510

3 585

8 710

12 810

Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

The cosecant of the angle is 0.2

From the question, we have the following parameters that can be used in our computation:

(5,-12)

This means that

(x, y) = (5,-12)

The csc(θ) is calculated as

csc(θ) = 1/x

Substitute the known values in the above equation, so, we have the following representation

csc(θ) = 1/5

Evaluate

csc(θ) = 0.2

Hence, the value of csc(θ) is 0.2

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 For recording the angular velocity we will use

     angular velocity, ω = dθ /dt

Angular velocity:

Angular velocity is a vector quantity, expressed as the angular velocity or rotational speed of an object and the rate of change of angular displacement that specifies the axis about which the object rotates. The amount of change in a particle's angular displacement over time is called its angular velocity. The trajectory of the angular velocity vector is usually perpendicular to the plane of rotation in the direction given by the right-hand rule.

Total Moment of Inertia:

The total moment of inertia is the sum of the moments of inertia of the mass elements in the body.

Unlike mass, which is a constant for a given body, the moment of inertia depends on the location of the center of rotation. In general, the moment of inertia is calculated by using integral calculus.

Thin cylindrical shell open at both ends, radius r, mass m.

This formula assumes that the thickness of the shell is negligible. This is a special case of a thick-walled cylindrical tube with r1=r2. A point mass m at the end of a rod of length r has the same moment of inertia and the value r is called the radius of gyration.

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The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

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The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

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For the given scatter plot of the data, the wrong with the conclusion was shown by option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect.

As given in the question,

Based on the class data of quiz3,

Teacher made scatterplot to represent the linear relation between amount of study time and quiz score

Pattern form was linear.

Using which correlation coefficient was computed to r = 0.8.

From the data scatterplot as it was linear the more time students study the good will the score.

Therefore, from the information of scatterplot option B. Since r = 0.80 slope will be negative 50 studying long time will give you lower score is incorrect answer.

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The minimum lateral surface area of the prism is approximately 1.194 square units.

The given base and height of the prism is y and x respectively.

Hence volume of the prism

V = 1/3 x²y

again 1/3 x²y  = 1/6

or, y = 1/2x²

The lateral surface area of the prism is given by :

F = √(4y²+x²)

By the equation 1 we get :

F = x √ (1/x⁴ + x²)

Now we will use differentiation:

[tex]\frac{df}{dx} = \frac{2x^6-1}{x^4(x^2+\frac{1}{x^2} )}[/tex]

Now for the critical points we have to take df/dx = 0

hence solving the equation for x we get :

[tex]x = (\frac{1}{2} )^{\frac{1}{6}}[/tex]

Hence the values of x is [tex](\frac{1}{2} )^{\frac{1}{6}}[/tex] and the value of y will be  [tex]\frac{1}{2^\frac{2}{3}}[/tex] units,

And the lateral surface are will be :

F (min ) = √(4y²+x²)

= √ (0.795 + 0.633)

= 1.194 square units

The approximate values of x and y are

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As per the given standard deviation, only (i) is true.

The term standard deviation refers the measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Here have given that the Bay Area Online Institute (BAOI) has set a guideline of 60 days for the time it should take to complete an independent study course.

Here by analyzing the times taken to complete the course for 16 random students, BAOI found the average time it took to complete the course was 72 hours with a standard deviation of 20 hours.

So, let us consider the possible inferences BAOI can make about the time it takes to complete this course if they assume that the time it takes is normally distributed:

i. For the 5% level, BAOI can infer that the average time to complete exceeds 60 hours.

ii. For the 1% level, BAOI can infer that the average time to complete exceeds 60 hours.

Here we are trying to determine if they should spend at least 480 minutes a day studying.

Now, our knoll is that the mean is 480 and then we are looking for evidence that they are studying less than 480.

Here we don't know the population standard deviation so we're going to use a distribution.

In the given, critical values are going to be a distribution with degrees of freedom.

So, if we look at a chart 11 of freedom, we can see our critical value. I'm going to center to zero if I draw our T.

Therefore, the tail probability of.05 and the rest of it is.95%.

Based on these value we have conform that option (1) is correct.

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Answer: 2 170 kilograms [kg] of Salt fit into 1 cubic meter. 135.46867 pounds [lbs] of Salt fit into 1 cubic foot. Salt weighs 2.17 gram per cubic centimeter or 2 170 kilogram per cubic meter, i.e. density of salt is equal to 2 170 kg/m³; at 20°C (68°F or 293.15K) at standard atmospheric pressure . In Imperial or US customary measurement system, the density is equal to 135.469 pound per cubic foot [lb/ft³], or 1.254 ounce per cubic inch [oz/inch³] .

Step-by-step explanation:

Answer:

Diana has 40 books in her collection.

Step-by-step explanation:

We can set up the equation 4x + x = 200 to represent the total number of books in the collection, where x is the number of books in Diana's collection and 4x is the number of books in Teri's collection. Solving for x, we get 5x = 200, so x = 40. This means that Diana has 40 books in her collection.

Answer:

Teri has 160 books

Step-by-step explanation:

Answer:

2.5

Step-by-step explanation:

Step-by-step explanation:

Given

Shelf Width = 3ft 9in

Copies = 18

Required

Determine the width of each book

This is calculated by dividing the shelf width by the number of copies.

Width = Shelf Width ÷ Copies

Width = (3 ft 9in) ÷ (18)

[Convert with to inches]

Width = (3 * 12 + 9) ÷ (18)

Width = (36 + 9) ÷ (18)

Width = 45 ÷ 18

Width = 2.5 inches

Answer:

The prime factors are 3 and 3

The given expression can be simplified to get the value as 19. The correct option is (A).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

[tex](12b - 2^{c}) /\sqrt[3]{a}[/tex]

Substitute a = 64, b = 9 and c = 5 to obtain the value as below,

⇒ (12 × 9 - 2⁵)/∛64

⇒ (108 - 32)/4

⇒ 76/4

⇒ 19

Hence, the value of the given expression is obtained as 19.

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The image of the complete problem is attached here.

Answer:

listed below

Step-by-step explanation:

5.) x=77 and y=63

6.)y=60 and x= 1230

7.)y=65 and x=92

8.)y=69 and x=175

The Total Income from this caster in the first year = $184,822 approximately

What is Total Income?

Total income is the sum of all earnings, save those specifically mentioned in Section 12 of this Act, that a person receives during a certain accounting period, before any deductions are taken into account.

Given that : f(t)=12,000e^0.04t (dollars per month)

We could calculate our twelve calculations and evaluate this function once a month, but it would take some time. Instead, we should keep in mind that a continuous function can be represented by an integral. This indicates that we can simplify our calculation by simply taking the integral of this function between 0 and 12.

∫₀¹² 12000e⁰·⁰⁴t dt

Since we will transform this integrand into something for which we have the antiderivative, we may utilise u-substitution to simplify the calculation of this integral.

u=0.04t

du=0.04

dt0.04(0)=0

0.04(12)=0.48

To get the substitute for d u, we must slightly modify our integrand. This can be accomplished by adding 0.04 inside and canceling it outside by its reciprocal. The Fundamental Theorem of Calculus will then be used to calculate this definite integral.

12000 (1/0.04) ∫₀¹² 0.04e⁰·⁰⁴t dt = 30000 ∫₀⁰·⁴⁸ e⁴du

30000[tex]e^{u}[/tex] | ₀ ⁰·⁴⁸

30000(1.61607 -1)

184822.32

Therefore, the total income over the first year is approximately $184,822.

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The x-axis of this graph is D) Individuals' life spans as a percentage of the maximum life span for the species.

In mathematics, "graph" can refer to (at least) two different things. The word "graph" in elementary mathematics refers to a plot or a function graph.

A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

Making a diagram that shows the link between two or more objects is known as developing a graph. Create a graph by placing a series of bars on graph paper.

Depending on age, survival curves display the likelihood of survival in a population. The y-axis represents the number of survivors (on a log scale), while the x-axis represents time (indicating relative age). The graph's x-axis (horizontal line) should contain the independent variable, and the y-axis should contain the dependent variable. At the origin, where the coordinates are, the x and y axes intersect.

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The correlation of the rates of return between x and y is the closest to = 0.4

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect.

Calculation for the correlation of the returns,

Using this formula,

Covariance of the returns = Correlation coefficient between the returns*Stock returns standard deviation*Mod T Stock returns standard deviation

The sample standard deviations of the rates of return for stock x and stock y were 0.20 and 0.12

The sample covariance between the returns of x and y is 0.0096.

Let plug in the formula

Covariance of the returns = Correlation * (0.20) * (0.12)

0.0096 = Correlation * (0.20) * (0.12)

0.0096 = Correlation * 0.024

0.0096 / 0.024 = Correlation

0.4 = Correlation

Correlation = 0.4

Therefore,

The correlation of the rates of return between x and y is the closest = 0.4

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The length of the Zambezi river is 838 × 10⁵ or 83.8 × 10⁶ or 8.38 × 10

What is scientific notation?

Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.

For example, 750,000,000 can be written in scientific notation as 7.5 ✕ 10⁸.

The length of the Zambezi river 83,800,000 feet.

Rewrite 83,800,000:

83,800,000 = 838 × 100000

83,800,000 = 838 × 10⁵ [Since the number of zeros is 5]

Multiply and divide 10:

83,800,000 = 838 × 10⁵ × (10/10)

83,800,000 = (838/10) × 10⁵ × 10

83,800,000 = 83.8 × 10⁵ × 10

83,800,000 = 83.8 × 10⁶

Multiply and divide 10:

83,800,000 = 83.8 × 10⁶ × (10/10)

83,800,000 = (83.8/10) × 10⁶ × 10

83,800,000 = 8.38 × 10⁷

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Answer:

Step-by-step explanation:

Given the conditional statement ~p → q, the statement logically equivalent is ~q → p.

Answer:

The number of degrees Celsius goes down 6 every week. (-6)

Step-by-step explanation:

If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).

The equation will look something like this:

w ÷ t = c

Fitting the numbers into this equation will look something like this:

2 ÷ -12 = -6

Every week, it changed -6 degrees Celsius.

Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.

The expression which represents the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).

It follows from the task content that the expression which represents the nth term of the given sequence, in terms of variable, n be determined.

According to the task content, the first term, a of the sequence is; 1.

Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.

Consequently, the required expression is an arithmetic sequence which can be modelled by;

T (n) = a + d (n - 1)

Since the constant common difference of consecutive terms in the sequence is; 7,

Therefore, the expression for the nth term of the expression is;

nth = 1 + 7(n -1)

On this note, the required expression which represents the nth term of the arithmetic sequence in discuss is; T (n) = 1 + 7 (n -1).

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a. The probability that the second marble is red is 2/5, since there are 2 red marbles and a total of 5 marbles.

b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.

c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.

d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.

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Answer:

x=44

y=32

Step-by-step explanation:

Given numbers x and y:

y=x-12

x+y+7=83

x+x-12+7=83

2x=88

x=44

y=32

The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.

When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.

This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.

Given that triangle AXY is similar to triangle ABC, it means that:

m<A = m<A

m<X = m<B

m<Y = m<C

AX/AB = AY/AC = XY/BC

To find the length of AB, we could use the following expression derived from the ratios stated above:

AX/AB = AY/AC

Cross multiply:

(AB) * (AY) = (AX) * (AC)

Divide both sides by AY

(AB) * (AY) / AY = (AX) * (AC) / AY

AB = AX * AC/AY

The expression to use is: A. AB = AX * AC/AY

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In order to find the value of f(-1), you can start by finding the value of f(1) and then proceed for the next step.

As you have already noted, writing z13+z14 as e13(ln|z|+iθ(z)+i2nπ)+e14(ln|z|+iθ(z)+i2mπ) will not give you a specific branch. Instead, you can write z13+z14 as follows:

(z-1)(z12+z11+z10+...+1)

Then, you can use the fact that f(1)=0 to solve for the value of z12+z11+z10+...+1. This will give you a specific value for f(1).

To find the value of f(-1), you can use the following relationship:

f(-1) = f(1) * (-1)13 * (-1)14

Substituting the value you found for f(1) and evaluating the expression will give you the value of f(-1).

As for the condition "not defined on the negative imaginary axis", this means that the branch of f(z) is not defined for any complex number with a negative imaginary part. This is because the 13th and 14th roots of a complex number are not unique when the imaginary part is negative, so the function is not defined for these values.

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The  interval containing the middle-most 86% of sample mean in the interval notation is  is (196.4, 203.5)

The 50 +/- 86/2 percentile will make up the center 86% of the sample means' distribution.

The 86th percentile's z-score is 1.08

sample mean population mean = 200

standard deviation from mean = 19

sample size = 33.

Standard error (SE) is equal to 19 / sqrt(33) = 3.3077.

86th percentile x can be located using the formula z = (x - population mean)/sample error.

1.08 = (x - 200)/3.3077

x = 3.3077* 1.08 + 200 = 203.57

that is the interval's upper bound.

it is 3.5721 over the population mean (203.57 - 200).

Due to the symmetry of the normal distribution, the interval's bottom bound will be 1.66 standard deviations below the population mean (200 - 3.572 = 196.428).

then the interval is (196.4, 203.5).

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Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

The decimal equivalent of the relative frequency, rounded to the closest tenth, is 1.

The proportion of outcomes when a certain event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Thirty male college students at random were chosen.

The following table lists their heights in inches. These heights are 12 44 70 73 68 66 73 70 23 23 64 74 and 68 69 70 71 73.

Therefore, the frequency of any height value in the data set is just its count. A value's relative frequency is simply the ratio of its corresponding frequency to  the total frequency.

So, the frequency table is

Height(xi) Frequency(fi) Relative frequency

66                  3                        3/30=0.1

67                  3                                3/30=0.1

68                 4                                 4/30=0.13

69                3                                3/30=0.1

70               2                                2/30=0.06

71                  4                                4/30=0.13

72                 2                                 2/30=0.06

73                  6                                 6/30=0.2

74                 3                                 3/30=0.1

Total    30                                1

the frequency distribution for the data is given above.

The relative frequency as decimals, rounded to the nearest tenth is 1

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