a board that is 12 feet long must be cut into two pieces that have lengths in a ratio of 3 to 2. find the legnths of the two pieces.

The sum of the angles equals 540

There are 3 angles that measure (x - 6) and 2 angles that measure (x)

We should know that the question address a pentagon

3(x - 6) + 2(x) = 540

Simplify the equation

3x - 18 + 2x = 540

Collecting the like terms to have

5x - 18 = 540

5x = 598

Making x the subject of the relation we have

x = 120⁰

Bu substitution, put x in the value x-6 to have the value of the angle

x - 6   = 120 - 6   = 114

Conclusively,  the value of x  = 114

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The equation of a line in the form y is y = 150 - 85x.

This equation can be used to determine the amount of money in the grocery account at any given week, x. To solve, we will use the information given in the question.

We know that the initial amount in the account is $150. This is the y-intercept of the line. Therefore, 150 = 150 - 85x. Solving this equation for x, we get x = 0. This means that at week 0 the account has a balance of $150.

Next, we know that money is withdrawn from the account every week. We can use this information to solve for the slope of the line. We know that every week $85 is withdrawn from the account, so the slope of the line is -85. Therefore, the equation of the line is y = 150 - 85x.

Using this equation, we can determine the amount in the account at any given week. For example, at week 5, y = 150 - 85(5) = $25. This means that the account has a balance of $25 at week 5.

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The correct option is option a) Yes, this is plausible for the population mean because the upper boundary of the 95% confidence interval is below 7 minutes.

A confidence interval is a range of values, derived from a sample of data, that is used to estimate an unknown population parameter. The interval has an associated confidence level, such as 90%, 95%, or 99%, which indicates the level of confidence that the interval contains the true population parameter.

The most commonly used method to calculate a confidence interval is the method of maximum likelihood estimation. The wider the interval, the less certain the estimate, and the narrower the interval, the more certain the estimate.

It is plausible that the true mean number of times for all mice to complete the maze may be less than 7 minutes, as the interval provided by the researcher (2.9 minutes to 6.83 minutes) does not include 7 minutes as an upper bound.

A 95% confidence interval indicates that if the study were to be repeated multiple times, 95% of the intervals created would contain the true mean, so there is a 5% chance that the true mean falls outside of the interval provided.

Therefore, The correct option is option a) Yes, this is plausible for the population mean because the upper boundary of the 95% confidence interval is below 7 minutes.

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Answer:Yes, this is plausible for the population mean because the upper boundary of the 95% confidence interval is below 7 minutes

Step-by-step explanation:

i took the quiz

The equation of the tangent line at x = 4 is:

y = 179*x  - 490

(your teacher or the person who wrote this problem made a mistake somewhere, as none of the options is near correct)

We have:

f(x) = 4x³ - 2x² + 3x - 10

When x = 4 we have:

f(4) = 4*4³ - 2*4² + 3*4 - 10 = 226

So we want a line tangent to the curve at the point (4, 226)

To find the slope of that line, we need to evaluate the derivative of f(x) in x = 4.

The derivative is:

f'(x) = 3*4x² - 2*2x + 3

f'(x) = 12x² - 4x + 3

Then the slope is:

f'(4) = 12*4² - 4*4 + 3 = 179

Then the tangent line is something like:

y = 179*x + b

To find the value of b, we replace the values of the point (4, 226)

226 = 179*4 + b

226 - 179*4 = b = -490

The line is:

y = 179*x  - 490

Notice that this is not in the options, meaning that the problem (or the options) are written incorrectly.

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The subtraction of the expression 27 g^7 k^3 z^4 - 9 g^2 K^5 z is 18(g⁷k³z⁴ - g²k⁵z)

Algebraic expressions are described as expressions that are known to consist of terms, coefficients, constants, variables and factors.

They are also described as expressions composed of arithmetic operations, such as;

It is also important to note that index forms are mathematical representation of variables or values too large or small in more convenient forms.

From the information given, we have the expression;

27 g^7 k^3 z^4 - 9 g^2 K^5 z

Subtract the coefficient

18(g⁷k³z⁴ - g²k⁵z)

Hence, the value is 18(g⁷k³z⁴ - g²k⁵z)

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(4x + 5) + (2x - 7)

4x + 5 + 2x - 7

6x - 2

The volumes of the prisms are 12 cm³, 135 cm³ and 1200 cm³

A prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases.

Given are prisms, We need to find their volumes,

Volume of a prism = 1/2 × area of the base × height

1) Area of the base = 1/2 × 3 × 4 = 6 cm²

Height = 4 cm

Volume = 1/2 × 4 × 6 = 12 cm³

2) Area of the base = 1/2 × 5 × 12 = 30 cm²

Height = 9 cm

Volume = 1/2 × 9 × 30 = 135 cm³

3) Area of the base = 1/2 × 15 × 16 = 120 cm²

Height = 20 cm

Volume = 1/2 × 20 × 120 = 1200 cm³

Hence, the volumes are 12 cm³, 135 cm³ and 1200 cm³

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Answer:

Let's represent the amount of shells Chen bought as x grams. Then the amount of eggs he bought is 320 - x grams.

We can use the price per gram to write two equations:

0.96x + 1.06(320 - x) = 0.9975 * 320

Expanding and simplifying the equation:

0.96x + 342.4 - 1.06x = 319.2

-0.1x = -23.2

x = 232

Answer:

Chen bought 232 grams of shells and 320 - 232 = 88 grams of eggs.

Geometric series should you use to find total amount of money after 30 days geometric series should you use to find total amount of money after 30 days

after 30 days the total is 0737418.23

Given that

A geometric series is a collection of terms in mathematics that have an unlimited number and a fixed ratio between each term. Because each succeeding term may be produced by doubling the previous term by half, for instance, the series

1/2+1/4+1/8+1/16+ ..........is geometric, because each successive term can be obtained by multiplying the previous term by 1/2.

The geometric series had an important role in the early development of calculus, is used throughout mathematics, and can serve as an introduction to frequently used mathematical tools such as the Taylor series, the complex Fourier series, and the matrix exponential.

Each term in a geometric series is the geometric mean of its two adjacent terms, as indicated by the name.

now, we need to find geometric series  should you use to find total amount of money after 30 days

geometric series = Σ[tex]\left \ {{30} \atop {n=1}} \right.[/tex]

= (1)[tex](2)^{1-1}[/tex] + (1)[tex](2)^{2-1}[/tex] + (1)[tex](2)^{3-1}[/tex] + (1)[tex](2)^{4-1}[/tex] + ......................+(1) [tex](2)^{29-1}[/tex] +(1)[tex](2)^{30-1}[/tex]

= 10737418.23

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Answer:

A and then the 2nd one is 10737418.23

Step-by-step explanation:

yw

The supplied figure's half is tipped downward; therefore, to make them symmetric, we must translate the figure upwards. Anden consider the negative image.

In mathematics, symmetry is the quality of an object being split into two identical, mirrored parts. What does axis of symmetry mean? The term "axis of symmetry" refers to a hypothetical line that can fold or divide an item into two identical mirror halves. If two halves can fit together, then anything is symmetrical. Drawing a mirror line in the center and making sure both halves are the same will allow you to determine the shape's symmetry. To put it another way, symmetry is when two things are facing one another or when two things have mating pieces that revolve about an axis.

The supplied figure's half is tipped downward; therefore, to make them symmetric, we must translate the figure upwards. Anden consider the negative image. We obtain the translational and reflective symmetry.

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Answer:  the maximum number of zeros that the polynomial function

f(x)= 4x^9+5x^8+4x^6+9x+1  is 9

Step-by-step explanation:

Firstly, it is important to rearrange the function in decreasing order. The function will now be f (x) = 4x^9+5x^8+4x^6+9x+1

Secondly, for finding the zeros, it is necessary to find the degree of the function. The maximum number of zeroes in a polynomial is the degree of the function. The degree of a function is the highest value of exponents in the function. Here, in this function, the degree is 9.

Lastly, the degree of the function is the number of zeroes. Since the degree is 9, the number of zeroes possible is also 9.

Answer:

The lake decreases by a factor of 3.038 in 10 years (to 3.038 km^2).

The lake decreases by a factor of 0.00167 each month.

Step-by-step explanation:

Use the given relationship A(t)=11x(.98)^t and find the value of A for t=10 years.

A(10) = 11*(0.98)^10

A(10) = 3.621 km^2

The lake has decreased by a factor of (11km^2/3.621km^2) or 3.038.

==

The lake decreases each month by (0.02/12) or 0.00167 each month.

Suppose X and Y are two random variables that have the same distribution. Does

P[X≤ t∣ Y=a]

be necessarily equal to

P[Y≤ t∣ X=a]?

Note that if X and Y are bivariate normal with correlation ρ and each is marginally N(μ,σ2), then it is necessarily true because both conditional distributions would be

N(μ+ρ(a−μ),(1−ρ2)σ2).

A simple counter example:

P(X=1,Y=2)=13P(X=2,Y=3)=13P(X=3,Y=1)=13

Then P(X≤1|Y=2)=1, but P(Y≤1|X=2)=0.

Because it is interesting to look at the general pattern.

The wanted property is a kind of symmetry,

so we should look for some asymmetrical joint distribution for X,Y).

Si if (X,Y) has a permutable distribution in the sense that (X,Y) and (Y,X) have the same distribution,

so that for the joint cumulative we have F(x ,y)=F(y ,x) for all (x ,y), then the sought-after property will hold.

Let us use copulas. Let F be the joint CDF (cumulative distribution function) and

C(u ,v)=P(F(x)≤ u ,F(Y)≤v)

By the Fréchet– Hoefdding copula bounds (see linked wiki article above) we have

W(u ,v)≤C(u ,v)≤M(u ,v)

where W(u ,v)=max(u+v−1,0) and M(u ,v)=min(u ,v). Both W,M are copulas. W describes the anti-monotonic case X=U,Y…

Not necessarily true. Let X and Y be discrete random variables that take the values in {1, 2, 3} each with probability 13;

i.e. they have a discrete uniform distribution. Consider the joint probability mass function represented by the matrix below where the element in row i and column j is P[X=i , Y=j]:

160⎡⎣⎢331461221154⎤⎦⎥

Note that all rows and columns add up to 13 and therefore the marginal distributions are the discrete uniform as stated. Now calculate the conditional probability

P[X≤2∣Y=1]=360+360360+360+1460=310.

On the other hand,

P[Y≤2∣X=1]=360+660360+660+1160=920.

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(x^2  - 5x -  14 = 0) has the solution set as F: "x = 7 , -2" .

Solve the equation by factorization method.

x^2 - 5x - 14 = 0

x^2 -  7.x + 2.x - 14 = 0

taking x common from the frist two terms and +2 common from the last two terms.

[ x(x - 7 ) PLUS (+) 2 (x -7) ] = 0

[( x - 7) . (x + 2)] = 0

x - 7 = 0 , &   x + 2  =0

x = 7  , & x = -2

Thus the solution is x = 7 and x = -2.

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The number that represents an area receiving several weeks (to months) of constant daylight during their summer is 10.

The number 10 is typically found at latitudes above the Arctic Circle (about 66.5 degrees North) during the summer solstice, the longest day of the year.

During the summer solstice, the tilt of the Earth's axis is such that the North Pole is tilted towards the sun, providing more direct sunlight to areas within the Arctic Circle. This results in several weeks to months of constant daylight, known as the "midnight sun."

On the other hand, areas south of the Antarctic Circle, which is located at about 66.5 degrees South latitude, experience "polar night" or 24-hour darkness during the winter solstice.

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AD = 2.6

DB = 4 and DC = 6 , We need to find AD using Euclid's theorem for the right triangle.

Euclid's theorem is a fundamental number theory theorem that asserts that for every two numbers a and b, where b does not equal 0, there exist unique integers q and r such that a = bq + r, where 0 r |b|. To put it another way, a may be divided by b with a remaining of r. Euclid's theorem is a subset of the division method that asserts that for every two integers a and b with b greater than zero, there exist unique numbers q and r such that a = bq + r, where 0 r |b|.

Using Euclid's theorem,

∴ DB² = AD * DC

∴ 4² = AD * 6

∴ 6 AD = 16

∴ AD = 16/6 = 8/3 ≈ 2.67

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Answer:

1, 3, 5, 7 and 19

Step-by-step explanation:

to find the first 4 terms, substitute n = 1, 2, 3, 4 into the rule, then

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 - 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

the first 4 terms are 1, 3, 5, 7

to find the 10th term , substitute n = 10 into the rule

a₁₀ = 2(20) - 1 = 20 - 1 = 19

The length of AD is 70.26.

A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.

The volume of a pyramid with a square base is given as:

Volume = 1/3 x base area x height

We have,

ΔBCD

Tan 33 = BC/BD

0.65 = 37/BD

BD = 37/0.65

BD = 56.92

Now,

ΔABD

Sin 54 = BD/AD

0.81 = 56.92/AD

AD = 56.91/0.81

AD = 70.26

Thus,

The length of AD is 70.26.

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The next 3 terms of the given geometric sequence are:

... 1, -1/3, 1/9

A geometric sequence is a sequence where to get the next term, we need to multiply the previous term by a constant number.

Such that the general recursive formula is:

Aₙ = k*Aₙ₋₁

By using the two first terms:

81 and -27, we can find the value of k.

-27 = k*81

-27/81 = k

-1/3 = k

Now, to get the next 3 terms we can use the recursive formula:

A₅ = -3*(-1/3) = 1

A₆ = (-1/3)*1 = -1/3

A₇ = (-1/3)*(-1/3) = 1/9

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Answer:

-9

Step-by-step explanation:

-7x = 63

Divide both sides by -7.

-7x/-7 = 63/-7

Simplify.

x = -9

Follow directions and input only the -9

[tex]-7x=63[/tex]

1. Divide both sides by -7.

[tex]\frac{-7x}{-7} = \frac{63}{-7}[/tex]

[tex]x=-9[/tex]

-9 would be your answer.

If set of ordered pairs (1,8.50) , (3,25.50) , (5,42.50) , (6,51) , (7,59.50) represents cost of tickets for school play , it means that the function that represents the relationship between the number of tickets and the cost for ticket is  [tex]y = 8.5\times x[/tex] .

The Ordered Pairs are given as : (1,8.50) , (3,25.50) , (5,42.50) , (6,51) , (7,59.50) ;

the input represents the number of ticket and

the output represents the total cost of number of tickets ,

So , the domain is = { 1 , 3 , 5 , 6 , 7 } ;

and the range for this function is = {8.50 , 25.50 , 42.50 , 51 , 59.50 } ;

Considering the first pair ,

when the number of ticket is 1 , then the cost is 8.50 ,

for second pair when the number of ticket is 3 , then the cost is 25.50 ;

So , we can say that the cost of 1 ticket is = 8.50 ;

if x represents number of tickets , and y represents the cost for that tickets , then  function that can represent given situation is [tex]y = 8.5\times x[/tex] .

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His pay to play this game per draw is $0.1413

0.015 of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Money mark recieves for diamond=$0.45

Money mark recieves for queen=$0.60

Money mark recieves for queen of diamonds=$0.80

Now,

Probability of getting a diamond = 13/52

Price of one heart =$0.45

Pay for one heart = 13/52×0.45=$0.1125

Probability of getting a queen =4/52

Price of one queen =$0.60

Pay for one queen =4/52×$0.60=$0.0115

Probability of getting a queen of diamonds =1/52

Price of one queen =$0.80

Pay for one queen =1/52×$0.80=$0.015

Total pay for one draw= $0.1125+$0.0115+$0.0173=$0.015

=0.1413

Therefore, the pay per draw by probability will be $0.1413

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The smaller of the numbers, given the ratio and the larger number, can be found to be 393.

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.

The ratio is given such that it is 5 : 3 . What this means is that for every 3 of the smaller number, there is 5 of the larger number.

Given that the larger number is 655 therefore, the smaller number would be:

= ( Ratio of smaller number x Larger number ) / Ratio of larger number

Ratio of smaller number = 3

Ratio of larger number = 5

Larger number = 655

The smaller number is:

= ( 3 x 655 ) / 5

= 1, 965 / 5

= 393

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There are 8 different colorings that can be made.

Color each of the six faces of a cube with either blue or red. note that two colorings are regarded the same if the cube looks identical after some rotation.

The number of colorings can be calculated by using the equation 2^6 = 64. This is because each of the six faces of the cube can be colored either blue or red, giving two options for each face.

As there are six faces, the total number of colorings is 2^6 = 64. However, some of these colorings are the same after a rotation, so the total number of distinct colorings is 8.

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If n=2k  (means even value) is always possible to dissect a rectangle into n right triangles.

Dissect means to separate a dead person's or animal's body into its component for closer examination.

Dissect is to consider or talk about the specifics of something in order to fully comprehend it.

To dissect is to separate into components.

For n=2, it is easy to show that it is possible (just insert the diagonal).

For n=3, it is not possible ( I tried on some examples but not able to do it).

For n=4, it is possible first make two rectangle from the original rectangle then use the case of n=2

So if n=2k  (means even) then it is always possible.

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The point that is equidistant of the points (7, 3) and (13, -1) is (3.33, -9)

Remember the distance between two points (x₁, y₁) and (x₂, y₂) can be written as:

distance = √( (x₂ - x₁)² + ( y₂ -  y₁)²)

We want to find a point (x, y), that lies on the line y = -9 that is equidistant to  (7, 3) and (13, -1)

We can rewrite our point as (x, -9)

And the distances to the given points are:

distance = √( (x - 7)² + ( -9 - 3)²)

distance = √( (x - 13)² + ( -9 + 1)²)

These distances must be equal, (that is what equidistant means) so we can write:

√( (x - 7)² + ( -9 - 3)²) = √( (x - 13)² + ( -9 + 1)²)

Now we can remove the square root and simplify the equation:

(x - 7)² + ( -9 - 3)² =  (x - 13)² + ( -9 + 1)²

(x - 7)² + 144 = (x - 13)² + 64

x^2 - 14x + 49 + 144 = x^2 - 26x + 169 + 64

-14x + 26x = 169 + 64 - 49 - 144

12x = 40

x = 40/12

x = 3.33

The point is (3.33, -9)

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Answer:

To solve this problem, we can use algebra. Let x be the number of student tickets sold and y be the number of adult tickets sold. We know that:

x + y = 500 (the total number of tickets sold)

5x + 10y = 3000 (the total revenue from ticket sales)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can use the first equation to solve for y in terms of x:

y = 500 - x

Now we can substitute this expression for y into the second equation:

5x + 10(500 - x) = 3000

5x + 5000 - 10x = 3000

-5x = -2000

x = 400

So, the number of student tickets sold is 400. The answer is d) 400

Total 400 students attended the play.

A function is a relation between a dependent and independent variable.

Mathematically, we can write → y = f(x) = ax + b.

Given is that student tickets cost $5 each and adult tickets cost $10 each. The total ticket sales were $3,000 for 500 tickets.

We can write the system of equations as -

5x + 10y = 3000

x + y = 500

Now -

x = 500 - y

So -

5(500 - y) + 10y = 3000

2500 - 5y + 10y = 3000

5y = 500

y = 100

x = 400

Therefore, total 400 students attended the play.

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Answer: "-99"

Step-by-step explanation:

You should begin evaluating the given expression from the innermost part.

So, you should find the s(5) firstly. And then, you should use this value for the other function to find r(s(5)).

If you calculate s(5) ==> (-2) * (5)^2 + 1 = -49

This means that the question is asking what is r(-49), indeed.

If you finally calculate r(-49) ==> 2 * (-49) - 1 = -99

The answer is -99.