x + 4y = 10
2x + 8y = 20

To calculate the slope of the line, we have that its points are A(x₁, y₁) and B(x₂,y₂), we apply the following formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{\Delta y}{\Delta x} \iff m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}[/tex]

To solve, we have that the points are:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{A(x_1=\underbrace{2} \ \ , \ \ y_1=\overbrace{7} \ ) \ and \ B(x_2=\underbrace{-4} \ \ , \ \ y_2=\overbrace{19} } \end{gathered}$}}[/tex]

What we do to solve is that we substitute this data in the formula provided above.

 [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\dfrac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}[/tex]

 [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{19-7}{-4-2} } \end{gathered}$}}[/tex]

 [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{12}{-6}=-2 } \end{gathered}$}}[/tex]

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 p-value when the test statistic is equal to 2.30 is 0.033.

A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data.

A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct.

The statistical significance of the difference that was found increases with decreasing p-value.

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

So, the p-value will be:

The t-value for (n-1 = 20-1 = 19) degrees of freedom serves as the test statistic in this experiment.

Using the formula: T.DIST.2T(2.3,19)

The p-value will be 0.033.

Therefore, the p-value when the test statistic is equal to 2.30 is 0.033.

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Complete question:

A restaurant decides to test their oven's thermostat to see if it is working properly, that is if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set to 350 degrees and then the temperature was measured with a thermometer.

H o: μ=350 and Ha: μ≠350

The test statistic is equal to 2.30. What is the p-value _____?

By using the principle of counting, it can be calculated that

Total number of ways to arrange the four face cards in a 52-card deck =  11880

What is principle of counting?

Principle of counting states that if there are m ways to do one job and m ways to do another job after that job, there are m [tex]\times[/tex] n ways to do both the jobs together.

There are three face cards of hearts, three face cards of diamonds, three face card of clubs and three face cards of spade

Total number of face cards = 3 + 3 + 3 + 3 = 12

We can arrange the four face card in  [tex]{12 \choose 4}[/tex] ways = 495 ways

The four cards should be arranged in a row.

Number of choices for the first card = 4

Number of choices for the second card = 3

Number of choices for the third card = 2

Number of choices for the fourth card = 1

Total number of ways  to arrange the four cards in a row = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1 = 24

Total number of ways to arrange the four face cards in a 52-card deck =

495 [tex]\times[/tex] 24 = 11880

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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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The dimensions that need to be used so that the enclosed area of the two adjacent rectangular corrals will be maximum is 90 by 120 feet.

What do you mean by adjacent?

Adjacent refers to something that is close to or nearby. Your next-door neighbor is the person who lives in the home or apartment that is next to yours, even though you may consider the individuals who live up and down your street to be your neighbor.

Two things can be considered adjacent if they contact each other or share a wall or border. If two angles in geometry share a side and a vertex, they are said to be adjacent. In other words, neighbor angles do not overlap and are adjacent to each other immediately.

Solution Explained:

So according to the question, we get the equation

Perimeter is 4x + 3y = 720

⇒ x = 180 - [tex]\frac{3}{4}y[/tex]

Taking Area = 2xy

= 2(180 - [tex]\frac{3}{4} y[/tex])y

= 360y - [tex]\frac{3}{2} y^{2}[/tex]

Differentiating the function w.r.t y

A'(y) = 360-3y

Setting to 0

0 = 360 - 3y

⇒ y = 360 / 3 ⇒ 120

Now putting the value of y in

x =  [tex]180- \frac{3}{4} X 120[/tex]

x = 180 - 90 = 90

So, the dimensions are 90 by 120 feet.

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The width of the rectangle, x is 2.76 cm

Given,

The area of a rectangle = 17.6 square centimeters

Length of the rectangle = 2.3x

Width of the rectangle = x

We have to find the value of x.

Here,

Area of rectangle = length × width

Then,

17.6 = 2.3x × x

17.6 = 2.3x²

x² = 17.6/2.3

x² = 7.65

x = √7.65

x = 2.76

Now,

Width of the rectangle =  2.76 cm

Length of the rectangle = 2.76 × 2.3 = 6.35 cm

Therefore,

The value of x, that is the width of the rectangle is 2.76 cm

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The account, will reach $5500 in 33.33 years. if Victoria deposits $5000 into a savings account.

The direct crediting of cash flows associated to an investment or deposit is referred to as simple interest. Simple interest is a quick and straightforward way to calculate the interest amount on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle by the number of days between payments.

The written formula is "Simple Interest = Principal x Interest Rate x Time." This is the most fundamental method of calculating interest.

Victoria deposited $5000 into a savings account with an annual basic interest rate of 0.3%.

Simple Interest Formula

A = P(1 + rt)

5500 = 5000(1 + 0.003t)

5500 = 5000 + 15t

15t = 500

The account will reach $5500 in 33.33 years.

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Answer:

  4) ∠J = ∠L = 88°; ∠K = 92°

  5) ∠P = ∠R = 34°; ∠S = 146°

  6) ∠T = 54°; ∠U = ∠W = 126°

Step-by-step explanation:

You want the remaining angles in each rhombus where one angle is specified.

In a rhombus, as in any parallelogram, opposite angles are congruent, and adjacent angles are supplementary.

In each of the rhombi, the adjacent angle is supplementary:

  4) 180° -92° = 88°

  5) 180° -146° = 34°

  6) 180° -54° = 126°

Then the angle measures of interest are ...

  4) ∠J = ∠L = 88°; ∠K = 92°

  5) ∠P = ∠R = 34°; ∠S = 146°

  6) ∠T = 54°; ∠U = ∠W = 126°

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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Answer:

15

Step-by-step explanation:

Given functions:

[tex]g(x)=14-\dfrac{2}{3}x[/tex]

[tex]h(x)=-x-7[/tex]

g(9) means to substitute x = 9 into function g(x):

[tex]\begin{aligned}\implies g(9)&=14-\dfrac{2}{3}(9)\\&=14-\dfrac{18}{3}\\&=14-6=8\end{aligned}[/tex]

h(-14) means to substitute x = -14 into function h(x).

[tex]\begin{aligned}\implies h(-14)&=-(-14)-7\\&=14-7\\&=7\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies g(9)+h(-14)&=8+7\\&=15\end{aligned}[/tex]

As one calculation:

[tex]\begin{aligned}\implies g(9) + h(-14)&=\left(14-\dfrac{2}{3}(9)\right)+\left(-(-14)-7\right)\\&=\left(14-\dfrac{18}{3}\right)+\left(14-7\right)\\&=\left(14-6\right)+\left(14-7\right)\\&=8+7\\&=15\end{aligned}[/tex]

Answer:

56 in^2

Step-by-step explanation:

The formula for calculating area of a triangle is:

The height is 7t and base is 4t:

the value of t = 4 so replace x with 4:

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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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.

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 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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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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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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The time that the car will travel when the average speed is 55mph is 11 hours.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

From the information, the car has an average speed of 55 mph and it's travelling at 605 miles.

It should be noted that time will be calculated as the distance divided by the speed that given and this will be:

Time = Distance / Speed

Time = 605 / 55

Time = 11

The time is 11 hours.

This simply illustrates the time.

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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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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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The decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place include 0.237, 0.893, 0.475, and 0.652.

An even number is any number that can be divided exactly by two. Even numbers always have a last digit of 0, 2, 4, 6, or 8. Even numbers include 2, 4, 6, 8, 10, 12, 14, and 16.

Odd numbers are those that cannot be divided evenly by two. It cannot be evenly divided into two separate integers. When we divide an odd number by 2, we get a remainder. Odd numbers include 1, 3, 5, 7, and so on.

A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.

A prime number is a whole number greater than one with only the number one and itself as factors. A factor is a whole number that can be divided into other numbers evenly.

In this case, 0.237, 0.893, 0.475, and 0.652 have an even number in the tenths place which is the first place after the decimal point. Also, there's an odd number in the hundredths place, and a prime number in the thousandths place.

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Complete question

Write four decimal numbers that have an even number in the tenths place, an odd number in the hundredths place, and a prime number in the thousandths place

Answer:

Step-by-step explanation:

B becuase the way the angle is

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).

Answer:

a) 12 · y = x

b) If the points show equivalent fractions and the line goes through (0,0)

Step-by-step explanation:

a1) divide any numbers from the x and y line (for example, 2 ÷ 24 would give us 12)

a2) This equation makes sense because any number from the x line (for example, 2) multiplied by 12 would give us the number from the y line (in this example, 24).

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,

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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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:

outpot=160

Step-by-step explanation:

outpot= 100+ 100×0.6=160