Use the quadrilateral below to help answer the next two questions.
If L is (-2,-5) and M is (4,-1), what should the slope of NO be in order for LMNO to be a parallelogram?
Note: Enter negatives when necessary with no space between the negative sign and the number.
If the answer is a fraction, leave as an improper fraction in simplest form. Ex. 4/3 for 8/6

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

a. two-tailed test

b. reject H0 if Z>1.96 or Z<-1.96

c. Z = 1.73

d. we have failed to reject the null hypothesis

e. P-value = 0.0418

We need to find our critical value:

Zα/2 = Z(0.05/2) = 0.025

The Z test will be done using the next equation:

Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2

Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73

Z<1.96, therefore we have failed to reject the null hypothesis

The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis

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The final amount of the money according to compound interest model is $ 5342.80.

Herein we find a case of a money deposited that increases its amount in time by compound interest, that is, the amount increases continuously in time. The compound interest model is described below:

C' = C · (1 + r / 100)ⁿ

Where:

If we know that C = 4232, r = 6 and n = 4, then the final amount of the money is:

C' = 4232 · (1 + 6 / 100)⁴

C' = 5232.802

The final amount is $ 5342.80.

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The expressions x - 5 and x - 5 gives the equal value for the different values of x, therefore expressions are equivalent.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expressions are,

x - 5 and x - 5

To determine the expressions are equivalent,

Since, in the both, the expression x is a variable, and 5 is an integer,

Therefore, for the values of x the value of expression should be equal.

Substitute x = 0,

x - 5 = 0 - 5 = - 5

And

x - 5 = 0 - 5 = - 5

Substitute x = 1

x - 5 = 1 - 5 = - 4

and

x - 5 = 1 - 5 = - 4

Since, for the different values of x the values of expressions are equal.

Hence, expression x - 5 and x - 5 are equivalent.

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(X=60,Y=47,Z=73),  the measures of the three angles.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question

x+y+z=180

The second and third angles' combined measurements equal twice the first angle's combined measurement, therefore

y+z−2x+y+z=2=0

Third angle has 26 more degrees than second angle, therefore

z−y+z=y+26=26

As a result, we obtain the equation system.

x+y+z=180−2x+y+z=0−y+z=26

(1)(2)(3)

By removing y and z, use equations (1) and (2) to determine x. To get rid of y and z, multiply equation (2) by one before adding it to equation (1).

x+y+z2x−y−z3xx=180=0=180=60(4)

To get rid of z, use equations (1) and 3). To get rid of z, multiply equation (3) by 1 and then add it to equation (1).

x+y+zy−zx+2y=180=−26=154(5)

To determine, substitute x=60 into equation (5).

x+2y(60)+2y2yy=154=154=94=47

In order to find, we can now change x=60 and y=47 in equation (1).

x+y+z(60)+(47)+zz+107z=180=180=180=73

Therefore, there is a solution.

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Answer:

-----------------------------------------

Given:

Find a function g which is a horizontal shrink by a factor of 1/3 of f(x).

Horizontal shrink by a factor of k is:

Apply this to the given function:

Answer:Put a one under the five then sop he last faction and start multiplying

Step-by-step explanation:

The total number of toys in the bag is 20

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

Frisbees = 5

Proportion of these Frisbees = 25%

Using the above as a guide, we have the following:

Number of Frisbees = Total number of Frisbees * The proportion of these Frisbees

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

Total number of Frisbees * 25% = 5

Divide both sides by 25%

Total number of Frisbees = 20

Hence, the total is 20

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The exact value for sin (∅) is √15/4 if  cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

In mathematics, the trigonometric functions—also known as circle, angle, or goniometric functions—are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths.  As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic phenomena.

The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals.

Given, cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

cos²∅+sin²∅=1

sin²∅=1-cos²∅

sin²∅=(1-(-1/4)²)

sin²∅=1-(1/16)

sin²∅=15/16

sin∅=√15/4

Therefore, the exact value for sin (∅) is √15/4 if  cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

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Answer:

Step-by-step explanation:

Clearly, it can be seen that 10/12 represents the largest fraction. Hence 5/6 (which is equivalent to 10/12) is larger than 2/3 or 3/4.

Answer: no they are equal either simplified to 5/6 or decimal 0.83 repeating decimal.

Step-by-step explanation:

By the Definition of a Correlation Coefficient,

x and y do not have a linear relationship.

Option B is the correct answer.

The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.

The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.

According to the question, If the correlation coefficient is zero, there is no linear relationship.

If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.

By the Definition of a Correlation Coefficient,

Option B is the correct answer.

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By the Definition of a Correlation Coefficient, X and Y do not have a linear relationship. Option B is the correct answer.

The correlation coefficient describes the movement of one variable in relation to another. A positive correlation indicates that the two are moving in the same direction, with 1 denoting a perfect positive correlation. A value of -1 indicates a perfect negative, or inverse, correlation, while a value of zero indicates that no linear correlation exists.

The number's value indicates the strength of the relationship: r = 0 indicates that there is no correlation. r = 1 indicates that there is a perfect positive correlation. r = -1 shows a perfect negative correlation.

According to the question, If the correlation coefficient is zero, there is no linear relationship.

If the correlation coefficient is zero, the relationship between x and y is not linear. Another possible relationship (such as an exponential or quadratic) could exist, but this is dependent on the scatter plot provided.

By the Definition of a Correlation Coefficient,

Option B is the correct answer.

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Answer:

He worked 26 hours at the vegetable farm and 4 hours at the paddy field.

Step-by-step explanation:

Let us take the working hour at a vegetable farm be x and at paddy field be y

He worked for both jobs for a total of 30 hours.

So,

x + y = 30 ...(1)

He earns Rs 200/- per hour from vegetable farm and Rs 250/- per hour from paddy field, total of Rs 6900.

So,

200x + 250y = 6900

2x + 5y = 138 ...(2)

From equation 1 we get,

x = 30 - y

Put the value of x = 30 - y in equation 2 we get,

2x + 5y = 138

2(30 - y) + 5y = 138

60 - 2y + 5y = 138

60 + 3y = 138

3y = 138 - 60

3y = 78

y = 26

Now, put the value of y in equation 1 we get,

x + y = 30

x + 26 = 30

x + 26 - 26 = 30 - 26

x = 4

Thus, He worked 26 hours at the vegetable farm and 4 hours at the paddy field.

The constant of proportionality for the relationship is 70.

From the given graph (2, 140), (4, 280), (6, 420), (8, 560) and (10, 700).

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the graph we can see it is direct proportion.

Here, y∝x

⇒ y=kx

⇒ k=y/x

⇒ k=140/2

⇒ k=70

Hence, the constant of proportionality for the relationship is 70.

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The probability of rolling an odd number or a number less than 4 is 2/3.

What is probability?

The degree to which something is likely; the probability that something will occur or will be the case.

Here, we have

Given

A single die is rolled.

Sample space = {1, 2, 3, 4, 5, 6}

Let P(A) be the probability of getting an odd number, where A = {1, 3, 5}

Let P(B) be the probability of getting a number less than 4,

where B = {1,2,3}

A ⋂ B ={1, 3}

P(A) = 3/6 = 1/2

P(B) = 3/6 = 1/2

P(A ⋂ B) = 2/6 = 1/3

Let P be the required probability of getting an odd number or a number less than 4

P = P( A ⋃ B ) = P(A) + P(B) - P(A ⋂ B)

P( A ⋃ B ) = 1/2 + 1/2 - 1/3

P( A ⋃ B ) = 1 - 1/3

P( A ⋃ B ) = 2/3

Hence, the probability of rolling an odd number or a number less than 4 is 2/3.

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The equation for total amount to be paid represented as y and pounds of potatoes represented as x will be y = 0.64x

Ax + By + C = 0 can be used to express a linear equation in two variables, where x and y are the two variables, and each has a degree of one.

Ex. -2x+3y=8

Total weight of potatoes in pounds Dontrell bought= x

Let total amount Dontrell he pays= $ y

It is given 5.5 pounds are bought by paying $3.52

5.5 pounds = $3.52

1 pound = $ 3.52/5.5

1pound=$0.64(Using Unitary method)

Dontrell buy x pounds potatoes and he pays $y

Therefore,

y=0.64x

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The area of the triangle below 8 yards

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Triangles are three-sided shapes. The many kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.7-15=8

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top I think he or she is right

The length of the AB in the given right triangle is √3/6

Given that, a right triangle with the base measure 6 units and an acute angle 30°,

We need to find the measure of side AB,

So, we will use the concept of trigonometric ratios,

Tan 30° = AB / AC

Tan 30° = AB / 6

1 / √3 = AB / 6

AB = √3/6

Hence the length of the AB in the given right triangle is √3/6

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The difference between 3894256 and 756533 by rounding each number to the nearest thousand is 3138000

The first number = 3894256

The second number = 756533

To find the difference between the numbers we have to use the subtraction

Difference between 3894256 and 756533 = 3894256 - 756533

Subtract the numbers

= 3137723

Rounding of a number is write the numbers to the nearest place values like tens, hundreds and thousand etc.

Here, the number is 3137723 and we have to round the number to nearest thousand

Round to nearest thousand = 3137000

Therefore, the result nearest to the thousand is 3138000

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The equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45  × d, so option B is correct.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.

Given:

The distance travelled = 315 miles,

The distance on the map =  7 inches,

Calculate the equation represents the actual miles traveled,

Actual distance = The distance traveled / The distance on the map × The distance on the map

m = 315 / 7 × d

m = 45  × d

Therefore, the equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45  × d.

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Triangles are congruent, then there is no additional angles/sides should we mark in each triangle.

What is congruent triangles?

If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.

Since reflexive angles means is an angle that is more than 180 degrees and less than 360 degrees.

And the reflexive sides means the reflexive property of congruence states that any shape is congruent to itself.

Vertical angles are angles opposite each other where two lines cross.

But to check the congruence of two triangles we only have the angles and sides of the two triangles are same.

So, there is no additional angles/sides should we mark in each triangle.

Hence, triangles are congruent, then there is no additional angles/sides should we mark in each triangle.

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Answer: It is crucial for students to look for and make use of a structure because this practice requires them to reason about the underlying mathematical structure and unity of mathematics ideas.

0.26 is  probability that a graduating senior receives two or three job offers.

What is probability in math?

Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.              

                                             Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.

P(2 or 3 jobs)=P(2 jobs)+P(3 jobs)-P(2 jobs and 3 jobs)=P(2 jobs) + P(3 jobs) since a student can not have 2 jobs as well as three jobs at a time.

So,

P(2 or 3 jobs)=0.15+0.11 = 0.26

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We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.

The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.

Therefore, the speed upstream is: (14 mi/h - S)

The speed downstream is (14 mph + S), where S is the stream's current flow rate.

We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:

14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.

In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:

T = (12 miles)/(14 miles per hour Plus S)

By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.

Taking only the favorable outcome, we obtain:

S = (24 - 25)/(-0.5) = 2 mph

2 mi/hr is the stream's current velocity.

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Answer:

106

Step-by-step explanation:

The pattern goes +6, +12, +18, etc

Thus, the final term is simply +30.

76+30 = 106

Hope it helps :) and let me know if you want me to elaborate.

Answer:

I've solved all of the above for you :)

Step-by-step explanation:

3q² + 7 = 55

3q² = + 7 - 7 = 55 - 7

3q² = 48

3q²/3 = 48/3

q² = 12

q = 2√3

√p - 4 = - 5

p - 4 = (-5)²

p - 4 + 4 = 25 + 4

p = 29

5√a/2 = 40

5√a/2 × 2 = 40 × 2

5√a = 80

5√a/5 = 80/5

√a = 16

a = 256

c³ - 4 = 23

c³ - 4 + 4 = 23 + 4

c³ = 27

c = 3

(k + 3)² = 4

k² + 6k + 9 = 4

k² + 6k + 9 - 4 = 0

k² + 6k + 5 = 0

k² + k + 5k + 5 = 0

k(k + 1) + 5(k + 1) = 0

(k + 5) (k + 1) = 0

k = (-5) or (-1)

√s + 4 = 6

s + 4 = (6)²

s + 4 - 4 = 36 - 4

s = 32

(√f - 5) = (√7 - f)

(√f - 5)² = (√7 - f)²

f - 5 = 7 - f

f - 5 + 5 + f = 7 + 5 - f + f

2f/2 = 12/2

f = 6

∛j + 9 = 0

∛j + 9 - 9 = -9

∛j = (-9)

j = (-9)³

j = (-729)

b² - 1 = 24

b² - 1 + 1 = 24 + 1

b² = 25

√b² = √25

b = 5

13 = (w - 2)² + 5

13 = w² - 4w + 4 + 5

13 - 9 = w² - 4w

w² - 4w = 4

w² - 4w - 4 = 0

w² - 2w - 2w - 4 = 0

w(w - 2) - 2(w - 2) = 0

(w - 2) (w - 2) = 0

w = 2 or 2

12 = 4√2x + 1

12/4 = 4√2x + 1/4

3 = √2x + 1

√2x + 1 = 3

2x + 1 = 9

2x + 1 - 1 = 9 - 1

2x/2 = 8/2

x = 4

(g + 1)³ = (-8)

g³ + 1³ + 3g(g + 1) = (-8)

g³ + 1 + 3g² + 3g = (-8)

g³ + 3g² + 3g = (-8) - 1

g³ + 3g² + 3g = -9

g³ + 3g² + 3g + 9 = 0

g = (-3)

∜(5m + 1) = 4

[∜(5m + 1)]⁴ = (4)⁴

5m + 1 = 256

5m + 1 - 1 = 256 - 1

5m/5 = 255/5

m = 51

∛(y³ - 19) = 2

(y³ - 19) = (2)³

y³ - 19 = 8

y³ - 19 + 19 = 8 + 19

y³ = 27

y = 3

The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

Step-by-step explanation:

12=666

Answer:

3.17×10^3

Step-by-step explanation:

Hope it helps!

Answer:

[tex]a=4, b=-8, c=-12[/tex]

Step-by-step explanation:

Compare the given equation with the general form [tex]y=ax^2 + bx+c[/tex].

The object's height was 300 ft above sea level when it was launched.

What is a quadratic equation?

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

Given, the height of the object can be modeled by the function

           h(t)=-16t^2+100 t+300

Height of object when it was launched

At the time of launched, t=0

h = -16(0)^2 + 100(0) + 300 = 300 ft above sea level

Hence, the object's height was 300 ft above sea level when it was launched.

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The first three terms of a sequence are given, so the 35th term is: [tex]a_n = 69[/tex]

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. A sequence is a list of elements that has been arranged in a certain way.

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should go forward. A phrase is used to describe each number in the series. The first word in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.

The first three terms are : 205, 201, 197, .......

The general term through the pattern is:

[tex]a_n = - 4n+209[/tex]

or, [tex]a_n = - 4(35)+209[/tex]    

here, n = 35

or, [tex]a_n = 69[/tex]

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