Tell whether each figure creates the conditions to form a unique triangle, more than one triangle, or no triangle.

_________3 in.
________6 in. ___
________10 in. _____________

In interval notation,  the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)

A function is said to be continuous in an interval if all the values in the interval satisfy the function.

Since we have the function (x² - 4)/(x² - 7x + 10), we desire to find the interval in which it is continuous. So, we proceed as follows.

For the function f(x) = (x² - 4)/(x² - 7x + 10) to be continuous, then the denominator (x² - 7x + 10) ≠ 0

So, solving this inequality, we have

x² - 7x + 10 ≠ 0

x² - 2x - 5x + 10 ≠ 0

Factorizing, we have that

x(x - 2) - 5(x - 2) ≠ 0

(x - 2)(x - 5) ≠ 0

x - 2 ≠ 0or x - 5 ≠ 0

x ≠ 2 or x ≠ 5

Also, since the coefficient of x² is positive the function f(x) tends to ±∞.

So, the interval of continuity of f(x) is 2 < x and x > 5

So, the interval of continuity of f(x) is (-∞, 2) ∪ (5, +∞)

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A parachutist falls 11 seconds before the parachute opens, so 1936 ft far the parachutist fall during this time.

We have to find how far does the parachutist fall during this time.

The formula for estimating the time in seconds it will take an object to fall d feet is given below.

t = [tex]\sqrt{\frac{d}{16}}[/tex]

We merely need to enter the specified time t into the formula to find the distance answer.

11 = [tex]\sqrt{\frac{d}{16}}[/tex]

taking square on both side, we get

121 = d/16

Multiply by 16 on both side, we get

d = 1936 ft

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The complete question is:

The approximate time t in seconds that it takes an object to fall a distance of d feet is given by

t = [tex]\sqrt{\frac{d}{16}}[/tex]

Suppose a parachutist falls 11 seconds before the parachute opens. How far does the parachutist fall during this time?

Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.

If both a and b have the same sign, point P could be located in one of the four quadrants:

For First quadrant (a > 0, b > 0)

For Second quadrant (a < 0, b > 0)

For Third quadrant (a < 0, b < 0)

For Fourth quadrant (a > 0, b < 0)

Hence, Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.

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Answer:

D

Step-by-step explanation:

Answer: Let x be the speed of the eastbound train.

Then the speed of the westbound train is x+3 mph.

We can set up the following equation using the distance formula (rate x time = distance)

x*4 = 648/2 + (x+3)*4

Solving for x,

x= 42

So the speed of the eastbound train is 42 mph and the speed of the westbound train is 45 mph.

Step-by-step explanation:

A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.

It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.

A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.

Although it is not taken into account in the study, it might affect how the variables are related.

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In a case whhereby container built for transatlantic shipping is constructed in the shape of a right rectangular prism and Its dimensions are 15 ft by 5 ft by 10 ft the total weight of the contents is 68 pounds.

The concept that will be usd here is rectangular prism.

Then to calculate the volume of a rectangular prism, we will need to to make the multiplication with 3 dimensions:( length×width×height).

the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.

the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

The dimensions of the container built are 15 ft by 5 ft by 10 ft. since the container is entirely full , considering the average, its contents weigh  0.09 pounds per cubic foot.

we can calculate the volume of the container  as:15 ft * 5 ft * 10 ft= 750ft^3

Then, the total weight of the contents  can be found as :

750 ft³×   0.09 pounds per cubic foot= 67.5 pounds = 68 pounds.

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The side lengths for Quadrilateral EFGH are 4, 5, 6, and 8 units.

Quadrilateral EFGH is a reduction of Quad WXYZ by a ratio of 1:2. To find the side lengths for Quad EFGH, divide the side lengths of Quad WXYZ by 2. Therefore, the side lengths of Quad EFGH will be 4, 5, 6, and 8 units.

There are four sides, four vertices, and four angles in a closed quadrilateral. It is a form of polygon. Quadrilaterals' inner angles add up to 360 degrees in total. The English word quadrilateral is derived from the Latin words quadra, which means four, and latus, which means sides.

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The individuals in this dataset consented to participate in this study after receiving a request for volunteers. This sampling design may be biased in favor of volunteers, given that every volunteer has recorded responses for each variable.

At any point during the trial—from recruitment to retention to follow-up—volunteer bias may manifest itself. Volunteers and the target community differ not only in terms of sociodemographic characteristics but also in terms of views about the experiment and the institutions involved.

Volunteer bias may also be related to the illnesses or conditions being investigated, as volunteers may be less likely to volunteer for research on illnesses or behaviors that are viewed as less acceptable by society, such as ailments linked to drug usage.

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After being asked for volunteers, the people in this dataset agreed to take part in the study. Given that each volunteer has recorded responses for each variable, this sample design may be skewed in favour of the volunteers.

Volunteer bias may appear at any time during the experiment, from recruitment to retention to follow-up. The target community and volunteers have different sociodemographic features, as well as different perspectives on the experiment and the participating institutions.

As volunteers may be less likely to volunteer for research on illnesses or behaviours that are perceived as less acceptable by society, such as conditions associated to drug use, bias may also be related to the illnesses or conditions being examined.

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The expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

So, we must keep in mind the following characteristics of the logarithms in order to solve the issue:

[tex]\begin{aligned}& \log (x . y)=\log (x)+\log (y) \\& \log \left(x^y\right)=y \cdot \log (x)\end{aligned}[/tex]

Then, the expression we have:

[tex]P=\log \left(6 x^4\right)[/tex]

The factor of 6=2*3:

[tex]P=\log \left(2 \cdot 3 x^4\right)[/tex]

Apply the product's feature:

[tex]P=\log (2)+\log (3)+\log \left(x^4\right)[/tex]

Apply the exponent's property now:

P=log(2)+log(3)+4.log(x)

Therefore, the expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

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Correct question:

Expand the logarithm fully using the properties of logs. Express the final answer in

terms of log .

log 6x^4

Answer:

yes ✔‍♀️

Step-by-step explanation:

just flip it over and dividend by 1.2

An expression that is equivalent to -56Z +28 can be -23z + 10 - 33z + 18

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, an expression that is equivalent to -56Z +28 can be:.

-23z + 10 - 33z + 18

= -23z - 33z + 10 + 18

= -56z + 28

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48.15% people visited one of the three coffee shops on monday

The scholars discovered that;

518 people went to Cool Beans, 974 to Planet Euro, and 1,160 to Frothies.

Assume that x% of Monday's customers at each of the three coffee shops were x.

One hundred thirty-five people went to Cool Beans on Monday.

Of the total number of customers who went to one of the three coffee shops on Monday, 52% went to Cool Beans.

Consequently, 52/100 * x = 135

The calculation for x is (135*100)/52.

x = 260 individuals

On Monday, the following number of visitors visited either PlanetEuro or Frothies:

260-135 =125

Calculating the percentage of Monday visitors to either PlanetEuro or Frothies;

135= 52%

125=?

Cross-product as you

(125*52)/135 =48.15%

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He rode 1 kilometer farther than her, which is equal to 1,000 meters.

He rode the farthest as he rode 4 kilometers and she rode 3,000 meters. To calculate how much farther he rode, we need to convert 3,000 meters into kilometers. 1 kilometer is equal to 1,000 meters. So, 3,000 meters is equal to 3 kilometers. Therefore, he rode 1 kilometer farther than her, which is equal to 1,000 meters.

To calculate the difference between the two distances, we can use the following formula:

Difference = km1 - km2

In this example, km1 is 4 kilometers and km2 is 3 kilometers.

Difference = 4 - 3

Difference = 1

Therefore, he rode 1 kilometer farther than her, which is equal to 1,000 meters.

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The area of the largest possible norman window with a perimeter of 25 ft is 43.75 ft²

Let r = the semicircle's radius

h = the rectangle's radius

2r = the window's width

C = 2πr is the formula for the perimeter of a circle,

The perimeter of the semicircle =πr

The perimeter of the window is

P=πr + 2h + 2r = 25

2h + (π +2)r = 25

h = ½[25 - (π + 2)r]

h = 12.5 - (π/2 +1)r ...............(1)

The formula for the area of a circle is A= πr²,  so

½πr² = the perimeter of the semicircle

The area of the window is

A = ½πr² + 2rh.............. (2)

Substitute (1) with (2).

A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²

A = 25r - (π + 2 - π/2)r²

A =  -(π/2 + 2)r² + 25r ........(3)

One way to notice the vertex is to set the first derivative equal to zero.

dA/dr =-2(π/2 + 2)r + 25 = 0

-(π + 4)r  + 25 = 0    

 r = 25/(π + 4)

 r ≈ 3.50 ft .......... (4)

Substitute (4) with (1).

h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50)

h  = 12.5 - 9.00 = 3.50  

h = 3.50 ft

Area =  1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50

Area = 43.75 ft²

So, the area is 43.75 ft².

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Assuming the interest is compounded monthly, the interest rate that would be required in order for Joshua to end up with $1,500 is 2.26%.

Mathematically, compound interest can be calculated by using this formula:

A(t) = P(1 + r/n)^{nt}

Where:

Substituting the given parameters into the compound interest formula, we have;

1,500 = 1,000(1 + r/12)^{12 × 18}

1.5 = (1 + r/12)^{216}

Taking the 216th root of both sides of the equation, we have:

1.00187891623 = 1 + 0.083333333r

0.083333333r = 1.00187891623 - 1

0.083333333r = 0.00187891623

r = 0.00187891623/0.083333333

r = 2.26

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Answer:

the interest rate that would be required in order for Joshua to end up with $1,500 is 2.26%.

Step-by-step explanation:

If the data for every person who took the tests were tabulated, the correlation between the Math and Verbal SATs would be less than 0.97.

Are the SAT verbal and SAT reading the same test?

The word used to designate the SAT Reading and Writing part is an older, outmoded one. The SAT Verbal section's material is still highly significant today, though. Many of the subjects and abilities from the old SAT Verbal portion are now included in the Evidence-Based Reading and Writing section.

Here we know that the correlation between these 51 pairs of averages was 0. 97.

And as we all know that the Educational Testing Service computed the average Verbal SAT score for each state, as well as the average Math SAT score for each state.

As we know that  the individual people tend to have more variation when you compare them to the average person

then if we look at the individual math and rebels course then there's probably a way more variation.

Here we know that the straight line wouldn't be there.

Then the whole thing would not be the same.

And which tells that It would be less of a correlation coefficient.

So it is less that 0.97.

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Answer:

The distance traveled by the car in each second is increasing by 4 cm each time. This is an example of an arithmetic sequence, where the common difference is 4 cm.

To find the total distance traveled by the car in 30 seconds, we can use the formula for the sum of an arithmetic series:

S_n = n/2 * (a_1 + a_n)

where S_n is the sum of the first n terms of the series, a_1 is the first term (4 cm in this case), a_n is the nth term, and n is the number of terms.

Substituting the values into the formula:

S_n = 30/2 * (4 + (4 + (30 - 1) * 4))

S_n = 30/2 * (4 + 4 + 116)

S_n = 30/2 * 124

S_n = 3720 cm

So the total distance travelled by the car in 30 seconds is 3720 cm.

It take 43 seconds to the object to travel the full length.

Constant rate refers to a fixed rate of change over a specific period of time. It can be used to describe a variety of situations such as the rate of population growth, the rate of inflation, or the rate of decline in a company's profits.

Constant rate can be used to measure a variety of factors in order to track progress or gauge the success of a particular strategy.

This question uses the concept of constant rate.

Constant rate means that the marble is travelling at a constant speed over the entire length of the path.

This means that the time it takes to travel the full length is the same as the time it took to travel a certain portion of the path.

In this case, it took 43 seconds to travel a certain portion of the path, so it will take 43 seconds to travel the full length.

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Answer:

itll take 8 pounds for both DHL and MPS to cost the same

Step-by-step explanation:

since DHL charges $4 for the first pound and $0.22 for each additional pound, and MPS charges $12 for the first pound and $0.12 for each additional pound, we can write that as 4 + 0.22x = 12 + 0.12x, with the left side representing DHL and the right representing MPS.

If this equation is solved, you will find out that x = 8, which is the number of pounds that DHL and MPS will cost the same at. Therefore, they will charge the same amount for 8 pounds.

If the average rate of inflation over the last hundred years was 3.22%, the amount of money one hundred years ago would be equivalent to a million dollars today is approximately 968,805 dollars.

If the average rate of inflation over the last hundred years was 3.22%, we have to determine the amount of money one hundred years ago would be equivalent to a million dollars today.

We know that formula of inflation is:

inflation = (FP−IP)/IP × 100

where, IP stands for the initial basket price or price index.

FP stands for the basket's final price or the price index.

From the question, inflation = 3.22%, FP = 1,000,000

Now putting the values in the formula

3.22 = (1,000,000 - IP)/IP  × 100

Divide by 100 on both side, we get

0.0322 = (1,000,000 - IP)/IP

Multiply by IP on both side, we get

0.0322IP = 1,000,000 - IP

Add IP on both side, we get

1.0322IP = 1,000,000

Divide by 1.0322 on both side, we get

IP = 968,804.5

IP = 968,805(approx)

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Answer:

93.312

Step-by-step explanation:

This would be decay so we use the formula [tex]y=a(1-r)^{2}[/tex]

in this case a would equal $1200, r would equal 40% (as a decimal) or 0.4 and x would equal 5

[tex]y=1200(1-0.4)^5[/tex] plug this into your calculator and you will get 93.312

I hope this helps (Lmk if im wrong )

The 32 inche flat screen televisions will be 19.35 inches in height based on the angle between diagonal and bottom

The diagonal, bottom and perpendicular forms

right angled triangle. The mentioned angle can be related with diagonal and height through sine function. The formula is expressed as follows -

sin theta = height ÷ diagonal

Keep the values in formula to find the value of height.

sin 35 = h/32

Rewriting the formula for h.

h = sin 35 × 32

Keep the value of sin 35 in the formula

h = 0.57 × 32

Performing multiplication on Right Hand Side of the equation

h = 18.35 inches

Hence, the TV screen is 18.35 inches high.

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A graph of the inequality w ≤ 200 is shown in the image attached below.

In this scenario, we would solve the given inequality by making "w" the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle is closed because of the less than or equal to (≤) symbol.

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The population of rabbits in the Butler County, where the starting rabbit population of 6,004 increases by 8% per year in 10 years is about 13,362 rabbits

A population is the set that comprises of all individuals or items that share a common specified characteristics.

The current population of the rabbit = 6,004

The rate at which the population is increasing per year = 8%

The number of rabbits in 10 years is found using the formula for population growth as follows;

P = P₀ × e^(r·t))

Where;

P = The population or number after the time t

P₀ = The initial or starting population = 6,004 rabbits

r = The percentage growth rate = 8%

t = The time of growth = 10 years

e = Euler number

Therefore;

P₁₀ = 6,004 × e^(0.08 × 10) ≈ 13362

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Answer:

You will need to pay $48.06.

Solution:

Given that,

The fixed fee of online recruiting website offers listings is $30,

and $0.42 per word.

Your listing has 43 words,

so,

No.of words*Cost per word = 43*0.42

                                              =$18.06

Total fee for 43 listings =$30 + $18.06

                                                  =$ 48.06

The number of sticks in pattern number n will be 6 + (n-1)(4).

What is a pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.

The given diagram states that -

The first figure of the triangle is made using - 6 sticks.

The second figure of the triangle is made using - 6 + 4 sticks.

The third figure of the triangle is made using - 6 + 4 + 4 sticks.

Similarly, the fourth figure of the triangle will be made using - 6 + 4 + 4 + 4 sticks.

So, the pattern followed here is -

First image = 6 + (1-1)(4)

Second image = 6 + (2-1)(4)

Third image = 6 + (3-1)(4)

Fourth image = 6 + (4-1)(4)

So, for pattern n the number of sticks will be -

nth image = 6 + (n-1)(4)

Therefore, the pattern is obtained as 6 + (n-1)(4).

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The length of Nigel's bedroom is 11 feet while the width is 9 feet

An equation is an expression that shows the relationship between numbers and variables.

For Colleen room:

length = 8 ft, width = 12 ft

Perimeter = 2(length + width)

substituting:

Perimeter = 2(8 + 12) = 2(20)

Perimeter = 40 feet

For Nigel room:

length = l ft, width = 3/4 times that of Colleen = (3/4)(12) = 9 feet

Perimeter = 2(length + width)

But Colleen and Nigel room has same perimeter

substituting:

40 = 2(l + 9)

l + 9 = 20

l = 11 feet

The length is 11 feet.

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