The equation of Pilar's line of fit is `c=-1t+120`
How many more cups of hot chocolate would Pilar expect to sell if the temperature decreased by `15°`F?

Table 4 shows proportional relationship between x and y.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional. If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.

The proportionality is given by the following equation:

y = kx

For table 1 substitute the value of x = 40 and y = 8.

8 = k (40)

k = 1/5

Table 1 does not follow the proportionality for all points hence option 1 is incorrect.

Similarly, table 2 and table 3 do not follow the proportionality for all points.

For table 4, substituting the value we have:

2 = k4

k = 1/2

The proportionality is followed for all the values.

Hence, table 4 shows proportional relationship between x and y.

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Step-by-step explanation:

all pairs of corresponding sides have the same scale factor.

so, we only need to find one to know it for all.

a)

we know 2 corresponding sides : 6 and 12.

that means

12 × s = 6

s = 6/12 = 1/2

b)

x = 5 × s = 5 × 1/2 = 2.5 = 2 1/2

y = 13 × s = 13 × 1/2 = 6.5 = 6 1/2

c)

to be right-angled triangles they need to fulfill the Pythagoras criteria :

c² = a² + b²

c is the Hypotenuse (the side opposite of the 90° angle).

a and b are the legs.

so, for the larger triangle we have

13² = 12² + 5²

169 = 144 + 25 = 169

correct. it is right-angled.

for the smaller triangle :

6.5² = 6² + 2.5²

42.25 = 36 + 6.25 = 42.25

as expected : also correct. so, yes, they are both right-angled.

Answer:

Yes, by AA

Step-by-step explanation:

A triangle adds up to 180 degrees.

This means:

angle E = 180-53-60

angle E= 67 degrees

Angle E=Angle H

Angle C= Angle F

2 angles equaling to each other when comparing triangles means they are similar by AA.

Answer:

C. Yes by AA

Step-by-step explanation:

The triangles have the smae anlges, one is just smaller, but they are the same size.

The complete expression that gives equivalent values is:

x⁻⁸ . x⁹ = x⁻⁶ . x⁷ = x⁻⁴ . x⁵ = x¹ = x⁻² . x³

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

x⁻ . x = x⁻ . x = x⁻ . x = x = x⁻ . x

Where the exponents are blank

There is no general answer to this, and one of the possible solutions is as follows:

To start with, we create an expression of the following format:

x⁻ⁿ . xⁿ⁺¹ = x¹

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

x⁻⁸ . x⁹ = x¹

x⁻⁶ . x⁷ = x¹

x⁻⁴ . x⁵ = x¹

x⁻² . x³ = x¹

So, the equivalent expression is x⁻⁸ . x⁹ = x⁻⁶ . x⁷ = x⁻⁴ . x⁵ = x¹ = x⁻² . x³

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The statement 'a correlational study is used to examine the relationship between two variables but cannot determine whether it is a cause-and-effect relationship" is true.

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

When examining the link between two variables, a correlational analysis cannot establish if there is a cause-and-effect relationship.

This assertion is absolutely accurate. The data can only be used to infer cause and effect relationships if a proper experiment has been conducted. A control group and a sample of participants drawn using random sampling techniques are required for the study to qualify as an experiment.

Therefore, the given statement is true.

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Triangles

Looking at the image, It is safe to say there are two similar triangles having similar base and sides there.

Triangle BAC has the same base as Triangle DAC

Therefore, the vertices of the angle B is equivalent to the vertice of angle D

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Answer:

Step-by-step explanation:

Answer: −a−5b

Step-by-step explanation:

How to simplify:

1. Rearrange terms

−4−(5−3)

−4−(−3+5)

2. Distribute

−4−(−3+5)

−4+3−5

3. Combine like terms

−4a+3a−5b

−a−5b

Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.

The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.

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Answer:

26 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

26 3/3 - 2/3 = 26 1/3

The polynomial f(x) of degree 4 that has the following zeros 3 (multiplicity 2), -2, 0 is f(x) = (x-3)^2 * (x+2) * (x-0).

To find the polynomial f(x), we can use the fact that the zeros of a polynomial are the values of x that make the polynomial equal to zero. In other words, if a polynomial f(x) has zeros at x=a, x=b, and x=c, then f(x) = (x-a) * (x-b) * (x-c).

In this case, we have zeros at x=3 (with multiplicity 2), x=-2, and x=0. This means that our polynomial will have factors of (x-3)^2, (x+2), and (x-0).

Multiplying these factors together gives us the polynomial f(x) = (x-3)^2 * (x+2) * (x-0), which simplifies to f(x) = (x^2 - 6x + 9) * (x+2) * x. Expanding this expression gives us the polynomial f(x) = x^4 - 4x^3 - 3x^2 + 12x.

Therefore, the polynomial f(x) of degree 4 that has the following zeros 3 (multiplicity 2), -2, 0 is f(x) = x^4 - 4x^3 - 3x^2 + 12x.

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Answer:

1/27

Step-by-step explanation:

Probability of DeeDee choosing Yogurt in diary = 1/3

Probability of DeeDee choosing pineapple as fruit = 1/3

Probability of DeeDee choosing cherries as toppings = 1/3

So the Probability of DeeDee's shake being made with yogurt pineapple and cherries = 1/3×1/3×1/3 = 1/27

Answer:

-15°

Step-by-step explanation:

We know that at 7 pm it started at -6°, and that every 2 hours until 2 am, it dropped by 2 degrees.

From that we can form this expression:

-6-2x, with x being the number of hours it dropped.

From 7 pm to 2 am is 7 hours, therefore -6-2(7) = -20°

From 2 am until 7 am, it began raising 1 degree per hour.

We can write that as:

-20 + x, with x being the number of hours it went up.

From 2 am to 7 am is 5 hours:

-20 + 5 = -15°

Therefore, the temperature at 7 am is -15°.

T statistic calculator displays the T-test value along with the mean and standard deviation for the two sets of data.

To find the t-value for a given set of data, enter the sample mean, population mean, standard deviation, and sample size into the t-statistic calculator. Given the other variables, this calculator can also determine the sample mean, population mean, standard deviation, and sample size.

The T-test, also known as the hypothesis testing tool or the hypothesis test static, is a statistical method for assessing whether the means of two sets of data differ in any way that affects their properties. It is a form of inferential static that aids in verifying whether assumption testing that is relevant to the population is being used.

The t-test comes in three varieties. As follows:

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The square of the expression 1/2 is given as the numeric value in the terms of the 0.7071.

The value that a number yields when multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For example, 16 minus 4 is 16. The root symbol or radicals is another name for the radical symbol. If an integer is a perfect square, we can quickly determine its square root.

square root of the 1/2 = √1/2

We can use this rule for radicals to write the expression.

√a/b = √a/√b

So, by multiplying by the right form of 1, we may rationalise the denominator or, in other words, remove the radical from the denominator:

√1/2 x √2/√2

√2/2

1.4142/2

0.7071

So the square of the 1/2 is 0.7071.

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Answer:

6/25

Step-by-step explanation:

you add the total number of green and yellow together to equal 12. you then divide this by the total 50 and then simplify!

hope this helps

94 kg is approximately equal to 207.2350 pounds ( rounded to four decimal places )

The conversion factor to convert kg to pounds is 2.20462

1 kg = 2.20462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in lbs = The mass in kg × conversion factor

Substitute the values in the equation

1 kg = 2.20462 pounds

94 kg = 94 × 2.20462

Multiply the numbers

= 207.235 pounds  ( rounded to four decimal places )

Therefore, 94 kg is 207.235 pounds

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8)

The indicated 3th root of 125 is 5.

9)

The indicated 4th root of 81 is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

8)

∛125

5 x 5 x 5 = 125

And,

5³ = 125

So,

= ∛5³

= 5

9)

[tex]\sqrt[4]{81}[/tex]

3 x 3 x 3 x 3 = 81

And,

[tex]3^4[/tex] = 81

So,

= [tex]\sqrt[4]{3^4}[/tex]

= 3

Thus,

8)

∛125 is 5.

9)

[tex]\sqrt[4]{81}[/tex] is 3.

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Found that a short stanza contains 8 lines and a long stanza contains 9 lines.

What is linear equation ?

A linear equation is an equation that describes a straight line in a two-dimensional coordinate system. The general form of a linear equation is:

y = mx + b

Explanation:
Let's use "s" to represent the number of lines in a short stanza and "l" to represent the number of lines in a long stanza.

From the problem, we know that Megan wrote 10 short stanzas and 2 long stanzas, for a total of 98 lines. This can be written as the equation:

10s + 2l = 98

We also know that Sebastian wrote 3 short stanzas and 7 long stanzas, for a total of 87 lines. This can be written as the equation:

3s + 7l = 87

We want to find the values of s and l that satisfy both of these equations. We can use algebra to solve for s and l.

Multiplying the first equation by 3, we get:

30s + 6l = 294

Multiplying the second equation by 2, we get:

6s + 14l = 174

Now we can add the two equations together to eliminate the variable s:

30s + 6l + 6s + 14l = 468

Simplifying and rearranging, we get:

36s + 20l = 468

Dividing both sides by 4, we get:

9s + 5l = 117

Now we have a new equation that relates the values of s and l that satisfy both sets of stanzas. We can use this equation along with one of the original equations to solve for either s or l.

Let's use the first equation, 10s + 2l = 98. We can solve for s in terms of l:

10s + 2l = 98

10s = 98 - 2l

s = (98 - 2l)/10

Now we can substitute this expression for s into the equation 9s + 5l = 117:

9[(98 - 2l)/10] + 5l = 117

Simplifying and solving for l, we get:

l = 9

Now we can substitute this value of l back into either of the original equations to solve for s. Using the first equation:

10s + 2l = 98

10s + 2(9) = 98

10s = 80

s = 8

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 To find the x-intercept using the straight-line equation, substitute y=0 and solve for x. To find the y-intercept, substitute x=0 and solve for y.

The equation of a straight line is

y=mx+c

is the gradient and

c

is the height at which the line crosses the y-axis, also known as the y-intercept.

The gradient m is the slope of the line - the amount by which the ycoordinate increases in proportion to the x-coordinate. If you have two points (x1,y1) and (x2,y2) on the line, the gradient ism=y2−y1x2−x1

, we must first work out the gradient using the gradient formula above, and then choose either point to substitute into the straight line equation with this gradient.

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After all these transformations, point A' will lie on the left side of the y-axis with the same y-coordinate as A, and point A''' will lie on the right side of the y-axis with the same x-coordinate as A.

What is parallelogram ?

A parallelogram is a quadrilateral with two pairs of parallel sides.

If parallelogram ABCD is reflected over the y-axis, all the x-coordinates of the vertices will change sign while the y-coordinates remain the same. This means that A will be reflected to a point A' on the left side of the y-axis with the same y-coordinate as A.

If the reflected parallelogram is then reflected over the x-axis, all the y-coordinates of the vertices will change sign while the x-coordinates remain the same. This means that A' will be reflected to a point A'' below the x-axis with the same x-coordinate as A'.

Finally, if the reflected and flipped parallelogram is rotated 180 degrees, all points will be reflected over the origin. This means that A'' will be reflected to a point A''' on the right side of the y-axis with the same x-coordinate as A'' (which is the same as A).

Therefore, after all these transformations, point A' will lie on the left side of the y-axis with the same y-coordinate as A, and point A''' will lie on the right side of the y-axis with the same x-coordinate as A.

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True. Rational functions are defined as the division of two polynomials. These functions are limited in their scope and, as a result, have specific properties. One such property is the existence of vertical asymptotes.

Vertical asymptotes occur when the denominator of a rational function approaches zero, resulting in a discontinuity in the graph of the function, or a point at which the function can approach but never reach. This creates a divide in the graph, resulting in two halves with a vertical line at the point where the denominator equals zero. This vertical line is the vertical asymptote of the rational function. In conclusion, all rational functions have vertical asymptotes due to their limited scope and specific properties.

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Answer:

Step-by-step explanation:

You want the measures of angles d° and e° in the given figure.

Usually, geometry problems tell you not to assume anything that isn't marked or stated regarding the figure. In order to answer this question, we need to assume ...

The base angles in an isosceles triangle are congruent. That means each of them is the complement of half the vertex angle.

  ∠D = 90° -1/2∠A = 90° -8°/2 = 86°

The segments CD and BE are parallel, so angle E is the supplement of angle D:

  ∠E = 180° -86° = 94°

The angle measures are d° = 86° and e° = 94°.

__

Additional comment

This is not a "word problem." All of the relations necessary for answering the question are shown in the diagram, not stated in words. (The question is necessarily written in words—for any problem.)

If b is a base angle and v is the vertex angle of an isosceles triangle, then the sum of angles is ...

  b + b + v = 180°

  2b = 180° -v . . . . . . subtract v

  b = 90° -v/2 . . . . . . divide by 2

Effectively, the altitude of an isosceles triangle bisects the vertex angle and creates two congruent right triangles. The acute angles in that triangle are the original base angle and half the vertex angle. They are complementary.

The price of each bagel sold when 312 bagels are sold and $280.80 earned  is $ 0.9.

One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups.

The number of bagels sold = 312

The total money earned by selling 312 bagels = $ 280 . 80

The price for each bagel,

[tex]=\frac{total money earned}{number of bagels sold} \\\\=\frac{280.80}{312} \\\\=$0.9[/tex]

So, the price of each bagel sold is $ 0.9.

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The net force acting on each ball can be ranked from largest to smallest as Fd>Fb>Fc=Fa, with Fd being the largest  number of force due to its the highest mass and Fa being the smallest force due to its lowest mass.

The net force acting on each ball is equal to the product of its mass and acceleration due to gravity (F=ma). Since all of the balls have the same acceleration due to gravity, the magnitude of the net force on each ball can be determined by its mass. Therefore, the net force acting on each ball can be ranked from largest number to smallest as follows: Fd>Fb>Fc=Fa.

Fd>Fb>Fc=Fa

The net force acting on each ball can be ranked from largest to smallest as Fd>Fb>Fc=Fa, with Fd being the largest force due to its the highest mass and Fa being the smallest force due to its lowest mass.

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The polynomial 250x³ - 42x² + 112x is a trinomial of degree 3.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

The given polynomial is 250x³ - 42x² + 112x.

To classify this polynomial by the number of terms, we count the number of terms it has, which is three. Therefore, we can classify it as a "trinomial".

To identify the degree of this polynomial, we look at the highest power of x in the polynomial. In this case, the highest power of x is 3, which is the coefficient of the x³ term. Therefore, the degree of this polynomial is 3.

So, the polynomial 250x³ - 42x² + 112x is a trinomial of degree 3.

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The area of the trepezium will be 80 sq. unit.

What precisely is a trepezium?

Trapezoids are made up of two parallel and two oblique sides. A Trapezium is another name for it. A trapezoid is a closed four-sided shape or figure with a space-filling perimeter. It is a 2D figurine rather than a 3D figure. A trapezoid's bases are the sides that are parallel to one another. Legs are non-parallel sides, often known as lateral sides. The space between its parallel sides determines its height.

A trepezium's area is equal to 1/2*(a+b)*h.

where h is the height or distance between two parallel lines

The lines a and b are parallel.

Now,

Given A rectangle with a length of 17 and a height of 4 has two right triangles on each side of it with long leg lengths of 5

then parallel sides of trepezium will be 17 and 17+3+3=23

because for the triangle base will be =√5²-4²

=3

and height of trepezium=4 unit

So, area of trepezium will be=1/2(23+17)*4

=40*2

=80 sq. unit

hence,

           The area of the trepezium will be 80 sq. unit.

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The probability that exactly 12 of the 15 adult smartphone users use their smartphones in meetings or classes is approximately 0.0040 (rounded to four decimal places).

We can solve this problem using the binomial probability formula:

[tex]P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)[/tex]

where:

P(X = k) is the probability of exactly k successes (using smartphones in meetings or classes)

n is the total number of trials (in this case, 15 adult smartphone users)

k is the number of successes (in this case, 12 adults using their smartphones in meetings or classes)

p is the probability of a success on a single trial (in this case, 0.44)

(1 - p) is the probability of a failure on a single trial (in this case, 0.56)

Using this formula, we can plug in the values and calculate:

[tex]P(X = 12) = (15 choose 12) * 0.44^12 * 0.56^(15-12)[/tex]

[tex]= 455 * 0.0001473577 * 0.215872256[/tex]

= 0.0040367

Therefore, the probability that exactly 12 of the 15 adult smartphone users use their smartphones in meetings or classes is approximately 0.0040 (rounded to four decimal places).

[tex]= 455 * 0.0001473577 * 0.215872256[/tex].

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Assume that when adults with smartphones are randomly selected, 44% use them in meetings or classes. If 15 adult smartphone users are randomly selected, find the probability that exactly 12 of them use their smartphones in meetings or classes?(Round to four decimal places as needed.)

There cannot be a point P on altitude BD that is equidistant from A and C, as this would mean that the two smaller triangles are congruent. This is because the altitude BD divides the triangle into two smaller triangles, ABD and CBD. If AB is unequal to BC, then these two smaller triangles cannot be congruent.

To prove this, let's assume that there is a point P on altitude BD that is equidistant from A and C. This would mean that AP = CP. However, since AB is unequal to BC, we know that AD is not equal to DC. Therefore, the triangles ABD and CBD are not congruent, and there cannot be a point P on altitude BD that is equidistant from A and C.

In conclusion, if AB is unequal to BC, then there does not exist a point P on altitude BD that is equidistant from A and C. This is because the altitude BD divides the triangle into two smaller triangles that cannot be congruent if AB is unequal to BC.

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If she is working at a constant rate, 12 rows had been completed before Elena started working.

To determine the number of rows that were completed before Elena started working, we need to find the equation of the line that represents the relationship between the number of rows completed and the time taken.

We can use the two given points (14, 19) and (20, 22) to find the slope of the line:

slope = (change in rows) / (change in time) = (22 - 19) / (20 - 14) = 3 / 6 = 1/2

Next, we can use the slope and one of the points to find the y-intercept of the line using the point-slope form of a line:

y - 19 = (1/2)(x - 14)

y - 19 = (1/2)x - 7

y = (1/2)x + 12

Now that we have the equation of the line, we can use it to find the number of rows completed when x (time) is equal to 0, which represents the point when Elena started working:

y = (1/2)(0) + 12 = 12

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The given question is incomplete, the complete question is :

Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting.

Assuming she worked at a constant rate, how many rows had been completed before Elena started working?