fill in the following statements with sometimes, always, or never in order to the statements true

[tex]\textit{area of the rectangle}\\\\ A=Lw \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=5\\ w=6 \end{cases}\implies A=(5)(6)\qquad \begin{cases} \textit{tripling the sides}\\[-0.5em] \hrulefill\\ L=3\cdot 5\\ w=3\cdot 6 \end{cases} \\\\\\ A=(3\cdot 5)(3\cdot 6)\implies (3\cdot 3)(5)(6)\implies 9(5)(6)\leftarrow \begin{array}{llll} \textit{new area is 9 times}\\ \textit{the old one}\\ \textit{a ratio of 9 : 1} \end{array}[/tex]

a) The quadratic function is factored as follows: f(x) = 4(x - 0.5)(x + 2.5).

b) The x-intercepts of the quadratic function are given as follows: x = -2.5 and x = 0.5.

c) The end behavior of the quadratic function is given as follows: as x -> ± ∞, f(x) -> ∞.

d) The graph is constructed at the end of the answer, considering the x-intercepts, the y-intercept, the end behavior and the vertex.

The quadratic function for this problem is defined as follows:

f(x) = 4x² + 8x - 5.

Hence the coefficients are given as follows:

a = 4, b = 8, c = -5.

The discriminant is given as follows:

D = 8² - 4 x 4 x (-5)

D = 144.

Hence the x-intercepts are given as follows:

Considering the intercepts and the leading coefficient of a = 4, the function is factored as follows:

f(x) = 4(x - 0.5)(x + 2.5).

As the leading coefficient is positive, the parabola is concave up, meaning that the end behavior is that the function increases to infinity both at the left tail and at the right tail.

The y-intercept is given as follows:

f(0) = 4(0)² + 8(0) - 5

f(0) = -5.

The coordinates of the vertex are given as follows:

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The equations are n + s = 76 and 2n + 1.50 s = 125.

let n = number of Nachos sold

let s = number of sodas sold

Two equations are presented to us, and we can use them together to solve one variable at a time.

Eq. 1: n + s = 76

Eq. 2: 2n + 1.50 s = 125

So, s = 76 - n

Put (76 - n) for s in the second equation

2n + 1.50 (76 - n) = 125

2n + 114 - 1.50 n = 125

2n - 1.50 n + 114 = 125

0.5n + 114 = 125

0.5n = 125 - 114

0.5n = 11

n = 22

s = 76 - 22

s = 54

22 nachos sold and 54 sodas sold.

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Answer:

I'm pretty sure the answer for this is 28 :))

Adding all of the remaining pizzas, and dividing the total pizza into 5 equal fractions, the fraction of pizza that each person gets would be 11/24

A mixed number is a combination of a whole number and a fraction. For example, 3 1/2 is a mixed number. It is different from an improper fraction, which is a fraction where the numerator is greater than or equal to the denominator. For example, 7/4 is an improper fraction.

To convert a mixed number to an improper fraction, you must first multiply the whole number by the denominator of the fraction. Then add the result to the numerator. Finally, place the sum over the denominator. For example, to convert 3 1/2 to an improper fraction, you would first multiply 3 by 2 (the denominator of the fraction 1/2) to get 6, then add 1 (the numerator of the fraction 1/2) to get 7. So 3 1/2 is equivalent to 7/2 as an improper fraction.

So to find out the fraction of a whole pizza  that each person gets out of the different remaining pizzas, first we need to all the remaining pizzas as shown below,

3/4 of pepperoni + 5/8 of cheese + 11/12 of sausage = 55/24

Now to equally divide this into 5 person, we need to divide this fraction by 5,

i.e 55/(24*5) = 11/24

Therefore, each person gets 11/24 of the whole pizza.

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Answer: x = 10

Step-by-step explanation:

1. To find x, you need x to be by itself and the only way for it be like that in this situation is by dividing both sides by 7.

2.  7 divided by 7 cancels out and 70 divided by 7 = 10. This means x = 10.

Answer:

10

Step-by-step explanation:

since we have 7x=70

the multiply goes and becomes divide we get 70/7

and by dividing it we get the ans 10

The  polynomial Y⁴+ 4y²+ 5 does not have zeroes.

Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.

Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.

We know that,   (a +b)² = a² + b² + 2ab

Here given that,

⇒ y⁴ + 4y² + 5 = 0

⇒ y⁴ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

Because the first term is a square, the expression (y² + 2)² + 1  will never be zero for any value of y.

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The product of (2x-3y)(2x+3y) is 4x^2-9y^2

Product= (2x-3y)(2x+3y)

Let the product of (2x-3y)(2x+3y) be P

P=2x(2x+3y)-3y(2x+3y)

P= 2x(2x)+2x(3y)-3y(2x)-3y(3y) {using distributive property of multiplication}

This property states that  multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. The multiplication of (a-b)(a+b) is equal to a^2 - b^2. This result is used as an identity.

P= 4x^2 +6xy - 6xy -9y^2

solving 6xy-6xy=0

P= 4x^2 - 9y^2

4x^2-9y^2 is the product of (2x-3y)(2x+3y).

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According to the probability, there are 540 arrangements that can the cars stack up so that all three lanes are occupied.

Mathematicians use addition and division as well as counting to calculate probability.

There are three partitions of six using digits 1-3.

(4,1,1), (3,2,1), (2,2,2) (2,2,2)

These could be dispersed between the lanes in order that

(3) Possible solutions to (4,1,1)

There are six possible ways to solve the equation (3,2,1).

There is only one possible solution to the equation (2,2,2).

Cars must now move in the lanes in proper order.

The arrangements for (4,1,1) will be 6C4 * 2C1 = 30. Six cars are chosen, sorted, and placed in the appropriate lanes. then decide on 1 of the 2 surviving vehicles.

then place it in a lane.

The arrangements for (3,2,1) will be 6C3 * 3C2 = 60.

There will be 6C2 * 4C2 = 90 arrangements for (2,2,2).

Consequently, there will be 540 arrangements (3*30 + 6*60 + 1*90 = 90+360 + 90).

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The approximate value of ㏒(b) to the nearest hundredth is 1.23.

The other method to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to some other number. A logarithm performs exponentiation's exact opposite function. 

In Logarithms, ㏒ₐ(b) = ㏒(b)/ ㏒(a)

Given that

The two expressions below have the same value when rounded to the nearest hundredth

=> ㏒₅ (b) = ㏒₉ (48)  

As we know  ㏒ₐ(b) = ㏒(b)/ ㏒(a)

=> ㏒₅ (b) = ㏒(b)/㏒(5)

=> ㏒(b)/㏒(5) = ㏒₉ (48)  

=> ㏒(b) = ㏒₉ (48) ㏒(5)

=> ㏒(b) =  (1.7618)(0.6989)  

=> ㏒(b) = 1.23132202  

=> ㏒(b) = 1.23  

Therefore,

The approximate value of ㏒(b) to the nearest hundredth is 1.23.

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Answer:

Tamicca made 12 monthly payments of $115, for a total payment of 12*$115 = $<<12*115=1380>>1380.

She bought a computer for $1200, so the finance charge that she paid is $1380-$1200 = $<<1380-1200=180>>180.

Therefore, the finance charge that Tamicca paid was $180, rounded to the nearest cent.

Step-by-step explanation:

a) The minimum number of dogs that could have a mass of more than 27 kg is 6.

b) The maximum number of dogs that could have a mass of more than 27 kg is 18.

We have a table which shows information about the masses of some dogs.

Now , we need to determine the minimum number of dogs could have a mass more than 27 kg . Let us see dogs with mass of more than 27 kg present in the following intervals , 20≤x<30 and 30≤x<40 with 12 and 6 respectively.

But we wants minimum of 12 and 6 is 6 .

so, the minimum number of dogs with mass more than 27 kg is 6.

b) We need to determine maximum number of dogs with mass more than 27 kg ,so Maximum is equals to sum of number of dogs present in interval 20≤x<30 and in interval 30≤x<40 = 12+6 = 18. So, required maximum number of dogs are 18.

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Complete question:

The above table shows information about the masses of some dogs.

a) Work out the minimum number of dogs that could have a mass of more than 27 kg

b) Work out the maximum number of dogs that could have a mass of more than 27 kg

a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given

by pythagoras theorem

c2 = a2 + b2

18*18 = a2 + 12*12

324  - 144 = a2

a2 = 180

a = [tex]6\sqrt{5}[/tex]

a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.

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The ratio is 1:4, which means for every 1 butterfly, there are 4 caterpillars.

This ratio represents the relationship between the number of butterflies and the number of caterpillars. In this case, the ratio is saying that for every 1 butterfly, there are 4 caterpillars. This could mean that for every butterfly that is observed, there are 4 caterpillars that are also present or for every butterfly that is caught, there are 4 caterpillars that are also caught.

This ratio may also indicate that for every butterfly that is born, 4 caterpillars are also born. It could also indicate the population ratio of butterflies to caterpillars in a specific habitat.

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Answer:32 17/18

Step-by-step explanation:

33 + (1/9)(x)

x = -1/2

33 + (1/9)(-1/2) =

33 + -1/18

= 32 17/18

The interest rate is 2.5 %.

Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:

I = Prt

where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

I = $25, P = $500, r = ?, t = 2 years

∴ I = Prt

∴ r = I / Pt

∴ r = 25 / ( 500 * 2)

∴ r = 25 / 1000

∴ r = 0.025

∴ r = 0.025 * 100 %

∴ r = 2.5 %

Therefore, the interest rate is 2.5 %.

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It will take the toaster about 175 seconds to make 20 slices.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

Given that The toaster takes 35 seconds to make 4 slices of toast.

It takes 70 seconds to make 8 slices of toast, It also takes 105 seconds to make 12 slices.

We are required to calculate how long it may probably take the toaster to make 20 slices.

To calculate the time it takes the toaster to make 1 slice:

4 slices ---------- 35 seconds

1 slice ----------- ? seconds

1/4 × 35 = 35/4 seconds

Now, if 1 slice will be made in 35/4 seconds,

20 slices will be made in:

1 slice --------- 35/4 seconds

20 slices ------ ? seconds

(20/1) × 35/4 = 175 seconds

Hence It will take the toaster about 175 seconds to make 20 slices.

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The relationship exists between N and K are the endpoints of the side KN.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions.

It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length.

we know that for a parallelogram KLMN is a quadrilateral whose two sides are parallel to each other and has two non-parallel sides.

for N and K we could say that the two are endpoints of the line segment KN; which is one of a side of a parallelogram KLMN.

Therefore, The relationship exists between N and K are the endpoints of the side KN.

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The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Given, k(x) = 4 ÷ 5x - 6.

k(x) = (4/5x) - 6.

Let, y = k(x).

y =  (4/5x) - 6.

(4/5x) = y + 6.

1/x = 5(y + 6)/4.

x = 4/{5(y + 6)}.

y = 4/{5(x + 6)}.

k⁻¹(x) = 4/{5(x + 6)}.

k⁻¹(8) = 4/{5(8 + 6)}.

k⁻¹(8) = 4/{5(14)}.

k⁻¹(8) = 4/70.

k⁻¹(8) = 2/35.

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Answer:

AC = PF

Step-by-step explanation:

Joshua will need 7 additional customers.

The parameters that will help us to determine the number of customers is give as follows:

Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.

Since Joshua's goal is to sell more than 20 items at a farmers' market and he has sold 6 items. and If each of his customers buys 2 items, the number of additional customers needed will be:

= (20 - 6) / 2

This is given as  14 / 2

The the number of customers needed = 7

In conclusion He will  need 7 additional customers.

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Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .

It tells about how  dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed variable from the mean. Any distribution will have roughly 95% of its values within two standard deviations of the mean.

Here,

We know population SD= Σ(xi-mu)2/n where mu is the population mean and n is the number of observation.

Here

we have n=7 and mu can be taken as x- =310.142

Standard deviation = SD=Σ(xi-mu)2/n

=>(Σxi2/n)-x-2

=>(704883/7)-(310.14)2=67.15=σx

Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .

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Answer:

Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.

So (x + 4) + (2x + 4) + (4x + 4) = 61.

7x + 12 = 61 => 7x = 49 => x = 7.

So the answer is

Pat = 7

Mattie = 14

Jon = 28

The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.  

If we take Pat's age as = 'x' years,

so, Mattie's age will be = '2x' years.

and then, Jon would be = 2(2x)

                                        = '4x' years.

Now, the sum of their ages after 4 years =

 => (x+4) + (2x+4) + (4x+4) = 61

 => 7x+12 = 61

 => 7x= 61-12

 => 7x= 49

 => x= 49/7

 => x = 7

Therefore, Pat's age is  = 7 years.

              Mattie's age is = 14 years (2×7).

                  Jon's age is = 28 years (4×7).

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Jamal’s test scores are 84, 88, 92, and 94. Natalia’s test scores are 86, 88, 90, 92. Jamal has a greater test average than Natalia. Natalia has more consistent test scores than Jamal.

To find the test average, you add up all the test scores and divide by the number of test scores.

Jamal's average: (84+88+92+94) / 4 = 89.50

Natalia's average: (86+88+90+92) / 4 = 89

Jamal has a greater test average.

To find the consistency of test scores, you can use the range, which is the difference between the highest and lowest scores.

Jamal's range: 94-84=10

Natalia's range: 92-86 = 6

Natalia has the most consistent test scores, as the range of her scores is smaller than Jamal's.

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Answer:2

Step-by-step explanation:

The equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the equation of the line as -

y = 14x - 4

The given equation of line is -

y = 14x - 4

Slope of the line perpendicular to the given line is -

m{p} = -1/14

The equation of this line will be -

y = -(1/14)x + c

For the point (28, 16), we can write -

16 = -(1/14) x 28 + c

c = 16 + 2

c = 18

So, the equation will be -

y = - (1/14)x + 18

Therefore, the equation of the line perpendicular to {y = 14x - 4} and passes through the point (28, 16) is y = - (1/14)x + 18.

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The half-life of caffeine in the body is approximately 5-6 hours, not 666 hours. Given this information, we can calculate the latest time Charlotte can drink a 222-ounce shot of espresso that contains 80mg of caffeine and still have no more than 2020mg of caffeine in her system at 11pm.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

We know that after 5-6 hours, the amount of caffeine in the body decreases by 50%. Therefore, in 11 hours, the amount of caffeine in the body would decrease by approximately 87.5%.

If we let x be the number of hours before 11pm that Charlotte can drink the espresso, then the amount of caffeine in her body at 11pm would be:

80mg * (1 - (87.5% ^ (x/5-6))) = 2020mg

Solving for x, we find that the latest time Charlotte can drink the espresso is approximately 6:30pm.

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On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Month / Brent / Gretel

0/4/ 128

1/ 16 / 256

2 / 64 / 512

3 / 256 / 1024

4 / 1024 / 2048

5 / 4096 / 4096

They will have the same amount of fish in 5 months.

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I’ve added my work attached :)
n = 250

Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(4)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{20})}}\implies 80+50\implies \text{\LARGE 130}~m^2[/tex]