Colette bought 1/4 of a pound of green grapes and 1/8 of a pound of red grapes. How much more did the green grapes weigh than the red grapes?

The discontinuity of our given function is at point (-6, -7).

The zero of our given function is, (1, 0).

What is discontinuity and zero of the function?

A discontinuous function is a graph function that is not connected to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first kind at x = a.

The x-intercept(s) of the function's graph represent the real zero of the function.

Consider the given function,

[tex]f(x) = \frac{x^2+5x-6}{x+6}[/tex]

We know that a function is discontinuous, when its denominator is equal to zero.

To find the discontinuity for our given function, we will equate denominator to 0 as:

x + 6 = 0

    x = -6

Now simplify the given function.

[tex]f(x) = \frac{x^2+5x - 6}{x+6}\\ f(x) = \frac{x^2 +6x - x - 6}{x+6}\\ f(x) = \frac{x(x+6)-1(x+6)}{x+6}\\ f(x) = \frac{(x-1)(x+6)}{x+6} \\f(x) = x-1[/tex]

Take  y = x - 1

Since the denominator term is cancelled out, so our give function has a removable discontinuity.

Now, we will find value of y by substituting  x = -6

⇒ y = -6 - 1

   y = -7

Therefore, the discontinuity of our given function is at point (-6, -7).

Now, we will find zero of our given function by substituting  f(x) = 0,as zero of the function is the point, where graph intersects x-axis and value of y is 0 at x-axis:

⇒  0 = x - 1

x - 1 = 0

    x = 1

Therefore, the zero of our given function is, (1, 0).

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Answer:

R'>R

Step-by-step explanation:

To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.

We know the range is defined by R

R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.

Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5.  So, our range also becomes

R = X(n) + 5 - X(1)

So,  R'>R. Hence, the range of the new score will be greater than that of the original score distribution.

Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9

First term, T(1) = 3

nth term, T(n+1) = T(n) +5 for n>1

Second term, T2 = T(n) +5

= 2 + 5

= 7

Third term, T3 = T(n) +5

= 3 + 5

= 8

Fourth term, T3 = T(n) +5

= 4 + 5

= 9

Therefore, the first four terms of the sequence are 3, 7, 8, 9

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Using confidence interval concepts, it is found that the correct options are:A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.

There is a 99% chance that the mean of the population is between 14.3 and 30.4.

The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.

In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.

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Answer:

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

First, solve the inequality:

This is option C (you have chosen it correctly).

Now, graph it:

Answer:

x < -11  or  x > 8

Step-by-step explanation:

Given absolute value inequality:

[tex]|2x+3| > 19[/tex]

[tex]\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}[/tex]

Apply the absolute rule:

[tex]\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}[/tex]            [tex]\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}[/tex]

To graph the solution:

By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.

In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:

sin θ = y / r

cos θ = x / r

tan θ = y / x

cot θ = x / y

sec θ = r / x

csc θ = r / y

Where:

First, obtain the length of side BD:

cos θ = BD / AB

BD = AB · cos θ

BD = 5 · cos 30°

BD = 5√3 / 2 cm

Second, calculate the length of side BC:

sin θ = BD / BC

BC = BD / sin θ

BC = 5√3 / 2 / sin 22°

BC ≈ 11.6 cm

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The following are binomial random variable,

A)A Roll a fair die 5 times and X = the number of rolls that land showing a "4", is a binomial random variable.

B) Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6), is a binomial random variable.

C) Roll 5 fair dice at once and let Y = the number of dice that land showing a "4" , is a binomial random variable.

A random binomial variable should satisfy the following conditions:

1. The number of trials are defined or fixed.

2. Each trial is independent of others.

3. The probability of success is same in all trials.

4. There should be only two outcomes in each trial.

Lets we evaluate the options based on the above conditions:

(A) Rolling fair dice 5 times have 5 trials, each rolling is independent, probability of 4 is 1/6 in all cases and the dice will either land 4 or will not land 4. So, X will have values from 0 to 5, 0 when dice doesn't land 4 even once in 5 rolls and 5 when dice land 4 in all rolls. This variable satisfies the condition to be a random binomial variable. So, X is a random binomial variable.

(B)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice with even number to all 5 dices with even number. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Z is a random binomial variable as it satisfies all the conditions.

(C)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice land with 4 to all 5 dices land with 4. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Y is a random binomial variable as it satisfies all the conditions.

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The function plotted in the graph is given by - g(x) = 3.5 sin(x)

        [tex]$\sin \theta=\frac{a}{h}[/tex]

      {θ} = angle theta

      {a} = length of opposite side a

      {h} = length of hypotenuse h

        [tex]${\displaystyle {\begin{aligned}\sin(x)&=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \;= \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}[/tex]

        {sin(A) / a = sin(B) / b = sin(C) / c}

Given is a graph as shown in the image.

A sine function has its maximum value of [1] and the minimum value of [-1]. The given graph g(x), is a amplitude scaled version of the function f(x) given by -

f(x) = sin(x)

and

g(x) = Asin(x)

Here, [A] is equal to 3.5. So, the function g(x) is equal to -

g(x) = 3.5 sin(x)

Therefore, the function plotted in the graph is given by -

g(x) = 3.5 sin(x)

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Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.

To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.

According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.

This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.

Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.

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Answer:

y = [tex]\frac{1}{2}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 10 ← is in slope- intercept form

with slope m = - 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (10, 7 ) into the partial equation

7 = 5 + c ⇒ c = 7 - 5 = 2

y = [tex]\frac{1}{2}[/tex] x + 2 ← equation of perpendicular line

For the quiz score of 100, the time will be equal to 5.26 hours.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.

The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.

Given that the relationship can be represented by the equation y=7.6x+60. Here x is the time and y is the score of the quiz.

At the score of the quiz of 100, the value of x will be calculated as,

y = 7.6x+60

100 = 7.6x + 60

40 = 7.6x

x = 40 / 7.6

x = 5.26 hours

The meaning of the value of x = 5.26 hours is that for scoring 100 on the quiz the time will be 5.26 hours.

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Therefore, the length of a rectangle is 13m and width is 8m

A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.

Here,

width=x

length=2x-3

Area =l x w

104=(2x-3)(x)

104=2x^2-3x

52=x^2-3/2(x)

52+9/16=x^2-3/2(x)+9/16

841/16=(x-3/4)^2

29/4=x-3/4

x=32/4

x= 8m

Thus width = 8m

length =  2(8)-3  = 13m

Therefore the length of a rectangle is 13m and width is 8m

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The correct option is (d) i.e. log [ √x × (x-1)^3 / ∛ (x+1)^2 ] is as the single logarithm.

What is logarithm?

Logarithm is a mathematical operation which is used to determine the exponential power of a number. It is the inverse operation of exponentiation. Logarithm is commonly used in calculus, algebra, and other areas of mathematics. It can also be used to solve problems involving exponents, roots, and powers. Logarithm is denoted by the symbol log, and is read as "log to the base". The base is the number which the logarithm is taken to. For example, log2 10 is the logarithm to the base 2 of 10. This is equivalent to saying "2 to the power of what equals 10?" The answer is that 2 raised to the power of 3 (2^3) would equal 10.

Given, log x / 2 + 3 [ log(x-1) - 2/9 log(x+1) ]

        = log √x + 3 log(x-1) - 2/3 log (x+1)            {∵ log x^a = a log x }

        = log √x + log (x-1)^3 - log (x+1)^2/3

        = log √x + log [(x-1)^3 / (x+1)^2/3]              {∵ log a - log b = log a/b }

        = log [√x × (x-1)^3 / (x+1)^2/3 ]

        = log [ √x × (x-1)^3 / ∛ (x+1)^2 ]

Hence, (d) is the correct option.

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The inequality that shows the relationship between thier heights is g < r or r > g

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

Reese is taller than Gage.

Also, from the question; we have

Reeses's height = r

Gage's height = g

Because Reese is taller than Gage, then it means that

The value of r is greater  than the value of g

So, we have the following inequality expression

r > g

Also, we have

g < r

Hence, the inequality is g < r

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Answer:

the first option

Step-by-step explanation:

in an "and" statement both parts need to be true, so that the overall condition is true.

is x = 6 a valid solution ?

no, it violates both, x <= -8 and x <= 4

is a value between -8 and 4 a valid solution like x = -2 ?

no, it violates x <= -8, even though it is true for x <= 4.

only values that are smaller or equal to -8 (like -9) are true for both.

and therefore the first answer option is correct.

The expected number of students that pick soda is 80

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

Ice cream = 40

Soda = 20

popsicle = 10

This means that the proportion of soda is

Soda = 20/(40 + 20 + 10)

Evaluate the sum

Soda = 20/70

So, we have

Soda = 2/7

For a group of 280 students, we have

Soda = 2/7 *280

Evaluate

Soda = 80

Hence, the number of students is 80

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You would need to deposit $2,500 in order to have $5,000.00 in the account in 1633 days.

1st method: This can be found by using the simple interest formula I=PRT. In this case, I=5000, P=2500, R=.42, and T=1633. Solving for I gives you the answer.

2nd Method: If you deposit $2,500 in an account now, you will have $5,000 in the account in 1633 days. $2,500 * 1.42 = $3,550 $3,550 + $2,500 = $6,050 $6,050 / 2 = $3,025

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Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly,

a) You will be refinancing $122536.

b) New monthly payment be after refinancing is

$794.1858 or 79 418.58 cents.

We have given that

Initial loan amount = $ 130,750

Number of year of loan = 30 year

Nomber of month of loan "n" = 30x12= 360

Annual interest rate = 6.6%

monthly rate "r" = 6.6% /12 =

monthly payment on the loan is

PMT= loan× r / [1 - (1+r)⁻ⁿ]

= $ 130750 X 12/(1 - (1+ 6.6%/12)⁻³⁶⁰)

= $719,125/(1- (1+0.0055) ⁻³⁶⁰

= $835.046

Monthly payment, $835.046 on initial loan.

Now after 5 years refinishing is done . So, amount and remaining balance is for 30-5 = 25 years and 25×12 = 300 months . The present value of unpaid monthly payment is

= PMT× ( (1 - (1+r)⁻ⁿ)/r)

= $835.046( 1 - (1+6.6%/12)⁻³⁰⁰/ 6.6%/12]

= $835.046× 196.74179

= $122536

Hence, amount refinanced is $122536.

b) New monthly payment will be on loan =$122536

Annual rate = 2.1%

monthly rate, r' = 2.1%/12

Number of years for refinancing = 15 years

Number of months , n' = 15× 12 = 180

Using the formula new monthly payment is

PMT = new loan× r'/ [1 - (1+r')⁻ⁿ´ ]

= $122536× 2.1%/12[ 1 - (1+2.1%/12)⁻¹⁸⁰]

= $214.43826/0.2700104

= $794.1858

Hence, new monthly payment is $794.1858.

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Answer:

Step-by-step explanation:rate = minute/meter => 20/5

so, 5/1 for rate

so for 11 meter,  (5m/1min)(11)

The answer is 55 minutes

In the factorization, the bottom triangular matrix L is the only one.

The exponent of a number indicates how many times it has been multiplied by itself.

Exponent-related issues can be solved using either exponent laws or exponent characteristics. When a number is repeated numerous times by itself, writing the product without the use of exponents becomes very difficult. Major exponentiation rules are also thought of as having these characteristics.

Given that A is a positively defined symmetric matrix with a Cholesky decomposition,

A = L[tex]L^{T}[/tex]  = [tex]R^{T} R[/tex]

Let A be our positive define symmetric matrix,

suppose A has Cholesky decomposition,

A = L₁L₂ = L₁L₂ , for L₁, L₂ lower triangular matrix with positive diagonal entries,

thus (A x ,x) = (Lx, Lx) = (Lx, Lx)

pick x = eₓ  the last coordinate vector,

then (Aₓ, x) = Axx = || L₁x||² = || L₂x||²

Given that L1, and L2 are lower triangular, which necessitates that their lower right entry be the same,

The Kth entry is currently the last row.

given by (L₁, eₓ, eₓ) = 1/√Axx (L₁eₓ, L₂eₓ) = 1/ Aₓ = (Aeₓ, eₓ)

so the last row of L₁, L₂ be the same,

we reduce our A to new (n - 1)x(n - 1) submatrix,

which will likewise be true, and then repeat the process to discover each row's unique value.

Thus, the inductive process shows that L1 = L2.

As a result, the factorization's bottom triangular matrix L is exclusive.

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The volume of the first and second designs are  2.7 m³ and 2.64 m³ so, the second design will hold more sand.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.

Given:

One design is 3 m by 3 m by 30 cm,

A second design is 3.25 m by 3.25 m by 25 cm,

Calculate the volume for the first design as shown below,

Volume of first design = 3 × 3  × 30/ 100   (1 m = 100 cm),

The volume of the first design = 270 / 100

The volume of the first design = 2.7 m³

Calculate the volume of the second design as shown below,

The volume of the second design = 3.25 × 3.25 × 25 / 100

The volume of the second design = 264.06 / 100

The volume of the second design = 2.64 m³

The difference in the volume of both designs = The volume of the first design - The volume of the second design

The difference in the volume of both designs = 2.7 - 2.64

The difference in the volume of both designs =0.06 m³

Thus, the first design will hold more volume of sand.

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The true statement regarding the probabilities on the spinner is given as follows:

The probability that the spinner will point to yellow is less than 1/4.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

Hence, for the spinner given in this problem, the probabilities are given by the fraction occupied by each area, as shown by the image given at the end of the answer.

From the text, these fractions, representing the probabilities, are given as follows:

The problem is given by the image shown at the end of the answer.

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The linear equation we need to solve is:

$27.50*w = $309.99 - $144.99

And the solution is w = 6.

How to write and solve the equation?

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:

f(w) = $144.99 + $27.50*w

So the linear equation we need to solve is:

$144.99 + $27.50*w = $309.99

To solve this we need to isolate w.

$144.99 + $27.50*w = $309.99

$27.50*w = $309.99 - $144.99

w = ($309.99 - $144.99)/$27.50 = 6

So they can buy the chair after 6 weeks.

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The required butter she needed is given as 1.67 cups of butter.

As given in the question, Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels,

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

here,
Let the nutter need be x cups,
now,
Taking the ratio o butter to kernels
[1 / 2] / 3 = x / 10
x = 10 / 6
x = 1.67

Thus, As of the given proportion, she requires 1.67 cups of butter.

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Answer:Printmaking is the process of creating artworks by the process of printing. It can be done on paper, brick, wood, and even metal.A lithographic is a planetographic process where the design is drawn into a flat stone and is prepared by use of metal. As per the paintings shows the artwork shows us the rhinosaruers. The painting is made from water and oil.Hence the painting B shows us the use of lithography.

Type I regions- ∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx

Type II regions- ∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy

Curves of type I can be described for yy in terms of xx and often "lay above and below" one another.

Type II curves, on the other hand, can be defined for xx in terms of yy and are more or less "left and right" of one another.

Type II regions can be divided into horizontal slices, but Type I regions can be divided into vertical slices.

When a location is simultaneously classified as Type I and Type II, you can choose to examine it in any manner.

Type I regions are regions that are bounded by vertical lines x=a and x=b, and curves y=g(x) and y=h(x), where we assume that g(x)<h(x) and a<b. Then we can integrate first over y and then over x:

∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx

Type II regions are bounded by horizontal lines y=c and y=d, and curves x=g(y) and x=h(y), where we assume that g(y)<h(y) and c<d. Then we can integrate first over x and then over y:

∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy

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Answer:

y=12x+20

Step-by-step explanation:

Your question and a graph of picture are different. So I just considered your question.

m= (80-44)/(5-2) = 36/3=12

(y- y_1)=m(x-x_1)

(y-44)= 12(x-2)

y-44=12x-24

y= 12x-24+44

y=12x+20

The amount earned by Damian on Friday, if The function f(x) = 12 x + 10, and he works for 2.75 hours, is $43.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Given:

The function f(x) = 12 x + 10, where x is working hours,

Calculate the amount by putting the value of x = 2.75 in the function as shown below,

f(x) = 12 × 2.75 + 10

f(x) = 33 + 10

f(x) = $43

Thus, the amount earned is $43.

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