E
Solving a word problem using a system of linear equations of th...
QUESTION
ODD 03
Zachary
A store is having a sale on walnuts and chocolate chips. For 4 pounds of walnuts and 8 pounds of chocolate chips, the total cost is $25. For 2 pounds of walnuts
and 3 pounds of chocolate chips, the total cost is $11. Find the cost for each pound of walnuts and each pound of chocolate chips.

The Jeweler makes the number of Pendants  from the total weight of gold alloy = 12

The Jeweler has the total weight of gold alloy = 5 [tex]\frac{5}{8}[/tex] = 45/8  troy ounces.

Weight of a single gold alloy pendant = 15/32 troy ounces.

Jeweler makes the number of Pendants  from the total weight of gold alloy = 45/8 ÷ 15/32.

Dividing Fractions by Fractions

We just learned how to divide fractions by taking the reciprocal. Now, let us see the method of dividing fractions by fractions with an example. Have a look at the formula of the division of a fraction by fraction given below. If x/y is divided by a/b, this implies,

x/y ÷ a/b

⇒ x/y × b/a (reciprocal of a/b is b/a)

⇒ xb/ya

Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.

45/8 ÷ 15/32 = 45/8 × 32/15 = 12

∴ The value of 45/8 ÷ 15/32 = 12.

Hence the Jeweler makes the number of Pendants  from the total weight of gold alloy = 12

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Answer:

m∠1 = 126°

m∠2 = 154°

Step-by-step explanation:

First, find the measure of angle that is supplementary to ∠1. (I will call it ∠A)

We know that the measures of the interior angles of a triangle add to 180°.

Therefore,

m∠A + 96° + 30° = 180°

m∠A + 96° = 150°

m∠A = 54°

From this value, we can solve for m∠1, since it is supplementary to ∠A:

m∠A + m∠1 = 180°

54° + m∠1 = 180°

m∠1 = 126°

To solve for ∠2, we must first solve for the adjacent supplementary angle that I have named ∠B.

First, the measures of the interior angles of a triangle add to 180°:

28° + m∠1 + m∠B = 180°

28° + 126° + m∠B = 180°

m∠B = 26°

Finally, we can solve for m∠2 because it is supplementary to ∠B.

m∠B + m∠2 = 180°

26° + m∠2 = 180°

m∠2 = 154°

Answer: 6,001 milliliters

Step-by-step explanation: 6 Liter translates to 6,000 milliliters, which is 1 less than 6,001 milliliters.

Answer:

I believe 6 liters is more.

Banerjee Company is  liable for FUTA tax this year and the net FUTA tax for the year is $528.60.

a. Yes. Banerjee Company liable for FUTA tax this year.

b. FUTA tax

FUTA tax =0.6%

Hence,

Net FUTA tax = (Wages paid  × tax rate ) +(Taxable wages × Tax rate)

Net FUTA tax = ($23,400 × 0.6%) + ($64,700 ×0.6%)

Net FUTA tax = $140.40 + $388.30

Net FUTA tax =$528.60

Therefore $528.60 is the Net FUTA tax.

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The probability that are a normally distributed variable is less than 23 is 0.3216

The most significant probability distribution in statistics for independent, random variables is the normal distribution, sometimes referred to as the Gaussian distribution.

In statistical reports, its well-known bell-shaped curve is generally recognized.

While calculating for probability for normally distributed variables the relationship the relationship is written in the form

P > 23 = 1 - P < 23

0.6784 = 1 - P < 23

P < 23 = 1 - 0.6784

P < 23 = 0.3216

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Answer:

=30

Step-by-step explanation:

The required speed is 45 mph in each direction.

What is speed?

The definition of speed is a measurement of how quickly an object's location changes in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance.

We know that distance=rate*time

d=rt

45=rt

45=(r+30)(t-2)

rt=(r+30)(t-2)    

This shows,

rt=rt+30t-2r-60

0=30t-2r-60

if 45=rt, then r=45/t

substitute in the equation

0=30t-2(45/t)-60

multiply both sides by t

0=30t²-90-60t

on solving this quadratic equation, we get  t= 3 s, t=-1 s

consider positive value

t=3 hours

45=rt

45=r*3

r=45/3 =15 mph to new site

r+30=15+30=45 mph returning

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The properties of operations to multiply the expression are commutative property,  associative property, and distributive property.

Let us understand the properties of operations to multiplication:

The foundation of arithmetic is the Properties of Operations; we use them when performing computations and recalling basic facts.

There are basically three properties of operations to multiplication which are:

Thus, the properties of operations to multiply the expression are commutative property,  associative property, and distributive property.

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Since the congruent angle is a right angle and it is not included, the two congruent sides of the triangles must include their hypotenuses and one of their legs.The triangles would be congruent by the hypotenuse leg theorem, which states that if the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.Answer:hypotenuse leg theorem

The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.

What is transformation of function?

Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the function f (x) = x 2 + 3 is obtained by just moving the graph of g (x) = x 2 by 3 units up.

Given,

function g(x) = (x − 4)3 + 5 and compares to function f(x) = x3,

The graph of g(x) = (x-4)3+5 compare to the parent function f(x) is g(x) is shifted 4 units to right and 5 units up.

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Answer:

y = A cos B(x - C) + D

Step-by-step explanation:

The equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -

y = √180 sin (π/12.5)(t - 25) + 12  

The sinusoidal wave is of the form -

y{x} = A sin (ωt - kx + Ф)

Given is that during a certain time of year, the daily temperature in a certain city (in degrees Celsius) follows a periodic pattern.

We can write the amplitude as -

A = √(18 - 12)² + (13 - 1)²

A = √(36 + 144)

A = √180                            ... { 1 }

{K} = 12                                       ... { 2 }

The time taken to complete one complete wave is 25 hours. So, we can write -

{T} = 25                                     ... { 3 }

ω = 2π/T = 2π/25 = π/12.5

{ω} = π/12.5                                  ... { 4 }

So, we can write the equation as -

y = √180 sin (π/12.5)(t - 25) + 12    

Therefore, the equation for the graph given in terms of Y(temperature in degrees Celsius) and T(time in hours) is -

y = √180 sin (π/12.5)(t - 25) + 12    

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The reflection of (-2, -2) and (-1, 1) are

preimage    image

(-2, -2)         (-4, -2)

(-1, 1)             (-5, 1)

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is over line x = -3

However, reflection over line x = -3 which is (-3, 0) is  done as follows

from -2 to -3 = -2 - -3 = 1 unit

reflecting 1 unit over x = -3

-3 - 1 = -4

(-4, -2)

(-2, -2) ⇒ (-2 - -3, -2) ⇒ (1, -2) ⇒ (-3 - 1, -2) → (-4, -2)

from -1 to -3 = -1 - -3 = 2 units

reflecting 2 units over x = -3

-3 - 2 = -5

(-5, 1)

(-1, 1) ⇒ (-1 - -3, 1) ⇒ (2, 1) ⇒ (-3 - 2, 1) → (-5, 1)

The calculation is simply saying put

(-2, -2) this point is just before the reflection line, the image will formed at the point just after the reflection line -3 which is -4 hence (-4, -2)

(-1, 1) this point is a line before the reflection line, the mirror image will be formed skipping a line (-4) to get to -5 hence the point  (-5, 1)

the y coordinate is constant for both situations

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Answer:

[tex]\sqrt{6}, -\sqrt{6}[/tex]

Step-by-step explanation:

[tex]f(x)=x^3+3x^2-6x-18 \\ \\ =x^2(x+3)-6(x+3) \\ \\ =(x^2-6)(x+3) \\ \\ \implies (x^2-6)(x+3)=0 \\ \\ x=\pm \sqrt{6}, -3[/tex]

Answer:

skewed  to the right

Step-by-step explanation:

look at the graph

divide it in half

if both the sides are not equal then it is skewed

then to find out which way it is skewed look which side has more.

Answer:

I'm assuming that you want to find x and y.

x = 18

y = 42

Step-by-step explanation:

Angle ACD = 138°

(5x + 2) + (2x + 10) = 138

7x + 12 = 138

7x = 126

x = 18

y + (5x + 2) + (2x + 10) = 180 (sum of adjacent angles on a straight line)

Substitute x = 18 into the equation.

y + 5(18) + 2 + 2(18) + 10 = 180

y + 90 + 2 + 36 + 10 = 180

y = 42

The library’s December record is 29442  

Mathematical operations are Operators which emphasize particular actions like adding, subtracting, adding multiple times, dividing, etc.

There are 4 basic operations in mathematics as given below.  

1. Addition  =>  (+)

2. Subtraction  => (-)

3. Division  => (÷)

4. Multiplication  =>  (x)  

Here we have

In 2017 the library was able to record 4907 borrowed books  

By December of the same year, the library has 6 times its January record.  

[ Here we use Multiplication to find the December record ]

The December record = 6 times of January record

⇒ 6 × January record

⇒ 6 × 4907    

⇒ 29442

Therefore,

The library’s December record is 29442

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Answer:

create a line between (0,0) and (1,3)
the unit rate is 3/2 or 1.5

Step-by-step explanation:

pls mark

AS per the combination method, Mr. Walters receive both payments in the same month in the 6th time.

Combination method:

A way of adding equations together in such a way that the variables are set aside, one by one is called as combination.

Given,

Mr. Walters receives a dividend every 5 months and a royalty check every 6 months. He received both payments in May 2019.

Here we need to find the next time he would receive both payments in the same month.

While looking into the given question we have identified he following things,

Dividend payment = 5 months

Royalty payment = 6 months

Both payment received = May 2019.

So, according to the combination method,

The value of n = 6 and the value of x = 5

So, the next time he would receive both payments in the same month is

=> 6 C 5 = 6! / 5! (6 - 5)!

Which results the value as 6.

Therefore, on 6th time from this payment he will receive both in the same month.

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well, we know the price is $18, now, if we jack it up by 70%, well, what's 70% of 18?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 18}}{\left( \cfrac{70}{100} \right)18}\implies 12.6~\hfill \underset{price}{\stackrel{18~~ + ~~12.6}{\text{\LARGE 30.60}}}[/tex]

Answer:

m = 37

Step-by-step explanation:

The interior and corresponding exterior angle of a triangle are always supplementary.

Therefore, we can set the sum of the two given angle measures to 180°:

[tex](2m-12) \textdegree + (3m+7) \textdegree = 180 \textdegree[/tex]

and solve algebraically for m.

[tex]2m-12 + 3m+7 = 180[/tex]

[tex](2m + 3m) + (-12+7) = 180[/tex]

[tex]5m-12+7 = 180[/tex]

[tex]5m - 5 = 180[/tex]

[tex]5m = 185[/tex]

[tex]m=37[/tex]

The value of m is 37.

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Given:

m ∠Z = (2m − 12)° and exterior angle ∠Z =(3m + 7)°.

int. m <Z + ext. <Z= 180

2m - 12 + 3m + 7 = 180

5m - 5 = 180

5m = 185

m = 185/ 5

m = 37

Hence, the value of m is 37.

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The number of students that chose band as an elective is 50

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic

let the total number of seats for choir be x and that for band be y

if there are 4 times as many seats as there in band then mathematically,

x = 4y.--------------------1

If there are 250 students, then, there would be 250 seats for the combined class.

so,

x + y = 250--------------2

substitute x = 4y in equation 2

4y + y = 250

5y = 250

y = 250/5

y = 50

In conclusion, 50 students can choose band.

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as x -> -infinity, y -> -infinity and as x-> infinity, y-> infinity

So, last option is correct

The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .

In the question,

it is given that ,

the sum of speed of two trains = 723.5 miles per hour

let the speed of the first train = x miles per hour

let the speed of the second train = y miles per hour ,

also given that , the speed of the first train is 4.5 mph faster than that of the second train , which means

x = y + 4.5 .

the sum is 723.5 ,

so , the equation is

x + y = 723.5

y + 4.5 + y = 723.5

2y + 4.5 = 723.5

2y = 719

y = 719/2

y = 359.5

So , x = 359.5 + 4.5 = 364 .

Therefore , The speed of first train is 364 miles per hour and the speed of second train is 359.5 miles per hour .

The given question is incomplete , the complete question is

The sum of the speed of the two trains is 723.5 miles per hour. if the speed of the first train is 4.5 mph faster than that of the second train, find the speeds of each train ?

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The group that travels faster when groups of hikers left camp at the same time and each traveled at a constant rate is group B.

From the information, two groups of hikers left camp at the same time. each traveled at a constant rate.

Since group A covered 3/4 mile in 1/2 hour, the speed will be:

= Distance / Time

= 3/4 ÷ 1/2

= 1.5 miles per hour.

It took Group B 3/4 hour to travel 1/3 mile. The speed will be:

= Distance / Time

= 3/4 ÷ 1/3

= 2.25 miles per hour.

Group B had a faster speed.

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Complete question

Two groups of hikers left camp at the same time. each traveled at a constant rate

group A covered 3/4 mile in 1/2 hour

It took Group B 3/4 hour to travel 1/3 mile

Which group so travelling at a faster rate?

The answer is -9.

-2 -(+7) = -2 -7

-2 -7 = -9

The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.

Given that,

The list of numbers are 3,6,9,7,4,6,7,0,7

The mean, median, mode, and range must be determined.

The "mean" is the standard "average," which is calculated by adding up all the numbers and dividing the result by the total number of numbers.

The value that sits in the middle of a set of numbers is known as the "median." Before you can find the median, your numbers must be listed in numerical order from smallest to greatest. This means that you might need to redo your list.

The "mode" value is the one that shows up the most often. There is no mode for the list if no number on the list is repeated.

A list of numbers' "range" is just the range between the largest and lowest values. It conveys "spread," which is the degree to which the values are scattered (or how concentrated they are).

Mean=(3+6+9+7+4+6+7+0+7)/9

Mean = 49/9

Mean = 5.4

Median is 0,3,4,6,6,7,7,7,9

The median is 6

Mode is 7

Range is

Greater number is 9 and the smallest number is 0

Difference is 9-0=9

Range is 9.

Therefore, The mean is 5.4, median is 6, mode is 7 and the range is 9 when the given list of numbers are 3,6,9,7,4,6,7,0,7.

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The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute, using the normal distribution and the central limit theorem, is of:

0.663 = 66.3%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the problem are given as follows:

[tex]\mu = 75, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]

The probability that these four females have pulse rates with a mean between 69 beats per minute and 81 bears per minute is the p-value of Z when X = 81 subtracted by the p-value of Z when X = 69, hence:

X = 81:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (81 - 75)/6.25

Z = 0.96

Z = 0.96 has a p-value of 0.8315.

X = 69:

Z = (69 - 75)/6.25

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.8315 - 0.1685 = 0.663 = 66.3%.

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The subtotal before the surcharge and sales tax is $12.2

In this question, we have the following parameters

Total = $13.73

Sales tax = 4%

Surcharge = $1

The above parameters imply that:

Total = Subtotal * (1 + sales tax) + Surcharge

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

13.73 = Subtotal * (1 + 4%) + 1

This gives

Subtotal * (1 + 4%) = 12.73

Divide both sides by 1.04

Subtotal = 12.2

Hence, the subtotal is $12.2

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