At a community barbecue, Mrs. Garcia and Mr. Clayton are buying dinner for their families. Mrs. Garcia purchases 2 hot dog meals and 1 hamburger meal, paying a total of $18. Mr. Clayton buys 3 hot dog meals and 3 hamburger meals, spending $42 in all. How much do the meals cost?

The equation in terms of log(x), log(y)  and log(z) is,  

log x + 1/4 log y -1/2 log z.

A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.

here, we have,

log x√√y/z = log(x√(√y)/z)

Consider, the given logarithmic expression,

we get,

By using the logarithmic rule: log(ab) = log(a) + log(b)

So, log(x√(√y)/z)

   =logx + log(√(√y)/z)

   =log x + 1/2 log (√y)/z

   =logx + 1/2 log (√y) - 1/2 log z

   = log x + 1/4 log y -1/2 log z

Hence, the expression in terms of x , y and z is, log x + 1/4 log y -1/2 log z.

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The possible outcomes for each event are given as follows:

Event J is composed by the multiples of 25 that are between 70 and 200, hence we start at 75, as 25 x 3 = 75, and then keep adding 25 until we reach 200, as follows:

J = {75, 100, 125, 150, 175, 200}

Event K is composed by the multiples of 70 that are between 70 and 200, hence we start at 70, as 70 x 1 = 70, and then keep adding 70 until we reach 200, as follows:

K = {70, 140}.

The union set is composed by the elements that belong to at least one of these two sets, hence:

J U K = {70, 75, 100, 125, 140, 150, 175, 200}.

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A point that is a solution to this system of linear inequalities is (0, 1).

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

y ≥ 2x - 4

x > -3

y < 5

Using the point (0, 1)

To see why this is a solution, we need to check if it satisfies each of the inequalities:

Since the point (0, 1) satisfies all of the inequalities, it is a solution to the system of linear inequalities.

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Answer:

yes

Step-by-step explanation:

4 > j ( substitute j = 1 )

4 > 1 ← is a true statement

so j = 1 is a solution to the inequality

The amount of Earl Grey tea to mix is  225 pounds.

The amount of Orange Pekoe tea to mix is 75 pounds.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let x be the amount of Earl Grey tea to mix.

So, the amount of Orange Pekoe tea to mix = 300-x

then, 6x+4 (300-x) = 5.5 x 300

6x+1200-4x=1650

2x=450

x=225

and, amount of Orange Pekoe tea to mix = 300-225=75

Thus, the amount of Earl Grey tea to mix = 225 pounds

and, the amount of Orange Pekoe tea to mix=75 pounds.

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Answer:

$199.98

Step-by-step explanation:

To calculate the amount that Kendall will save in finance charges during the six-month promotional rate period, we need to calculate the finance charges he would have incurred with his standard APR and then compare it to the finance charges he will incur with the promotional rate.

First, let's calculate the monthly finance charges with the standard APR. To do this, we need to know the average daily balance for each month. Assuming Kendall has a previous unpaid balance, let's say it is $500. And assuming he makes no other purchases, his average daily balance for each month would be:

$1,014 + $500 = $1,514The finance charges for each month with the standard APR would be:

$1,514 * (22.65/100) / 12 = $38.37

So, the total finance charges for the six-month promotional rate period with the standard APR would be:

$38.37 * 6 = $230.22

Next, let's calculate the finance charges with the promotional rate:

$1,514 * (3/100) / 12 = $5.04

So, the total finance charges for the six-month promotional rate period with the promotional rate would be:

$5.04 * 6 = $30.24

Finally, we can calculate the amount that Kendall will save in finance charges during the six-month promotional rate period:

$230.22 - $30.24 = $199.98

Therefore, Kendall will save $199.98 in finance charges during the six-month promotional rate period.

1) The sales tax is an additional rate that is paid along with the cost of the meal.

2) The amount paid in taxes for a meal costing $15.00 and a rate of 7% is given as follows: $1.05.

The sales tax is obtained applying the proportions in the context of this problem.

A proportion is applied as the sales tax is obtained with the multiplication of the cost of the meal by the decimal equivalent of the percentage of tax.

The decimal equivalent for a percentage of 7% is given as follows:

7/100 = 0.07.

Hence the amount of tax paid is given as follows:

0.07 x 15 = $1.05.

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Therefore , the solution of the given problem of linear equation comes out to be  x = 21.75.

A linear regression curve is built on the equation y=mx+b. The y-intercept is m, and the slope is B. The previous sentence is sometimes referred as a "mathematical equation merging multiple variables," even if y or y are independent parts. The only variables in bivariate linear equations are two. There are no known solutions to application issues involving linear equations. Y=mx+b, also written as mx+b, is the expression for a straightforward system of equations.

Here,

Given :

From a mixed number, you must convert it to a decimal number. You can do this by following the instructions below:

In order to start, you must reduce the fraction's denominator by its numerator.

Step 2: You must now multiply the resulting quotient by the whole number component.

You therefore obtain:

=> 7 1/4 = 7 + 0.25 = 7.25

The scale picture that transforms "Figure a" into "Figure b" is then: 1: 71

The specified length of the appropriate side of "Shape a" must then be multiplied by in order to determine the value of "z."

The outcome is as follows:

=>x = (3)(7.25)

=> x = 21.75

Therefore , the solution of the given problem of linear equation comes out to be  x = 21.75.

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The complete question is "Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:7 1/4 enter the value of x

Both figures are triangles

Figure a is smaller than figure b

Figure a to the right has a 3

Figure b to the right has a x"

The value of the expressions will be:

2x² + 3x + 4, when x=1 is equal to 9.

(x+y)², when x=2 and y=2 is equal to 16.

5x² + 2x, when x=2 is equal to 24.

(x+y)³, when x=7 and y=3 is equal to 1000.

2x² + 3x + 4, when x=1 is:

= 2(1)² + 3 + 4

= 2 + 3 + 4

= 9.

(x+y)², when x=2 and y=2 is equal to:

= (2 + 2)²

= 4²

= 16.

5x² + 2x, when x=2 is equal to:

= 5(2)² + 2(2)

= 20 + 4

= 24.

(x+y)³, when x=7 and y=3 is equal to:

= (7 + 3)³

= 10³

= 1000.

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1: cscX = 1/sinX = 5/2√5.

2: Using the reciprocal identity of tanA and sinA,

tanA/sinA = 1/cosA

√2/2 / -√3/3 = 1/cosA

-2√2/2√3 = 1/cosA

cosA = -2√3/2√2.

3: Using the Pythagorean theorem, sinX = √(1 - cos^2X)

√(1 - cos^2X) = √((1/cot^2X) - 1) = √((√3/2)^2 - 1) / (-√3/2)

sinX = √2/2.

4: Using the Pythagorean theorem,

cotθ = cosθ / sinθ = 1 / tanθ = 1 / (√(1 - cos^2θ) / cosθ) = cosθ / √(1 - cos^2θ) = 1 / (√(1 - (1/7)^2)) = √(48) / 7.

5: Using the cofunction identity, tan(-x) = -tan(x).

Using the identity that tan(π/2 -x) = cot(x),

-tan(x) = -1/cot(π/2 -x) = -1/(-1.84) = 1.84.

6: Using the even-odd identity, cos(-θ) = cos(θ), and

sin(-θ) = -sin(θ),

cos(θ-π/2) = cosθcos(π/2) + sinθsin(π/2) = 0cos(π/2) + (-0.57)sin(π/2) = -0.57.

7: Using the identity sin^2X + cos^2X = 1,

secX ⋅ sin^2X + cosX = secX ⋅ (1 - cos^2X) + cosX = secX - secXcos^2X + cosX = secX + cosX.

8: Using the identity 1 + tan^2θ = sec^2θ,

(sinθ + 1)(tanθ - secθ) = (sinθ + 1)(tanθ - 1/cosθ) = (sinθ + 1)(tanθcosθ - 1) = (sinθ + 1)sinθ(tanθ/sinθ) - (sinθ + 1) = sinθ + sin^2θ - sinθ - 1 = sin^2θ - 1.

Proof:

Using the identity tan^2X = sin^2X / cos^2X,

1+sec^2X / 1+tan^2X = (1 + 1/cos^2X) / (1 + sin^2X / cos^2X) = cos^2X / (cos^2X + sin^2X) = cos^2X / (1) = 1 + cos^2X.

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Answer:

M = 10 + 2f

Step-by-step explanation:

Please see the attachment for detail explanation

Answer:

A and D

Step-by-step explanation:

Given the function:

[tex]\displaystyle{f(x)=\sqrt{5-x^2}}[/tex]

In order to find the first-order derivative of square root function, we have to convert the form of surd to exponent form. Therefore:

[tex]\displaystyle{f(x)=\left(5-x^2\right)^{\frac{1}{2}}}[/tex]

Since the exponent is a constant and that the base is an expression with variable, we can apply the chain rule (power rule variation):

[tex]\displaystyle{f(x) = u^n \to f'(x) = nu^{n-1} \cdot \dfrac{du}{dx}}[/tex]

Therefore:

[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-1} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{\frac{1}{2}-\frac{2}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot \dfrac{d}{dx}\left(5-x^2\right)}[/tex]

Deriving 5 - x²:

[tex]\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = 0 - 2x^{2-1}}\\\\\displaystyle{\dfrac{d}{dx}\left(5-x^2\right) = -2x}[/tex]

Thus:

[tex]\displaystyle{f'(x)=\dfrac{1}{2}\left(5-x^2\right)^{-\frac{1}{2}} \cdot (-2x)}\\\\\displaystyle{f'(x)=\dfrac{1}{2}(-2x)\left(5-x^2\right)^{-\frac{1}{2}} }\\\\\displaystyle{f'(x)=-x\left(5-x^2\right)^{-\frac{1}{2}} }[/tex]

You can also convert to the square root form of:

[tex]\displaystyle{f'(x)= \dfrac{-x}{\sqrt{5-x^2}}}[/tex]

Therefore, A and D are correct.

Therefore , the solution of the given problem of probability comes out to be probability of winning a  3 game out of 5 is 0.5 .

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any quantity between 0 and 1, whereby 1 frequently represents certainty range 1 and 0 normally denotes possibility, can be used to represent chance. A probability diagram illustrates the likelihood that a particular event will take place.

Here,

Given :

Since,

the probability to win a game is 50% .

So they have to win 3 games ,

and so , the probability to win the game is:

=> 1/2 * 1

=> 0.5

thus,

probability of winning a  3 game out of 5 :

=> 0.5

Therefore , the solution of the given problem of probability comes out to be probability of winning a  3 game out of 5 is 0.5 .

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The required lowest cost for the trip of 200km is given as $657.1.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
A truck travelling at x km/h, where 30 ≤x≤ 120, uses gasoline at the rate of r(x) L/100 km, where r(x) = 1/400(4900/x + x)

Since,
For r(x) maximum, r(x) = 0
1/400(4900/x + x) = 0
4900 = x²
x = 70 km/hr

Now,
Cost of the fuel for 200km = 200 / r(70) × $1.15/L
                                         = 200/(1/400× (4900/70 + 70)) × 1.15
                                         = $657.1

Thus, the required lowest cost for the trip of 200km is given as $657.1.

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The graph of the equation x^2 - 4x + 4y - 4 = 0 is a circle, so it doesn't have a direction of opening.

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

x^2 - 4x + 4y - 4 = 0

The equation x^2 - 4x + 4y - 4 = 0 is of a conic section

i.e. the equation of a circle

The equation of a circle does not have a particular direction it opens to

Hence, it is a closed shape

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On solving the provided question, we can say that by percentage 9.6  gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

by percentage

mix with 96 gallons of a 10% sugar solution

the resulting mixture is an 18%

10/100 X 96 = 9.6

9.6  gallons of a 34% sugar solution do we need to mix with 96 gallons of a 10% sugar solution

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Answer:

0.67

Step-by-step explanation:

10/15＝0.666666......

＝0.67

A: Mai answered 5  open-ended questions correctly,

B: Priya answered 15 multiple-choice questions correctly,

C: expression for the condition is y = 10 + 4a + 6b.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given points on each multiple choice question = 4

points on each open-ended question = 6

extra credit for winners = 10 points

A. If Mai answered 13 multiple-choice questions correctly and earned a total score of 92,

the total score of multiple choice questions = 13*4

the total score of multiple choice questions = 52

score left  = 92 - 52 - 10 (reducing 10 for extra points)

score left  = 30

open-ended questions she answers correctly = 30/6

open-ended questions she answers correctly = 5

B:  If Priya answered 4 open-ended questions correctly and earned a total score of 94,

the total score of open-ended questions = 4*6

the total score of open-ended questions = 24

the score left  = 94 - 24 - 10 (reducing 10 for extra points)

score left  = 60

multiple choice questions she answers correctly = 60/4

multiple choice questions she answers correctly = 15

C:  an expression that will represent a student's score in first period,

let y be the total score,

a be the number of multiple choice questions answered,

the total score of multiple choice questions = 4a

and b be the number of  open-ended questions answered,

the total score of open-ended questions = 6b

expression is,

y = 10 + 4a + 6b  (adding 10 for extra points)

Hence Mai answered 5  open-ended questions correctly,

Priya answered 15 multiple-choice questions correctly,

and expression is y = 10 + 4a + 6b.

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The value of function at f(-1) = -13,

f(0) = -8 and f(2) = 10.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given equations,

f(x) = 9x - 4 where x < 0

f(x) = 9x - 8  where x ≥ 0

to find f(-1),

substitute value in equation f(x) = 9x - 4 where x < 0

f(x) = 9x - 4

f(-1) = 9(-1) - 4

f(-1) = -13

now f(0) and f(2),  substitute in equation f(x) = 9x - 8  where x ≥ 0

f(x) = 9x - 8

f(0) = 9(0) - 8

f(0) = -8

f(2) = 9(2) - 8

f(2) = 10

Hence  f(-1) = -13,

f(0) = -8 and f(2) = 10.

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Answer:

2X-3=0

2X=3

X=3/2

Step-by-step explanation:

Answer:

2x- 3 = 0

2x=3

x = 3/2

Step-by-step explanation:                                                                                   best of luck to you

The mean of the numbers is 22.625

The average of all the data in a set. The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

The mean or average of the set of the data is calculated thus

(6+7+5+8+6+7+6+8)/8

181/8 = 22.625

Therefore,  the mean for the number of hours of sleep: 6 7 5 8 6 7 6 8 is 22.625

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The two plans cost the same when the amount is $200.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the miles driven = x.

Given that,

The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. This is represented as:

A = 40 + 0.70x

The second plan has no initial fee but costs $0.90 per mile driven.

B = 0.90x

The two plans cost the same when A = B:

40 + 0.70x = 0.90x

40 = 0.90x - 0.70x

40 = 0.20x

x = 200

The two plans cost the same when the amount is $200.

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Answer: The annual premium for a 27-year-old female purchasing a 20-Year Endowment insurance policy with a face value of $25,000 is $42.67.

Step-by-step explanation:

When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs of the equations, we can reasonably infer and logically deduce that they both would produce the same output (dependent value or y-value) at the ordered pair (4, 6).

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The description of the parts of the expression are:

The coefficient of x² is 1/2.

The coefficient of x is 1.

The constant is 7.

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,

(1/2)x² + x + 7

Now,

The coefficient of x² is 1/2.

The coefficient of x is 1.

The constant is 7.

Thus,

The description of the expression is given above.

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Answer:

The description of the parts of the expression are:The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.What is an expression?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,(1/2)x² + x + 7Now,The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.Thus,The description of the expression is given above.Learn more about expressions here:brainly.com/question/3118662#SPJ1The description of the parts of the expression are:The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.What is an expression?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,(1/2)x² + x + 7Now,The coefficient of x² is 1/2.The coefficient of x is 1.The constant is 7.Thus,The description of the expression is given above.Learn more about expressions here:brainly.com/question/3118662#SPJ1

Step-by-step explanation:

1. PM:MQ and KM:ML  (Given)

2. KM/MQ = PM/ML (Property of cross multiplication)

3. ∠ PMK = ∠ LMQ (vertical angles are congruent)

4. ΔPMK ~ ΔLMQ  (SAS~)

Similar triangles are triangles that have the same shape, but their sizes may vary, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Given,

PM:MQ and KM:ML

To prove

ΔPMK ~ ΔLMQ

By the figure,

PM:MQ = KM:ML (Given)

Cross multiplying

KM/MQ = PM/ML

∠ PMK = ∠ LMQ (vertical angles)

Using Side - Angle - Side theorem

ΔPMK ~ ΔLMQ

Hence,

1. PM:MQ = KM:ML , since its given

2. KM/MQ = PM/ML using cross multiplication

3. ∠ PMK = ∠ LMQ both are vertical angles

4.  ΔPMK ~ ΔLMQ using side-angle-side theorem of similarity

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Best Mortgage Option 3 because this mortgage option offers a lower interest rate.

After reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.

Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.

In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.

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[tex]\textit{sum of all exterior angles in a polygon}\\\\ S=360^o \\\\[-0.35em] ~\dotfill\\\\ x+2x+3x+4x+5x+6x+7x+8x=360\implies 36x=360 \\\\\\ x=\cfrac{360}{36}\implies x=10[/tex]

Answer:

The exterior angles of an octagon add up to 360°. So, 8x° = 360°, and x = 45°.

Given that the volume of the rectangular prism is 120 cubic inches, we can write the equation:

l * w * h = 120

where l, w, and h are the length, width, and height of the prism, respectively.

Since the length is 3 and the width is 10, we can plug in these values into the equation:

3 * 10 * h = 120

Solving for h, we get:

h = 120 / (3 * 10) = 120 / 30 = 4

So the height of the rectangular prism is 4 inches.

To find the surface area of the rectangular prism, we can add up the areas of all six faces:

2 * l * w + 2 * w * h + 2 * h * l

Plugging in the known dimensions, we get:

2 * 3 * 10 + 2 * 10 * 4 + 2 * 4 * 3 = 60 + 80 + 24 = 164 square inches

So the surface area of the rectangular prism is 164 square inches.

Answer: Hight 4 inch, surface area 164 square inch

Step-by-step explanation: multiply with l * w * h  

* = x