You work at a hardware store earning $8. 50 per hour. You work no more than 40 hours each week. Your friend says that the function y = 8. 5x represents the amount of money you earn each week where the domain of x > 40 represents the number of possible hours you work. Is your friend correct? Explain

Answer:

  C.  4x²√(3x)

Step-by-step explanation:

You want to simplify √(48x⁵).

Square root expressions can be simplified by removing perfect squares from under the radical:

  [tex]\sqrt{48x^5}=\sqrt{16x^4\cdot3x}=\sqrt{(4x^2)^2}\cdot\sqrt{3x}=\boxed{4x^2\sqrt{3x}}[/tex]

The measure of angle x is 70°  

For a triangle, the exterior angle is the angle formed by extending one of the sides of the triangle

The Triangle Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Here we have

A triangle where 105° is an exterior angle

And 'x' is an interior angle

Name the given triangle as given below

If we take AC as Transversal which cuts AB and DC  

=> ∠A = 35°    [ Alternate Interior Angles ]      

In a triangle,

The measure of an exterior angle will equal to the sum of measures of opposite interior angles.  

=> x° + 35° = 105°  

=> x° = 105° - 35°  

=> x° = 70°  

Therefore,

The measure of angle x is 70°

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Answer:

A + B must lie between 90 and 450 degrees.

Explanation:

Since sin A and cos B are both negative, A and B must lie in the third quadrant or the fourth quadrant. In the third quadrant, sin A and cos B are both negative, while in the fourth quadrant, sin A is negative and cos B is positive.

Let's consider the case where A and B are both in the third quadrant. In this case, both A and B are between 180 and 270 degrees. Since A + B is the sum of two angles in this range, it follows that A + B must be between 360 and 450 degrees.

Now let's consider the case where A is in the fourth quadrant and B is in the third quadrant. In this case, A is between 270 and 360 degrees, while B is between 180 and 270 degrees. Since sin A is negative and cos B is positive, it follows that cos A and sin B are both negative. Using the identities sin(180 - x) = sin x and cos(180 - x) = -cos x, we can write:

sin A + cos B = sin(180 - (180 - A) - B) + cos(180 - (180 - A) - B)

= sin(180 - A) - cos(180 - B)

= -sin A - cos B

Therefore, A + B is the difference of two angles in the third quadrant, and it must be between 90 and 180 degrees.

Putting the two cases together, we see that A + B must lie between 90 and 450 degrees.

The original price of the article without the discount is %60.

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods.

Let us suppose original price = x.

Given that, after a discount, the marked price of an article is 48$ and the discount is 20%.

Thus,

48 = x(1 - 20/100)

48 = x(80/100)

x = 60

Hence, the original price of the article without the discount is %60.

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On converting 159 lbs to Kg , we get 159 pounds is equivalent to 72.1211 Kilogram .

The various units that are used to measure the weight of an object , some of them are : Kilogram (Kg) , Pounds (lb) , Gram (gm) .

We have to convert 159 lbs to Kilogram ;

We know that , 1 pound is equal to 0.453592 Kg ;

So , the conversion factor is 0.45359237 kg per pound.

For the conversion , we multiply the given weight by this conversion factor ,

We get ;

⇒ 159 lbs × 0.45359237 kg/lb = 72.1211 Kg ;

Therefore, 159 pounds is equal to 72.1211 Kilograms .

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The translation vector is

a = 6

b = -2

The transformation rule for 90 degrees clockwise rotation is

(x, y) → (y, -x)

Using reference side (-3, -3). 90 degrees clockwise rotation will result to

(-3, -3) → (-3, 3)

The location  (-3, 3) is compared with (3, 1) we have that

-3 + x = 3, x = 3 + 3 = 6

3 + y = 1, y = 1 - 3 = -2

hence the vector is (6, -2), a = 6 and b = -2

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In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent categorical data. The Option A is correct.

Categorical data refers to collection of data that is organized into categories. For instance, the data obtained when an organization or agency tries to collect the biodata of its employees is referred to as categorical data. Because the variables in the biodata, like sex, state of residence, etc., can be used to categorize the data, it is known as categorical data.

It is also regarded as a type of data that can be categorized or grouped using names or labels. Through a process known as matching, this grouping is typically created in accordance with the data characteristics and similarities of these characteristics.

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Answer:

8.5 cm

Step-by-step explanation:

A regular pentagon has 5 congruent sides , then

length of each side = perimeter ÷ 5 = 42.5 ÷ 5 = 8.5 cm

"Karen wants to buy a new smartphone that costs $46. She currently has some money saved up, represented by the expression 6x - 4, where x is the number of weeks she has been saving. Can Karen buy the smartphone now, or does she need to save for more weeks? Use the inequality 6x - 4 < 46 to help you answer the question."

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent and solve problems in various areas, including science, engineering, economics, and mathematics.

An algebraic expression can contain one or more variables, which represent unknown or changing quantities, and one or more constants, which represent fixed values. The variables are usually represented by letters, such as x, y, or z. The operations of addition, subtraction, multiplication, and division are represented by the symbols +, -, ×, and ÷, respectively. Parentheses are also used to group terms and indicate the order of operations.

For example, the algebraic expression 3x + 2y - 5 represents a combination of two variables, x and y, and three constants, 3, 2, and 5. The terms 3x and 2y are the variables multiplied by their coefficients, while -5 is a constant term.

Algebraic expressions can be simplified by combining like terms, which are terms that have the same variable raised to the same power. For example, in the expression 3x + 2y - 5 + 4x - 3y, the like terms are 3x and 4x, and 2y and -3y. Combining these terms yields the simplified expression 7x - y - 5.

Algebraic expressions are used in various mathematical operations, such as solving equations, graphing functions, and evaluating formulas. They are also used in real-world applications, such as calculating interest rates, solving optimization problems, and modeling physical phenomena.

Sure, here's a word problem that fits the inequality 6x - 4 < 46:

"Karen wants to buy a new smartphone that costs $46. She currently has some money saved up, represented by the expression 6x - 4, where x is the number of weeks she has been saving. Can Karen buy the smartphone now, or does she need to save for more weeks? Use the inequality 6x - 4 < 46 to help you answer the question."

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After conversion of 80 ounces into gallon we get 0.625 gallons.

A fluid ounce is the U.S. popular units system.

Ounces and fluid ounces are two unlike units.

1 fluid ounce is equal to the 1.04 oz weight.

US fluid ounce contain 29.6 milliliters and British fluid ounce contain 28.4 milliliters.

Ounce expressed by notation oz.

To convert ounces (oz) to gallons,

We know that

One gallon = 128 fluid ounces.

We want to convert 80 ounces to gallons,

we can use the following formula:

80 oz ÷ 128 oz/gal = 0.625 gallons

Hence,

We get 80 ounces is equal to 0.625 gallons.

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We can convert the unit  Nm to ft-lbs by using the formula 1Nm = 0.71 Lbs-ft.

We are provided with the unit Nm that means Newton meter.

we have to covert it into Lbs - ft.

Now, we know, from the standard conversion rates that one newton is equal to 0.2 lbs and one meter is roughly equal to 3.2 feet.

So, if we want to do the unit conversion, we should write,

= Lbs-ft

= 0.2 Lbs(3.2)ft

1Nm = 0.71 Lbs-ft.

Now, the above mentioned relation is our formula for the conversion of the two unit.

So, now we can write that, 1 Nm(Newton - meter) is equal to 0.71 Lbs-ft.

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Answer:

1) Put equation or function in y= form.

2) Multiply out (expand) any factored polynomials in the numerator or denominator.

3) Remove everything except the terms with the biggest exponents of x found in the numerator and denominator. These are the "dominant" terms.

A statistical package is likely to be used with quantitative research but not with qualitative research - True.

The collection and analysis of numerical data, such as survey responses or experimental measurements, is common in quantitative research, and statistical analysis is frequently used to summarise and interpret this data. In quantitative research, statistical software such as SPSS, R, or Stata are widely used to do data analysis and statistical tests.

In contrast, qualitative research often entails gathering and interpreting non-numerical data, such as interview transcripts or observational notes. Although statistical analysis may not be suited for this type of data, several software packages, such as NVivo, MAXQDA, or ATLAS.ti, can be used to manage and analyse qualitative data.

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Mr. Jericho needs to teach his students how to make change. Vygotsky would recommend that he set up a pretend shop and have all of the students act as cashiers in it.

One of the four methods of teaching is the interactive or participative method of teaching. In this method, students are taught certain stuff with the use of hands-on techniques. These include acting out whatever is being taught so that students have a better view of whatever is happening around them.

This method is quite useful and this is exactly what Vygotsky suggested for the students in the class in the very first place.

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The correct answer to this question is option D: (0.60 minus 0.70) plus-or-minus 1.96 StartRoot StartFraction 0.60 (1 minus 0.60) Over 50 EndFraction + StartFraction 0.70 (1 minus 0.70) Over 50 EndFraction EndRoot.

To find the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups, we need to use the formula:

CI = (p1 - p2) ± z*√[(p1(1-p1)/n1) + (p2(1-p2)/n2)]

Where p1 and p2 are the proportions of patients experiencing stress relief in the yoga and meditation groups, respectively, n1 and n2 are the sample sizes of the yoga and meditation groups, respectively, and z is the critical value from the z-table corresponding to the 95% confidence level.

Plugging in the given values:

p1 = 30/50 = 0.60
p2 = 35/50 = 0.70
n1 = 50
n2 = 50
z = 1.96 (from the z-table for a 95% confidence level)

CI = (0.60 - 0.70) ± 1.96*√[(0.60(1-0.60)/50) + (0.70(1-0.70)/50)]
CI = (-0.10) ± 1.96*√[(0.24/50) + (0.21/50)]
CI = (-0.10) ± 1.96*√[0.009]
CI = (-0.10) ± 1.96*(0.095)
CI = (-0.10) ± 0.186

Therefore, the 95% confidence interval for the difference in proportions of patients experiencing stress relief from the yoga and meditation groups is (-0.286, 0.086).

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The function family based on the information is a linear function.

A linear function is a type of mathematical function that has the form:

f(x) = ax + b

where a and b are constants, and x is a variable. The variable x is often called the independent variable, and the variable f(x) is called the dependent variable.

The value of a determines the slope of the line, while the value of b determines the intercept of the line with the y-axis. The slope of the line represents the rate of change of the dependent variable with respect to the independent variable, and the intercept represents the value of the dependent variable when the independent variable is zero.

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Answer:

248 feet

Step-by-step explanation:

Since each curtain is 48 inches long, or 4 feet long, Fabrizio will need:

62 curtains × 4 feet per curtain = 248 feet of fabric

Therefore, Fabrizio's curtain company will need 248 feet of fabric to make 62 curtains.

Answer:

248 feet...

Step-by-step explanation:

Each curtain is 48 inches long, which is 4 feet (since there are 12 inches in a foot). Therefore, 62 curtains will require:

62 curtains x 4 feet per curtain = 248 feet of fabric.

So Fabrizio's curtain company will need to purchase 248 feet of fabric from the store...

A negative relationship exists when two connected variables move in opposite directions. As a result, Option A is right which has a downward slope and variables that are negatively correlated.

An inverse correlation, sometimes referred to as negative correlation, is a relationship between two variables in which, when one variable's value is high, the other variable's value is likely low.

For instance, with the variables A and B, when A is high, B is low, and when A is low, B is high. In statistical nomenclature, an inverse correlation is frequently expressed by the correlation coefficient "r," which has a value between -1 and 0, with r = -1 signifying complete inverse correlation.

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =300 \end{cases}\implies s=\cfrac{(300)\pi (3)}{180}\implies s=5\pi \implies s\approx 15.71~mm[/tex]

Answer:

To convert GB to MB multiply the value of a GB by 1000 to get mb.

1gb x 1000 equals 1000 mb

By the current exchange rate for Japanese Yen to US Dollar , 1500 Yen is equivalent to 11.187  USD .

In order to convert 1500 YEN to USD, we need the current exchange rate between the "Japanese Yen" and the "US Dollar" .

The exchange rate varies constantly due to fluctuations in the global financial markets ,

According to the current exchange rate of 1 US Dollar = 134.08 Japanese Yen  ,

We convert 1500 yen to USD by dividing 1500 by 134.08  ;

⇒ 1500/134.08 = 11.187 USD ;

Therefore, 1500 Japanese yen is approximately equal to 11.187 US Dollars .

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Answer:

−16n² −4n −4

Step-by-step explanation:

=(4)(−4n²+−n+−1)

=(4)(−4n²)+(4)(−n)+(4)(−1)

=−16n² −4n −4

So, the product of two irrational numbers may be rational or irrational, depending on the specific irrational numbers being multiplied.

A real number is said to be irrational if it cannot be expressed as the quotient of two integers, p/q, where p and q are both integers. The square root of two, for example, cannot be stated as an integer or a fraction.

No, that statement is not always correct.

In general, the product of two irrational numbers is not necessarily irrational. For example, consider the square roots of 2 and 8:

sqrt(2) * sqrt(8) = sqrt(2) * 2 * sqrt(2) = 2 * 2 = 4,

which is a rational number.

However, there are some cases where the product of two irrational numbers is irrational. For example, the product of the square root of 2 and the square root of 3 is irrational:

sqrt(2) * sqrt(3) = sqrt(6),

which is irrational.

So, the product of two irrational numbers may be rational or irrational, depending on the specific irrational numbers being multiplied.

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Answer:

Measuring Spoon

Step-by-step explanation:

The tool you would use is a measuring spoon.

Answer:

Measuring spoon

Step-by-step explanation:

Answer and Step-by-step explanation:

To write the quadratic equation, we need to find the values of a, b, and c in the general form of a quadratic equation:

y = ax^2 + bx + c

Using the given data, we can plug in the x- and y-values to get a system of equations:

-12 = 16a - 4b + c

-5 = 9a - 3b + c

0 = 4a - 2b + c

We can solve this system of equations using substitution or elimination to get:

a = -1

b = 3

c = 4

Substituting these values into the general form of the quadratic equation, we get:

y = -x^2 + 3x + 4

Therefore, the quadratic equation from the table is:

y = -x^2 + 3x + 4

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On converting the weight , 151 lbs is equivalent to  68.492 Kilogram .

The Units of measuring weight are used to measure the mass or heaviness of an object. There are several units of measuring weight such as : Kilogram (kg) , Gram (g) , Pound (lb) .

We have to convert the weight 151 pounds (lbs) to kilograms (kg),

We use the conversion factor of 0.45359237 kg per pound.

We multiply the number of pounds by conversion factor to get the equivalent weight in kilograms.

By using this method, we get ;

⇒ 151 lbs × 0.45359237 kg/lb = 68.492 kg ;

Therefore, 151 pounds is equal to  68.492 Kilograms .

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The 55-gallon drum size is a popular choice for storing and transporting materials because it is convenient, cost-effective, and safe.

The size of the 55-gallon drum is not arbitrary. It is a standard size that has been adopted by industry and regulatory agencies for many practical reasons.

Firstly, the 55-gallon drum is a convenient size for handling and transport. It is large enough to hold a significant amount of material but still small enough to be moved around with relative ease. Its cylindrical shape makes it easy to roll and stack, which saves space and simplifies handling.

Secondly, the 55-gallon drum is a cost-effective option for storage and transport. Its size allows for efficient use of space and materials, which translates into lower costs for manufacturers and shippers.

Thirdly, the 55-gallon drum size is closely linked to regulatory standards. Many regulations and guidelines in the industry specify the use of 55-gallon drums for storing and transporting hazardous materials. This is because the size is considered to be a safe and manageable option for handling such materials.

Its dimensions have been standardized by industry and regulatory agencies, making it a common sight in many settings.

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Answer:

Therefore, adding 10 to the numerator is the better option if we want to increase the value of 46/224.

Step-by-step explanation:

To find which option will give a larger final number, we should calculate both the possibilities and compare them ,

Firstly,add 10 to the numerator

Now,

The new rational number will be,

(46 + 10) / 224

= 56 / 224

= 7 / 28

2ndly,

Add 10 to the denominator

The new rational number will be,

46 / (224 + 10)

= 46 / 234

After comparing these two rational numbers and converting them to decimals or simplify them ,

7 / 28

= 0.25

46 / 234

= 0.196581...

Since 0.25 is larger than 0.196581...,

Now,adding 10 to the numerator will result in a larger final number.

Therefore, adding 10 to the numerator is the better option if we want to increase the value of 46/224.

The greatest volume of mortar mix, she could make, is 1.5 cubic meters.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Mortar mix is made by mixing cement, sand, and quicklime in a ratio of 1:2:3.

Julie has 0.75 m³ of quicklime.

Let the volume of cement, sand, and quicklime be x, 2x, and 3x.

So,

3x = 0.75

Divide by 3 into both sides,

we get,

3x/3 = 0.75/3

x = 0.25

The total volume = the greatest volume of mortar mix

=  x + 2x + 3x

Substituting the value of x to the expression,

we get,

x + 3x + 3x = (0.25) + 2(0.25) + (90.25)

The greatest volume of mortar mix,

= 1.5 cubic meters.

Therefore, the required amount of volume is 1.5 cubic meters.

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The complete question:

Mortar mix is made by mixing cement, sand, and quicklime in a ratio of 1:2:3.

Julie has 0.75 m³ of quicklime.

She has plenty of sand and cement.

Work out the greatest volume of mortar mix she could make.