Paula bought a ski jacket on sale for $4 less than half its original price. She paid $89 for the jacket. What was the original price?

The required exponent form is obtained as 2 x 2 x 2 x 2 = 2⁴.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The given expression is 2 x 2 x 2 x 2.

It can be written in exponent form as,

2 x 2 x 2 x 2

The number 2 is multiplied to itself by four times,.

Thus, the exponent form is given as 2⁴.

Hence, the exponent form of the given expression is 2⁴.

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The algebraic expression for the given statement total number of hours present in y hours and 45 minutes is equal to ( y + 0.75 ) hours.

As given in the question,

Given statement is equal to :

The total number of hours present in y hours and 45 minutes .

Here we have to convert whole equation into hours we have :

1 hour = 60 minutes

⇒ 1 minute = ( 1 / 60 ) hours

⇒ 45 minutes = ( 45 / 60 ) hours

⇒ 45 minutes = 0.75 hours

Algebraic expression for the given statement in hours  is given by :

y hours and 45 minutes

= y hours + 45 minutes

= y hours + 0.75 hours

= ( y + 0.75 ) hours

Therefore, the algebraic expression for the given statement is given by

( y + 0.75 ) hours.

The complete question is:

Write an algebraic expression for the total number of hours in y hours and 45 minutes.

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Answer:

The conclusion is incorrect because there is exactly one solution to the equation.

Step-by-step explanation:

8x - 12 = 4(12x - 6)

4 x 12x = 48x    4 x -6 = -24

8x - 12 = 48x - 24

Move the terms

8x - 12 - 48x = -24

Move the constant to the right-hand side and change its sign

8x - 48x = -24 + 12

-40x = -24 + 12

-40x = -12

Divide both sides by -40

40x  =  -12

40    =   40

x = [tex]\frac{3}{10}[/tex]  or, alternate form, x = 0.3

a. The diagram that represents this situation is given by the image shown at the end of the answer.

b. The height of the building is of: 33.4 feet.

The three trigonometric ratios are defined as follows:

As shown by the diagram given at the end of the answer, this situation is represented by a right triangle in which:

Then the height of the building is calculated as follows:

tan(24º) = x/75

x = 75 x tangent of 24 degrees

x = 33.4 feet. -> height of the building.

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Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5

The closure property of addition states that the sum of two whole numbers will always be a whole number.

A whole number is a set of all positive integers from 0 to infinity.  Now we all know that if we add two positive numbers up, the sum will either remain constant (if the number is 0) or be greater than both numbers. This means that the sum of two whole numbers has to be a whole number.

Example 1 If we add 0 and 45

0 + 45

= 45

We already know that 45 is a whole number.

Example 2- If we add 486 and 354

486 + 354

= 840

From the definition, we can say that 840 is a whole number.

This is the closure property.

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The best prediction of the population in the year 2015 will be 4150

rate of decrease involves The rate of reduction expressing a decrease as a percentage of the initial value.To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100.

Given that an island's peasant population is falling at a rate of 1.7% per year,

A 1.7% decrease means that 98.3% will remain.

as a result, decrease = 0.983/year

A(t) = A(original) multiplied by (0.983)^t

As a result, after 6 years, A(6) = 4600 x (0.983)6 = 4150

As a result, the population in 2009 will be 4150.

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Answer:

Step-by-step explanation:

g

Step-by-step explanation:

16.            +.        5

__.                    ____
7(x+4).                7 (x-3)

Answer:

4.82803

Step-by-step explanation:

3 x 1.6

Yes, the sum of 2 whole numbers is always a whole number.

Any number that ranges from 0 to infinity with 1 as the denominator in its smallest form is called a whole number.

For example- 0, 3, 78, 9363, etc.

Now if we take up two numbers say 34 and 78.

34 + 78

= 112

According to the definition of the whole number, we can say that this is a whole number.

Another example can be 0 + 237

The sum is 237

which again is a whole number.

The last example can be 2365 + 930

= 3295

This too is a whole number.

Hence the sum of two whole numbers will always be a whole number.

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Answer:

.33m+65=C

Step-by-step explanation:

to solve the equation you will need to multipy .33 x the amount of miles drove after you get the answer for that you will need to add 65 then thats your final answer

118,813,760 different combination license plates can the country produce

Permutations and combinations:

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor. By considering the ratio of the number of desired subsets to the number of all possible subsets for many games of chance in the 17th century, the French mathematicians Blaise Pascal and Pierre de Fermat gave impetus to the development of combinatorics and probability theory.

Given that

In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the roman alphabet

X = 10 × 26 × 26 × 26 × 26 × 26

  = 10 × 11881376

  = 118,813,760

118,813,760 different combinations license plates can the country produce

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6% slope means on a run of 100 units, there is just a 6-unit rise. The basic definition of slope is the gradient or incline of the terrain.

A steep slope is an abrupt incline, and a gentle slope is a gradual incline. The river's route flows between the steep, forested hills and their softer counterparts.

This is accomplished by comparing the vertical and horizontal changes, which are frequently stated as rise/run.

Since "percent" or "%" denotes "out of 100" or "per 100," x% can be expressed as

For instance

You can come across a road sign that says "6% Grade" or "Steep Grade" while driving down a highway. The road's grade is essentially its slope, multiplied by 100.

6% thus equals 6/100.

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Because it permits one to assume that the sampling distribution of the mean would typically be normally distributed, the central limit theorem is helpful when examining big data sets. This makes statistical analysis and inference simpler.

Hypothesis :

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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The surface area of that part of the plane 10x+7y+z=4 inside the elliptic cylinder x^2/25+y^2/9=1 is equal to πab, where a=5 and b=3. Therefore, the surface area is equal to 45π.

Total area on a three-dimensional shape's surface is known as surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas of each face. Alternatively, you can write down the cuboid's length, width, and height and use the formula surface area (SA)=2lw+2lh+2hw.

The general formula for a cube's surface area is as follows: The area of the base plus the area of the cube's vertical surfaces will add up to the cube's total surface area. The cube's total surface area is calculated using the formula 6a2, where an is the side length.

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Answer:

Available credit = $2,416.42

Step-by-step explanation:

$1,374.90

$266.21

39.46

$903.01

Sum = $2,583.58

$2,583.58 was spent. Subtract this from $5,000 to find Marianne's available credit.

$5,000

- $2,583.58

Available credit = $2,416.42

There are two ways to find the remainder when a polynomial in x is divided by a binomial of the form x-r, the use of synthetic division or calculate P(r).

Synthetic division

The Synthetic division is a shortcut way of polynomial division, especially if we need to divide it by a linear factor. It is generally used to find out the zeroes or roots of polynomials and not for the division of factors.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

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By using Pythagoras' theorem the required length of the cable  is 85 feets.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case because it is opposite the angle of 90°.

The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of a right-angled triangle. Alternatively, the sum of the squares of a right triangle's two legs equals the square of its hypotenuse.

Given:

Height of the tower = 68 feet = perpendicular

distance of box form tower = 51 feet = base

Let's assume lenght of the cable = L = hypotenous

Acoording to the question by using Pythagoras' theorem,

[tex]hyp^{2}= perpendicular^{2} +base^{2} \\(L)^2 = (68)^2 + (51)^2\\L^2 = 4624 + 2601\\L^2 = 7225\\L =\sqrt{7225}\\L = 85 feet[/tex]

Hence by using Pythagoras' theorem the required length of the cable  is 85 feets.

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To graph a rational function on a graphing calculator, enter the equation into the Y= editor, then press the graph button. The calculator will display the graph of the rational function.

1. Enter the equation for the rational function into the Y= editor of your graphing calculator. Be sure to include all terms, coefficients, and operators.

2. Press the graph button. This will tell the calculator to generate the graph of the equation.

3. The calculator will display the graph of the rational function, including any asymptotes, zeroes, and intercepts.

4. Adjust the window settings as desired to get a better view of the graph. This can be done by pressing the WINDOW button, then setting the appropriate Xmin, Xmax, Ymin, and Ymax values.

5. Press the GRAPH button again to view the adjusted graph.

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On your entire strategy at the expiration of the contract if the stock price at that time is $81.50 then the profit is $2189.

A portfolio is a collection of financial investments like stocks, bonds, commodities, cash and cash equivalents, including closed-end funds and exchange traded funds.

A stock is a security that represents the ownership of a fraction of the issuing corporation. Units of stock are called "shares" which entitles the owner to a proportion of the corporation's assets the owner equal to how much stock they own.

We know that,

Profit on the strategy

        = Profit on the shares + Profit from long calls + Profit from short puts

        = 200(81.50 - 70) + 200(Max(81.50-72,0)-5.75) + 300(-Max(68 - 81.50,0)+2.87)

        = 2300 + 750 - 861

        = 2189

Therefore profit on strategy is $2189.

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The formula is = 7 and 3. It may be used to calculate the number regular mall boxes as well as the number of big boxes.

What is the world's most difficult arithmetic problem? A mathematical conundrum that has baffled mathematicians over decades is finally solved earlier this week. Diophantine Equation, sometimes referred to as the "sum of three cubes," is what it is: Find x, y, & z such that, for any k between 1 and 100, x3+y3+z3=k.

Let x= Number of small boxes , y = Number of large boxes.

As per given , 30x+55y=375 (i)

x+y=10 (ii)

Multiply (ii) by 30, we get

30x+30y=300 (iii)

Eliminate (iii) from (i), we get

25y=75

⇒ y= 3

Put y=3 in (ii), we get

x+3=10 ⇒ x=7

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Answer: 7

Step-by-step explanation:

Answer:

both cost the same price of 6 dollars for each

Step-by-step explanation:

we can make a system of equation

d- daylilies

o- ornamental glass

5d+5o=60

8d+5o=78

-8d.      -8d

5o=78-8d

5d+78-8d=60

-3d+78=60

     -78. -78

-3d= -18

/-3.   /-3

d=6

5(6)+5o=60

30+5o=60

-30.      -30

5o=30

/5.  /5

o=6

they both are 6 dollars each

hopes this helps

The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. A perpendicular line to Y = -4x + 7 would be Y = 4x + 7.

To find the equation of a line perpendicular to Y = -4x + 7, we need to switch the x and y variables and then change the sign of the slope.

The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Since the original equation has a slope of -4, the perpendicular line will have a slope of 4.

Therefore, the equation for the perpendicular line is y = 4x + b.

We can find the y-intercept by plugging in a point from the original equation.

For example, if we plug in (0,7), we get 7 = -4(0) + b, or b = 7.

Therefore, the equation for the perpendicular line is y = 4x + 7.

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Answer:

Step-by-step explanation:

0.0154, I think, I apologize if this is wrong.

Answer: 7w + 6

Step-by-step explanation:

Your question was "7w + 6". When we simplify this, we get 7w + 6. So your answer is 7w + 6.

The sample size be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence is 4148 , the correct option is (b)    .

In the question ,

it is given that ,

the confidence interval is 99% .

let us consider ,

A sociologist wishes to estimate the percent of the U.S. population living in poverty .

Here , preliminary estimate of population has been ,

p = q = 0.50 .

for given , 99% confidence interval z = 2.756 .

the error percent is 2% , the means E = 0.02  .

So , the required sample size (n) can be calculated using the formula ,

n = (0.50)(0.50)(2.576/0.02)²

n = 0.25 * 16589.44

n = 4147.36

n ≈ 4148 .

Therefore , the sample size is 4148 .

The given question is incomplete the complete question is

A sociologist wishes to estimate the percentage of the U.S. population living in poverty. What size sample should be obtained if she wishes the estimate to be within 2 percentage points with 99% confidence ?

(a) 2401

(b) 4148

(c) 1692

(d) 2.575

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The linear function decreases when x is between –6 and 0.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+2. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=2.

A function can be classified as:

From the graph is possible to see that the function decreases when x is between –6 and 0 because the values of y decrease with the increasing of x-values.

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