(Chapter 13) If |r(t)| = 1 for all t, then r'(t) is orthogonal to r(t) for all t.

Answer:

Step-by-step explanation:

There are two consecutive positive even integers such that the square of the first is 364 more than five times a second. What are the two numbers?

Two consecutive year positive integers are represented by

x and x + 1

First integer = x

Second integer = y

There are two consecutive positive even integers such that the square of the first is 364 more than five times a second.

This is represented mathematically as:

x² = 364 + 5(x + 1)

x² = 364 + 5x + 5

x² -5x -5 - 364

x² - 5x - 369

Answer:

3.6%, 6/17, 0.36

Step-by-step explanation:

Convert to decimal:

6/17 ≈ 0.3529

0.36 = 0.36

3.6% 3.6/100 = 0.036

Order:

0.036, 0.3529, 0.36

Hope this helps.

Answer:  y=1/2x+-4

(You cant give a certain number of points btw)

A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer:

24099000

Step-by-step explanation:

To find the percentile rank using the mean and standard deviation, you need to calculate the z-score and then use the z-table to determine the corresponding percentile rank.

To find the percentile rank using the mean and standard deviation, you can follow these steps:

1. Determine the given value for which you want to find the percentile rank.
2. Calculate the z-score of the given value using the formula: z = (X - mean) / standard deviation, where X is the given value.
3. Look up the z-score in the standard normal distribution table (also known as the z-table) to find the corresponding percentile rank. The z-score represents the number of standard deviations the given value is away from the mean.
4. If the z-score is positive, the percentile rank can be found by looking up the z-score in the z-table and subtracting the area under the curve from 0.5. If the z-score is negative, subtract the area under the curve from 0.5 and then subtract the result from 1.
5. Multiply the percentile rank by 100 to express it as a percentage.

For example, let's say we want to find the percentile rank for a value of 85, given a mean of 75 and a standard deviation of 10.

1. X = 85
2. z = (85 - 75) / 10 = 1
3. Looking up the z-score of 1 in the z-table, we find that the corresponding percentile is approximately 84.13%.
4. Multiply the percentile rank by 100 to get the final result: 84.13%.

In conclusion, to find the percentile rank using the mean and standard deviation, you need to calculate the z-score and then use the z-table to determine the corresponding percentile rank.

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Answer:

<2 <4 <5

Step-by-step explanation:

When two lines are parallel and crossed by a transversal, the opposite interior angles are congruent.

The ratio strength of the final product is 1:0.4.

One technique to indicate concentration is through ratio strength, which uses a ratio to characterize drug concentration. In this context, concentration is defined as the quantity of a solute that makes up one unit in the whole volume of a solution or combination. You should be an expert in ratio strength calculations as a pharmacy student. Ratio strength uses a ratio to describe the medication concentration. So, what it implies is, you have one unit of solute contained in the complete amount of preparation and so generally your ratio strength is expressed as one is to something. In the case of a weight-in-weight, volume-in-volume, or weight-in-volume situation, you would interpret a ratio of 1:2,000 differently.

Drug strength = 800mg

whole volume =2ltrs

The ratio of the solution in 1 ltr is = 400 mg

The ratio strength of the solutions is = 1:0.4

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The confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.

A trait that cannot be quantified is referred to as a categorical variable (also known as a qualitative variable).

Nominal or ordinal categorical variables are also acceptable.

Since the variable of interest is a person's opinion, which is a qualitative variable, the confidence interval for a proportion should be built.

Statistical Variables Qualitative variables also referred to as categorical variables are variables without a built-in sense of hierarchy.

As a result, they are quantified using a nominal scale.

For instance, a qualitative variable is a name as well as hair color (Black, Brown, Gray, Red, Yellow).

Therefore, the confidence interval for a proportion should be constructed since the variable of interest is a person's opinion, which is a qualitative variable.

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To find out how the amount of fabric required to make the cylindrical bag compares to the amount of fabric required to make the square-based-prism bag, we can use the formula for the surface area of each shape.

The amount of fabric required to make a bag is proportional to its surface area. Therefore, we can compare the surface areas to determine which bag will require more fabric. Let's assume the dimensions of each bag are as follows:

Cylindrical bag: height = 10 inches,

radius = 5 inches
Square-based-prism bag: height = 10 inches,

base length = 6 inches,

base width = 6 inches

Now, let's find the surface areas of each bag:

Surface area of cylindrical bag = 2πrh + 2πr²
= 2π(10)(5) + 2π(5)²
= 100π + 50π
= 150π square inches

Surface area of square-based-prism bag = 2lw + 2lh + 2wh
= 2(6)(6) + 2(6)(10) + 2(6)(10)
= 72 + 120 + 120
= 312 square inches

Therefore, the square-based-prism bag requires more fabric than the cylindrical bag.

Next, let's find out how much each bag will hold. We can use the formula for the volume of each shape to find out. The volume of each bag will give us an idea of how much they can hold.

Volume of cylindrical bag = πr²h
= π(5)²(10)
= 250π cubic inches

Volume of square-based-prism bag = lwh
= 6(6)(10)
= 360 cubic inches

Therefore, the square-based-prism bag can hold more than the cylindrical bag.

Based on this information, the cpm sports company should make the square-based-prism bag if they want to maximize the amount of items each bag can hold.

However, if the company is more concerned with using less fabric to make each bag, then they should make the cylindrical bag. The decision ultimately depends on the company's priorities and goals.

The amount of fabric required to make the cylindrical bag is less than the square-based-prism bag. However, the square-based-prism bag can hold more than the cylindrical bag.

The cpm sports company should make the square-based-prism bag if they want to maximize the amount of items each bag can hold.

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Answer:

GCF = x

Step-by-step explanation:

The greatest common factor is "x"

\(5\,x^2+3\,x=x\,(5x+3)\)

it is the only common factor we can extract from both terms

Marta's theory lacks practical significance or real-world applicability.

Marta's theory suggests that filling out a job application in crayon leads to a lower probability of being hired.

However, she mentions that almost nobody fills out an application in crayon.

This means that the finding or theory has no practical significance because it doesn't affect a significant number of people or have a real impact in real-world scenarios.

If the vast majority of job applicants do not use crayon to fill out their applications, Marta's theory becomes inconsequential because it doesn't provide any meaningful insight or guidance for job seekers.

The theory lacks practical significance because it doesn't have any practical implications or relevance in the context of job applications and hiring processes.

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Answer:

sin (0.35) = 0.57638, cos (0.35) = 0.96512, and tan (0.35) = 0.67578

These values can be found by going to the 'Calculator' tab and entering the values for 'Sine', 'Cosine' and 'Tangent' as shown above.

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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This refers to the tax paid to a governing body for the sales of certain goods and services.

In  Williamson County, the sales tax rate is 9.75% = 9.75% × $1,000 = $1,097.5

In Davidson County , the sales tax rate is 9.25% =  9.25%  × $1,000 = $1,092.5

The amount saved will therefore be $1,097.5 - $1,092.5 = $5.

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Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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Answer:

A

Step-by-step explanation:

- \(\frac{1}{2}\) (x + 3) > x - 3 ( multiply both sides by 2 to clear the fraction )

- (x + 3) > 2x - 6 ← distribute parenthesis on left side by - 1

- x - 3 > 2x - 6 ( subtract 2x from both sides )

- 3x - 3 > - 6 ( add 3 to both sides )

- 3x > - 3

divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity

x < 1

Answer:

A. x<1

Step-by-step explanation:

-1/2 (x+3) > x - 3

(-1/2)x-3/2>x-3

Multiply both sides by 2:

-x-3>2x-6

add both sides by 3:

-x-3+3>2x-6+3

-x>2x-3

minus both sides by 2x

-x-2x>2x-2x-3

-3x>-3

x<1

The value of x and z are x° = 6.71°, z° = 75.26° simulataneously,

What is the linear pair angles?

Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.

We have,

Angles:

6x° + 35°

z°

8x° + 51°

To find the values of x and z

from the given figure

Linear pair angles:

6x° + 35° + 8x° + 51° = 180

14x° + 86° = 180

14x° = 180° - 86°

14x° = 94°

x° = 94°/14°

x° = 6.71°

Vertically opposites angles are equal

6x° + 35° = z°

z° =  6( 6.71°)° + 35

z° = 40.26 + 35

z° = 75.26°

Hence, the value of x and z are x° = 6.71°, z° = 75.26° simulataneously.

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Answer:

AC=42

EB=21

BC=26

thats all i know, sorry hope u figure it out

Step-by-step explanation:

The sides are AC = 42, EB = 21, BC = 26, AB = 38 and the measures of angles are ∠ADC = 90°, ∠ABD = 38°, ∠BCA = 52°, ∠DEC = 104°.

Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles

Given is a rectangle ABCD.

AC and BD are diagonals intersecting at E.

Given  DB=42, AD=26 and m ∠DAE=52°

(a) Diagonals of a rectangle are of equal length.

AC = DB = 42

(b) Diagonals of a rectangle bisect each other.

DE = EB = DB / 2 = 42/2 = 21

(c) Opposite side are equal.

BC = AD = 26

(d) Using Pythagoras theorem,

AB = \(\sqrt{(AC)^2-(BC)^2}\) = \(\sqrt{42^2-26^2}\) = 37.947 ≈ 38

(e) Measure of all the interior angles in a rectangle is 90°.

So, ∠ADC = 90°

(f) Given ∠DAE = 52°

∠BAE = 90° - 52° = 38°

ΔBAE is an isosceles triangle, since the two sides which are the bisectors of the diagonals are equal.

So, ∠ABD = ∠BAE = 38°

(g) ∠BCA = ∠DAE [Alternate interior angles]

∠BCA = 52°

(h) Sum of interior angles of a triangle is 180°.

∠DEC + ∠BDC + ∠ACD = 180°

∠BDC = ∠ABD = 38° and ∠ACD = ∠BAE = 38°

∠DEC = 180° - (38° + 38°)

          = 104°

Hence the measures are found.

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Answer:

14,000

Step-by-step explanation:

13,649

the 6 in the hundredths place rounds up therefore the 3 in the thousands place turns into a 4

Yes, its a rectangle because it has one right angle. A rectangle is a shape having all sides 90° and pair of two opposite same sides.

Answer:

bk

Step-by-step explanation:

jlvlivh

Answer:

dunno what the other guy said but I'm pretty sure the answer is -12/11, or -1.09.

The angle x of the isosceles triangle is 64 degrees.

The side and angle of the similar polygon are 7.5 units and 20 degrees.

The triangle above is an isosceles triangle. An isosceles triangle is a triangle that has 2 sides equal to each other and two angles equal to each other.

Therefore, the base angle of the isosceles triangle are equal.

Hence,

52 + x + x = 180

52 + 2x = 180

2x = 180 - 52

2x = 128

x = 128 / 2

x = 64 degrees

Similar polygons are two polygons with the same shape, but not the same size.  Similar polygons have corresponding angles that are congruent, and corresponding sides that are proportional.

Therefore, let's find x and y in the polygon.

x / 5 = 6 / 4

cross multiply

4x = 30

x = 30 / 4

x = 7.5

y - 73 = 360 - 90 - 61 - 116

y - 73 = 93

y = 93 - 73

y = 20

Therefore, the angle x of the isosceles triangle is 64 degrees and the sides x of the polygon is 7.5 units and the angle y of the polygon is 20 degrees.

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Check the picture below.

\(2a=8\sqrt{2}\implies a=\cfrac{8\sqrt{2}}{2}\implies a=\cfrac{8}{\sqrt{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 45-45-90 rule}}{a=x\sqrt{2}\implies} \cfrac{8}{\sqrt{2}}=x\sqrt{2}\implies \cfrac{8}{\sqrt{2}\cdot\sqrt{2}}=x\implies \cfrac{8}{2}=x\implies \boxed{4=x}\)

Answer:

rise over run (change in y divided by change in x)

so it would go as follows

\(\frac{(3-1)}{(4-9)}\)

= \(\frac{2}{-5}\)

= \(-\frac{2}{5}\)

Answer: - (2/5)

Step-by-step explanation:

(y2-y1) / (x2- x1) =

(1-3) / (9-4)

= - (2/5)

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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Answer:

B. Going up the elevator 14 floors

Step-by-step explanation:

Choice A can't be right because you are going below sea level (negative).

Choice C can't be correct either because the word "losing" let's you know that it's negative.

Choice D isn't right because if you are taking $20 from your checking account, it would be a negative number.

Hope this helps!

Answer:

2.61625

Step-by-step explanation:

Answer:

b. 9 (5+8)

Step-by-step explanation:

Answer:

Step-by-step explanation: (5+9)