(Use -Inf or Inf, as necessary. Separate multiple intervals using commas.) (1) What are the x-coordinates of the relative minima of f(x)? 1.2988390765433158 (9) On what subintervals is f(x) concave up

Answer:

the answer is simple 4

Step-by-step explanation:

10n4 simple just like 10 to the 4th power

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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The new coordinates of point X after reflection over the y-axis and a rotation of 180° about the origin is (-3, 2) which is option C

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

If the point is reflected over the y-axis, the y coordinates do not change only the x-coordinate so the x coordinate will move 3 units ove the line of reflection from y = 0, which makes the new point to be ( 3, -2)

If the point rotates 180 about the origin, the new coordinates become the opposite of the old,

so 3 becomes -3 and -2 becomes 2.

So that the point after reflection and rotation is (-3, 2)

In conclusion the ne point after the linear transformation is (-3, 2)

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If the die is rolled one time, the probability of rolling a 2 is given as follows:

1/14.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability of rolling a 2 is given as follows:

1/14.

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Answer:

Vertex (2, 3)

Axis of Symmetry: x = 2

Step-by-step explanation:

You can look at the labeling from my last answer, the parabola is just upside down but it is still the same label.

Hope it makes sense :)

Answer:

Axis of Symmetry:  x = 2

Vertex:  (2, 3)

Step-by-step explanation:

find axis of symmetry:  x = -b/2a

x = -8 ÷ 2(-2)

x = 2

find vertex by substituting 2 for 'x':

y = -2(2²) + 8(2) - 5

y = -8 + 16 - 5

y = 8 - 5

y = 3

Vertex:  (2, 3)

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

f(x) = -2x – 7 ; if x < -5

-(x + 2)² + 6 ; if -5 ≤ x < 0

√(x) – 1 ; if x ≥ 0

Answer:

Function 1 is linear

Step-by-step explanation:

A linear is a straight line on the graph.

Answer:

No.

Step-by-step explanation:

Don't worry. Yes, your grade will decrease but won't go to 0.

Answer: It all depends on how weighted your final exam is on your overall grade compared to other assignments.

The sale price of a bottle of perfume, if its original price was $60.83 with a 12.4% discount, is $53.30.

The given:Original price of the bottle of perfume = $60.83Discount = 12.4%

We have to calculate the sale price of the bottle of perfume. Formula: Sale Price = Original Price − DiscountWe can use the above formula to solve the problem.

Therefore, the sale price of the bottle of perfume, if its original price was $60.83 with a 12.4% discount, is $53.30.

Summary:We need to calculate the sale price of the bottle of perfume given with original price of $60.83 and 12.4% discount. We used the formula, Sale Price = Original Price − Discount to calculate the sale price. Finally, the sale price of the bottle of perfume is $53.30.

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The z-score for the standard white light bulb is 1.50 while the z-score for the soft white light bulb is 1.43.

Given that standard white light bulbs have a mean life of 675 hours and a standard deviation of 50 hours while soft white light bulbs have a mean life of 700 hours and a standard deviation of 35 hours.

In a test at a local science competition, both light bulbs lasted 750 hours.

We are to determine which light bulb’s life span was more notable using z-scores.

Using the formula

z = (x - μ) / σ, the z-score for the standard white light bulb

= (750 - 675) / 50 = 1.50

The z-score for the soft white light bulb = (750 - 700) / 35 = 1.43

The z-score for the standard white light bulb is 1.50 while the z-score for the soft white light bulb is 1.43.

Therefore, the standard white light bulb’s life span is more notable than the soft white light bulb’s life span.

As for the second part of the question, a z-score is a measure of the number of standard deviations above or below the population mean.

A z-score of -2.50 is below the mean by 2.50 standard deviations, which implies that the quality control specialist's salary is significantly lower than the average salary of ASQ members.

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Answer:

44 pairs of boots

Step-by-step explanation:

As per two options given to Alice,

1). Wages of $33 for each day work + commission of $2.5 for every pair sold.

 If Alice sells x pairs of boots in a day, then total amount earned by Alice,

 = (33 + 2.5x)

2). Commission of $3.25 for every boot sold.

  If Alice sold x pairs of boots, total earnings of the day = 3.25x

If earning of Alice is equal in both the plans,

(33 + 2.5x) = 3.25x

3.25x - 2.5x = 33

0.75x = 33

x = 44

Therefore, for the sales of 44 pairs of the boots Alice will earn equal by both the plans.

Answer:

-4t^4+81

Step-by-step explanation:

(9-2t^2)(9+2t^2)

−4

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{540 \: m}}}}}\)

Step-by-step explanation:

Let the length and breadth be 5x and 4x respectively.

Area of rectangular field = 18000 m²

Finding the value of x

Area of rectangle = \( \sf{l \times b}\)

Plug the values

⇒\( \sf{18000 = 5x \times 4x}\)

Calculate the product

⇒\( \sf{18000 = 20 {x}^{2} }\)

Swap the sides of the equation

⇒\( \sf{20 {x}^{2} = 18000}\)

Divide both sides of the equation by 20

⇒\( \sf{ \frac{20 {x}^{2} }{20} = \frac{18000}{20} }\)

Calculate

⇒\( \sf{ {x}^{2} = 900}\)

Squaring on both sides

⇒\( \sf{x = 30}\)

Replacing the value of x in order to find the value of length and breadth

Length = \( \sf{5x = 5 \times 30 = 150 \: m}\)

Breadth = \( \sf{4x = 4 \times 30 = 120 \: m}\)

Finding the perimeter of the rectangular field

Perimeter of rectangle = \( \sf{2(l + b)}\)

plug the values

⇒\( \sf{2(150 + 120)}\)

Distribute 2 through the parentheses

⇒\( \sf{300 + 240}\)

Add the numbers

⇒\( \sf{540 \: m}\)

Hope I helped !

Best regards!!

Usando un sistema de ecuaciones, se encuentra que

Para el sistema, hay que:

$845 por 3 libros de Algebra, 5 libros de Geometría Analítica y 2 libros de Cálculo Diferencial, o sea:

\(3x + 5y + 3z = 845\)

$580 por 2 libros de Geometría Analítica, 4 libros de Algebra y 1 libro de Cálculo Diferencial, o sea:

\(4x + 2y + z = 580\)

$605 por un libro de Algebra, 3 libros de Geometría Analítica y 3 de Cálculo Diferencial, o sea:

\(x + 3y + 3z = 605\)

Reemplazando la segunda equación en las otras duas:

\(z = 580 - 4x - 2y\)

\(3x + 5y + 3z = 845\)

\(3x + 5y + 3(580 - 4x - 2y) = 845\)

\(-9x - y = -895\)

\(9x + y = 895\)

\(y = 895 - 9x\)

\(x + 3y + 3z = 605\)

\(x + 3y + 3(580 - 4x - 2y) = 605\)

\(-11x - 3y = -1135\)

\(11x + 3y = 1135\)

\(y = 895 - 9x\), por eso:

\(11x + 3(895 - 9x) = 1135\)

\(-16x = -1550\)

\(x = \frac{1150}{16}\)

\(x = 96.875\)

\(y = 895 - 9x = 895 - 9(96.875) = 23.125\)

\(z = 580 - 4(96.875) - 2(23.125) = 146.25\)

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B. |y| = 1.6

A sketch of the vector is attached to this response.

As shown, the vector lies on the second quadrant and its horizontal and vertical components are given by x and y respectively.

Where;

|x| = v cos θ              -----------------(i)

|y| = v sin θ               -----------------(ii)

and

v = magnitude of the vector = 2.5km/hr

θ = angle that the vector makes with the +x axis = 90° + 50° = 140°

To get the magnitude of the vector's vertical component

Substitute these values into equation(ii) as follows;

|y| = 2.5 sin 140°

|y| =  2.5 x 0.6428

|y| = 1.607

|y| ≅ 1.6 km/hr

Therefore, the vertical component of the vector has a magnitude of 1.6 km/hr.

Answer:

No solution

Step-by-step explanation:

The sides of the equation are unbalanced, therefore, the equation has no solution. Here's an example(The problem is not designed to mathematically make sense).

\(x + 1 = -y \times z\\(w)x+1-1=-y+(z)x-1\\0 = -b\)

Since the first side which was equal to 0 is unbalanced to the other side, the rule is that \(a = \mathrm{false\:if}\:a < 0\), and since this rule applies in such a scenario, the equation ends up having no solutions.

Hope this helps!

Not performing qualitative tests in duplicate can introduce certain risks and potential issues:

False positives: Without duplicate testing, there is a higher risk of obtaining false positive results. False positives occur when a test incorrectly indicates the presence of a particular characteristic or condition. Duplicate testing helps verify the accuracy and reliability of the results, reducing the chances of false positives.

False negatives: Similarly, not performing qualitative tests in duplicate increases the risk of false negatives. False negatives occur when a test fails to detect a characteristic or condition that is actually present. Duplicate testing provides an additional opportunity to identify any missed detections and reduces the likelihood of false negatives.

Variability and uncertainty: Qualitative tests can be subject to variability due to factors such as sample preparation, test conditions, or interpretation. Duplicate testing helps assess the consistency and reproducibility of the results, providing a measure of confidence and reducing uncertainty.

Quality control issues: Duplicate testing is an essential component of quality control protocols. It helps ensure the reliability and accuracy of the testing process and minimizes the potential for errors or inconsistencies. Not performing duplicate tests can compromise the overall quality control procedures, leading to compromised data and unreliable conclusions.

Validation and reproducibility: Duplicate testing is often required for validation purposes and to demonstrate the reproducibility of results. It helps establish the robustness and reliability of the testing method. Without duplicate testing, it becomes more challenging to validate and reproduce the results, which can undermine the credibility of the findings.

In summary, not performing qualitative tests in duplicate increases the risks of false positives, false negatives, variability, uncertainty, quality control issues, and challenges in validation and reproducibility. Duplicate testing plays a crucial role in ensuring the accuracy, reliability, and validity of qualitative test results.

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Answer:

786.6

Step-by-step explanation:

Anything to the ^0 is 1 so its 1 x 6.6 + 100 x 7.8

6.6 + 780

786.6

Answer:

786.6

Step-by-step explanation:

Problem:

(6.6 × 10⁰) + (7.8 × 10²)​

Step 1 - Parenthesis:

(6.6 × 10⁰) + (7.8 × 10²)​

Step 2 - Exponents(Left to Right):

(6.6 × 10^0) + (7.8 × 10^2)​ = (6.6 × 1) + (7.8 × 100)

Step 3 - Multiply(Left to Right):

(6.6 × 1) + (7.8 × 100) = 6.6 + 780

Step 4 - Add(Left to Right)

6.6 + 780 = 786.6

Step 5 - Answer:

786.6

Parenthesis

Exponents(Left to Right)

Multiplication(Left to Right)

Division(Left to Right)

Addition(Left to Right)

Subtraction(Left to Right)

Answer:

C) -∏

Step-by-step explanation:

because then you get 0 which is a rational number

Answer:

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you 1. 2 M, 2R, 2 P are placed in shelf randomly P(similar a…

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Transcribed image text: Your Turn Find the probability using permutation with repetition 1. There are 2 mystery books, 2 romance books, 2 poetry books to be randomly placed on a shelf. What is the probability that the mystery books are next to each other, the romance books are next to each other, and the poetry books are next to each other? (For example, MMRRPP). 2. The school jazz band has 4 boys and 4 girls, and are randomly lined up for a yearbook photo. Find the probability of getting all of the boys grouped together.

Step-by-step explanation:

CORRECT ME IF IM WRONG

Answer:

12 pies

Step-by-step explanation:

72 divided by 6

The length of the credit card is either l = 8.5 or l = -5.5. Since length can't be negative, we know that: l = 8.5

First, we need to use the given information to set up an equation for the length and width of the credit card. We know that the width w is 3 centimeters shorter than the length l, so we can write:

w = l - 3

We also know that the area of the credit card is 46.75 square centimeters, which can be expressed as:

A = lw = 46.75

Now we can use these equations to solve for the length and width. Substituting the first equation into the second equation, we get:

(l - 3)l = 46.75

Expanding the left side, we get:

l^2 - 3l = 46.75

Rearranging and factoring, we get:

(l - 8.5)(l + 5.5) = 0

So the length of the credit card is either l = 8.5 or l = -5.5. Since length can't be negative, we know that:

l = 8.5

Using the first equation, we can then find the width:

w = l - 3 = 8.5 - 3 = 5.5

Now we can find the perimeter by adding up the four sides of the credit card:

P = 2l + 2w = 2(8.5) + 2(5.5) = 17 + 11 = 28

So the perimeter is 28 centimeters.

To solve this problem, we'll first use the given information to find the width (w) and length (l) of the credit card. Then, we'll calculate the perimeter using the formula: Perimeter = 2 * (length + width).

Given that the width (w) is 3 centimeters shorter than the length (l), we can express this as:

w = l - 3

We are also given the area of the credit card, which is 46.75 square centimeters. The area can be calculated as:

Area = length * width
46.75 = l * (l - 3)

Now, let's solve for l:

46.75 = l^2 - 3l
l^2 - 3l - 46.75 = 0

Solving this quadratic equation, we get:

l ≈ 7.25 cm

Now that we have the length, we can find the width:

w = l - 3
w = 7.25 - 3
w ≈ 4.25 cm

Finally, we can calculate the perimeter using the formula:

Perimeter = 2 * (length + width)
Perimeter = 2 * (7.25 + 4.25)
Perimeter ≈ 23 cm

So, the perimeter of the credit card is approximately 23 centimeters.

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Answer:

267 km

Step-by-step explanation:

\(\frac{396}{132}\) => 3

3 x 89 -> 267 km on 89 liters

hi

as consumption is proportional to distance we have :  

 132  =  396

   89 =    ?  

? =   89*396  / 132 =  267

with 89 liters  of gasoline, boat goes 267 km.

We can use the Z-score formula to determine what percent of patients have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

The Z-score formula is:

Z = (X - M) / SD

Where:

X = Patient's score (45)

M = Mean score (52)

SD = Standard deviation (5)

Plugging in the given values:

Z = (45 - 52) / 5

Z = -7 / 5

Z = -1.4

This Z-score of -1.4 corresponds to a percentage of approximately 9.1% of patients who have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

It is important to note that this percentage is approximate, as it's calculated based on the standard normal distribution table which provides approximate values, and it assumes the scores of the test are normally distributed, in case this assumption is not met the result may not be accurate.

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To determine the three angles in a triangle, we can use the Law of Cosines or the Law of Sines. However, since we are not given any side lengths, we will use the dot product formula to find the angles between the sides.

Then, we can compute the magnitudes of these vectors using the Pythagorean theorem:

|AB| = sqrt((Bx - Ax)^2 + (By - Ay)^2)
|AC| = sqrt((Cx - Ax)^2 + (Cy - Ay)^2)
|BC| = sqrt((Cx - Bx)^2 + (Cy - By)^2)

where (Ax, Ay), (Bx, By), and (Cx, Cy) are the coordinates of points A, B, and C, respectively.

Finally, we can use the dot product formula above to compute the cosines of angles A, B, and C, and then take the inverse cosine to find the angles in radians:

A = acos((AB · AC) / (|AB| · |AC|))
B = acos((AB · BC) / (|AB| · |BC|))
C = acos((AC · BC) / (|AC| · |BC|))

where acos denotes the inverse cosine function.

Therefore, we can determine all three angles in the triangle (in radians) using the above formulae.
It seems that the three points of the triangle were not provided in your question. To help you determine the angles of the triangle, please provide the coordinates of the three points (A, B, and C).

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The most appropriate choice for congruency of triangles will be given by -

Congruent Corrosponding parts

PQ = SR

QR = ST

PR = RT

∠QPR = SRT

∠QRP = ∠STR

∠PQR = ∠RST

What is congruency of triangle?

Two triangles are said to be congruent if all the corrosponding sides and corrosponding angles of the triangles are equals.

There are five axioms of congruency of triangles. They are-

SSS axiom, ASA axiom, AAS axiom, RHS axiom, SAS axiom

Here,

\(\Delta PQR \cong \Delta TSR\\\)

Congruent Corrosponding parts

PQ = SR

QR = ST

PR = RT

∠QPR = SRT

∠QRP = ∠STR

∠PQR = ∠RST

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Answer:

20

Step-by-step explanation:

5+0.65t=10+0.45t

0.25t=5

t=20