Find the proper answer

Answer:

\(x=-\dfrac{1}{6}\)

Step-by-step explanation:

For a quadratic function in standard form  \(y=ax^2 + bx + c\), the axis of symmetry can be expressed as \(x=\dfrac{-b}{2a}\)

For the equation \(y=3x^2+x\)

\(a=3, b=1, c=0\)

Therefore, the axis of symmetry is \(x=-\dfrac{1}{6}\)

In the scenario where she does the hypothesis test, the student should take into account the decision to reject H0 and the P-value.

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis.

We can make probabilistic claims regarding population parameters through hypothesis testing.

The null hypothesis would be that 50% is true, and the alternative hypothesis would be that 50% is untrue, if someone wanted to test, for instance, whether a penny has an exact 50% chance of landing on heads.

There are 4 ways to test a hypothesis.

The student should incorporate the choice to reject H0 and the P-value in e the scenario in which she conducts the hypothesis test.

Therefore, in the scenario where she does the hypothesis test, the student should take into account the decision to reject H0 and the P-value.

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In complex analysis, the orbit of a complex number refers to the sequence of numbers produced when a function is iteratively applied to the number. In other words, it is the sequence of numbers obtained by repeatedly applying a function to a starting complex number.

The orbit of a complex number under iteration can provide information about the behavior of the function being iterated.

For example, it can help determine if the function converges or diverges, if it has any fixed points or periodic points, or if it exhibits chaos or other complex behavior.

The orbit can also be graphed in the complex plane, with each point in the sequence represented as a dot or a line connecting the dots.

This can provide a visual representation of the behavior of the function and the points that it converges to or diverges from.

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Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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The constant rate of change of the surface area of the circle would be 14 feet per second.

The circumference of a circle is defined as the area round the circle which is also the perimeter of the circle. The formula that is used to find the circumference of a circle;

Circumference= 2πr

where r= 7 feet

π = 22/7

circumference= 2×22/7×7

= 308/7 = 44ft

The surface area of circle= πr²

= 22/7 ×7²

= 1078/7

= 154feet²

The rate of change for circumference;

44ft = 4ft/sec

154 ft = X

Make X the subject of formula;

X = 154 × 4/44

X = 616/44

X = 14 feet per second.

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To evaluate 2^2 × 2^2, we can simplify it using the properties of exponents Therefore, the final answer is 16.

To evaluate 2^2 × 2^2 , we can use the property of exponents that states, "When multiplying two numbers with the same base, you add the exponents." In this case, the base is 2, and the exponents are both 2. Applying the property, we have:

2^2 = 2× 2=4

Adding the exponents, we get:

4 × 4

Now, 2 raised to the power of 4 can be computed as:

4 × 4= 16

Therefore,

2^2 × 2^2 = 16

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Question

Evaluate the equation 2^2 × 2^2.

Since the current price of $440 results from a discount of 18% on the original price, $440->100-18=82%. Thus,

Solving for x,

Once rounded, the answer is $536.59

An integral calculator with steps is a tool that allows you to compute integrals of functions and provides a step-by-step solution to the problem.

This type of calculator is especially useful for students learning calculus, as it allows them to see how the integral is computed and helps them to understand the underlying concepts and techniques.

To use an integral calculator with steps, you typically enter the function you want to integrate and the limits of integration. The calculator then applies a variety of techniques to compute the integral, such as substitution, integration by parts, partial fractions, or trigonometric substitutions.

The output of the calculator usually includes the solution to the integral, as well as a detailed explanation of the steps involved in the computation. Some calculators may also provide graphs of the function and the area under the curve.

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Answer:

y = 1

Step-by-step explanation:

the equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through

the line passes through (- 8, 1 ) and (7, 1 )

both with y- coordinates of 1 , then

y = 1 ← is the equation of the line

What is the question?

The volume of the given solid is πa³/4 cubic units.

Given that the base of a solid is a quadrant of a circle of radius a and each cross-section perpendicular to one edge of the base is a semicircle whose diameter lies in the base.

To find the volume of the solid, we'll integrate the area of the cross-section over the height of the solid.

Let us consider a cross-section with thickness dx at a distance x from the vertex of the quadrant, as shown in the figure below.

Here, the diameter of the semicircle forming the cross-section is 2(x + a).

Therefore, the radius of the semicircle is (x + a).

Area of the cross-section = Area of the semicircle= π[(x + a)²]/2

Volume of the solid = ∫Area dx from 0 to a= ∫π[(x + a)²]/2 dx from 0 to a= π/2 ∫(x² + 2ax + a²) dx from 0 to a= π/2 [(a³/3 + 2a²/2 + a³/2) - (0)] = πa³/4 cubic units

Therefore, the volume of the given solid is πa³/4 cubic units.

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Answer:

38.91

Step-by-step explanation:

link to awnswer:

https://quizlet.com/362606734/applying-tax-and-tip-remember-to-always-round-up-flash-cards/

Answer:

38.59

Step-by-step explanation:

O>o

The length  of LM is approximately 4.8 cm to the nearest 10th of a centimeter.

How to find angle of the triangle ?

To find the angle of a triangle, you need to know the lengths of its sides or the relationship between the lengths of its sides. There are different methods for finding angles depending on the information you have about the triangle. Here are a few examples:

Law of sines: If you know the lengths of two sides of a triangle and the angle between them, you can use the law of sines to find the angle opposite the longer side. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. So, you can set up the equation:

sin(A) / a = sin(B) / b

where A and B are the angles opposite the sides a and b, respectively. Solve for the angle A to find the measure of the angle.

Law of cosines: If you know the lengths of all three sides of a triangle, you can use the law of cosines to find the angle opposite the longest side. The law of cosines states that:

c² = a² + b² - 2ab*cos(C)

where c is the length of the longest side (the side opposite angle C), and a and b are the lengths of the other two sides. Solve for cos(C) and then use the inverse cosine function to find the measure of angle C.

Right triangles: If you have a right triangle, you can use the properties of right triangles to find the angles. The sum of the measures of the two acute angles in a right triangle is always 90 degrees, so if you know one of the acute angles, you can find the other one by subtracting it from 90 degrees.

These are just a few methods for finding angles in a triangle. There are many other techniques depending on the specific information you have about the triangle.

To find the length of LM, we can use the law of sines which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. That is,

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite those sides.

In this case, we know the length of KL is 1.2 cm, and we want to find the length of LM. Let's call the length of LM x. Then, we can use the law of sines to set up the following equation:

1.2/sin(93°) = x/sin(81°)

Solving for x, we get:

x = (1.2 × sin(81°)) / sin(93°)

Using a calculator, we get:

x ≈ 4.8 cm

Therefore, the length of LM is approximately 4.8 cm to the nearest 10th of a centimeter.

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Answer:

draw a diagram, ASA law of sines, find another angle, plug in, opposite sides go together.

≈1.2133≈1.2

Answer:

8 : 6 , 16 : 12 , 24 : 18

Answer:

8 : 6 12 : 9 16 : 12  

Step-by-step explanation:

Answer:

the cost of the tire=341.4$

Point B is not the midpoint of line AC, because angle AOB is not half of angle  AOC.

If point B is the midpoint of line AC, then angle AOB must be equal to angle  BOC.

The value of angle AOC is calculated as follows;

let angle AOC = θ

cos θ = 100 yds / 500 yds

cos θ = 0.2

θ = cos⁻¹ (0.2)

θ = 78.5⁰

The value of length AC is calculated as follows;

AC = √ (500² - 100²)

AC = 489.9

If point B is the midpoint, then AB = BC = 489.9/2 = 244.95

The value of angle AOB is calculated as follows;

tan β = AB/AO

tan β = 244.95/100
tan β = 2.4495

β = arc tan (2.4495)

β = 67.8⁰

Half of angle AOC = 78.5⁰/2 = 39.25⁰

β  ≠ 39.25⁰

So point B is not midpoint of line AC, since angle AOB is not half of angle  AOC.

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Answer:

c

Step-by-step explanation:

Based on the given information, the question is asking about the apparent relationship between two variables: study hours and test score. The correct answer is c.

Test score tends to increase as the number of study hours increases. This suggests a positive correlation between the two variables, meaning that as one variable (study hours) increases, the other variable (test score) also tends to increase.
The apparent relationship between the two variables under consideration, which are study hours and test score, can be described as follows:
Your answer: c. Test score tends to increase as the number of study hours increases.
This is because, generally, the more time a person spends studying, the better their understanding of the material, which often leads to a higher test score.

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The height of the tree is approximately 48 feet.

In the given situation, we have a girl standing 40 feet away from a tree. She sights along a yardstick, and when the bottom of the yardstick is 4 feet from her eye, she aligns the top of the yardstick with the top of the tree.

To find the height of the tree, we can create a right triangle. The girl's eye, the bottom of the yardstick, and the top of the tree form the three vertices. The distance from the girl's eye to the bottom of the yardstick is 4 feet, and the distance from the girl to the tree is 40 feet.

Using the concept of similar triangles, we can set up the proportion:

(height of the tree) / (distance from the girl to the tree) = (length of the yardstick) / (distance from the girl to the bottom of the yardstick)

Let's substitute the given values:

(height of the tree) / 40 = 3 / 4

Cross-multiplying, we get:

(height of the tree) = (40 * 3) / 4 = 120 / 4 = 30 feet

Therefore, the height of the tree is approximately 48 feet.

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Answer:

b is the correct answer

A vector that is not in the span(B) can be found by creating a linear combination of the basis vectors in B that does not yield the desired vector.

The set B = {<1,0,0,0>, <0,1,0,0>, <1,0,0,1>, <0,1,0,1>} is being considered as a basis set for 4D vectors in R^4. To find a vector not in the span(B), we need to find a vector that cannot be expressed as a linear combination of the basis vectors in B.

One approach is to create a vector that has different coefficients for each basis vector in B. For example, let's consider the vector v = <1, 1, 0, 1>. We can see that there is no combination of the basis vectors in B that can be multiplied by scalars to yield the vector v. Therefore, v is not in the span(B), indicating that B does not span all of R^4.


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The average value of the function f(x) = \(9 - x^2\) over the interval [-3, 3] is 6.0000. The values of x in the interval for which the function equals its average value are x = -2.4495 and x = 2.4495.

To find the average value of a function over an interval, we need to calculate the definite integral of the function over the interval and divide it by the length of the interval. In this case, we have the function

f(x) = \(9 - x^2\) and the interval [-3, 3].

First, we calculate the definite integral of f(x) over the interval [-3, 3]:

\(\(\int_{-3}^{3} (9 - x^2) \, dx = \left[9x - \frac{x^3}{3}\right] \bigg|_{-3}^{3}\)\)

Evaluating the definite integral at the upper and lower limits gives us:

\(\((9(3) - \frac{{3^3}}{3}) - (9(-3) - \frac{{(-3)^3}}{3})\)\)

= (27 - 9) - (-27 + 9)

= 18 + 18

= 36

Next, we calculate the length of the interval:

Length = 3 - (-3) = 6

Finally, we divide the definite integral by the length of the interval to find the average value:

Average value = 36/6 = 6.0000

To find the values of x in the interval for which the function equals its average value, we set f(x) equal to the average value of 6 and solve for x:

\(9 - x^2 = 6\)

Rearranging the equation gives:

\(x^2 = 3\)

Taking the square root of both sides gives:

x = ±√3

Rounding to four decimal places, we get:

x ≈ -2.4495 and x ≈ 2.4495

Therefore, the values of x in the interval [-3, 3] for which the function equals its average value are approximately -2.4495 and 2.4495.

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Answer: 12.5

Step-by-step explanation:

Given all the weights and the total capacity of the elevator, we have the following expression:

where 'x' denotes the weight of the third case.

Solving for x, we get the following:

therefore, the third case must weigh 60.3 kg or less.

The correct true statement is the swimmer comes back up 9 seconds after the timer was started.

The maximum height of a function is the  point where the velocity the body is zero.

Given the function that represent the height of the swimmer as  h(t)=t^2−12t+27

If the velocity of the function is zero, hence;

h'(t) = 2t - 12

0 = 2t - 12

2t = 12

t = 6secs

Substitute t = 6 into the function as shown:

h(6) = 6^2−12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.

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The mass of ingredient is given by 66g, 45g, 100g, 150g.

What is mass?

Mass is a parameter of measurement that calculates how much matter is contained in a body.

Mass is a physical quantity. Mass is measured in terms of the weight of a body. Gram, kilogram, and pounds are some standard mass units to measure it. The SI unit of mass is the kilogram; however, smaller objects are measured in grams.

Given, the ratio of the ingredients by mass as 2:2:1.

Let x be the mass of the ingredients.

A) total mass is given by 330g

therefore, 2x+2x+1x = 330

5x = 330

x = 330/5

x = 66

Hence the mass of oat = 2(66) = 132g

mass of cereal = 2(66) = 132 g

mass of nuts = 66g

B) 2x+2x+1x = 210

5x = 210

x = 210/5

x = 42g

Hence,  the mass of oat = 2(42) = 84g

mass of cereal = 2(42) = 84 g

mass of nuts = 84

C) 2x+2x+1 = 500

5x = 500

x = 100

hence,  the mass of oat = 2(100) = 200g

mass of cereal = 2(100) = 200 g

mass of nuts = 100g

D) 2x+2x+1 = 750g

5x = 750

x = 750/5

x = 150

Hence, the mass of oat = 2(150) = 300g

mass of cereal = 2(150) = 300 g

mass of nuts = 150g

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Answer:

A

Step-by-step explanation:

the other options have a common difference

Answer:

A is not arithmetic series

Step-by-step explanation:

In B,C and D there is arithmetic series as a2-a1=a3-a2

In A. there is no such series.....

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the  t-value (-1.732) is less than the critical value (-2.429).

Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.

Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.

Level of significance = 1%

We can use a one-sample t-test to test the hypothesis.

t = (X - μ) / (s / √n)

where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Substituting the values, we get

t = (998,946 - 1,000,000) / (23,876 / √65)

t = -1.732

Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.

Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.

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