Please answer this.. ​

To find the value of "a", we assumed that the total area under the density function is equal to 1, since this is a continuous probability distribution. The value of "a" that satisfies the conditions is a = ∛(5) ≈ 1.71.  

The integral of the density function over its entire domain should be equal to 1:

∫[1,a] x^3 dx = 1

Using the power rule of integration:

[1/4 x^4]_1^a = 1

Substituting the limits of integration and simplifying:

1/4 a^4 - 1/4(1)^4 = 1

1/4 a^4 - 1/4 = 1

1/4 a^4 = 5/4

a^4 = 5

Taking the fourth root of both sides:

a = ∛(5)

Therefore, the value of "a" that satisfies the conditions is a = ∛(5) ≈ 1.71.

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Answer: \(\lim_{x \to \infty} (\frac{sinh(x)}{e^x})\)\(= 0\)

Step-by-step explanation:

\(\lim_{x \to \infty} (\frac{sinh(x)}{e^x})\)

\(\lim_{n \to \infty} \frac{sinh(\infty)}{e^(\infty)}\)

As x approaches infinity, the exponential term e^x becomes much larger than the hyperbolic sine function sinh(x), so the entire expression sinh(x)/e^x becomes very close to zero.

Therefore, the limit of the expression as x approaches infinity is 0:

\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)

Answer:

a) Domain: All real numbers

b) Domain: -4<x<=4

a) Range: All real numbers greater than 2

b) Range: 0<=y<=4

Step-by-step explanation:

Domain is the possible x values

Range is the possible y values

Open circle means not included

Close circle means included

Answer: a) Domain: x = (-∞, ∞)              b) Domain x = (-4, 4]

                  Range y = [2, ∞)                        Range y = [0, 4]

Step-by-step explanation:

Domain represents the x-values. Range represents the y-values.

a) the graph doesn't end so every x-value is possible

  x = All Real Numbers       x = (-∞, ∞)

The lowest y-value (minimum) is at y = 2.  All other y-values are greater than that. y ≥ 2      y = [2, ∞)

b) The graph starts at x = -4 with an open dot so it doesn't include -4.  It ends at x = +4 with a closed dot so it does include +4.

     -4 < x ≤ 4           x = (-4, 4]

The lowest y-value (minimum) is at y = 0.  All other y-values are greater than that up to y = 4. 0 ≤ y ≤ 4      y = [0, 4]

The p-value for study B is 0.98.

With the same set of data, two studies were conducted.

Study A was a two-sided test while study B was a one-sided test.

The p-value of the test in study A is 0.040.

If the test statistic from your sample has a negative value, the p-value for a two-sided test is equal to twice the p-value for the lower-tailed p-value. If the test statistic from your sample has a positive value, the p-value is two times that of the upper-tailed p-value.

So, in conclusion:

The one-tail p-value equals one minus half the two-tailed value.

The two-tail p-value is twice the one-tail p-value.

As study A is a two-sided test with p-value = 0.04.

The p-value of study B will be:

p = 1 - ( 1/2 ) × 0.04

p = 1 - 0.02

p = 0.98

The p-value for study B is 0.8.

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Therefore, the probability that a randomly selected point within the square falls in the red-shaded area is 68%.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event A is denoted as P(A). To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.

Here,

The area of the red-shaded region is the area of the square minus the area of the white right-angled triangle. The area of the square is the length of one side squared, which is:

Area of square = 5 cm × 5 cm

= 25 cm²

The area of the right-angled triangle is one-half the base times the perpendicular height, which is:

Area of triangle = (1/2) × base × height

= (1/2) × 4 cm × 4 cm

= 8 cm²

Therefore, the area of the red-shaded region is:

Area of red-shaded region = Area of square - Area of triangle

= 25 cm² - 8 cm²

= 17 cm²

To find the probability that a randomly selected point within the square falls in the red-shaded area, we need to divide the area of the red-shaded region by the total area of the square, which is:

Probability = Area of red-shaded region / Area of square

Probability = 17 cm² / 25 cm²

= 0.68 or 68%

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Answer: 33.33 megabytes per day

Step-by-step explanation:

From the question, we are informed that in June, Clarissa used 1 gigabytes of data on her cell phone. Since June has 30 days, the amount of data she uses on average per day? will be:

= 1000megabyte/30

= 33.33mb

Note that:

1000 megabytes = 1 gigabyte

Answer: A <N is congruent to <Z

Answer: <N=<Z

Step-by-step explanation:

Answer:

you would put a full dot on 7 and make an arrow going to the left

Step-by-step explanation:

Answer:

A solid dot over the 8 with the arrow going to the left

Step-by-step explanation:

56/8=7

Answer:

34 days

Step-by-step explanation:

if you do six assignments a week, you have finished 42 assignments in one week. then multiply that with four, which is 168 (not exceeding 174) and add  6 days. 4 weeks and 6 days is 34 days.

have a great day and thx for your inquiry :)

A: √50x^2 and d: √72x^2 are like radicals.

Like radicals are square roots with the same coefficient outside the radical. For example, √50x^2 and √72x^2 can be simplified to √2 * √25x^2, which makes them like radicals. Simplifying the expressions helps to see if they are alike.

Expressions such as √32x and √18n cannot be simplified to have the same coefficient outside the radical and hence, they are not like radicals.

In conclusion, only √50x^2 and √72x^2 are like radicals after simplification.

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Answer:

A&D

Step-by-step explanation:

Got it right on edge

Answer:

Two-thirds

Step-by-step explanation:

slope is

∆y/∆x = (y2-y1) divided by (x2-x1)

= (-8-(-6)) divided by (-6-(-3))

= -2 divided by -3

= 2/3

Answer:

He was gone for 36 minutes

Step-by-step explanation:

Sorry if wrong

98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

mean x = 16

standard deviation σ = 2.4

sample size n = 65

z score for 98% = 2.576

Interval = x±z*s/

= 16±2.576*2.4/

= 16±2.576*0.39629

= 16±1.0208

Interval = (21.0208,18.9792)

Therefore 98% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

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Answer:

It's c. sorry if its not right

Answer:

D) x= 2 , B) x= - 6

Step-by-step explanation:

D) 2 + 3x = 6x - 4

Arrange x with x and constant with constant, (the signs +ve and - ve changes while arranging them to other side)

2 + 4 = - 3x + 6x

6 = 3x

(Here the 3 was multiplying with x and when you bring it to the other side it divides by 6)

6/3 = x

2 = x

B) 18 + 4x = - 6

Arrange them again,

4x = - 18 - 6

4x = - 24

x = - 24/4

x = - 6

Answer: Giuseppe is taller.

Step-by-step explanation:

Giuseppe is 74 inches tall, and we know that 12 inches is one foot, so 74/12 is ~6.1677777... versus 6.1.

Another way you can check this is by converting feet to inches. So 6 feet 1 inch would be (6 x 12) + 1 which is ~73.

Answer:

You Used 20%

How I Found The Answer:

$1245 ÷ 5 = $249

$249 Is 20%

The value of sin(D) is 7/25 after the application of the Pythagoras theorem.

The Pythagorean theorem is a fundamental theorem in geometry that describes the relationship between the sides of a right triangle. It claims that the hypotenuse's square length, which is the side that faces the right angle, is equivalent to the total of the squares of the lengths of the other two sides in a right triangle. The theorem can be formulated mathematically as:

c² = a² + b²

where, even the lengths for the remaining two sides (the legs) of the right triangle are a and b, and c is the length of the hypotenuse.

The Pythagorean theorem may be employed to determine the triangle's third side's length:

DE²= FD² + EF²

25² = 24² + EF²

625 = 576 + EF²

EF² = 49

EF = 7

Now, we can use the definition of sine to find sin(D):

sin(D) = opposite/hypotenuse = EF/DE = 7/25

Therefore, the value of sin(D) is 7/25.

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\(12 {x}^{2} + 8x + 1\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\((4 {x}^{2} + 6x + 7) - ( - 8 {x}^{2} - 2x + 6) \\ = 4 {x}^{2} + 6x + 7 + 8 {x}^{2} + 2x - 6 \\ = 4 {x}^{2} + 8 {x}^{2} + 6x + 2x + 7 - 6 \\ = 12 {x}^{2} + 8x + 1\)

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

3/8 unit

Step-by-step explanation:

\( \sqrt[3]{ \frac{27}{64} } = \frac{3}{8} \)

Answer:

The length of the cube is 3/4 units.

Step-by-step explanation:

The notation used for a vector pointing into the point is X.

A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.

Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.

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The correct option is A, which is {(5/7, 12/7)}.

equation 1, 5x + 2y = 7,

equation 2, y = x+1

To solve the question, as given in equation 2 the value of y which is equal to x+1, Substitute the value of  y in equation 1,

\(5x + 2y = 7\)

\(5x + 2(x+1) = 7\\5x+2x+2=7\\7x+2=7\\7x=7-2\\7x=5\\\\x= \dfrac{5}{7}\)

Now, we have the value of x, substitute the value in equation 2, to get y,

\(y=x+1\\y=(\frac{5}{7})+1\\\)

Taking LCM,

\(y=\frac{5+(1\times 7)}{7} \\y= \dfrac{12}{7}\)

Hence, the correct option is A, which is {(5/7, 12/7)}.

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Answer:

terrells' age is 18 years old

Step-by-step explanation:

d represents dantes' age

t represents terrells' age

d= 3t

d+ t = 72

substitute d to the second equation

d+ t = 72

3t+t=72

4t = 72

t = 18

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The answers are: (a) The function f is not continuous at x = 3.

(b) The function f is not differentiable at x = 3.

To determine the continuity of the function f at x = 3, we need to check if the left-hand limit and the right-hand limit exist and are equal at x = 3.

(a) To find the left-hand limit:

lim(x → 3-) f(x) = lim(x → 3-) x^2 = 3^2 = 9

(b) To find the right-hand limit:

lim(x → 3+) f(x) = lim(x → 3+) (3x - 2) = 3(3) - 2 = 7

Since the left-hand limit (9) is not equal to the right-hand limit (7), the function f is not continuous at x = 3.

To determine the differentiability of the function f at x = 3, we need to check if the left-hand derivative and the right-hand derivative exist and are equal at x = 3.

(a) To find the left-hand derivative:

f'(x) = 2x for x < 3

lim(x → 3-) f'(x) = lim(x → 3-) 2x = 2(3) = 6

(b) To find the right-hand derivative:

f'(x) = 3 for x > 3

lim(x → 3+) f'(x) = lim(x → 3+) 3 = 3

Since the left-hand derivative (6) is not equal to the right-hand derivative (3), the function f is not differentiable at x = 3.

Therefore, the answers are:

(a) The function f is not continuous at x = 3.

(b) The function f is not differentiable at x = 3.

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The circle at -6 is closed because the inequality does not include the possibility of y being equal to -6.

Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.

by the question.

the solution set of the inequality 1/2y < -3

Graph the solution set of the inequality 1/2y &lt; -3 - 1

To solve the inequality 1/2y < -3, we can begin by isolating the variable y on one side of the inequality:

1/2y < -3

Multiplying both sides by 2 yields:

y < -6

So, the solution set of the inequality is all real numbers y that are less than -6.

To graph the solution set on a number line, we can draw a closed circle at -6 and shade to the left of it, indicating that all values to the left of -6 are solutions to the inequality. The graph would look like this:

<=======o----------------------

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Step-by-step explanation:

Since it varies directly, we can set up a ratio and solve for x

\( \frac{ - 4}{ - 2} = \frac{x}{12} \)

Next we would cross multiply... multiply the numbers diagonally

\(( - 4)(12) = ( - 2)(x)\)

Simplifying

\( - 48 = - 2x\)

Now to get X alone, we would divide by the number attached to it, so -2. We'd do -2 on the -48 also

\(x = 24\)

The total weight of the 4 heaviest pumpkins is given as follows:

D. 41 and 3/4 pounds.

The dot plot shows the number of times that each measure appears in the data-set.

Hence the weights of the four-heaviest pumpkins are given as follows:

Then the total weight of all these pumpkins is obtained as follows:

2 x (10.375 + 10.5) = 41.75.

The fraction equivalent to a decimal of 0.75 is given as follows:

3/4.

Which means that the correct option is given by option D.

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Answer:

370 stores

Step-by-step explanation:

Given data

initial number of stores P= 200

r= 8%

t= 1999-2007=  8 years

Let us apply the compound interest expression to find the final amount of stores

A= P(1+r)^t

A= 200(1+0.08)^8

A= 200(1.08)^8

A= 200*1.85

A=370

Hence the number of stores in 2007 is 370 stores