four fiths of a number is 64 work out the number

Answer: The diver descended 20 meters below sea level and then ascended 8 meters.

Step-by-step explanation: The expression 2 + (-20) + 8 describes the diver's movements in relation to sea level. The first number, 2, represents the diver's initial position at sea level. The second number, -20, represents the diver's descent below sea level by 20 meters. The third number, 8, represents the diver's ascent back up to sea level. This can be interpreted as the diver starting at sea level, descending 20 meters below sea level, and then ascending 8 meters back up to sea level.

a) Area (Ф(R)) = 5184 (b) Area (Ф(R)) = 25920

Let J be the Jacobian of Ф. We have J = det(DФ) = det([3 9; 9 9]) = -72.

(a) For R = [0,9] × [0,6], we have

Ф(R) = {(3u+9v,9u+9v) | 0 ≤ u ≤ 9, 0 ≤ v ≤ 6}.

The area of Ф(R) is given by the double integral over R of the Jacobian:

Area (Ф(R)) = ∬R |J| dudv

= ∫0^9 ∫0^6 72 dudv

= 5184.

Therefore, the area of Ф(R) is 5184.

(b) For R = [2,20] × [1,17], we have Ф(R) = {(3u+9v,9u+9v) | 2 ≤ u ≤ 20, 1 ≤ v ≤ 17}. The area of Ф(R) is given by the double integral over R of the Jacobian:

Area (Ф(R)) = ∬R |J| dudv = ∫2^20 ∫1^17 72 dudv = 25920.

Therefore, the area of Ф(R) is 25920.

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Answer:

2 Cube

Step-by-step explanation:

Compute u * v if u and v are unit vectors and the angle between them is Pie. U * v =  is u.v = -1

that u and v are unit vectors and the angle between them is π.To find u*v, we use the dot product of vectors. Dot product of two vectors a and b is given bya.

b = |a| |b| cosθ

Where |a| is the magnitude of vector a, |b| is the magnitude of vector b, and θ is the angle between the two vectors.Let's find u*v using this formula.

u.v = |u| |v| cos π(u.v) = 1 × 1 × (-1))= -1

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The perimeter of a triangle is the sum of the lengths of its three sides. The perimeter of a triangle is represented by the expression a + b + c, where a, b, and c are the lengths of the three sides of the triangle.

Let's say the lengths of the sides of the triangle are represented by the variables a, b, and c. The perimeter of the triangle can then be expressed as:

Perimeter = a + b + c

This equation represents the sum of the lengths of all three sides of the triangle. The variables a, b, and c represent the lengths of the individual sides.

For example, if the triangle has sides with lengths 4 cm, 5 cm, and 6 cm, the expression for the perimeter would be:

Perimeter = 4 cm + 5 cm + 6 cm

= 15 cm

So, in general, the perimeter of a triangle is represented by the expression a + b + c, where a, b, and c are the lengths of the three sides of the triangle.

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Laplace transform is an important and efficient mathematical technique used to solve linear ordinary differential equations with constant coefficients. It converts a differential equation into an algebraic equation using a Laplace operator.

Here are the solutions to the given initial value problems and differential equations:

Solution of the initial-value problem i)

+ 3y = 13 sin 2t, y(0) = 6

Taking the Laplace transform on both sides:

L[ y"+3y] = L[13 sin 2t]

⇒ L[y]s² + 3L[y] = 13L[sin 2t]

⇒ L[y](s² + 3) = 26/(s²+4)

⇒ L[y] = 26/(s²+4)(s²+3)

Applying the inverse Laplace transform on both sides, we get:

y(t) = 2 sin 2t + 3 cos √3t + sin √3t

Solution of the initial-value problem

ii) y + 16y=f(t), y(0) = 0, y' (0) = 1 where

f(t) = {cos 4t, 0≤t≤m 0, † Σπ

Taking the Laplace transform on both sides:

L[y] + 16L[y] = L[f(t)] + L[y'(0)]

⇒ L[y](s + 16) = s/(s²+16) + 0

⇒ L[y] = s/(s²+16)(s+16)

Applying partial fraction decomposition on the Laplace transform equation:

y(t) = [3/(16)]{1 - cos 4t} + [1/4]{1/2} e^-16t + [1/4]{1/2} t e^-16t

Solution of the initial-value problem

iii) y'+y=8(t-1), y(0) = 2

Taking the Laplace transform on both sides:

L[y'] + L[y] = 8 L[t-1] + L[y(0)](s+1)

⇒ L[y](s+1) - y(0) + L[y] = 8 (1/s²) - 2

⇒ L[y](s+2) = [8/(s²)] + 2

⇒ L[y] = [4/(s²(s+2))] + [2/(s+2)]

Applying partial fraction decomposition on the Laplace transform equation, we get:

y(t) = 2 - 2e^-2t - 2t e^-2t + 4 sin t Solution of the initial-value problem

iv) y" -7y' +6y=et + 8(t-2) + 8(t-4),

y(0) = 0, y'(0) = 0

Taking the Laplace transform on both sides:

L[y"] -7L[y'] + 6L[y] = L[et] + L[8(t-2)] + L[8(t-4)]

⇒ L[y](s² -7s + 6) = 1/(s-1) + 8 e^-2s/(s²) + 8 e^-4s/(s²)

⇒ L[y] = [1/(s²(s-6)(s-1))] + [8/(s-1)(s²)]{1 - e^-2s - e^-4s}

Applying partial fraction decomposition and inverse Laplace transform on the Laplace transform equation, we get:

y(t) = [1/30] {9e^6t - e^t - 8} + (1/4) t - [1/20] (3cos 2t + 2sin 2t)

Solution of the initial-value problem v)

y"+y = 8 (t-n) +8 (t-n), y(0) = 0, y'(0) = 0

Taking the Laplace transform on both sides:

L[y"] + L[y] = 8 L[t-n] + 8 L[t-n]

⇒ L[y](s² + 1) = 16 e^(-ns) (1/s)

⇒ L[y] = (8/s) e^(-ns)/(s² + 1)

Applying inverse Laplace transform on the Laplace transform equation, we get:

y(t) = 8 e^(-n t) sint

Use Laplace transform to solve the given system of differential equations i) dy/dt =-x+y, dx/dt = 2x, x(0) = 0, y(0) = 1

Taking the Laplace transform on both sides:

L[dy/dt] = -L[x] + L[y]L[dx/dt]

= 2L[x]

Initial conditions become:

L[x] = 0, L[y] = 1/s

Laplace transforms of x and y become:

L[x] = 0, L[y] = 1/s

Applying Laplace transforms of dx/dt and dy/dt to the Laplace transform equation, we get:

L[x](s) = 0⇒ L[x] = 0

Applying inverse Laplace transform on the Laplace transform equation of y(t), we get:

y(t) = 1 - e^t

Use Laplace transform to solve the given system of differential equations

ii) dx/dt - 4x + 3y = 6 sin t, dy/dt + 2x - 2y = 0, x(0) = 0, y(0) = 0, y'(0) = 0

Taking the Laplace transform on both sides:

L[dx/dt] - 4L[x] + 3L[y] = L[6 sin t]L[dy/dt] + 2L[x] - 2L[y]

= 0

Initial conditions become:

L[x] = 0, L[y] = 0, sL[y] = 0

Applying Laplace transforms of dx/dt and dy/dt to the Laplace transform equation, we get:

L[x](s) = L[6 sin t]/(s+4) - (3/2)L[y](s)/(s+4)

⇒ L[x] = [6/(s² + 4)] - (3/2) L[y]/(s+4)L[y](s)

= -2L[x](s)/(s-2)

Applying inverse Laplace transform on the Laplace transform equation of x(t), we get:

x(t) = (3/2) [cos 2t - 2 sin 2t]

Applying inverse Laplace transform on the Laplace transform equation of y(t), we get:

y(t) = (3/2) [cos 2t - cos 4t]

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The x- intercept of  y = x²-4x-2 is 4.44949 and −0.44949.

The line's point of intersection with the coordinate axes is known as an intercept. The y coordinate of the intersection point is zero if the line contacts the X axis, and the intercept is known as the x intercept.

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.

Given:

To find the x-intercepts of the function, y = x²-4x-2, we need to make the y-value of the function equal to zero,

So, x²-4x-2 = 0

Now, solving the above Quadratic Equation

x²-4x-2 = 0

D = √(-4)² - 4(1)(-2)

D = √16 + 8

D = √24

D = 2√6

So, x= 4 ±  2√6/ 2

x = 4 +  2√6/2  or x = 4-  2√6/2

x = 2 + √6 or x = 2- √6

x = 4.44949 or x = −0.44949

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The null hypothesis is that there is no significant difference in the mean fuel efficiency rating for highway driving among the three sizes of cars.

The alternative hypothesis is that there is a significant difference in the mean fuel efficiency rating for highway driving among the three sizes of cars.

The value of the test statistic for the overall model is 2.68.

The p-value for the overall model is 0.008.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis. Therefore, there is sufficient evidence to conclude that there is a significant difference in the mean fuel efficiency rating for highway driving among the three sizes of cars.

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The statement "A histogram with the hills to the far left means the image is overexposed" is not accurate. In fact, a histogram with the hills to the far left indicates that the image is underexposed, not overexposed.

A histogram is a graphical representation of the distribution of pixel values in an image. It displays the frequency of occurrence of different tonal values. The horizontal axis represents the tonal values, while the vertical axis represents the frequency or number of pixels.

When the hills of the histogram are concentrated towards the left side, it means that a significant portion of the image has darker or lower tonal values. This indicates an underexposed image, where the exposure settings were insufficient to capture enough light, resulting in a darker overall appearance.

Conversely, an overexposed image would have the hills of the histogram concentrated towards the right side, indicating that a significant portion of the image has brighter or higher tonal values.

Therefore, the correct interpretation is that a histogram with the hills to the far left means the image is underexposed, not overexposed.

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Answer:

-12x²

Step-by-step explanation:

Given expression:

\(-5x^{2} -7x^{2}\)

Since both terms in the expression have common terms, we can subtract the terms by combining like terms.

\(\implies x^{2} (-5 -7)\)

\(\implies x^{2} (-12)\)

\(\implies -12x^{2}\)

Answer:

31.25 gallons to go 500 miles

Step-by-step explanation:

Answer:

It is scalene and acute.

Step-by-step explanation:

Since it has all acute angles, it is an acute triangle, and since none of the sides are equal or congruent, it is scalene.

Answer:

No

Step-by-step explanation:

no

Answer:

Connected scatter plot. If the third variable we want to add to a scatter plot indicates timestamps, then one chart type we could choose is the connected scatter plot. Rather than modify the form of the points to indicate date, we use line segments to connect observations in order.

Step-by-step explanation:

The figure given is a circle with two tangents meeting at point M and touching the circle at points L and N.

The angle made by the arc is 138 degrees

In order to get a better understanding, we can redraw the figure.

This is done below:

As we can see, the angle subtended by the arc LN, is 138 degrees.

There is a theorem that says the angle that a radius (such as OL) makes with a tangent

(such as LM) is 90 degrees.

This is illustrated further below:

This new image highlights the 90 degree angles the two tangents make with the radius of the circle.

Thus, we can consider quadrilateral MNOL, we can finally solve for x.

A theorem says that the sum of angles in a quadrilateral is 360 degrees.

Therefore, we can say:

Therefore the final answer is: x = 42 degrees

The value of x corresponds to option B: 10.5 as the figure provided has two congruent figures inside it.

From the given image, we can consider that that the two triangles- one for which side x is given, and another for which measurements of both sides are given- are congruent. This is because they both have one common side and one angle equal to another at a vertex (refer image).

Thus, we have:

(x / 19.3) = (3.9 / 7.2)

Then, attempting to find the value of x we have:

x = (3.9 / 7.2) × (19.3)

= 10.5

Therefore, option B gives the measure of the side x of the given triangle, where x = 10.5.

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Answer:

-12.9

Step-by-step explanation:

Answer:

10 hours

Step-by-step explanation:

130-50-80

80 divided by 8 equals 10

Answer:

Hope this helps:)

Answer:

B

Step-by-step explanation:

The answer is B because it tells you the letter atound triangle.

Answer:

b

Step-by-step explanation:

The total number of acres planted for the optimal solution is not provided in the given information.

The amount of fertilizer (in tons) required to produce only corn is not provided in the given information.

The peak number of acres of wheat planted as fertilizer availability varies from 200 tons to 2200 tons in 100-ton increments cannot be determined without additional information.

I can help explain the general approach to answering the questions you mentioned.

To determine the total number of acres planted for the optimal solution, you would need to refer to the problem's constraints and objective function. The optimal solution would be obtained by solving the problem using linear programming techniques such as the simplex method or graphical method. By solving the problem, you can identify the values of the decision variables (such as acres planted) that maximize or minimize the objective function while satisfying the given constraints. The total number of acres planted for the optimal solution would depend on the specific problem setup and the solution obtained.

Similarly, to find out how much fertilizer would be needed to produce only corn, you would need to refer to the constraints and objective function of the problem. The specific requirements and coefficients associated with the corn production and fertilizer usage would determine the amount of fertilizer needed. By solving the problem, you can obtain the value of the decision variable representing fertilizer usage, which would indicate the required amount of fertilizer in tons.

SolverTable is a tool in Excel that allows you to perform sensitivity analysis by varying certain input values and observing the impact on the output. By using SolverTable, you can analyze the relationship between fertilizer availability (input) and acres planted (output) in the given problem. By varying the fertilizer availability from 200 tons to 2200 tons in 100-ton increments, you can observe how the acres of wheat planted change accordingly. The peak number of acres of wheat planted would be the maximum value observed during this range of fertilizer availability.

Since I don't have access to the specific problem you mentioned, I cannot provide precise answers or calculations. Please refer to the problem in your textbook or reference material to obtain the exact values and final answers.

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Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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The value of a, b, c or k that make the function continuous everywhere are:

To make the given functions continuous everywhere, ensure that the different parts of the function agree at their boundaries.

For f(x) = kx², x ≤ 3; 4x - 11, x > 3:

To make the function continuous at x = 3, two parts of the function to agree at x = 3.

Setting them equal and solving for k:

k(3)² = 4(3) - 11

9k = 12 - 11

9k = 1

k = 1/9

Therefore, the value of k that makes the function continuous everywhere is k = 1/9.

For g(x) = cx², x < 1; 4, x = 1; -x³ + kx, x > 1:

To make the function continuous at x = 1, two parts of the function to agree at x = 1.

Setting them equal and solving for c:

c(1)² = -1³ + k(1)

c = -1 + k

Therefore, the value of c that makes the function continuous everywhere is c = -1 + k.

For h(x) = π, x < 0; x² + ax + b, 0 ≤ x ≤ 1; 6x + 5, x > 1:

To make the function continuous at x = 0 and x = 1, three parts of the function to agree at their boundaries.

Setting the two boundaries equal and solving for a and b:

0² + a(0) + b = π

b = π

1² + a(1) + b = 6(1) + 5

1 + a + π = 6 + 5

a = 10 - π

Therefore, the values of a and b that make the function continuous everywhere are a = 10 - π and b = π.

For f(x) = x², x < 1; sin(bx), x ≥ 1:

To make the function continuous at x = 1, two parts of the function to agree at x = 1.

Setting them equal and solving for b:

1² = sin(b(1))

1 = sin(b)

Therefore, the value of b that makes the function continuous everywhere is b = π/2.

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Answer:

D

Step-by-step explanation:

H2CO3

ithink it is the answer maybe

Answer:

D. H2CO3

Step-by-step explanation:

D is the correct answer

The following data shows the daily production of cell phones. 7, 10, 12, 15, 18, 19, 20. Mean The formula for finding the mean is: mean = (sum of observations) / (number of observations).

Therefore, the mean for the daily production of cell phones is: Mean = (7+10+12+15+18+19+20) / 7

= 101 / 7

Mean = 14.43

Variance The formula for finding the variance is: Variance = (sum of the squares of the deviations) / (number of observations - 1) Where the deviation of each observation from the mean is: deviation = observation - mean First, calculate the deviation for each observation:7 - 14.43

= -7.4310 - 14.43

= -4.4312 - 14.43

= -2.4315 - 14.43

= 0.5718 - 14.43

= 3.5719 - 14.43

= 4.5720 - 14.43

= 5.57

Now, square each of these deviations: 56.25, 19.62, 5.91, 0.33, 12.75, 20.9, 30.96 The sum of these squares of deviations is: 56.25 + 19.62 + 5.91 + 0.33 + 12.75 + 20.9 + 30.96

= 147.72

Therefore, the variance for the daily production of cell phones is: Variance = 147.72 / (7-1) = 24.62 Standard deviation ) Mean = 14.43b) Variance per Day = 24.62c) Standard Deviation = 4.96

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Answer:

Step-by-step explanation:

If you are saying, Y is more than 9, then use this- Y>9

If you are saying Y more than 9 equals ? then use this- 9+Y=?

Hope i helped you!!

Answer:

because there is 1 arc on both meaning they are congruent

Step-by-step explanation:

Answer: Yes it is a rational number because you can wright it as a fraction

Answer:

\(\huge\colorbox{blue}{h$\approx$1.3 foot }\)

Step-by-step explanation:

we are given volume and redious

but r is in inches and V is in gallons

so we have to convert V into inches unit

\( \sf\displaystyle 1\: cubic\: foot=1728 \: cubic\: inches\)

first convert gallon to cubic foot

\( \sf\displaystyle 15\times 0.15\: (\text{since 1 gallon=0.15 cubic feet}) \\ \displaystyle \: = 2.25\)

now convert cubic feet to cubic inches:

\(\sf\displaystyle 2.25\times 1728 \\ = 3888\)

now we need a little algebra to figure out h

\(V_{cylinder}=\pi r^2 h\)

substitute the value of V and r:

\( \displaystyle \: \pi \times {9}^{2} \times h = 3888\)

simplify square:

\( \displaystyle \: \pi \times 81 \times h = 3888\)

divide both sides by 81:

\( \displaystyle \: \frac{ \pi \times 81 \times h}{81} = \frac{ 3 888}{81} \\ \pi \times h = 48\)

divide both sides by π:

\( \displaystyle \: \frac{\pi \times h}{\pi} = \frac{48}{\pi} \\ \: h \approx 15.3\)

12 inches = 1 foot

15.3 " =15.3/12

≈1.3 foot