A boy leaves home at 7:30 a.m and cycles to school, 6 km away, arriving at 7:45 a.m. The average speed of the boy as he cycles, in kmh, is (A) 32 (B) 24 (C) 18 (D) 16​

Answer:

The market equilibrium price is approximately $36.43 per barrel.

Step-by-step explanation:

To find the market equilibrium price, we need to set the quantity supplied (QS) equal to the quantity demanded (QD) and solve for the price (P).

Given:

QS = -250 + 7P

QD = 260 - 7P

Setting QS equal to QD:

-250 + 7P = 260 - 7P

Now, let's solve for P:

Add 7P to both sides:

-250 + 7P + 7P = 260 - 7P + 7P

Combine like terms:

14P - 250 = 260

Add 250 to both sides:

14P - 250 + 250 = 260 + 250

Simplify:

14P = 510

Divide both sides by 14:

14P/14 = 510/14

Simplify:

P = 36.43

The market equilibrium price can be found by setting the quantity supplied (QS) equal to the quantity demanded (QD) and solving for the price (P) that satisfies this condition.

In the given scenario, the supply function is QS = -250 + 7P, and the demand function is QD = 260 - 7P. To find the equilibrium price, we set QS equal to QD:

-250 + 7P = 260 - 7P

Simplifying the equation, we get:

14P = 510

Dividing both sides by 14, we find:

P = 36.43

Therefore, the market equilibrium price is approximately $36.43 per barrel. At this price, the quantity supplied and quantity demanded will be equal, resulting in a state of equilibrium in the perfectly competitive domestic crude oil market.

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[(h + 10) - 4] × (h - 4) = 1344. This equation to find the height and length of the unframed portrait, and then calculate the area.

Let's denote the height of the portrait as 'h' inches. According to the problem, the length of the portrait is 10 inches longer than its height, so the length would be 'h + 10' inches.

Now, we need to find the dimensions and area of the unframed portrait. To do this, we need to subtract the thickness of the frame from the dimensions of the framed portrait.

Dimensions of the framed portrait:

Length: (h + 10) inches

Height: h inches

Dimensions of the unframed portrait:

Length: (h + 10) - (2 + 2) inches (subtracting the thickness of the frame)

Height: h - (2 + 2) inches

Area of the unframed portrait:

Area = Length × Height

Area = [(h + 10) - 4] × (h - 4) square inches

We are given that the total area of the framed portrait is 1344 square inches. So, we can set up the equation:

[(h + 10) - 4] × (h - 4) = 1344

Solve this equation to find the height and length of the unframed portrait, and then calculate the area.

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it's a because b and c are 170 or lower and d is over 190

JUST ADD IF ANY OF THEM EQUAL 180 THEN ITS A TRIANGLE

The three angles of a triangle need to equal 180 when added together.

Add the three angles together and see which one equal 180.

The answer would be A. 89.1, 45.1, 45

Answer:

The factors of the number 18 are: 1, 2, 3, 6, 9, 18. If you add them up, you will get the total of 39.

Answer:

90 minutes

Step-by-step explanation:

it will take twice as long therefore 90 minutes

Answer:

93.2° (nearest tenth)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

From inspection of the given triangle:

Substitute the values into the sine rule to find the measure of angle C:

\(\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

\(\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}\)

\(\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}\)

\(\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)\)

\(\implies C=48.80523914...^{\circ}\)

Interior angles of a triangle sum to 180°.

\(\implies A+B+C=180^{\circ}\)

\(\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}\)

\(\implies A=93.19476086...^{\circ}\)

Therefore, the size of angle A is 93.2° (nearest tenth).

x(1) = [0 - y / (1 - (2 - 1))] the given equation x(1) = [0 - y / (1 - (2 - 1))] is proven.

To prove the given equation x(1) = [0 - y / (1 - (2 - 1))], we need to manipulate equations (i) and (ii) and substitute the given expressions for A1, A2, and Y.

From equation (i), we have:

ln(A1) = ln(A0) - kt1

Substituting A1 = A0 - x1, we get:

ln(A0 - x1) = ln(A0) - kt1

Similarly, from equation (ii), we have:

ln(A2) = ln(A0) - kt2

Substituting A2 = A0 - x2, we get:

ln(A0 - x2) = ln(A0) - kt2

Now, let's subtract equation (ii) from equation (i):

ln(A0 - x1) - ln(A0 - x2) = kt2 - kt1

Using the logarithmic property ln(a) - ln(b) = ln(a/b), we can simplify the equation as follows:

ln((A0 - x1) / (A0 - x2)) = k(t2 - t1)

Since Y = x2 - x1, we can rewrite the equation as:

ln((A0 - x1) / (A0 - x2)) = kY

Exponentiating both sides of the equation:

(e^ln((A0 - x1) / (A0 - x2))) = e^(kY)

Simplifying further:

((A0 - x1) / (A0 - x2)) = e^(kY)

Rearranging the equation:

x1 = A0 - (A0 - x2)e^(kY)

Since A0 - A0 = 0, the equation becomes:

x1 = x2e^(kY)

Now, substituting Y = x2 - x1, we have:

x1 = x2e^(k(x2 - x1))

Dividing both sides by x2 - x1:

x(1) = x2e^(k(x2 - x1))/(x2 - x1)

Simplifying further:

x(1) = -x2e^(k(x1 - x2))/(1 - (2 - 1))

Finally, we can write x(1) as:

x(1) = [0 - y / (1 - (2 - 1))]

Therefore, the given equation x(1) = [0 - y / (1 - (2 - 1))] is proven.

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Step-by-step explanation:

(A) (In the fig. triangle represented by small triangle with angle of elevation 30° and height h1 ) ( Using this explanation since the figure is not marked)

\(tan30 = \frac{h1}{40} \)

\(h1 = \frac{40}{\sqrt{3} } m\)

(B) (In the fig. triangle represented by small triangle with angle of depression 58° and height h2 )

\(tan58 = \frac{h2}{40} \)

\(h2 = 64m\)

(C)

\(Height \: of \: Building \: A = h2 = 64m\)

\(Height \: of \: Building \: B = h1+h2 = (64 + \frac{40}{ \sqrt{3} } )= 87m\)

Answer

0.¯¯¯¯81 or

Step-by-step explanation:

( the line is suppose to be over the .81)

It is the distributive property.

Answer:

15

Step-by-step explanation:

5y - 20 = 2y + 25 (opposite sides of a parallelogram are equal)

5y - 2y = 25 + 20

3y = 45

y = 45/3

y = 15

hope you understood❤

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\(5y - 20 = 2y + 25\)

Subtract sides 2y

\( - 2y + 5y - 20 = - 2y + 2y + 25 \\ \)

\(3y - 20 = 25\)

Add sides 20

\(3y - 20 + 20 = 25 + 20\)

\(3y = 45\)

Divided sides by 3

\( \frac{3}{3} y = \frac{45}{3} \\ \)

\(y = 15\)

Done....

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the number of cans that would be needed to cover the  pizza slice that is in form of a sector is 42 cans.

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

To calculate the number of cans that would be needed to cover the slice, we use the formula below

Formula:

Where:

Given:

Substitute these values into equation 1

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Answer:

-1.540

Step-by-step explanation:

H0 : μ = 18

H0 : μ ≠ 18

The sample size, n = 48

Sample mean, xbar = 17

Sample standard deviation, s = 4.5

α = 0.05

The test statistic :

(xbar - μ) ÷ (s/√(n))

(17 - 18) ÷ (4.5 / √48))

-1 ÷ 0.6495190

= -1.5396

= -1.540 (3 decimal places ).

To write the given expression in factored form using the greatest common factor and distributive property, we need to find the largest common factor of 9 and 6, which is 3. Then we can factor out 3 from both terms, giving us 3(3d+2e). Therefore, the equivalent expression in factored form is 3(3d+2e).

This expression is simplified and shows that 3 is a common factor of both terms. In 100 words, this process involves identifying the greatest common factor between the terms and then using the distributive property to factor it out. This simplifies the expression and allows for easier calculations in further operations.

It is important to always look for common factors and simplify expressions whenever possible.

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Answer: PV= $ 2292.10

Step-by-step explanation:

A= P(1+r/100)^n*r

where FV is the Future vale, PV is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years

5000 = PVe^(0.065*12)

PV = 5000/e^0.78

PV = 2292.10

The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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Answer:

7

Step-by-step explanation:

start by adding 3+ 11 in the parenthesis, that should give you 14. now you should have  7 + 14 over -5 + 8.  

-5 + 8 = 3  (another way to look at this problem is, 8 -5)

7+14 = 21

you should now have 21 over 3

to simplify this divide 21 by 3, this should give you 7  

Answer: 21 divided by 3

Step-by-step explanation:

If you solve the top and the bottom you get 21 for the top and 3 for the top and you can divide 21 by 3 and get 7. You can double check the math if you want, hope this helps!

Question 1-

To determine which two points would a line of fit go through to best fit the data on the scatter plot, we need to visually analyze the pattern of the data points and choose two points that the line would pass through to represent the overall trend.

Without the actual scatter plot provided, I am unable to directly analyze it. However, based on the given answer choices:

A. (1,9) and (9,5)

B. (1,9) and (5,7)

C. (2,7) and (4,3)

D. (2,7) and (6,5)

Since I don't have the scatter plot, I cannot accurately determine which points would best fit the data. I would recommend carefully reviewing the scatter plot and selecting the two points that seem to represent the general trend or pattern of the data. The two points that form a line that closely follows the general direction of the data points would be the best choices.

Question 2-

To determine the slope of the relationship between the number of hours Laila danced, x, and the money she raised, y, we need to examine the graph and calculate the slope using the formula:

Slope = (change in y) / (change in x)

However, since the graph is not provided, it is not possible to directly calculate the slope. However, we can still evaluate the given answer choices based on their explanations:

A. The slope is 1/4, which means that the amount the student raised increases by $0.75 each hour.

B. The slope is 4, which means that the amount the student raised increases by $4 each hour.

C. The slope is 12, which means that the student will finish raising money after 12 hours.

D. The slope is 20, which means that the student started with $20.

From the explanations provided, it seems that option B would be the most reasonable choice. A slope of 4 would indicate that for each additional hour Laila danced, she raised $4. However, without the actual graph, it is challenging to confirm the accuracy of the answer choice or its real-world interpretation.

Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.

The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).

Therefore, the answer is "translation , reflection , and dilation".

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Answer:

A) Translation

B) Reflection

C) Dilation

Step-by-step explanation:

\(\implies {\blue {\boxed {\boxed {\purple {\sf {A. \:-54}}}}}}\)

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

We have,

\('m = 18'\) and \('a = - 3'\)

Substituting the values of \(m\) and \(a\) in \(F=ma\),

➺\(\:F = 18 \times - 3\)

➺\( \: F = - 54\)

Therefore, the value of F is \(\boxed{-54}\).

F = force

m = mass

a = acceleration.

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}\)

The paths of two particles are described by parametric equations. The first particle follows a circular path, while the second particle follows a path with both circular and linear components.

We need to graph the paths and determine the number of points of intersection.

Additionally, we need to find the collision point where the particles occupy the same position at the same time.

Lastly, we need to determine if there is a collision when the x-coordinate of the second particle is modified.

(a) To graph the paths of both particles, we plot the parametric equations x1 = 3sin(t), y1 = 2cos(t) and x2 = -3 + cos(t), y2 = 1 + sin(t) on a coordinate plane for 0 ≤ t ≤ 2π. The paths of the particles will be represented by curves. By analyzing the graph, we can count the number of points of intersection.

(b) To find the collision point, we need to find the values of t where x1 = x2 and y1 = y2 simultaneously. By setting 3sin(t) = -3 + cos(t) and 2cos(t) = 1 + sin(t), we can solve for t. The obtained value(s) of t will give us the collision point (x, y) where the particles occupy the same position at the same time.

(c) If the x-coordinate of the second particle is modified to x2 = 3 + cos(t), we need to repeat the process of finding the collision point. By setting 3sin(t) = 3 + cos(t) and 2cos(t) = 1 + sin(t), we solve for t. Depending on the solution(s) of t, we can determine if there is still a collision or not.

Please note that since this question involves graphing and solving equations, it is best to draw the graphs and solve the equations visually or using numerical methods to obtain specific values.

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Answer:What is the next term in the geometric sequence 2 8 32?

If you notice in this sequence,the next number is a multiple of 4 of the previous number. 2 multiplied by 4 is 8,8 multiplied by 4 is 32. So, the geometric sequence is 2,8,32,128,512,2048,8192,32768. The sum of the sequence is 43,690.

Step-by-step explanation:

i hope this helps

Answer:

=8x+64

Step-by-step explanation:

Answer:

11. B.

12. 3

Step-by-step explanation:

\(\sqrt{81}-\sqrt{25}=9-5=4\)

\(\sqrt[3]{27}=3\) since \(3^{3}\)\(=27\)

Answer:

The question is asking what number times itself 3 times equals 27. 3*3*3=27

A Hessian matrix, D²u(x, y), is a square matrix consisting of second-order partial derivatives of a multivariable function. The matrix is symmetric by definition, so it suffices to compute half of the matrix. To verify whether the function u(r, g) is convex or concave, we'll use the Hessian matrix's determinants.

Thus, we can conclude that the Hessian matrix of the function u(r, g) is positive semi-definite. Hence, the function is a concave function.(a) We will take the second derivative of u with respect to each variable to compute the Hessian matrix. Here are the second derivatives of u:$$\begin{aligned} \frac{\partial u}{\partial x^2} &= \frac{2}{(1+x)^2} &\qquad \frac{\partial^2 u}{\partial x\partial y} &= 0 \\ \frac{\partial^2 u}{\partial y\partial x} &= 0 &\qquad \frac{\partial u}{\partial y^2} &= \frac{2z}{(1+y)^2} \end{aligned}$$Thus, the Hessian matrix D²u(x, y) is:$$D^2u(x, y)=\begin{pmatrix} \frac{2}{(1+x)^2} & 0 \\ 0 & \frac{2z}{(1+y)^2} \end{pmatrix}$$Since both diagonal entries of the matrix are positive, the function u(r, g) is concave.(b) A convex set is defined as follows:A set C in Rn is said to be convex if for every x, y ∈ C and for all t ∈ [0, 1], tx + (1 − t)y ∈ C.It means that all points on a line segment connecting two points in the set C should also be in C. That is, any line segment between any two points in C should be contained entirely in C.(c)We will use the Hessian matrix's positive semi-definiteness to show that I+(1) = {(x, y) = R²: u(x, y) ≥ 1} is a convex set.If D²u(x, y) is positive semi-definite, it means that the eigenvalues are greater than or equal to zero. The eigenvalues of D²u(x, y) are:$$\lambda_1 = \frac{2}{(1+x)^2} \quad \text{and} \quad \lambda_2 = \frac{2z}{(1+y)^2}$$Since both eigenvalues are greater than or equal to zero, D²u(x, y) is positive semi-definite. As a result, the set I+(1) is convex because u(x, y) is a concave function.(d) The second-order Taylor polynomial of u(x, y) at (0, 0) is given by:$$u(0,0)+\begin{pmatrix} 0 \\ 0 \end{pmatrix}^T \nabla u(0,0)+\frac{1}{2}\begin{pmatrix} 0 \\ 0 \end{pmatrix}^T D^2u(0,0)\begin{pmatrix} 0 \\ 0 \end{pmatrix}$$$$=u(0,0)+0+0=1$$Therefore, the 2nd order Taylor polynomial of u(x, y) at (0,0) is 1.

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A Hessian matrix, \(D^{2} u(x, y)\), is a square matrix consisting of second-order partial derivatives of a multivariable function. The matrix is symmetric by definition, so it suffices to compute half of the matrix. To verify whether the function u(r, g) is convex or concave, we'll use the Hessian matrix's determinants.

Here, we have,

Thus, we can conclude that the Hessian matrix of the function u(r, g) is positive semi-definite. Hence, the function is a concave function.

(a) We will take the second derivative of u with respect to each variable to compute the Hessian matrix.

Here are the second derivatives of u:

{∂ u}/{∂ x²} = {2}/{(1+x)²}  

{∂² u}/{∂ x∂ y} = 0

{∂² u}/{∂ y∂ x} = 0

{∂ u}/{∂ y²} = {2z}/{(1+y)²}

Thus, the Hessian matrix \(D^{2} u(x, y)\) is:

\(D^{2} u(x, y)\)=\(\begin{pmatrix} \frac{2}{(1+x)²} & 0 \\ 0 & \frac{2z}{(1+y)²} \end{pmatrix}\)

Since both diagonal entries of the matrix are positive, the function u(r, g) is concave.

(b) A convex set is defined as follows:

A set C in Rn is said to be convex if for every x, y ∈ C and for all t ∈ [0, 1], tx + (1 − t)y ∈ C.

It means that all points on a line segment connecting two points in the set C should also be in C.

That is, any line segment between any two points in C should be contained entirely in C.

(c)We will use the Hessian matrix's positive semi-definiteness to show that I+(1) = {(x, y) = \(R^{2}\): \(u(x, y)\geq 1\)} is a convex set.

If \(D^{2} u(x, y)\) is positive semi-definite, it means that the eigenvalues are greater than or equal to zero.

The eigenvalues of \(D^{2} u(x, y)\) are:

\(\lambda_1 = \frac{2}{(1+x)²} \quad \text{and} \quad \lambda_2 = \frac{2z}{(1+y)²}\)

Since both eigenvalues are greater than or equal to zero,\(D^{2} u(x, y)\) is positive semi-definite. As a result, the set I+(1) is convex because u(x, y) is a concave function.

(d) The second-order Taylor polynomial of u(x, y) at (0, 0) is given by:

\(u(0,0)+\begin{pmatrix} 0 \\ 0 \end{pmatrix}^T \nabla u(0,0)+\frac{1}{2}\begin{pmatrix} 0 \\ 0 \end{pmatrix}^T D²u(0,0)\begin{pmatrix} 0 \\ 0 \end{pmatrix}=u(0,0)+0+0=1\)

Therefore, the 2nd order Taylor polynomial of u(x, y) at (0,0) is 1.

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The value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.

The formula of sum of sin (a+b) is the trigonometry identity which is used to solve and simplify the problem based on trigonometry equation.

The formula of sum of sin (a+b),

Sin(A+B)=(sin A)(cos B)+(cos A)(sin B)

Here, (A and B) are the measure of angles.

The trigonometry equation given in the problem is,

(sin 60)(cos 30)+(cos 60)(sin 30)

Compare this expression with the above formula we get,

A=60

B=30

Thus, the value of the given expression is,

(sin 60)(cos 30)+(cos 60)(sin 30)=sin (60+30)

Thus, the value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.

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Answer:

18

Step-by-step explanation:

for the first one, 2(5+1)+10=22

for the second one, 2(6+4)+10=30

using the same concept, 2(3+1)+10=18

?=18

im not sure if im right or not lol