Kyla brought pies to a picnic. After the picnic, Kyla noticed 16/8 of the pies were eaten.

How many of the pies that Kyla brought to the picnic were eaten?


A. 16

B. 8

C. 2

D. 1

Answer:

To answer the questions regarding Mokoena's and his brother's ages, we'll use the given information:

Mokoena is p years old.

His brother is twice his age.

2.1 How old is his brother?

Since his brother is twice Mokoena's age, his brother's age would be 2p.

2.2 How old will Mokoena be in 10 years?

To find Mokoena's age in 10 years, we add 10 to his current age: p + 10.

2.3 How old was his brother 3 years ago?

To find his brother's age 3 years ago, we subtract 3 from his brother's current age: 2p - 3.

2.4 What will their combined age be in q years' time?

To find their combined age in q years' time, we add q to the sum of their current ages: p + 2p + q = 3p + q.

Therefore, the answers are:

2.1 His brother's age is 2p.

2.2 Mokoena will be p + 10 years old in 10 years.

2.3 His brother was 2p - 3 years old 3 years ago.

2.4 Their combined age in q years' time will be 3p + q.

Step-by-step explanation:

The tool that makes an exact duplicate of what it is sampling is called a "clone stamp" tool.

A "clone stamp" tool is a function included in image editing software such as Adobe Photoshop that allows you to sample a specific region of a picture and reproduce it elsewhere.

The clone stamp tool creates an identical copy of the original by copying pixels from the selected source area and pasting them onto the region where the tool is applied.

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Answer:

1st problem: x = 1.75

2nd problem: x = 16

Hope this helps!

Answer:

c. function g has A y intercept of (0,4)

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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To show that the function \(B: \mathbb{R}^2 \times \mathbb{R}^2 \to \mathbb{R}\), given by \(B((x_1, y_1), (x_2, y_2)) = ax_1y_1 + bx_2y_1 + cx_1y_2 + dy_2\), is negative definite, we need to prove that it satisfies two conditions:

For any non-zero vector\(v = (x, y) \in \mathbb{R}^2, B(v, v) < 0\).

The determinant of the matrix formed by the coefficients of B is positive: \(ac - b^2 > 0\).

Let's start with the first condition:

For \(v = (x, y) \in \mathbb{R}^2, B(v, v) = ax^2 + bxy + cxy + dy^2 = (a + c)x^2 + (b + d)xy + dy^2\).

Since we want B(v, v) to be negative for any non-zero vector v, the coefficient of \(x^2 (a + c)\) should be negative, and the determinant of the quadratic term \((b + d)^2 - 4ad\) should be negative as well.

Therefore, we have the following conditions:

\(a + c < 0 (1)\\\\(b + d)^2 - 4ad < 0 (2)\)

Now, let's move to the second condition:

We are given that B is negative definite, so we can assume that a, c, d ≠ 0 to avoid any degenerate cases.

To determine the sign of \(ac - b^2\), we can consider the determinant of the matrix formed by the coefficients:

\(\begin{bmatrix}a & b \\c & d \\\end{bmatrix}\)

The determinant is ad - bc, and for B to be negative definite, we want this determinant to be positive:

ad - bc > 0 (3)

Now, let's combine the conditions (1), (2), and (3):

From condition (1), we have a + c < 0, which implies c < -a.

From condition (2), we have\((b + d)^2 - 4ad < 0\), which implies \((b + d)^2 < 4ad\).

Now, let's multiply (1) by d and (2) by -c:

\(-d(a + c) > 0 (4)\\\\(c^2 - 4ac)d > 0 (5)\)

Adding (4) and (5), we get:

\(c^2 - 4ac - d(a + c) > 0\)

Rearranging terms, we have:

\(c^2 - 4ac - d(a + c) + 2ac - 2ac > 0\\\\c^2 - 2ac - d(a + c) + 2ac > 0\\\\(c^2 - 2ac) - (d(a + c) - 2ac) > 0\\\\c^2 - 2ac - (d - 2a)(a + c) > 0\)

Now, since c < -a, we have c + a < 0, which implies a + c < 0. Therefore, (a + c) is negative.

So, we can rewrite the inequality as:

\(c^2 - 2ac + (2a - d)(a + c) > 0\)

Since (2a - d) is negative, (a + c) is negative, and a < 0, we can conclude that:

\(ac - b^2 > 0.\)

Therefore, we have shown that B is negative definite if a < 0 and \(ac - b^2 > 0\).

Please note that in the given expression, there is a slight difference in the notation used (axıyı instead of \(ax_1y_1\)), but the approach and conclusion remain the same.

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Answer:

A reasonable range for the function y=0.1x+12 would be all real numbers greater than or equal to 12. This is because the minimum monthly phone bill that Ben could have would be $12 (if he does not use any minutes), and the monthly bill can increase to any higher value depending on the number of minutes he talks. In set builder notation, this range would be written as {y | y >= 12}.

Step-by-step explanation:

Answer:

3 meters per second

Step-by-step explanation:

all you need to do is devise 30 by 10

Answer:

The equation is 39=3r-6

Step-by-step explanation:

Let x = # of years from the start of the Great Depression to the first Presidential election of Nixon

Let r = Raul's age

The question gives us what x equals so...

x=39

Now we just turn the sentence into an equation.

"The number of years from the start of the Great Depression to the first Presidential election of Nixon [(x)] is six years less than three times Raul's age [(3r-6)]"

Remove the icky words...

x=3r-6

replace x with what it equals (39)

39=3r-6

Now you can go on to olve it

Overal Raul is only 15 :)

Answer:

y=-5, x=-1

Step-by-step explanation:

y=5x

/5 /5

y/5=x

y=9(y/5)+4

y=-5

-5=5x

/5   /5

-1=x

The zero input response y(t) can be written as: \(y(t) = -2/3e^{-3t} + 2/9te^{-3t} + 5/9 + 8/9e^{-3t}\)

Also ,  the zero input response y(t) is given as:\(y(t) = (8/9 - 2/3)e^{-3t} + 2/9te^{-3t} + 5/9\)

In the given question, we are given the transfer function of the system. The zero input response y(t) can be calculated using the following steps:

Step 1: Find the roots of the denominator of the transfer function. In the denominator, we have:s²+6s+9 = 0Using the quadratic formula, we get: s1 = s2 = -3Therefore, the denominator of the transfer function can be written as:

s²+6s+9 = (s+3)²

Step 2: Find the partial fraction of the transfer function. To find the partial fraction, we need to factorize the numerator of the transfer function.

G(s) = (3s+5):(s+3)²= A:(s+3) + B:(s+3)² + C Where A, B, and C are constants.

Multiplying both sides by (s+3)², we get:3s+5 = A(s+3)(s+3) + B(s+3)² + C On substituting s=-3 in the above equation, we get: C = 5/9On equating the coefficients of the terms with s and the constant term, we get:

A + 2B + 9C = 3A + 3B = 0On substituting C=5/9 in the above equation, we get: A = -2/3 and B = 2/9Therefore, the partial fraction of the transfer function can be written as: G(s) = -2/3:(s+3) + 2/9:(s+3)² + 5/9

Step 3: Find the inverse Laplace transform of the partial fraction of the transfer function. The inverse Laplace transform of the partial fraction of the transfer function can be calculated as: \(y(t) = -2/3e^{-3t} + 2/9te^{-3t} + 5/9\)

On substituting y(0) = 3 and y'(0) = −7, we get:3 = -2/3 + 5/9y'(0) = -2 + 10/9 = -8/9

Therefore, the zero input response y(t) can be written as: \(y(t) = -2/3e^{-3t} + 2/9te^{-3t} + 5/9 + 8/9e^{-3t}\)

Therefore, the zero input response y(t) is given as:\(y(t) = (8/9 - 2/3)e^{-3t} + 2/9te^{-3t} + 5/9\)

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Answer:

me kown it

Step-by-step explanation:

The p - value is, 0.3317.

What is test statistic?

In statistical hypothesis testing, a test statistic is a statistic that is employed. A hypothesis test is often defined in terms of a test statistic, which is a numerical summary of a data set that can be used to execute the test and reduces the data to one value.

Given: A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s.

In 1990s, the average amount of time spent playing computer games was 10. 2 hours per week.

Is the amount of time greater than that for this year? twenty students were surveyed and asked how many hours they spent playing video games.

The test statistics is equal to 0.45.

H0: μ = 10.2

H1: μ > 10.2

Test statistic:

t = 0.45          (since n is small)

P value = 0.3317

Hence, the p - value is, 0.3317

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Answer:

the answer is option A

Step-by-step explanation:

Distance between two points

/XY/ = √((X2-X1)²+(Y2-Y1)²)

Therefore

/XY/= √((7-(-5)²+(15-4)²)

Answer:

First a farl we should know,

Distance (d) = √(x2-x1)^2+ (y2-y1)^2

x(-5,4) = (x1, y1)

y(7,15) = (x2, y2)

Now,

Distance (d) = √(x2-x1) + (y2-y1)

Ans = √(7-5)^2 + (15-4)^2

Answred by : - ||Ziddiboy||

Answer:

y (is less than or equal to) 3

Step-by-step explanation:

i hope this helps :)

The value of the inequality will be : y ≥ -10 .

Given ,

y-5 ≥ -15

Here,

y-5 ≥ -15

To solve the given inequality,

Take -5 from LHS to RHS of inequality,

y ≥ -15 + 5
y≥ -10

Thus the value of y will be equal to or greater than -10 .

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Answer:

1.6

Step-by-step explanation:

x is 8 units,the length of a side of the hexagon or square, where the perimeter of the square increased by 32 units will be equal to the perimeter of the hexagon.

The concept of a six-sided shape is derived from the Greek word hexágnon, where the word gonia means "angle." This makes sense since a hexagon includes not only six sides, but also six angles, or vertices.

Hexagons are six-sided polygons in geometry. The term "regular hexagon" refers to a hexagon whose side lengths and angle measurements are all equal. In other words, a regular hexagon's sides are congruent.

In order to solve this problem, where we are given that a square and a regular hexagon have sides of the same length.

The perimeter of the square increased by 32 units will be equal to the perimeter of the hexagon.

So  we use the formula for the perimeter of a square which is:  

P = 4x,

and the formula for the perimeter of a regular hexagon is  P = 6x.

Compare this two equation and get -

4x + 32 = 6x,

so x = 8.

Therefore, the length of each side of the square and hexagon is 8 units.

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Given a block play problem, the minimum number of blocks Agnes can use to build a tower is 3 or 1.

To calculate the average (mean) of a set of values, first divide by the number of values in the set. Therefore, the sum of the values in the set is equal to their average multiplied by the number of values in the set. The average number of blocks in each tower was 25, and since there were 5 towers, the total number of blocks used was 5 × 25 = 125. Yuri's Tower used 32 blocks, so the remaining towers used a total of 125 minus 32 = 93 blocks.

To find the minimum possible number of blocks for Agne's tower, let the other three towers use as many blocks as possible. Now we know that Yuri's tower used the most blocks and each tower used a different number of blocks. So the other 3 towers can use up to 31, 30 and 29 blocks respectively. The result was an absolute minimum number of blocks that Agnes could use, 93 - 31 - 30 - 29 = 3

By the way, the minimum number of blocks Agnes can use is not 93 - 32 - 32 - 32 = - 3 , but negative value is not possible. so, if everyone could use the same number of blocks. Agnes must have used at least one block, as it is possible to use a negative number of blocks.

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On solving the problem, 160 square feet will be the area of the garden be  after he doubles the length and width.

A flat (2-D) surface's or an object's shape's total area is known as its area. On a piece of paper, use a pencil to draw a square. It is a 2-D figure. Its Area refers to the area that the shape occupies on the paper. Imagine that your square is now composed of smaller unit squares.

we have,

rectangular garden with an area = 40 square feet.

Each dimension of the rectangular has been increased by doubling.

Now

Area = L X W

if the area is doubled

= > (2XL)(2XW)

=>  ( 4 X L W)

= > 4X40

=>  160

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Answer:

C

Step-by-step explanation:

Answer:

The tip was 30% percent

Step-by-step explanation:

All you have to do is the following, total price difference/ original price. 4.20/14 is 0.3, so 30 percent.

The vector field F(x, y, z) = eyzi + xzeyzj + xyeyzk is conservative, and a potential function f is f(x, y, z) = xeyzi + xy²ezj + xyzek + C

How to determine vector field?

To determine if a vector field is conservative, we need to check if its curl is zero. If the curl is zero, it implies that the vector field can be expressed as the gradient of a scalar function.

Taking the curl of F, we have:

curl(F) = (∂F₃/∂y - ∂F₂/∂z)i + (∂F₁/∂z - ∂F₃/∂x)j + (∂F₂/∂x - ∂F₁/∂y)k

Evaluating the partial derivatives, we get:

curl(F) = (z - z) i + (x - x) j + (y - y) k

= 0

Since the curl of F is zero, the vector field F is conservative. We can find a potential function f by integrating each component of F with respect to its respective variable:

f(x, y, z) = ∫eyzi dx = xeyzi + g₁(y, z)

∫xzeyzj dy = xy²ezj + g₂(x, z)

∫xyeyzk dz = xyzek + g₃(x, y)

Here, g₁, g₂, and g₃ are arbitrary functions of the remaining variables. Combining these results, we obtain the potential function:

f(x, y, z) = xeyzi + xy²ezj + xyzek + C

Where C is the constant of integration. Therefore, a potential function f exists for the given vector field F, and it is given by f(x, y, z) = xeyzi + xy²ezj + xyzek + C.

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Answer:

all radii of the same circle are congruent

tangents to a circle that intersect are congruent

side CO is congruent to side CO

SSS congruency theorem

Step-by-step explanation:

The triangle △ACO ≅ △BCO are congruent to each other by SAS postulate.

Given: ∠AOB is a central angle and ∠ACB is a circumscribed angle.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

We know that the radius and the tangent are perpendicular to each other.

Then the angle ∠CAO and angle ∠CBO are of 90°.

We know that the tangent of the circle drawn from the point outside the circle will be 2, and these tangent are of equal length.

In triangle △ACO ≅ △BCO, we have

CO = CO (Common side)

∠CAO = ∠CBO = 90°

OA = OB (Radius)

Thus, the triangle △ACO ≅ △BCO are congruent to each other by SAS postulate.

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Answer:

y = x/2 -14

Step-by-step explanation:

Since the lines are parallel, their slopes are equal

For the first line, we have

y = 0.5x -8

so comparing this with the standard form y = mx + c

Our m is the slope which is 0.5 here

kindly recall that 1/2 is same as 0.5

so the slope of the line we want to form also is 0.5

Now, we use the point slope form to find the equation of this new line

Mathematically that would be;

y-y1 = m(x-x1)

So;

y-(-17) = 0.5(x-(-6)

y + 17 = 0.5(x + 6)

y + 17 = 0.5x + 3

y = 0.5x + 3-17

y = 0.5x -14

or y = x/2 -14

The domain of g(x) is all real numbers, and the range is (61, ∞) and the range is (61, ∞).

The domain of a function is the set of all possible input values for which the function is defined, while the range is the set of all possible output values.

For the given function g(x) = -1/4 (x−17)² + 61, the domain is all real numbers since there are no restrictions on the input values.

To find the range, we can use the fact that the vertex of the parabola is at (17, 61) and the coefficient of the squared term is negative, indicating a downward opening parabola.

Thus, the maximum value of the function occurs at the vertex and is 61, which is also the minimum possible value. Therefore, the range is (61, ∞).

In summary, the domain of g(x) is all real numbers, and the range is (61, ∞).

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Answer:

The domain of the function is ( -2, -1, 0, 1, 5)

Step-by-step explanation:

The domain is referring to the x-values.

Answer:

Step-by-step explanation:

Corresponding sides of similar triangles have same ratio.

Correct option is D

Answer:

\(m = -2\)

Step-by-step explanation:

Given

\(y = mx - 4\)

See attachment for graph

Required

Find m

From the graph, we have:

\((x,y) = (-4,4)\) at point G

Substitute these values for x and y, respectively in: \(y = mx - 4\)

\(4 = m * -4 - 4\)

\(4 = -4m - 4\)

Collect like terms

\(-4m=4+4\)

\(-4m=8\)

Solve for m

\(m = -2\)

In the given public good provision game, player 1's expected payoff for contributing and not contributing depends on player 2's cutoff point (C*₂). When player 1 contributes, their payoff is v - C₁ if C₁ < C*₂, and 0 if C₁ ≥ C*₂. When player 1 does not contribute, their payoff is always 0.

In this public good provision game, player 1's decision to contribute or not contribute depends on their private cost, C₁, and player 2's cutoff point, C*₂. If player 1 contributes, they incur a cost of C₁ but gain access to the public good valued at v dollars. However, if C₁ is greater than or equal to C*₂, player 1's expected payoff for contributing would be 0 since player 2 would not contribute.

On the other hand, if player 1 does not contribute, their expected payoff is always 0, as they neither incur any cost nor receive any benefit from the public good. Therefore, player 1's expected payoff for not contributing is constant, irrespective of the cutoff point.

To determine player 1's expected payoff for contributing, we consider the case when C₁ is less than C*₂. In this scenario, player 2 contributes to the public good, allowing both players to consume it. Player 1's payoff would then be v - C₁, which represents the value of the public good minus their cost of contribution. However, if C₁ is greater than or equal to C*₂, player 1's contribution would be futile, as player 2 would not contribute. In this case, player 1's expected payoff for contributing would be 0, as they would not gain access to the public good.

In summary, player 1's expected payoff for contributing is v - C₁ if C₁ < C*₂, and 0 if C₁ ≥ C*₂. On the other hand, player 1's expected payoff for not contributing is always 0. Therefore, when C₁ is low, player 1 would prefer to contribute, as long as the cost of contribution is less than player 2's cutoff point.

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