Chad is making a cake for the first time. His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try. He uses a small spoon to remove the extra sugar. If he needs to remove 12 spoonfuls, how many milligrams of sugar does his spoon hold?

Answer:

sqrt(95)

Step-by-step explanation:

c^2 = a^2 +  b^2

12^2 = 7^2 + b^2

144 = 49 + b^2

95 = b^2

sqrt(95) = b

Answer:

(0, 7)

Step-by-step explanation:

Using the midpoint formula expressed as;

M (X, Y )= [(ax1+bx2/a+b), (ay1+by2/a+b)]

where a and b are the ratios

Given

a = 2

b = 1

x1 = -3

y1 = 6

x2 = 6

y2 = 9

Get the coordinate of B

Get X;

X = ax1+bx2/a+b

X = 2(-3)+1(6)/2+1

X = -6+6/3

X = 0/3

X = 0

Get Y;

Y = ay1+by2/a+b

Y = 2(6)+1(9)/2+1

Y = 12+9/3

Y = 21/3

Y = 7

Hence the coordinate of B is (0, 7)

TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

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The absolute value of the determinant gives us the area of the parallelogram, which is 21 square units.

To begin, we need to find the vectors that represent the edges of the parallelogram. Recall that a vector is a quantity that has both magnitude and direction. The vector that represents an edge of the parallelogram is simply the difference between the coordinates of its endpoints. For example, the vector that represents the edge connecting the points (3,0) and (9,1) is given by:

<9-3, 1-0> = <6,1>

Similarly, we can find the other three vectors:

<0-3, 3-0> = <-3,3>

<6-0, 4-3> = <6,1>

<0-6, 3-4> = <-6,-1>

Next, we need to arrange these vectors as the rows or columns of a 2x2 matrix. It doesn't matter which arrangement we choose, as long as we are consistent. For this problem, let's use the rows:

| 6 1 |

|-3 3 |

Now, we can take the determinant of this matrix, which is given by:

det(S) = (6)(3) - (1)(-3) = 21

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Complete Question:

Let S be the parallelogram with vertices (3, 0), (9,1), (0,3), and (6,4) in R2. Find the area of S using determinants. Hint: you will first want to find the vectors that represent the edges of the parallelogram

The greatest common factor of the polynomial expression 16y^3-8y^2-20y is; 4y.

As evident in the task content, the greatest common factor of the expression 16y³ - 8y² - 20y is to be determined.

On this note, we have that;

Since 4y is the greatest of all common factors to all terms of the polynomial expression;

16y³ - 8y² - 20y = 4y (4y² - 2y - 5).

Ultimately, the required greatest common factor is; 4y.

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Answer:

The volume of only the cheese popcorn is 392.5 cubic inches.

Step-by-step explanation:

To determine the volume of only the cheese popcorn,

First, we will determine the volume of the cylindrical tin

The volume of a cylinder is given by

V = πr²h

Where V is the volume of the cylinder

π is a constant, (Take π = 3.14)

r is the radius of the cylinder

and h is the height of the cylinder

From the question, the tin is 10 inches in diameter and 15 inches tall.

Diameter = 10 inches, therefore, we can find radius

Radius = Diameter/2 = 10/2 = 5 inches

r = 5 inches

h = 15 inches

Now, putting the values into the equation, we get

V = 3.14 × 5² × 15

V = 1177.5 cubic inches

This is the volume of the cylindrical tin.

Since the cylindrical tin is divided into three equal sections of caramel, cheese, and buttered flavors, then the volume of only the cheese popcorn will be one-third of the total volume of the cylindrical tin.

∴ The volume of only the cheese popcorn = 1/3 × 1177.5 = 392.5 cubic inches

Hence, the volume of only the cheese popcorn is 392.5 cubic inches.

P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

1) The statement is true. Suppose (x^,y^) is an extreme point of P. To show that x^ is an extreme point of Q, we need to prove that for any two distinct points x_1, x_2 in Q, the line segment connecting x_1 and x_2 lies entirely in Q. Since Q is the projection of P onto x-space, it means that for any x in Q, there exists y in R^k such that Ax + By ≥ b.

Now, let's assume x_1 and x_2 are two distinct points in Q. Since they belong to Q, there exist corresponding y_1 and y_2 in R^k such that Ax_1 + By_1 ≥ b and Ax_2 + By_2 ≥ b. Since P is a polyhedron, the set of points that satisfy Ax + By ≥ b is a convex set. Therefore, the line segment connecting x_1 and x_2, denoted by [x_1, x_2], lies entirely in P. Since the projection of a convex set onto a subspace is also a convex set, [x_1, x_2] lies entirely in Q. Thus, x^ is an extreme point of Q.

2) The statement is false. Suppose x^ is an extreme point of Q. It does not necessarily imply the existence of a corresponding y^ such that (x^, y^) is an extreme point of P. This is because the projection Q onto x-space may not capture all the extreme points of P. It is possible for multiple points in P to project to the same point in Q, making it impossible to uniquely determine y^.

3) The statement is true. If x^ is an extreme point of Q and P does not contain a line, then there exists a corresponding y^ such that (x^, y^) is an extreme point of P. Since P does not contain a line, it means that for any x in R^n, there exists a unique y in R^k such that Ax + By ≥ b. Therefore, x^ is uniquely determined by y^, and (x^, y^) is an extreme point of P.

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To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data

The answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.

In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.

Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.

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Answer:

27.

Step-by-step explanation:

3 to the power of 3 = 3*3*3

3*3 = 9.

9*3 = 27

Hope this helps!

Answer: 60

Step-by-step explanation:

-10 x -6 = 60

Negative x Negative = Positive

Answer: 60

Step-by-step explanation: When multiplying integers,

if the signs are the same, the product is positive.'

So a negative times a negative always equals a positive.

So in this problem, -10 × -6 is 60.

The expression represents the probability that both students chosen are sophomores is C( 6 , 1 ) * C ( 5 , 1 ) / C ( 20 , 2 ) .

Given :

The requested probability can be computed as the ratio between the number of ways to choose two sophomores in alternate positions \(N_s\) and the total number of possible choices \(N_t\) .

p = \(N_s\) / \(N_t\)

There are 6 sophomores and 14 freshmen to choose from each separate set. There are 20 students in total .

We'll assume the positions of the selections are NOT significative, i.e. student A/student B is the same as student B/student A.

To choose 2 sophomores out of the 6 available, the first position has 6 elements to choose from, the second has now only 5.

C( 6 , 1 ) * C ( 5 , 1 ) ways .

The total number of possible choices is C ( 20 , 2 )

Probability = C( 6 , 1 ) * C ( 5 , 1 ) / C ( 20 , 2 )

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Full question :

Six sophomores and 14 freshmen are competing for two alternate positions on the debate team. Which expression represents the probability that both students chosen are sophomores? StartFraction (6 C 1) (5 C 1) Over 20 C 2 EndFraction StartFraction (6 P 1) (5 P 1) Over 20 P 2 EndFraction StartFraction (20 C 6) (19 C 5) Over 20 C 2 EndFraction StartFraction (20 P 6) (19 P 5) Over 20 P 2 EndFraction

Answer:

last one. 9 × 10^4 is 300 times larger than 3 × 10^2

Step-by-step explanation:

this is because

9 × 10 × 10 × 10 × 10 = 90,000

and

3 × 10 × 10 = 300

there difference is x300 for the second one to reach it.

Answer:5

Step-by-step explanation:

30 chapters in 6 hours. 30/6 =5

The value of a for which the function g(x) is continuous at x = -2 is a = 1/4.

Given function:

g(x) = ax + 3 for x < -2and g(x) = x² + 2x for x ≥ -2.

Now, to check the continuity of the function at x = -2, we have to equate both functions at x = -2.

In other words,

g(-2) = a(-2) + 3

= (-2)² + 2(-2)

In simplification,

we get:

4a - 1 = 0

⇒ 4a = 1

⇒ a = 1/4

Thus, the value of a for which the function g(x) is continuous at x = -2 is a = 1/4.

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(50 - 45) / (90 - 45) = 0.5.

The probability that the painting time of an automobile will be more than 50 minutes is 0.5 because the painting time is uniformly distributed between 45 minutes to 90 minutes.

Mathematically speaking, the probability can be calculated by subtracting the lower limit of the time range (45 minutes) from the given time (50 minutes) and then dividing it by the difference between the upper limit of the time range (90 minutes) and the lower limit of the time range (45 minutes).

So, the probability of the painting time being more than 50 minutes is: (50 - 45) / (90 - 45) = 0.5.

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Answer:

Primero, dibuje el escenario. El camino tomado por Shane forma un triángulo rectángulo. La distancia desde el punto de partida forma la hipotenusa.

By using the SSS triangle property we will find the angle of the triangle.

SSS means-Side Side Side

"SSS" is when we know three sides of the triangle, and want to find the missing angles.

To solve an SSS triangle we use the following steps:

First to calculate one of the angles we use the Law of Cosines

Apply the same process the Law of Cosines again to find another angle.

finally, use the angles of a triangle to add to 180° to find the last angle.

We use the "angle" of the Law of Cosines:

\(cos(C)=\frac{a^2+b^2-c^2}{2ab}\)

\(cos(A)=\frac{b^2+c^2-a^2}{2ab}\)

\(cos(B)=\frac{a^2+c^2-b^2}{2ab}\)

By using these formulas the angles of a triangle are measured.

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Step-by-step explanation:

Given Function

f(x) = 2.5x + 150

f^-1(x) = ?

Let y = f(x)

y = 2.5x + 150

Interchanging the role of x and y we get,

x = 2.5y + 150

x - 150 = 2.5y

y = (x - 150) / 2.5

So therefore

f^ -1(x) = (x - 150) / 2.5

Hope it will help :)

Answer:

2/7

Step-by-step explanation:

✓To determine the fraction of the bag of trail mix gotten by each friends, we will need to divide the 2 bags of the trail mix by the number of friends ( 7 friends)

✓ The division can be written in terms of fraction which is

( 2 bags / 7 friends)

= 2/7

✓ The share of each friend = 2/7 of the bag of the trail mix

✓ Hence, fraction of a bag of trail mix that each friend get is 2/7

Answer:

1 second - 0.5m

2 seconds - 1m

3 seconds - 1.5m

4 seconds - 2m

Step-by-step explanation:

Answer:

1) The equation for the of the ball in y = a·(x - h)² + k is;

y = -16·(x - 5)² + 25

2) The height of the dock, d =  -375 feet below the water level

Step-by-step explanation:

1) The question is with regards to quadratic function representing projectile motion

The given parameters are;

The height the ball reaches 4 seconds after Sarah kicked the ball = 9 feet

The time the ball hits the water = 6 seconds after reaching the 9 feet height

The form of the quadratic equation representing the motion is given as follows;

y = a·(x - h)² + k = a·x² - 2·a·h·x + a·h² + k

Let 'x' represent the time of motion of the ball, and let 'a', represent the acceleration due to gravity, we have;

The equation for the ball, y = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

h = The horizontal component of the vertex coordinate = 0

Therefore, we have;

When x = 0, y = d

d = -16·(0 - h)² + k =  -16·h² + k

d = -16·h² + k  

When x = 4, y = 9 - d

9 - d = -16(4 - h)² + k = -16(4 - h)² + k

When x = 2, y = d

d = -16(2 - h)² + k

When x = 6, y = 9

9 = -16(6 - 5)² + k

When x = 8, y = d

d = -16(8 - h)² + k

-16(8 - h)² - (-16(2 - h)²) = 0

h = 5

From 9 - d = -16(4 - h)² + k = -16(4 - 4)² + k

d = 9 - k

9 = -16(6 - h)² + k

k = 9 + 16(6 - 5)² = 25

d = 9 - k = 9 - 25 = -16

Therefore, h = 5, k = 25

The equation for the of the ball in y = a·(x - h)² + k is therefore;

y = -16·(x - 5)² + 25

2) When x = 0, y = d, ∴ d = -16(0 - 5)² + 25 = -375 feet below the water

The height of the dock, d =  -375 feet below the water level

Answer: Sam is 14 years old.

Step-by-step explanation:

Equation: 20/2+4= 14

Solution: Do order of operations or PEMDAS. Parentheses, exponents, multiplication or division, addition or subtraction.

20/2= 10+4= 14.

Answer:

es 51.75

Step-by-step explanation:

por que al sumar 45 + 15 porciento da 51.75

Answer:

See below ↓↓

Step-by-step explanation:

(a) Most variability

(b) Highest scores on average

Answer:

82

Step-by-step explanation:

10z^2 - 2z - 2 =

10(3)^2 - 2(3) - 2 =

10(9) - 2(3) - 2 =

90 - 6 - 2 = 82