48:09
Simone applied the distributive property using the greatest common factor to determine the expression that is equivalent to 24 + 56. Her work is shown below.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56

24 + 56 = 8 (4 + 7)

What statement best describes Simone’s error?
Simone did not use the correct factors for 24 in the equation.
Simone did not use the correct factors for 56 in the equation.
Simone did not use the greatest common factor in the equation.
Simone did not use the correct operations in the equation.

Answer:

67

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

x + 55 = 90 (Right angle triangle)

x = 90 - 55

x = 35

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The projection of the point (4,4) onto the line passing through (3,1) is the point on the line that is closest to (4,4). To find this projection, we need to first find the direction vector of the line, which is (3-1, 1-0) = (2,1).

Next, we need to find the vector from the point (3,1) to the point (4,4), which is (4-3, 4-1) = (1,3).

Then, we can use the formula for projecting a vector onto another vector:

proj_v u = ((u · v) / (v · v)) v

where u is the vector we want to project, v is the vector we want to project onto, and · denotes the dot product.

Applying this formula, we get:

proj_v u = ((1,3) · (2,1)) / ((2,1) · (2,1)) (2,1)

= (5/5) (2,1)

= (2,1)

So the projection of (4,4) onto the line passing through (3,1) is the point (3,1) + (2,1) = (5,2).

To find the projection of vector (4, 4) onto vector (3, 1), you can follow these steps:

Step 1: Calculate the dot product of the two vectors.
Dot product = (4 * 3) + (4 * 1) = 12 + 4 = 16

Step 2: Calculate the magnitude squared of the vector you are projecting onto (3, 1).
Magnitude squared = (3 * 3) + (1 * 1) = 9 + 1 = 10

Step 3: Divide the dot product by the magnitude squared.
Scalar = 16 / 10 = 1.6

Step 4: Multiply the scalar by the vector you are projecting onto (3, 1) to find the projection.
Projection = 1.6 * (3, 1) = (4.8, 1.6)

So, the projection of (4, 4) onto (3, 1) is (4.8, 1.6).

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Two circles are concentric circles if and only if they have congruent radii.

When we say that two circles are concentric, it means that they share the same center point. In other words, the centers of the two circles coincide. The main characteristic that makes two circles concentric is that they have the same radius.

The radius of a circle is the distance from the center to any point on the circumference. When two circles have the same radius, it means that the distance from their centers to any point on their circumferences is equal. This makes the circles identical in size and shape.

Conversely, if two circles have congruent radii, it implies that their centers coincide, making them concentric circles. The congruence of the radii ensures that the distance from the center to any point on the circumference is the same for both circles.

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The point needed for the relation is \(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.

The point needed for the relation is \(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.

In this exercise we are supposed to determine the coordinates of a point P under an assumption of rigid transformation. Now, we must use the following symmetry transformations:

Reflection about the x-axis

\(S'(x,y) = S(x,y) - 2\cdot (0, s_{y})\) (1)

Reflection about the y-axis

\(S'(x,y) = S(x,y) - 2\cdot (s_{x}, 0)\) (2)

Where:

If we know that \(P'(x,y) = (3, -4)\), the coordinates for each reflection are, respectively:

Reflection about the x-axis

\(P(x,y) = (3,-4) - 2\cdot (0, -4)\)

\(P(x,y) = (3, 4)\)

\(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.

Reflection about the y-axis

\(P(x,y) = (3, -4) - 2\cdot (3, 0)\)

\(P(x,y) = (-3, -4)\)

\(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.

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Answer:

45

Step-by-step explanation:

1/4 of a number means the number divided by 4. 60/4=15. That's how much she spent, and we have to find the rest. So we do 60-15=45.

Answer:

6

Step-by-step explanation:

150+5x=180(linear pair)

30=5x

x=6

Answer:

Dimensions of the original rectangle:

Length = 19 cm

Width = 11 cm

Step-by-step explanation:

Let

Length = x

Width = y

Original rectangle:

2(Length + width) = 60

2x + 2y = 60

New rectangle has same length with original rectangle but half of the width of the original rectangle when folded

Length = x

Width = 1/2y

2(Length + 1/2width) = 49

2x + y = 49

2x + 2y = 60 (1)

2x + y = 49 (2)

Subtract (2) from (1) to eliminate x

2y - y = 60 - 49

y = 11

Substitute y = 11 into (2)

2x + y = 49

2x + 11 = 49

2x = 49 - 11

2x = 38

x = 38/2

x = 19

Dimensions of the original rectangle:

Length = 19 cm

Width = 11 cm

From the given question the prices of the same car in different countries best value for the car is in the USA with a price of 16000 euros.

We can use the currency conversion rates to compare the prices of the same car in different countries.

The prices of the same car in different countries are as follows:

USA: $20000

Ireland: €17500

England: £15000

Japan: ¥3000000

To compare these prices, we need to convert them to a common currency.

Here, we can use the conversion rates given in the question:

1 pound = 1.18 euro

1 pound = 140 yen

1 pound = 1.25 dollars

Price of car in euros in Ireland: 17500 euros

Price of car in pounds in England: 15000 pounds = 15000 x 1.18

= 17700 euros

Price of car in dollars in USA: 20000 dollars

= 20000 / 1.25 = 16000 euros

Price of car in yen in Japan: 3000000 yen = 3000000 / 140

= 21428.57 euros

Best value for the car is in the USA with a price of 16000 euros.

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The surface area of the cylinder is 2262.9 \(cm^{2}\)

Cylinder is a three-dimensional solid shape that consists of two identical and parallel bases linked by a curved surface. it is made up of a circled surface with a circular top and a circular base.

To find the surface area of a cylinder,

Surface area = 2πr (r + h)

Where π = 22/7

r = 12 cm

h = 18 cm

So, the surface area = 2 * 22/7 * 12 (12 + 18)

SA = 44/7 * 12(12 + 18)

SA = 44/7 * 12(30)

SA = 44/7 * 360

SA = 15840/7

SA = 2262.9 \(cm^{2}\)

Therefore, the surface area of cylinder 2262.9 \(cm^{2}\)

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The composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

To find the composite function k(t(x)), we substitute the expression for t(x) into the function k(t) as follows:

k(t(x)) = 4.5 + 3 - 7t(x)^2 + 3t(x) - 4

k(t(x)) = 4.5 + 3 - 7(ln x)^2 + 3(ln x) - 4

Simplifying this expression, we obtain:

k(t(x)) = -2.5 - 7(ln x)^2 + 3(ln x)

To find the derivative of the composite function, we use the chain rule as follows:

k'(t(x)) = k'(t) * t'(x)

where k'(t) is the derivative of the function k(t) with respect to t, and t'(x) is the derivative of the function t(x) with respect to x.

The derivative of k(t) with respect to t is:

k'(t) = -14t + 3

The derivative of t(x) with respect to x is:

t'(x) = 1/x

Substituting these expressions into the chain rule, we obtain:

k'(t(x)) = (-14t(x) + 3) * (1/x)

k'(t(x)) = (-14ln x + 3/x)

Therefore, the composite function k(t(x)) is -2.5 - 7(ln x)^2 + 3(ln x), and its derivative is -14ln x + 3/x.

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a) The probability of making a type I error, assuming p = 0.7, is 0.2515, or 25.15%.

b) The probability of committing a type II error, assuming p = 0.9, is 0.4029, or 40.29%.

a) Probability of Type I Error (assuming p = 0.7):

A type I error occurs when we reject the null hypothesis (p = 0.7) when it is actually true.

In this case, we reject the null hypothesis if fewer than 11 stains are removed out of 12.

Using the binomial distribution formula,

We have fewer than 11 successes (stains removed) out of 12 attempts, assuming the null hypothesis is true (p = 0.7).

So, P(X < 11) = Σ (nCr) x \(p^r (1-p)^{(n-r)\), where X follows a binomial distribution.

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

P(X < 11) ≈ 0.2515

Therefore, the probability of making a type I error, assuming p = 0.7, is 0.2515, or 25.15%.

b) A type II error occurs when we fail to reject the null hypothesis (p = 0.7) when the alternative hypothesis (p > 0.7) is true.

In this case, we fail to reject the null hypothesis if 11 or more stains are removed out of 12.

Similarly, using the binomial distribution formula,

P(X ≥ 11) = P(X = 11) + P(X = 12)

P(X = 11) = (12C11) x 0.9¹¹ x (1-0.9)⁽¹²⁻¹¹⁾

P(X = 12) = (12C12) x 0.9¹² x (1-0.9)⁽¹²⁻¹²⁾

Calculating these probabilities:

P(X ≥ 11) = P(X = 11) + P(X = 12)

          = (12C11) x 0.9¹¹ x (1-0.9)⁽¹²⁻¹¹⁾+ (12C12) x 0.9¹² x (1-0.9)⁽¹²⁻¹²⁾

          ≈ 0.4029

Therefore, the probability of committing a type II error, assuming p = 0.9, is 0.4029, or 40.29%.

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Answer:

the answer is 48m²

Step-by-step explanation:

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In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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Answer:

35

Step-by-step explanation:

Each line above the numbers multiply it by 1000. So this number is being multiplied by 1000000.

Each "C" is equal to 100, since there are "CCC" the number is 300.

"XL" is equal to 40, because "X" is equal to 10 and "L" is equal to 50, but since he X is on the left of the L we subtract them.

The number CCCXL is then 340, but there are the two lines. So we have:

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

The values of a and b are:

a = 10sin(132-B)/sin(84)

b = 10sin(96-B)/sin(48)

The law of sines, which relates the side lengths of a triangle to the sine of the opposite angles, can be utilized to solve this issue. In particular, for a triangle with sides a, b, and c and inverse points A, B, and C, we have:

a/sin(A) = b/sin(B) = c/sin(C)

let say we have triangle ABC AB=b ,BC = 10  AC =a ,and angle C is 48 degree.

Using this formula, we can find the length of side AC as follows:

a/sin(A) = 10/sin(84) (since angle C is 48 degrees, we know that angle A is 180 - 48 - B = 132 - B degrees)

a = 10*sin(132-B)/sin(84)

To find the length of side AB, we can involve the way that the amount of the points in a triangle is 180 degrees:

A + B + C = 180

B = 180 - A - C = 180 - (132 - B) - 48 = 96 - B

So we know that angle B is 96 - B degrees. Using the law of sines again, we have:

b/sin(B) = 10/sin(48)

b = 10*sin(96-B)/sin(48)

Therefore, the values of a and b are:

a = 10sin(132-B)/sin(84)

b = 10sin(96-B)/sin(48)

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The true statements for the given function f(x) are:

The value of g(1) is 3 and the y- intercept of g(x) is at the point (0, 1) .

The function g(x) = f( x - 3 )

g (1) = f (1 -3 )

       = f (-2 )

       = 3

g (-1) = f (-1 -3)

       = f (-4)

       = - 1

Substituting , x = 0 to find the y intercept of g(x)

g ( 0 ) = f ( 0 - 3)

          =f (-3)

          =1

The y intercept of g(x) is at the point (0, 1)

Thus, options 1 and 4 are the true statements for the given function.

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The calculated value of x in the expression x^(1/12) = 49^(1/24) is 7

From the question, we have the following parameters that can be used in our computation:

x^(1/12) = 49^(1/24)

Express 49 as 7^2

So, we have

x^(1/12) = 7^(2 * 1/24)

Evaluate the products

This gives

x^(1/12) = 7^(1/12)

When both sides of the equations are compared, we have

x = 7

Hence, the value of x in the expression is 7

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f(-5) = 1
f((-7)(5/7)) = f(-5) = 1
When x = 5/7: f(-7(5/7)) - 4 = 1 - 4 = -3

(5/7, -3) is a point on the graph of y = f(-7x) -4

Answer:

 Length is 13 meters

Step-by-step explanation:

  Length:  x + 5

  Width: x

  2L + 2W = Perimeter

  2(x+5) + 2x = 42

  2x + 10 + 2x = 42

  4x + 10 = 42

  4x = 32

    x = 8

Length:  8 + 5 = 13

Width: 8

The homogeneous difference equation for this system is: y[k] = 0.379*y[k-1] - 0.145*y[k-2]

The homogeneous difference equation for a discrete-time system with a sampling period of t=0.2s, a rise time of 1s, and an overshoot of 0.2 can be given as follows:
y[k] = a*y[k-1] + b*y[k-2]
Where y[k] is the output at time k, y[k-1] is the output at time k-1, and y[k-2] is the output at time k-2. The coefficients a and b are determined by the system's sampling period, rise time, and overshoot.
To find the coefficients a and b, we can use the following equations:
a = (2*exp(-t/tau))/(1+exp(-2*t/tau))
b = -(exp(-2*t/tau))/(1+exp(-2*t/tau))
Where tau is the time constant of the system, t is the sampling period, and exp is the exponential function. For this system, t=0.2s and tau=1s/ln(1+0.2)=0.223s. Plugging these values into the equations for a and b gives:
a = (2*exp(-0.2/0.223))/(1+exp(-2*0.2/0.223)) = 0.379
b = -(exp(-2*0.2/0.223))/(1+exp(-2*0.2/0.223)) = -0.145
Therefore, the homogeneous difference equation for this system is:
y[k] = 0.379*y[k-1] - 0.145*y[k-2]

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The solutions for the given polynomial function are:

a) The equation for the cubic function is: f(x) = 2(x + 3)(x + 3)(x - 2)

b) The equation for the quartic function is: f(x) = -1/6(x + 2)(x + 2)(x - 3)(x - 3)

a) To determine the equation for the cubic function with zeros -3 (multiplicity 2) and 2 and a y-intercept of -36, we can use the factored form of a cubic function:

\(f(x) = a(x - r_1)(x - r_2)(x - r_3)\)

where \(r_1\), \(r_2\) and \(r_3\) are the function's zeros, and "a" is a constant that scales the function vertically.

In this case, the zeros are -3 (multiplicity 2) and 2. Thus, we have:

f(x) = a(x + 3)(x + 3)(x - 2)

To determine the value of "a," we can use the y-intercept (-36). Substituting x = 0 and y = -36 into the equation, we have:

-36 = a(0 + 3)(0 + 3)(0 - 2)

-36 = a(3)(3)(-2)

-36 = -18a

Solving for "a," we get:

a = (-36) / (-18) = 2

Therefore, the equation for the cubic function is:

f(x) = 2(x + 3)(x + 3)(x - 2)

b) To determine the equation for the quartic function with a negative leading coefficient, zeros -2 (multiplicity 2) and 3 (multiplicity 2), and a constant term of -6, we can use the factored form of a quartic function:

\(f(x) = a(x - r_1)(x - r_1)(x - r_2)(x - r_2)\)

where \(r_1\) and \(r_2\) are the zeros of the function, and "a" is a constant that scales the function vertically.

In this case, the zeros are -2 (multiplicity 2) and 3 (multiplicity 2). Thus, we have:

f(x) = a(x + 2)(x + 2)(x - 3)(x - 3)

To determine the value of "a," we can use the constant term (-6). Substituting x = 0 and y = -6 into the equation, we have:

-6 = a(0 + 2)(0 + 2)(0 - 3)(0 - 3)

-6 = a(2)(2)(-3)(-3)

-6 = 36a

Solving for "a," we get:

a = (-6) / 36 = -1/6

Therefore, the equation for the quartic function is:

f(x) = -1/6(x + 2)(x + 2)(x - 3)(x - 3)

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Answer:

how many toys are in each group?

Answer:

TS = 6.6 (nearest tenth)

Step-by-step explanation:

Secant: a straight line that intersects a circle at two points.

Tangent: a straight line that touches a circle at only one point.

Theorem

When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Given:

⇒ QR² = TR · SR

⇒ 19² = (TS + 16) · 16

⇒ 361 = (TS + 16) · 16

⇒ 22.5625 = TS + 16

⇒ TS = 22.5625 - 16

⇒ TS = 6.5625

⇒ TS = 6.6 (nearest tenth)