What is the number of degrees in the measure of the smaller obtuse angle formed by the hands of a standard clock at 2:48pm

Answer:

3

Step-by-step explanation:

subtract 3y from both sides

add 9 to both sides

3y=12x+9

divide everything by 3

y=4x+3

y-intercept is 3

By using uniform distribution of probability,

Probability that washing dishes will take between 10 and 12 minutes  = \(\frac{2}{5}\)

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, uniform distribution of probability is used

The time taken to wash the dish is uniformly distributed between 9 and 14 minutes

Probability that washing dishes will take between 10 and 12 minutes =

\(\frac{12 - 10}{14 - 9}\\\frac{2}{5}\)

Probability that washing dishes will take between 10 and 12 minutes  = \(\frac{2}{5}\)

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The population was 6.98 million in 1900. The population of New York decreased with respect to time.

What is an exponential function?

An exponential function is a mathematical function with the formula f (x) = axe, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

The population of New York state can be modeled by

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513t}}\)

P is the population and t is the number of years since 1800.

The difference between the year 1900 to 1800 is 100.

Putting t = 100 in the given model:

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513\times 100}}\)

\(P(t)=\frac{19.71}{1+61.22e^{-3.513}}\)

P(t) = 19.71/2.8248

P(t) = 6.9774

P(t) = 6.977 (rounded to the nearest thousands)

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Answer:

So basically the answer is where the lines intersect if they do not intersect there is no solution if they are on top of one another it is infinite solutions

Step-by-step explanation:

Answer:

(a) 0.278

(b) 0.236<p<0.321

Step-by-step explanation:

The explanation is attached below.

Answer:

B. Substitution Property of Equality

(a) To find the upward-pointing unit normal vector at (2,2,1), we need to compute the gradient of the quadratic surface given by 4x² - y² - 2z² = 10.

The gradient is given by:
∇f = <∂f/∂x, ∂f/∂y, ∂f/∂z>
∇f = <8x, -2y, -4z>

At point (2,2,1), the gradient is:
∇f(2,2,1) = <16, -4, -4>

To find the upward-pointing unit normal, we normalize this vector and ensure the z-component is positive:
Unit normal = <16, -4, -4> / |<16, -4, -4>| = <16/18, -4/18, -4/18> = <8/9, -2/9, -2/9>

(b) To find the equation of the tangent plane P at (2,2,1), use the point-normal form of a plane equation:
P: (x - x₀, y - y₀, z - z₀) · <8/9, -2/9, -2/9> = 0
Substitute the point (2,2,1):
P: (x - 2, y - 2, z - 1) · <8/9, -2/9, -2/9> = 0

Expanding this equation, we get:
P: 8(x-2)/9 - 2(y-2)/9 - 2(z-1)/9 = 0

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Answer: i dont know sorry

Step-by-step explanation:

Answer:

118

Step-by-step explanation:

Answer:

1865=100%

1240=less

1240/1865*100

=66,48%

100%-66,48

=33,5 (percent decrease)

Answer:

33.5%

Step-by-step explanation:

Answer:

$26.25

Step-by-step explanation:

I multiply each fee with the number of cards it goes along with, then I added it up all together which is 315. To get the monthly fee I divide 315 by 12 to get the answer.

45(2)+35(3)+30(4)

90+105+120 = 315

315/12 = 26.25

Two point three tens times m equals zero point forty six hundredths

The given equation in the form of a statement can be written as Two times of the sum of the t and 4 times of q is equal to the sum of two times of q and  four times of t.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be written in the form of an statement as:

Two times of the sum of the t and 4 times of q is equal to the sum of two times of q and  four times of t.

Hence, the given equation in the form of a statement can be written as Two times of the sum of the t and 4 times of q is equal to the sum of two times of q and  four times of t.

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1. The slope of the water table between the two wells can be calculated by determining the difference in water table levels and dividing it by the distance between the wells. 2. The slope of Deer Creek can be determined by calculating the difference in elevation between its source and the valley floor and dividing it by the length of the creek. 3. To determine the ground measurements corresponding to 3.5 inches on the map, we need to use the map's scale. The scale of 1:24000 means that 1 inch on the map represents 24000 inches on the ground.

1. To calculate the slope of the water table between the wells, we subtract the water table level at one well (100 feet) from the level at the other well (300 feet), resulting in a difference of 200 feet. Since the wells are half a mile apart (2640 feet), we divide the difference in water table levels by the distance between the wells, giving us a slope of approximately 0.076 ft/mi.

2. The slope of Deer Creek can be determined by subtracting the elevation of its source (2700 meters) from the elevation at the valley floor (1290 meters), resulting in a difference of 1410 meters. Since the creek flows for 8 kilometers, we divide the elevation difference by the length of the creek, giving us a slope of approximately 176.25 m/km or 0.176 m/m.

3. To determine the ground measurements corresponding to 3.5 inches on the map, we use the scale of 1:24000. Since 1 inch on the map represents 24000 inches on the ground, 3.5 inches on the map would represent 84000 inches on the ground, which is approximately 7000 feet or 1.32 miles.

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The context that could be modeled by a linear function is A. A smartphone data plan charges $65/month and $0.46/GB of data used.

The total cost of the data plan depends linearly on the amount of data used.  The monthly fixed cost of $65 represents the y-intercept, and the variable cost of $0.46/GB represents the slope of the linear function.

A linear function is a rule in Maths that links two things on a graph using a straight line.

For instance: y = mx + b

In this equation

y = the thing that depends on something else (like time),

x = the thing it depends on (like distance),

m = how much y changes when x changes and

b = where the line starts on the up-and-down axis.

So, the slope (m) shows how y changes when x changes and the starting point (b) tells us where the line begins.

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B. \( \sqrt{x} + \sqrt{x - 1} \) ✅

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

\( \frac{1}{ \sqrt{x} - \sqrt{x - 1} } \\ \\= \frac{1}{ \sqrt{x} - \sqrt{x - 1} } \times \frac{ \sqrt{x} + \sqrt{x - 1} }{ \sqrt{x} + \sqrt{x - 1} } \\ \\ = \frac{ \sqrt{x} + \sqrt{x - 1} }{ ({ \sqrt{x} })^{2} - { (\sqrt{x - 1} })^{2} } \\\\ [∵(a + b)(a - b) = {a}^{2} - {b}^{2} ] \\ \\= \frac{ \sqrt{x} + \sqrt{x - 1} }{x - (x - 1)} \\ \\= \frac{ \sqrt{x} + \sqrt{x - 1} }{ x - x + 1} \\ \\= \sqrt{x} + \sqrt{x - 1} \)

\(\bold{ \green{ \star{ \orange{Mystique35}}}}⋆\)

The three integers found by solving the system of equations are 16, 116, and -40.

Let's represent the three integers as x, y, and z. From the given information, we can set up the following system of equations:

x + y + z = 92 (Sum of three integers is 92)

x + y = z + 60 (Sum of first and second integers exceeds the third by 60)

z = x - 56 (Third integer is 56 less than the first)

To solve this system of equations, we can use substitution or elimination method. Using substitution method: From equation 3, we have z = x - 56.

Substituting this into equation 2, we get x + y = (x - 56) + 60, which simplifies to y = 116 - x.

Substituting these expressions into equation 1, we have: x + (116 - x) + (x - 56) = 92. Simplifying, we get 2x + 60 = 92, and solving further gives x = 16.

Substituting this value back into equation 3, we get z = 16 - 56 = -40. Finally, substituting the values of x and z into equation 1, we have: 16 + y - 40 = 92, which simplifies to y = 116.

Therefore, the three integers are x = 16, y = 116, and z = -40.

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Answer:

4*x

Step-by-step explanation:

Rachel spent 4 times more, so you multiply.

You need to multiply 4 and x.

The expression would be 4*x

Approximately 2.28% of the data is more than 2 standard deviations above the mean in a normal distribution.

The data follows a symmetrical bell-shaped curve in a normal distribution. The data's average is located in the middle of the curve, and the standard deviation is used to calculate how much the data vary from the average. An outlier is a value that is two or more standard deviations apart from the mean. Approximately 68.27% of the data, 95.45% of the data, and 99.73% of the data are within one standard deviation, two standard deviations, and three standard deviations, respectively, of the mean. As a result, more than two standard deviations are above the mean for 2.28% of the data.

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The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

The area is the total area occupied by a flat (2-D) surface or the form of an object.

Create a square on paper by using a pencil.

Two dimensions make it up.

A form's area on paper is the space it takes up.

So, given, a square metal frame encircles a circular mirror.

The mirror has a 4x radius.

The metal frame's side length is 12x.

According to the basic formula for the area of a circle and a square:

area of a circle = pi * radius * radius

Square Area = Side * Side

In the given situation:

Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x

Squared mirror's Area = 12x * 12x = 144x²

The area of the metal frame is the sum of the areas of the squared and round mirrors.

Metal frame area =   144x² -  50.24x²

Metal frame size = 93.76x²

Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

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Correct question:

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal​ frame?

Answer:

\(AB=4\sqrt{5}\) (Which is the same as \(\sqrt{80}\))

Step-by-step explanation:

In order to find the length of AB, we first need to know the length of AC.

The length of the sides for ACD are

\(a=2\\b=?\\c=10\)

Knowing these values, we can plug them into the pythagorean theorem and solve for the missing side, b

\(a^2+b^2=c^2\\\\b^2=c^2-a^2\\\\b=\sqrt{c^2-a^2} \\\\b=\sqrt{(10)^2-(2)^2} \\\\b=\sqrt{100-4}\\ \\b=\sqrt{96}\)

This means that \(AC=\sqrt{96}\)

Now, let us find the values of a,b and c for our second triangle

\(a=4\\b=x\\c=\sqrt{96}\)

And now time for the pythagorean theorem

\(b=\sqrt{c^2-a^2} \\\\b=\sqrt{(\sqrt{96})^2-(4)^2 } \\\\b=\sqrt{96-16}\\\\b=\sqrt{80} \\\\b=4\sqrt{5}\)

This means that \(AB=4\sqrt{5}\) (Which is the same as \(\sqrt{80}\))

Answer:

2.5, 3, 6, 9, 2.8, 6, 1.5

Is this what you're asking for?

Step-by-step explanation:

Answer: 64

Step-by-step explanation:

Answer:

plzz me

Step-by-step explanation:

The total amount paid for the mortgage will be $123750 and the cost of the mortgage is $178750.

From the information, Kerri takes out a mortgage for $55,000 at 9% for 25 years. The total amount paid will be:

= ($55,000 × 9% × 25)

= $123750

The cost of the mortgage will be:

= $55000 + $123750

= $178750

The monthly payment will be:

= ($55000 + $123750) / 25 years

= $178750/(25 × 12)

= $178750/300

= $595

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Answer:

length × width × height.

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

(a)

To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.

\( (\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) = \)

\( = \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6 \)

\(= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}\)

\( = \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2} \)

(b)

No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.

Answer:3h^2 + 7g^4 + 5f^2 - 4h - 4g^4

Step-by-step explanation:To simplify the expression 2h+3h^2−4g^4+5f^2+11g^4−4h+f^2, we can follow these steps:

Group together like terms:

2h + (-4h) = -2h

3h^2 + f^2 = 3h^2 + f^2

-4g^4 + 11g^4 = 7g^4

This gives us the expression: -2h + 3h^2 + 5f^2 + 7g^4

Combine the constants:

3h^2 + 5f^2 + 7g^4 = 3h^2 + f^2 + 7g^4

Combine the like terms:

-2h + 3h^2 + f^2 + 7g^4 = 3h^2 + f^2 + 7g^4 - 2h

So, the simplified expression is: 3h^2 + 7g^4 + 5f^2 - 4h

After simplifying, the expression we'll get,  2h+3h^2+7g^4+6f^2-4h.

To simplify these algebraic expressions, we need to group the like terms. Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different.

After grouping like terms, perform the required operations. Here we have two operations i.e addition and subtraction. So group the like terms which need to add and those which need to subtract.

For example, Here -4g^4+11g^4 are like terms and 5f^2+f^2 are like terms. So we'll subtract 4 from 11, we'll get 7 and the variable will remain the same that is g^4. Similarly, we'll add 5 and 1, we'll get 6 and the variable will remain the same that is f^2.

Other terms will remain as it is.

2h+3h^2+(-4g^4+11g^4)+(5f^2+f^2)-4h

2h+3h^2+7g^4+6f^2-4h

Therefore the answer is, 2h+3h^2+7g^4+6f^2-4h

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The maximum rate of change always occurs in the direction of the gradient.

The directional derivative of a function f(x, y) in the direction of a unit vector v = ⟨a, b⟩ is defined as follows:

D_vf(x, y) = ∇f(x, y) · v

∇f(x, y) represents the gradient vector of f(x, y), which is defined as ∇f(x, y) = ⟨∂f/∂x, ∂f/∂y⟩. It is a vector that points in the direction of the steepest ascent of the function at a given point (x, y).

v = ⟨a, b⟩ is the unit vector that determines the direction in which we want to compute the derivative.

To show why the maximum rate of change of a function always occurs in the direction of the gradient, we can use the definition of the directional derivative.

Let's consider the dot product ∇f(x, y) · v, where v is a unit vector:

∇f(x, y) · v = ||∇f(x, y)|| ||v|| cosθ

In this equation, ||∇f(x, y)|| represents the magnitude (or length) of the gradient vector, ||v|| is the magnitude of the unit vector v (which is 1), and θ is the angle between ∇f(x, y) and v.

Since ||v|| = 1, the equation simplifies to:

∇f(x, y) · v = ||∇f(x, y)|| cosθ

The maximum value of the cosine function is 1, which occurs when the angle θ between the vectors is 0° (or when they are parallel). In this case, cosθ = 1, and the equation becomes:

∇f(x, y) · v = ||∇f(x, y)||

Therefore, the maximum rate of change of the function f(x, y) occurs when the angle between the gradient vector ∇f(x, y) and the direction vector v is 0°, or when they are parallel. In other words, the maximum rate of change happens when we move in the direction of the gradient.

This result is intuitive since the gradient vector points in the direction of the steepest ascent of the function. Moving in the direction of the gradient allows us to maximize the rate of change of the function at a given point.

If we were to move in a different direction, the dot product would be smaller than the magnitude of the gradient vector, resulting in a slower rate of change.

Therefore, the maximum rate of change always occurs in the direction of the gradient.

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Answer:

3000

Step-by-step explanation:

The solution to the inequality is x ≤ 3.75 and is shown on the number line.

An inequality shows the nonequal comparison of numbers and variables arranged in an expression.

Given the expression:

(-1/3)x + 1/2 ≥ -3/4

Multiply through by 12:

-4x + 6 ≥ -9

Subtract 6 from both sides:

-4x ≥ -15

Divide through by -4:

x ≤ 3.75

The solution to the inequality is x ≤ 3.75

See attachment for the number line

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Answer:

wow thats a lot let me write this down