4.4^x+4/4^x=10 solve​

Answer:

Grade 8 Worktext-Science Quarter 3

With 450 kids and chaperone there are 451 passengers to be transported, Using simple unitary method, The answer is 6 buses.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value.

The arithmetic operator is used to carry out mathematical operations on the provided operands, including addition, subtraction, multiplication, division, and modulus.

total members to be transported = 451

each bus hold = 80

Number of bus needed = 451/80 = 5.63

So, We need 6 buses in total.

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Answer: Can you tell me how do you want it answered?

Step-by-step explanation:

Answer:

its 3 3/4 :)

Step-by-step explanation:

Answer:

turtle biscuit believes in you

Answer: g

( 2x+6) = 4x^2+26x+44

Step-by-step explanation: Set up the composite function and evaluate. Hope this helps! :)

Given:

Total investments = $25000

She estimates the following:

Probability 0.2 of a $15,000 loss (-$15,000)

Probability 0.05 of a $20,000 loss (-$20000)

Probability 0.3 of a $35,000 profit (+35000)

Probability 0.45 of breaking even ($0)

Total probability = 0.2 + 0.05 + 0.3 + 0.45 = 1

Since the total probability is 1, to find the expected value of profit, we have:

Solving further:

Therefore, the expected value of the profit is $6,500

ANSWER:

a) $6,500

The probability distribution of X is 0.5, 0.25, 0.25, and 0.125. Mean value ∑ X × P (X) = 1.875. Standard Deviation of X = 1.0533

a) For a fair coin,

P(H) = P(T) = 0.5

Outcome  X                            Probability

T                  1                                  0.5

HT              2                       0.5×0.5 = 0.25

HHT          3                       0.5×0.5×0.5 = 0.125

HHHT          4                           0.5×0.5×0.5×0.5 = 0.0625

HHHH          4                           0.5×0.5×0.5×0.5 = 0.0625

So, probability distribution of X is

X P(X)

1 0.5

2 0.25

3 0.125

4 0.0625+0.0625 = 0.125

b)

X     P(X)    X×P(X)         X2×P(X)

1     0.5     0.5          0.5

2     0.25      0.5               1

3     0.125    0.375         1.125

4     0.125       0.5            2

sum 1     E(X) = 1.87

c) Variance = E(X²) - E(X)²

= 4.625 - 1.875²

= 1.1094

Standard Deviation of X = √ Variance

= √1.1094

= 1.0533

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Answer:

26.56

Step-by-step explanation:

tan x = 3/6=1/2

26.56

Answer:

h(5) = 20

Step-by-step explanation:

Assume that '2' is an exponent.

So the question for you should be:-

\( \displaystyle \large{h(x) = {x}^{2} - x}\)

We want to find h(5); we substitute x = 5 in.

\( \displaystyle \large{h(x) = {5}^{2} - 5}\)

5^2 is 5•5 = 25.

\( \displaystyle \large{h(x) = 25 - 5} \\ \displaystyle \large{h(x) = 20}\)

Therefore, h(5) is 20.

Only D is true. The rest are not true

The area of the polygon with the given vertices is

Area=9

This is further explained below.

Generally, A regular polygon is a polygon that is straight equiangular, and equilateral, according to the Euclidean geometry definition. Convex, star, or skew profiles may be assigned to regular polygons.

In conclusion, The specified vertices are used to calculate the area of the polygon.

A=9

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Answer:

Step-by-step explanation:

We cannot measure the period T using the elapsed time for a single revolution because they are not the same thing. Elapsed time is the amount of time that has passed since the beginning of an event, while the period is the amount of time it takes for an event to repeat itself. Let's explore these concepts further.

Single revolution: This refers to a complete rotation or cycle around an object, for example, one rotation of the Earth around its axis. In this case, one revolution would be 24 hours, or 1440 minutes, or 86400 seconds, depending on the units used to measure the elapsed time.

Elapsed time : This refers to the time that has passed since the beginning of an event or process. For example, if you start timing how long it takes a pendulum to complete one cycle when it is at rest and you stop the timer when it completes the next cycle, you would have measured the elapsed time for one cycle. The elapsed time can be measured in seconds, minutes, hours, or any other unit of time.

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The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .

The charge at which anything happens is referred to as the velocity at which it happens.

The required details for mean rate :

(a) H0: µ = 21.62

Ha: µ ≠ 21.62

(b) t = -1.231

p-value = 0.2253

(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.

(d) H0: µ = 21.62

Ha: µ ≠ 21.62

t = -1.231

check statistic ≥ 2.020

Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.

The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.

The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.

The crucial values for t at this level of significance are t=2.019.

Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.

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The circumference of a circle: C = 67.98 cm

Radius of the circular lawn, which is difference between outer radius of  path and inner radius of path.

outer radius:  \(r1 = (132 + 2T)/2 = (132 + 2(22))/2 = 88 ft\)

inner radius:  \(r2 = 132/2 = 66 ft\)

radius of circular lawn is r = r1 - r2 = 22 ft

Now using formula for the area of a circle:

A = πr^2 = π(22^2) ≈ 1520.53 ft^2

To find the circumference of a circle with area 367 cm^2, we can use the formula for the area of a circle to find the radius:

\(A = \pi r^2 \\r^2 = A/\pi = 367/\pi\)

r ≈ 10.80 cm

Then we can find the circumference using the formula for the circumference of a circle:

C = 2πr ≈ 2π(10.80) ≈ 67.98 cm

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A line needs 2 points.

To solve the number of lines you can have use the combination formula

8C2 = 8! / 2!(8-2)! = 28

The answer is D. 28

The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.

v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)

= -2 - 6 + 1 = -7

|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

=\(\sqrt{(4 + 9 + 1)}\)

=\(\sqrt{14}\)

|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16) }\)

= (\(\sqrt{21}\)

θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))

=  |A| (-7/21*14)

=  |A|(-7/294)

= 137.8 degrees

The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is

\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

= \(\sqrt{(4 + 9 + 1)}\)

= \(\sqrt{14}\).

The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is

\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16)}\)

= \(\sqrt{21}\)

Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.

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Answer:

(-1,-1)

Step-by-step explanation:

First thing to consider: the expression is y<-2+3 not y<-2x+3

When plotting this on a graph a possible answer is (-1,-1)

Answer:

r

Step-by-step explanation:

r is like a unit

you can subtract terms with the same unit

10r-9r= 1r

1r=r

Answer:

x = 12

y = 13

Step-by-step explanation:

Let's assume the two numbers as x and y.

The sum of the two numbers is 25

So,

The product of the two numbers is 156

Hence, the two numbers are 13 and 12.

Example: we have to find 2 number : a and b

(1)(2) ⇒ 156/b =  25 - b

⇒ 156/b - 25 + b = 25 - b - 25 + b

⇒ b - 25 + 156/b = 0

⇒ (b - 25 + 156/b) × b = 0 × b = 0

⇒ b² - 25b + 156  = 0

⇒ b² - (13b + 12b) + 156 = 0

⇒ b² - 13b - 12b + 156 = 0

⇒ (b² - 13b) + (- 12b + 156) = 0

⇒ b(b - 13) - 12(b - 13) = 0

⇒ (b - 13)(b - 12) = 0

⇒ b = 13 or b = 12

Answer: 12 and 13

OK done. Thank to me :>

The correct answer  is 2.3 with a repeating decimal is equivalent to the simplified fraction 7/3.

To rewrite 2.3 with a repeating decimal as a simplified fraction, we can use a mathematical technique called algebraic manipulation. We start by letting x be equal to 2.3 with a repeating decimal, and then we subtract x from 10x to eliminate the repeating part of the decimal. 10x - x = 23.3333... - 2.3333... = 21

Simplifying, we get: 9x = 21

Dividing both sides by 9, we get: x = 21/9

This fraction can be simplified further by dividing the numerator and denominator by their greatest common factor, which is 3. x = 21/9 = (21 ÷ 3)/(9 ÷ 3) = 7/3

Therefore, 2.3 with a repeating decimal is equivalent to the simplified fraction 7/3.

Repeating decimals can be challenging to work with, but the technique of algebraic manipulation allows us to convert them to equivalent fractions, which can be easier to understand and work with in many contexts.

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To find the shortest distance from a point to a curve/surface using Lagrange multipliers, we need to minimize the distance function subject to the constraint equation.

1. Shortest Distance from (0, b) to the Parabola \(y = x^2\):

Let's define the distance function \(\(D\)\) between the point \(\((0, b)\)\) and the parabola \(\(y = x^2\)\) as:

\(\[D(x, y, \lambda) = x^2 + (y - b)^2 + \lambda(y - x^2)\]\)

We want to minimize \(\(D\)\) with respect to \(\(x\), \(y\), and \(\lambda\).\)

Taking partial derivatives and setting them equal to zero:

\(\[\frac{\partial D}{\partial x} = 2x - 2\lambda x = 0 \implies x(1 - \lambda) = 0\]\)

\(\[\frac{\partial D}{\partial y} = 2(y - b) + \lambda = 0 \implies y = b - \frac{\lambda}{2}\]\)

\(\[\frac{\partial D}{\partial \lambda} = y - x^2 = 0\]\)

From the first equation, we have two possibilities:

1. \(\(x = 0\)\), which leads to \(\(y = b - \frac{\lambda}{2}\) and \(y = x^2\)\) (from the third equation). Substituting \(\(x = 0\)\) into the third equation gives \(\(y = 0\)\).

2. \(\(1 - \lambda = 0\)\), which leads to \(\(\lambda = 1\) and \(x = 1\).\)

Substituting \(\(x = 1\)\) into the third equation gives \(\(y = 1\)\).

Thus, we have two potential solutions: \(\((x, y) = (0, 0)\) and \((x, y) = (1, 1)\).\)

Now, we calculate the distances from \(\((0, b)\)\) to the parabola for each of these solutions:

1. For \(\((x, y) = (0, 0)\)\):

\(\[D(0, 0, \lambda) = 0^2 + (0 - b)^2 + \lambda(0 - 0^2) = b^2\]\)

2. For \(\((x, y) = (1, 1)\)\):

\(\[D(1, 1, \lambda) = 1^2 + (1 - b)^2 + \lambda(1 - 1^2) = 2 - 2b + \lambda\]\)

Comparing the distances, we see that \(\(b^2\)\) is always non-negative, while \(\(2 - 2b + \lambda\)\) can take negative values. Therefore, the shortest distance is \(\(b^2\)\) when \(\((x, y) = (0, 0)\)\).

Hence, the shortest distance from the point \(\((0, b)\)\) to the parabola \(\(y = x^2\)\) is \(\(b^2\)\).

2. Shortest Distance from (0, 0, b) to the Paraboloid \(z = x^2 + y^2\):

Let's define the distance function \(\(D\)\) between the point \(\((0, 0, b)\)\) and the paraboloid \(\(z = x^2 + y^2\)\) as:

\(\[D(x, y, z, \lambda) = x^2 + y^2 + (z - b)^2 + \lambda(z - x^2 - y^2)\]\)

We want to minimize \(\(D\)\) with

respect to \(\(x\), \(y\), \(z\), and \(\lambda\).\)

Taking partial derivatives and setting them equal to zero:

\(\[\frac{\partial D}{\partial x} = 2x - 2\lambda x = 0 \implies x(1 - \lambda) = 0\]\)

\(\[\frac{\partial D}{\partial y} = 2y - 2\lambda y = 0 \implies y(1 - \lambda) = 0\]\)

\(\[\frac{\partial D}{\partial z} = 2(z - b) + \lambda = 0 \implies z = b - \frac{\lambda}{2}\]\)

\(\[\frac{\partial D}{\partial \lambda} = z - x^2 - y^2 = 0\]\)

From the first and second equations, we have two possibilities:

1. \(\(x = 0\)\) and \(\(y = 0\)\), which leads to \(\(z = b\)\) and \(\(\lambda\)\) can take any value.

2. \(\(1 - \lambda = 0\)\), which leads to \(\(\lambda = 1\)\) and \(\(x = y = 0\)\). Substituting \(\(x = 0\)\) and \(\(y = 0\)\) into the fourth equation gives \(\(z = b\)\).

Thus, we have two potential solutions: \(\((x, y, z) = (0, 0, b)\)\) and \(\((x, y, z) = (0, 0, b)\).\)

Now, we calculate the distances from \(\((0, 0, b)\)\) to the paraboloid for each of these solutions:

1. For \(\((x, y, z) = (0, 0, b)\)\):

\(\[D(0, 0, b, \lambda) = 0^2 + 0^2 + (b - b)^2 + \lambda(b - 0^2 - 0^2) = 0\]\)

2. For \(\((x, y, z) = (0, 0, b)\)\):

\(\[D(0, 0, b, 1) = 0^2 + 0^2 + (b - b)^2 + 1(b - 0^2 - 0^2) = 0\]\)

Comparing the distances, we see that both solutions give a distance of 0. Therefore, the shortest distance is 0.

Hence, the shortest distance from the point \(\((0, 0, b)\)\) to the paraboloid \(\(z = x^2 + y^2\)\) is 0.

3. Shortest Distance from (0, 0, b) to the Paraboloid \(z = x^2 + 1/4 y^2\):

Let's define the distance function \(\(D\)\) between the point \(\((0, 0, b)\)\) and the paraboloid \(\(z = x^2 + \frac{1}{4}y^2\)\) as:

\(\[D(x, y, z, \lambda) = x^2 + \frac{1}{4}y^2 + (z - b)^2 + \lambda(z - x^2 - \frac{1}{4}y^2)\]\)

Hence, the shortest distance from the point \(\((0, 0, b)\)\) to the paraboloid \(\(z = x^2 + \frac{1}{4}y^2\)\) is 0.

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When you develop an argument with a major premise, a minor premise, and a conclusion, you are using deductive reasoning. When constructing an argument using deductive reasoning, three components are involved: a major premise, a minor premise, and a conclusion.

Deductive reasoning is a logical process where the conclusion is derived from the major and minor premises. The major premise is a general statement or principle that establishes a broad context or rule.

The minor premise is a specific statement or evidence that relates to the major premise. Finally, the conclusion is the logical inference or outcome that follows from the combination of the major and minor premises.

Deductive reasoning allows for the logical progression from general principles to specific conclusions, making it a valuable tool in fields such as mathematics, logic, and philosophy.

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a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

$390

Step-by-step explanation:

Multiply 600 by 0.35

210

Subtract 210 from 600

$390

This is the new price

Hope this helps :)

A function is even if the graphic is symmetric with respect to the y-axis.

You can symbolize an even function as -f(x)=f(x) for all values of x on the domain of the function f.

A)

The expression |y| indicates that its the absolute value of y. This means that y can be positive or negative.

This function is even.

B)

In this example x is expressed as an absolute value and can be either positive or negative:

This function is symetrical with respect to the y-axis, so it an even function.

C)

This function is not symetrical with respect to the y-axis

D)

This function is not symmetrial with respect to the y-axis

At t = 1.5 the height is 119 feet.

Distance is the measurement of an object from a specific point in the horizontal direction, and height is the measurement of an object in the vertical direction.

Without actually measuring the distances, heights, or angles, one of the principal applications of trigonometry is to determine the angles subtended by any object at a particular position, the height of the object, or both.

Given:

A window washer drops a tool from their platform 155 ft high.

and, polynomial =  -16t² + 155 tells us the height, in feet.

Now, the height after after t = 1.5 seconds.

h(t) = -16r² + 155

h(1.5) = -16t² + 155

h(1.5) = -16(1.5)² + 155

h(1.5) = -16(2.25) + 155

h(1.5) = -36 + 155

h(1.5) = 119 feet

Hence, the height is 119 feet.

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Answer:

y=32

Step-by-step explanation:

y/2 +22=38

y/2= 16

y=32

Answer: Y=32

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

because there's less humidity