Combine the like terms to create an equivalent expression:
-2x-x+8

Answer:

156.25

Step-by-step explanation:

8x2 (2 years) = 16. 2500 / 16 = 156.25

We can use trigonometry to solve this problem. Let h be the height of the radio tower. Then we have:

tan(69°) = h/60

Multiplying both sides by 60, we get:

h = 60 tan(69°)

Using a calculator, we find that:

h ≈ 178.37 feet

Therefore, the height of the radio tower is approximately 178.37 feet.

Answer:

3%

Step-by-step explanation:

11.18 x .03 = .33

Answer:

x = cd-by/ a

Step-by-step explanation:

ax + by / c = d

ax + by = cd

ax = cd-by

x = cd-by/a

Answer:

B

Step-by-step explanation:

You can multiply both sides by c to remove the fraction part.

d(c) = ax + by/c(c)

dc = ax + by

Then subtract "by" from both sides to isolate x.

dc - by = ax - by + by

dc - by = ax

Then divide both sides by a to completely isolate the variable x.

(dc - by)/a = ax/a

(dc - by)/a = x

B

Answer:

17

Step-by-step explanation:

5y - 8 = 9y - 28

-8 = 4y - 28

4y = 20

y = 5

9(5) - 28

45 - 28

17

Answer:

Step-by-step explanation:

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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Answer:

cheap.....

7/10 + 3/10

solve d rest

Find the area of the full circle:

Area = pi x r^2

Area = 3.14 x 17^2

Area = 907.46 square units

A full circle is 360 degrees. The sector is 120degrees.

Multiply the area of the circle by the sector degrees/ full circle degrees

907.46 x 120/360 = 302.486 square units round off as needed.

Answer:

289/3\(\pi\) m² or 302.6400923... m²

Step-by-step explanation:

These type of questions are very simple, you just have to know how to approach them properly. I'll give you the general structure using this as an example for your understanding.

The general structure goes like this:

Area of a circle is \(\pi r^{2}\), so \(\pi\)×17² = 289\(\pi\) m²

The angle is 120° out of 360°, think of a sector as the percentage of the area of the circle.

120/360 = 1/3

1/3 × 289\(\pi\) = 289/3\(\pi\) m² or 302.6400923... m²

Answer:

median = 78.5

Step-by-step explanation:

the median is the middle value of the data set arranged in ascending order. If there is no exact middle value then it the average of the values either side of the middle.

arrange scores in ascending order

45 , 63 , 77 , 80 , 86 , 93

                  ↑ middle

median = (77 + 80) ÷ 2 = 157 ÷ 2 = 78.5

Answer:

Approximately 328.067

Step-by-step explanation:

The value of 19,356 ÷ 59 is approximately 328.068.

Full Answer: 328.06779661

The cracking moment of the cantilever beam is 109,319.79 Nm. The effective moment of inertia of the cantilever beam is 16,783,570.08 mm^4. The instantaneous deflection of the cantilever beam is 4.53 mm.

1. Cracking Moment:
The cracking moment is the moment at which the tensile stress in the bottom fibers of the beam reaches the allowable tensile strength of the concrete. To calculate the cracking moment, we need to determine the moment of inertia of the beam and the distance from the neutral axis to the extreme fiber in tension.

The moment of inertia (I) can be calculated using the formula:
I = (b × h^3) / 12
where b is the width of the beam (300 mm) and h is the height of the beam (450 mm).

I = (300 × 450^3) / 12 = 14,062,500 mm^4

The distance from the neutral axis to the extreme fiber in tension (c) can be calculated using the formula:
c = h / 2 = 450 / 2 = 225 mm

Now, we can calculate the cracking moment (Mc):
Mc = (0.5 × fctm × I) / c
where fctm is the mean tensile strength of the concrete.

Given that fc′ = 21 MPa, we can convert it to fctm using the formula:
fctm = 0.3 × fc′^(2/3)
fctm = 0.3 × 21^(2/3) = 3.13 MPa

Substituting the values into the cracking moment formula:
Mc = (0.5 × 3.13 × 14,062,500) / 225 = 109,319.79 Nm

Therefore, the cracking moment of the cantilever beam is 109,319.79 Nm.

2. Moment of Inertia Effective:
The effective moment of inertia (Ie) takes into account the presence of reinforcement in the beam. To calculate the effective moment of inertia, we need to consider the contribution of the reinforcement to the overall stiffness of the beam.

The effective moment of inertia can be calculated using the formula:
Ie = I + As × (d - d')^2
where As is the area of reinforcement, d is the distance from the extreme fiber to the centroid of the reinforcement, and d' is the distance from the extreme fiber to the centroid of the compressive reinforcement.

Given that we have 3-20 mm diameter rebar for tension, we can calculate the area of reinforcement (As) using the formula:
As = (π/4) × (20)^2 × 3 = 942.48 mm^2

The distance from the extreme fiber to the centroid of the reinforcement (d) can be calculated as half the height of the beam minus the cover to the reinforcement (cc) minus the diameter of the reinforcement (20 mm):
d = (h/2) - cc - (20/2)
d = (450/2) - 40 - 10 = 180 mm

The distance from the extreme fiber to the centroid of the compressive reinforcement (d') is given as 58 mm.

Now, we can substitute the values into the effective moment of inertia formula:
Ie = 14,062,500 + 942.48 × (180 - 58)^2 = 16,783,570.08 mm^4

Therefore, the effective moment of inertia of the cantilever beam is 16,783,570.08 mm^4.

3. Instantaneous Deflection:
To calculate the instantaneous deflection of the cantilever beam, we need to determine the bending stress caused by the combined effect of the dead load and live load.

The bending stress (σ) can be calculated using the formula:
σ = (M × c) / Ie
where M is the moment at a particular section, c is the distance from the neutral axis to the extreme fiber in tension, and Ie is the effective moment of inertia.

At the support, the moment (M) can be calculated as the sum of the dead load moment (Mdl) and the live load moment (Mll):
M = Mdl + Mll
Mdl = (dead load per unit length × span^2) / 8 = (20 × 3^2) / 8 = 22.5 kNm
Mll = (live load per unit length × span^2) / 8 = (10 × 3^2) / 8 = 11.25 kNm
M = 22.5 + 11.25 = 33.75 kNm

Substituting the values into the bending stress formula:
σ = (33.75 × 225) / 16,783,570.08 = 0.453 MPa

The instantaneous deflection (δ) can be calculated using the formula:
δ = (5 × σ × L^4) / (384 × E × Ie)
where L is the span of the beam and E is the modulus of elasticity of concrete.

Given that the modulus of elasticity of concrete (E) is approximately 21,000 MPa, we can substitute the values into the deflection formula:
δ = (5 × 0.453 × 3000^4) / (384 × 21,000 × 16,783,570.08) = 4.53 mm

Therefore, the instantaneous deflection of the cantilever beam is 4.53 mm.

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Answer:

A

Step-by-step explanation:

6 minues -2 equals 8 because when subtracting a negative, (thats double negative), you add instead. If you substitute -2 for x in the other part of the situationadn solve it also equals 8 so yeah. Hope this helps :)

Two motorcycles are initially traveling with different velocities and experience different accelerations for a four-second interval. The problem asks for the initial speed difference between the motorcycles and which motorcycle was moving faster.

Let's denote the initial velocities of cycles A and B as vA and vB, respectively. During the four-second interval, cycle A has an average acceleration of 1.8 m/s^2, and cycle B has an average acceleration of 3.8 m/s^2. We can use the formula for average acceleration, a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

From the given information, we have:

Cycle A: aA = 1.8 m/s^2, t = 4 s

Cycle B: aB = 3.8 m/s^2, t = 4 s

Using the formula, we can solve for the initial velocity difference:

aA = (vfA - vA) / 4

1.8 = (vfA - vA) / 4

vfA - vA = 7.2

aB = (vfB - vB) / 4

3.8 = (vfB - vB) / 4

vfB - vB = 15.2

From the above equations, we can see that the speed difference at the beginning of the four-second interval is 7.2 m/s (cycle A) and 15.2 m/s (cycle B).

To determine which motorcycle was moving faster, we compare the initial velocities. Since 7.2 m/s is less than 15.2 m/s, cycle A was moving faster initially.

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The y-coordinate is 2 when x=0.

The slope or gradient of the line is a mathematical term used to describe the direction and steepness of a line. The ratio of the change in the y coordinate to the change in the x coordinate is known as the slope of a line. Δ y and Δx are the net changes in the y and x coordinates, respectively.

The slope of a line is calculated as the proportion of the rise to the run, or the increasing divide by the run. The coordinate plane, it describes the slope of the line. Finding the slope between two different points and calculating the slope of a line are similar tasks.

The slope-intercept form is y= mx +c

Here, given that slope m=2

Let us consider that the above equation is passing through (2,2)

2=2(2)+c

c=2

y=2x+2

Therefore, when x=0,

y=2(0)+2

y=2

Therefore, the y-coordinate is 2 when x=0

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The slope of the tangent line to the function f(x) = 6 - 5x² at the point where x = -1 is 10. This means that at x = -1, the function has a tangent line with a slope of 10.

To find the slope of the tangent line to the function f(x) = 6 - 5x² at the point where x = -1, we need to take the derivative of the function and evaluate it at x = -1. Let's go through the steps:

Find the derivative of f(x):

Taking the derivative of f(x) = 6 - 5x² with respect to x, we get:

f'(x) = d/dx(6) - d/dx(5x²) = 0 - 10x = -10x.

Evaluate the derivative at x = -1:

Plugging x = -1 into the derivative, we have:

f'(-1) = -10(-1) = 10.

Interpret the result:

The value obtained, 10, represents the slope of the tangent line to the function f(x) = 6 - 5x² at the point where x = -1.

To find the slope of the tangent line, we first took the derivative of the given function with respect to x. The derivative represents the instantaneous rate of change of the function at any given point.

By evaluating the derivative at x = -1, we found that the slope of the tangent line is 10. This means that at x = -1, the function has a tangent line with a slope of 10.

The slope of the tangent line provides information about how the function behaves locally around the given point. In this case, the positive slope of 10 indicates that the tangent line at x = -1 is upward-sloping, showing the steepness of the curve at that specific point.

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Answer: I know this is a bit late but for anyone looking the answer to this question, i got it right here :D.

Step-by-step explanation: I guessed and got it correct.

The graph representing Sondra's weekly earnings is plotted and attached.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Sondra receives an allowance of $10 per week, plus an additional $5 for each chore she completes.

Assume that her weekly earnings is $y. Assume she does [x] extra chores in a week. Then, we can model her earnings by the equation -

y = 5x + 10.

Refer to the graph attached.

Therefore, the graph representing Sondra's weekly earnings is plotted and attached.

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The Cartesian equation of a plane containing the following points:

P(3,-1,-2), Q(2,2,0) and R(-5,2,1) is 3x - 19y - 27z - 20 = 0.

In order to find the Cartesian equation of a plane in the 3-dimensional space, we need to determine the normal vector n of the plane, which is perpendicular to the plane.

Let's first find two vectors that lie on the plane.

One vector can be the vector connecting points P and Q, and the other can be the vector connecting points P and R. We will use these vectors to find the normal vector of the plane.

Thus, we have:

PQ = Q - P = (2-3, 2-(-1), 0-(-2)) = (-1, 3, 2)

PR = R - P = (-5-3, 2-(-1), 1-(-2)) = (-8, 3, 3)

Now, we will find the normal vector n of the plane.

This can be done by computing the cross product of vectors PQ and PR.

n = PQ x PR= ( -1   3   2  )   x   ( -8   3   3  )i   j   k  

=   3i - 19j - 27k

Therefore, the Cartesian equation of the plane containing points P, Q, and R is:

3(x - 3) - 19(y + 1) - 27(z + 2) = 0

Simplifying, we have:

3x - 19y - 27z - 20 = 0

So, the Cartesian equation of the plane is 3x - 19y - 27z - 20 = 0.

The Cartesian equation of the plane is 3x - 19y - 27z - 20 = 0..

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Answer: X coordinate can be anything.

Step-by-step explanation:

It can be 1, 2, 3, 4 , 5 .........

There must be an equation or something else, to we can work out the answer.

Answer: Multiply the centimeters number by 10.

Step-by-step explanation: There are 10 millimeters in every centimeter.

Step-by-step explanation:

this distance YZ is the height of the triangle WXY.

it splits the main triangle into 2 right-angled triangles WYZ and XYZ.

we can use Pythagoras

c² = a² + b²

with any of the 2 smaller right-angled triangles to get YZ.

remember, "c" is the Hypotenuse (the side opposite to the 90° angle). a and b are the legs.

so, when picking the larger one :

26² = 24² + YZ²

676 = 576 + YZ²

100 = YZ²

YZ = sqrt(100) = 10 = distance of Y to WX.

The mass of 6.56 pints of blood is 3.92 grams.

Given

The density of blood = 1.060 g/mL and mass of 6.56 pints

We have 1L = 2.113 pints

The density of a substance can be defined as the ratio of the mass of the substance to the volume of the substance. In chemistry, density is used to measure the concentration of the substance in the solution.

The expression for density = mass/volume

ρ = m/V

m = ρV

Mass = 1.060(1000ml/1L) × 6.56(1L/ 2.113)

= 3290.8 /1000

= 3.29g

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When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.

We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.

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Answer:

D. y=-2x+4

Step-by-step explanation:

In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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The general solution of the given differential equation is:

y = (1/7) + C * \(exp(-x^7)\)

The exponential of the integral of the coefficient of y, in this case 7x6, provides the integrating factor. The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is 7x⁶.

The integrating factor is therefore exp(∫ 7x⁶ dx), which can be calculated as exp(x⁷/7).

Multiplying both sides of the differential equation by the integrating factor, we have:

exp(x⁷/7) * y' + 7x⁶ * exp(x⁷/7) * y = x⁶ * exp(x⁷/7)

Using the product rule on the left side, we can rewrite the equation as:

d/dx (exp(x⁷/7) * y) = x⁶ * exp(x⁷/7)

Integrating both sides with respect to x, we get:

exp(x⁷/7) * y = ∫ x⁶ * exp(x⁷/7) dx

The integral on the right side can be solved using integration by parts. Let's denote u = x⁶ and dv = exp(x⁷/7) dx. Then, du = 6x⁵ dx and v = 7/7 * exp(x⁷/7) = exp(x⁷/7).

Using the formula for integration by parts:

∫ u dv = uv - ∫ v du

We have:

∫ x⁶ * exp(x⁷/7) dx = x⁶ * exp(x⁷/7) - ∫ exp(x⁷/7) * 6x⁵ dx

Simplifying the integral on the right side, we obtain:

∫ exp(x⁷/7) * 6x⁵ dx = 6 * ∫ x⁵ * exp(x⁷/7) dx

We can apply integration by parts again to this integral, with u = x⁵ and dv = exp(x⁷/7) dx.

Continuing this process, we will eventually reach an integral of the form ∫ exp(x⁷/7) dx, which can be expressed in terms of special functions called exponential integrals.

Once we have the value of this integral, we can substitute it back into the expression for the integral of x⁶ * exp(x⁷/7) dx.

Finally, we divide both sides of the equation by exp(x⁷/7) and solve for y:

y = (1/exp(x⁷/7)) * (∫ x⁶ * exp(x⁷/7) dx)

The resulting expression will give the general solution to the given differential equation.

To solve this linear first-order ordinary differential equation, we can use an integrating factor. The integral of the coefficient of y's exponential integral, in this case 7x⁶, provides the integrating factor.

The integrating factor is therefore exp(∫ 7x⁶ dx), which can be calculated as exp((7/7) * x⁷) = exp(x⁷).

Multiplying both sides of the differential equation by the integrating factor, we have:

exp(x⁷) * y' + 7x⁶ * exp(x⁷) * y = x⁶ * exp(x⁷)

We can rewrite this equation as follows:

d/dx (exp(x⁷) * y) = x⁶ * exp(x⁷)

Integrating both sides with respect to x, we get:

exp(x⁷) * y = ∫ x⁶ * exp(x⁷) dx

To evaluate this integral, we can make a substitution. Let's substitute u = x⁷, then du = 7x⁶ dx.

The integral becomes:

(1/7) ∫ exp(u) du = (1/7) * exp(u) + C = (1/7) * exp(x⁷) + C

Now, dividing both sides of the equation by exp(x⁷), we have:

y = (1/7) + C * exp(-x⁷)

Therefore, the general solution of the given differential equation is:

y = (1/7) + C * exp(-x⁷)

where C is an arbitrary constant.

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Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

Answer:

basketball player scored 40 points in a game. The number of three-point field goals the player made was 22 less than three times the number of free throws (each worth 1 point). Twice the number of two point field goals the player made was 11 more than the number of three point field goals made. Find the number of free-throws, two point field goals, and three point field goals that the player made in the game.

Once I have the equations I understand how to do the problem, but I am obviously doing something wrong because each time I write out the equations I end up getting fractions.