What are the solutions of the equation 3x + 8x=12

Answer:

Isosceles triangle I think

Step-by-step explanation:

The triangle that will always have at least 1-fold reflectional symmetry is the isosceles triangle. That is option D.

Reflectional symmetry is found in geometric shapes that can be folded over onto itself along a line.

The isosceles triangle has only one line of symmetry or 1-fold reflectional symmetry.

Therefore, the triangle that will always have at least 1-fold reflectional symmetry is the isosceles triangle.

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Answer:

Step-by-step explanation:

same

No, the sum of the magnitudes of two vectors can never be equal to the magnitude of the sum of the same two vectors.

The magnitude of the sum of two vectors is determined by the vector addition process, which takes into account both the magnitudes and the directions of the vectors. The magnitude of the sum of two vectors is generally greater than or equal to the sum of their individual magnitudes.

Mathematically, for two vectors A and B, the magnitude of the sum (|A + B|) is given by the triangle inequality:

|A + B| ≤ |A| + |B|

Equality in the triangle inequality occurs only when the vectors are collinear, meaning they have the same direction or are in opposite directions. In such cases, the vectors can be scaled such that their magnitudes add up to the magnitude of their sum. However, in general, when vectors have different directions, the sum of their magnitudes will always be greater than the magnitude of their sum.

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

Answer:

C

Step-by-step explanation:

I might be wrong. I hope it helps:)

Answer:

23 gallons per hour

Step-by-step explanation:

5 3/4 * 4 = 23

times the amount drank in 1/4 hours by 4 to get the amount drank in 1 hour

(1/4 * 4 = 1 hour (example))

If the distance an athlete throws a hammer follows a normal distribution with mean= 50 feet and standard deviation= 5 feet, then the probability he throws it between 50 feet and 60 feet is 0.4772

To find the probability he throws it between 50 feet and 60 feet, follow these steps:

Hence, the probability he throws a hammer between 50 feet and 60 feet is 0.4772

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The answer is: a. Yes, the forecast fails the bias test.

To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.

If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.

In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.

Therefore, the answer is:

a. Yes, the forecast fails the bias test.

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Answer:

288

Step-by-step explanation:

8x12x3

Answer:

B

Step-by-step explanation:

5^9•5^9/10•5^6/100•5^9/1000 = 5^(9+0.9+0.06+0.009) = 5^9.969

The rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

The Gompertz function is a solution of the differential equation:

dP/dt = c ln(K/P) P

where P(t) is the population at time t, c is a constant, and K is the carrying capacity, i.e., the maximum population that can be sustained by the available resources.

To solve this differential equation, we can use separation of variables:

dP/P ln(K/P) = c dt

Integrating both sides, we get:

∫ dP/P ln(K/P) = ∫ c dt

Integrating the left-hand side requires a substitution. Let u = ln(K/P), then du/dP = -1/P and the integral becomes:

-∫ du/u = -ln|u| = -ln|ln(K/P)|

The right-hand side is just:

c t + C

where C is an arbitrary constant of integration.

Putting these together, we get:

-ln|ln(K/P)| = ct + C

Taking the exponential of both sides, we get:

|ln(K/P)| = e^(-ct-C)

Using the absolute value is unnecessary, since ln(K/P) is always positive, so we can drop the absolute value and write:

ln(K/P) = e^(-ct-C)

Solving for P, we get:

P = K e^(-e^(-ct-C))

This is the Gompertz function, which gives the population as a function of time, under the assumption that the rate of population growth is proportional to the logarithm of the ratio of the carrying capacity to the current population.

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Answer:

the answer is B

x = 1

Step-by-step explanation:

the symmetry is in the middle of the curve like a mirror and the equation of the mirror or symmetry line is x=1

Answer:6

Step-by-step explanation:

day one-2 bread

day two-4 bread

10-4=6

6 at the end of the day

The number of loaves of bread remaining at the end of second day = 6 loaves of bread

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let number of loaves of bread remaining at the end of second day be A

The total number of loaves of bread = 10 loaves

The number of loaves of bread sold each day = 2 loaves

Substituting the values in the equation , we get

So , the number of loaves of bread remaining at end of first day = 10 - 2 = 8

Now , the number of loaves of bread remaining at end of second day = 8 -2

The number of loaves of bread remaining at the end of second day = 6

Therefore , the value of A is 6 loaves of bread

Hence , the equation is A = 6 loaves

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The area of a shape is the amount of space on it:

The shaded area is 314 square centimeters

Start by calculating the area of sectors OFG and OAD using:

\(A = \frac{\theta}{360} * \pi r^2\)

So, we have:

\(OFG = \frac{40}{360} * \pi * 18^2\)

\(OFG = 36\pi\)

Also, we have:

\(OAD = \frac{40}{360} * \pi * 18^2\)

\(OAD = 36\pi\)

Next, calculate the area of the sectors BOE and COH

Note that the radius of these sectors is 6 cm.

So, we have:

\(COH =BOE = \frac{140}{360} * \pi * 6^2\)

\(COH = BOE = 14\pi\)

The shaded area is then calculated as:

\(Shaded = OFG + OAD + COH + BOE\)

This gives

\(Shaded =36\pi + 36\pi + 14\pi + 14\pi\)

\(Shaded =100\pi\)

The equation becomes

\(Shaded =100 * 3.14\)

\(Shaded = 314\)

Hence, the shaded area is 314 square centimeters

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Answer:

153.6

Step-by-step explanation:

Answer:

153.6

Step-by-step explanation:

32x4=128

128x3=384

384x2=768

768/5=153.6

The correlation is a significant non-zero value.

The number of samples is n.

n = 25

The correlation of the coefficient is r.

r = -0.40

When correlation is significant,

\(H _{0} : p = 0\)

When correlation is non-zero,

\(H _{ \alpha } : p ≠0\)

The test statistic is,

\(TS = \frac{r \times \sqrt{n - 2} }{ \sqrt{1 - r {}^{2} } } \)

\( = \frac{0.4 \times \sqrt{25 - 2} }{ \sqrt{1 - ( - 0.4) ^{2} } } \)

\( = \frac{ - 1.918 }{ \sqrt{0.84} } \)

= -2.093

The test statistic is -2.093.

The correlation is,

\(H _{ \alpha } : - 2.93 ≠0\)

The correlation is not equal to zero and is significant.

Therefore, the correlation is a significant non-zero value.

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Using the Lagrange coefficient method, the sub-values are x = 1 and y = 3 - λ, where λ can have any value.

To find the sub-values of x and y using the Lagrange coefficient method, we need to set up the Lagrange function by incorporating the given objective function and constraint equation. Let's proceed step by step.

Define the objective function and constraint equation:

Objective function: f(x, y, z) = x²z + yz

Constraint equation: g(x, y, z) = 2x + y + z - 5 = 0

Set up the Lagrange function:

L(x, y, z, λ) = f(x, y, z) - λ * g(x, y, z)

L(x, y, z, λ) = x²z + yz - λ(2x + y + z - 5)

Find the partial derivatives

∂L/∂x = 2xz - 2λ = 0 -- (1)

∂L/∂y = z - λ = 0 -- (2)

∂L/∂z = x² + y - λ = 0 -- (3)

∂L/∂λ = -(2x + y + z - 5) = 0 -- (4)

Solve the system of equations

From equation (2), we get z = λ.

Substituting z = λ in equation (3), we have x² + y - λ = 0.

Rearranging equation (1), we get x = λ/z = λ/λ = 1.

Substituting x = 1 in equation (4), we have 2(1) + y + λ = 5.

Simplifying, we get y + λ = 3.

Now, we have the following equations

x = 1 -- (5)

y + λ = 3 -- (6)

z = λ -- (7)

2(1) + y + λ = 5 -- (8)

From equation (6), we can solve for λ:

y = 3 - λ -- (9)

Substituting equation (9) into equation (8):

2(1) + (3 - λ) + λ = 5

2 + 3 - λ + λ = 5

5 = 5

The equation 5 = 5 is always true. It indicates that λ can have any value.

Determine the sub-values of x and y:

From equation (5), we have x = 1.

Substituting y = 3 - λ (from equation (9)), we have y = 3 - λ.

Substituting z = λ (from equation (7)), we have z = λ.

Therefore, the sub-values of x and y are x = 1 and y = 3 - λ, respectively.

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Answer:

Good Night comrade !!

Step-by-step explanation:

Answer:

xy = 3y² - 4

Step-by-step explanation:

Hope it is helpful....

In the file i have attached, you will find the equation graphed, hope this helps.

Answer: 10 more

Step-by-step explanation:

Because 2 x 79 -89 =69

69-59=10

The general solution for the given differential equation is: \(y(t) = y_h(t) + y_p(t)\)

\(= (C_1 + C_2t)e^t + C_3e^t + (C_4t - (1/2)e^st)te^t\)

To find the general solution of the given differential equation using the method of variation of parameters, we assume a solution of the form y(t) = C₁\(e^(rt),\) where C₁ is an arbitrary constant and r is a constant to be determined.

The characteristic equation for the homogeneous equation is obtained by substituting y(t) = \(e^(rt)\)into the homogeneous equation:

\(r^2 - 2r - 1 + 2 = 0\)

Simplifying the equation, we have:

\(r^2 - 2r + 1 = 0\)

\((r - 1)^2 = 0\)

This equation has a repeated root r = 1.

Therefore, the homogeneous solution is given by y_h(t) = (C₁ + C₂t)e^t, where C₁ and C₂ are arbitrary constants.

Next, we find the particular solution using the method of variation of parameters. We assume the particular solution has the form y_p(t) = \(u_1(t)e^t + u_2(t)te^t.\)

To find u₁(t) and u₂(t), we substitute y(t) and its derivatives into the differential equation:

y" - 2y' - y + 2y =\(e^st\)

Taking the derivatives of \(y_p(t)\), we have:

\(y_p'(t) = u_1'(t)e^t + u_1(t)e^t + u_2'(t)te^t + u_2(t)te^t + u_2(t)e^t\)

\(y_p"(t) = u_1"(t)e^t + 2u_1'(t)e^t + u_1(t)e^t + u_2"(t)te^t + 2u_2'(t)e^t + 2u_2(t)e^t + u_2(t)e^t\)

Substituting these derivatives into the differential equation, we get:

u₁"(t)e^t + 2u₁'(t)e^t + u₁(t)e^t + u₂"(t)te^t + 2u₂'(t)e^t + 2u₂(t)e^t + u₂(t)e^t - 2(u₁'(t)e^t + u₁(t)e^t + u₂'(t)te^t + u₂(t)te^t + u₂(t)e^t) - (u₁(t)e^t + u₂(t)te^t) + 2(u₁(t)e^t + u₂(t)te^t) = e^st

Simplifying and grouping the terms, we have:

u₁"(t)\(e^t\)+ 2u₂'(t)\(e^t\) = 0

\(u_1"(t)e^t + 2u_2"(t)e^t - 2u_1'(t)e^t - 2u_2'(t)te^t = e^st\)

To solve this system of equations, we can equate the coefficients of like terms on both sides. We have:

For e^t:

u₁"(t) - 2u₁'(t) = 0 ...(1)

For te^t:

2u₂"(t) - 2u₂'(t) = e^st ...(2)

Solving equation (1), we find the general solution:

u₁(t) = C₃e^t, where C₃ is an arbitrary constant.

Solving equation (2), we use the method of undetermined coefficients to find a particular solution for u₂(t). Assume u₂(t) = C₄t + C₅. Substituting this into equation (2), we get:

2(C₄) - 2(C₄ + C₅) = \(e^st\)

Simplifying, we have:

-2C₅ = \(e^st\)

Therefore, C₅ = -1/2e^st.

The particular solution for u₂(t) is u₂(t) = C₄t - \((1/2)e^st,\) where C₄ is an arbitrary constant.

Finally, the general solution for the given differential equation is:

\(y(t) = y_h(t) + y_p(t)\)

= (C₁ + C₂t)\(e^t\)+ C₃\(e^t\) + (C₄t - \((1/2)e^st)te^t\)

This is the general solution of the given differential equation using the method of variation of parameters. The arbitrary constants are C₁, C₂, C₃, and C₄.

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If your train travels at 65 miles per hour for 3.5 hours, it go 227.5 miles.

What is Speed ?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

Given:

Speed S = 65 miles per hour

Time T = 3.5 hours

We know that,

S= D/T  Where D is the distance traveled.

Therefore,

65 miles per hour = D/ 3.5 hours

D = 65 x 3.5 miles

=227.5 miles

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Assuming the side lengths in the new phone are proportional to the old phone Then the width of the new phone will be 4.760 inches

Define Proportions

A direct proportion is a relation between variables where their ratio is a constant value.

The original length of a cell phone was L=1.2 inches and the original width was 3.4inches.

A new version of the cell phone is to be released with proportional dimensions with respect to the original cell phone.

We are given the length of the new phone L'=1.68 inches. The ratio of the lengths is 1,2/1.68=0.71428

The new width should be W'=3.4/0.71428=4.760 inches

The width of the new phone will be 4.760 inches

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The sample mean is 89.45, the sample standard deviation is 2.327, and the sample median is 91 and the leaf plot of the data is illustrated below.

The sample standard deviation is a measure of how much the ratings vary from the sample mean. It tells us how spread out the data is. A larger standard deviation means the data is more spread out, while a smaller standard deviation means the data is more tightly clustered around the mean.

To calculate the sample standard deviation, we first need to calculate the variance. The variance is the average of the squared differences between each rating and the mean. The formula for variance is:

variance = (sum of (rating - mean)²) / (number of ratings - 1)

In this case, the sum of the squared differences is 301.9, and there are 39 degrees of freedom (40 ratings minus 1), so the variance is 7.741. To get the sample standard deviation, we take the square root of the variance. In this case, the sample standard deviation is approximately 2.78.

The sample median is the middle rating when the ratings are arranged in order from lowest to highest. In this case, there are 40 ratings, so the median is the average of the 20th and 21st ratings, which are both 91.

Finally, we can determine what proportion of the taste-tasters considered this particular pinot noir truly exceptional (above 90 points). To do this, we count the number of ratings that are above 90 and divide by the total number of ratings. In this case, there are 30 ratings above 90, so the proportion is 30/40, or 0.75. This means that 75% of the taste-tasters considered this pinot noir truly exceptional.

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Complete Question:

A group of wine enthusiasts taste-tested a pinot noir wine from Oregon. The evaluation was to grade the wine on a 0-to-100-point scale. The results follow. Construct a stemand- leaf diagram for these data and comment on any important features that you notice. Compute the sample mean, the sample standard deviation, and the sample median. A wine rated above 90 is considered truly exceptional. What proportion of the taste-tasters considered this particular pinot noir truly exceptional?

94 90 92 91 91 86 89 91 91 90

90 93 87 90 91 92 89 86 89 90

88 95 91 88 89 92 87 89 95 92

85 91 85 89 88 84 85 90 90 83

Answer:

Hello mate here’s the answer 32 ounces

Step-by-step explanation:

2 pounds = 2x1(1 pound)

=2x(16 ounces)

=32 ounces

Answer:

y=½x-6

Step-by-step explanation:

m= ½

equation of the line: y-y1=m(x-x1)

y+5=½(x-2)

y=½x-6

Answer:

\(y =\dfrac{1}{2}x-6\)

Step-by-step explanation:

Point-slope formula

\(y-y_1=m(x-x_1)\)

where:

Given:

Substitute the given values into the formula:

\(\begin{aligned}y-y_1 & =m(x-x_1)\\\\\implies y-(-5) & =\dfrac{1}{2}(x-2)\\\\y+5 & =\dfrac{1}{2}x-1\\\\y & =\dfrac{1}{2}x-1-5\\\\y & =\dfrac{1}{2}x-6\end{aligned}\)