5x-11=3x+5 solve for ”x”

The surface area of the trapazoid based prism is 289.6 ft². The right option is b. 289.6 ft².

A prism is a solid shape that is bound on all its sides by plane faces.

To calculate the surface area of the trapazoid based prism, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is b. 289.6 ft².

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Answer:

253.75

Step-by-step explanation:

Total height of the cylinder is  8 ft . Since the tank holds 580 gallons when filled to capacity so in 1 ft height there will be  \frac{580}{8}  gallons oil when filled to capacity .

Answer:

A drink cost 1.50

Reasoning:

3×2=6

6+1.50=7.50

7.50+1.50=9

4×2=8

8+1.50=9.50

Answer:

shorter piece = 7 ft

longer piece = 19 ft

Step-by-step explanation:

L = longer board

S =  shorter board

L+S = 26   then  L =26-S

L = 5+2S

substitute for L

26-S = 5+2S

add S to each side & subtract 5 from each side

3S = 21

divide both sides by 3

3S/3 = 21/3

S = 7

L = 19

The parameter estimate's t-statistic calculates the discrepancy between the estimate and the actual parameter. If the absolute value is high, the true parameter is probably very different from the estimate.

The parameter estimate's t-statistic calculates the discrepancy between the estimate and the actual parameter. It is derived by multiplying the discrepancy between the two by the estimate's standard error. The true parameter is probably far from the estimate, according to a large absolute value of the t-statistic. As a result, one cannot have confidence in the estimate because it is not a trustworthy representation of the real parameter. This is because a significant t-statistic indicates that the estimate is likely to be inaccurately estimating the true parameter and is either too high or too low. As a result, it is obvious that the true parameter is unlikely to be represented by the estimate when the t-statistic for a parameter estimate has a high absolute value.

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The complete question is

when the t-statistic for a parameter estimate is large in absolute value, you can be confident that the true parameter is not .How do you interpret a large t-statistic in a parameter estimate?

The given set is (3, 4, 5, ...} is infinite set.

A set with an infinite number of elements is one that cannot be numbered. A set that has no last element is said to be endless. A set that can be put into a one-to-one correspondence with a suitable subset of itself is said to be infinite. No issue with the in-class assignment.

The stars in the clear night sky, water droplets, and the billions of cells in the human body are just a few examples of endless sets of objects that surround us. A set of natural numbers, however, serves as the best illustration of an infinite set in mathematics. There is no limit to the amount of natural numbers.

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The domain of the inverse of the function f(x) = 5e^x + 3 is found being all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

Suppose that the given function is

\(f:X\rightarrow Y\)

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

\(f^{-1}: Y \rightarrow X\)

such that:

\(\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X\)

(and vice versa).

It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'

The domain of the inverse of a function (if it exists) is the range of the function it is inverse of. Similarly range of the inverse of that considered function is the domain of that considered function.

The function given is:

\(f(x) = 5e^x + 3\)

The domain of the inverse of this function is this function's range.

Assuming only real values are allowed, for any real number x, we have:

\(e^x > 0\)

And therefore, we get:

\(5e^x > 0 \: \forall x \in \mathbb R\\5e^x + 3 > 3 \: \forall x \in \mathbb R\\\)

Also, since the function \(f(x) = 5e^x + 3\) is strictly monotonically increasing and continuous, it touches all the values as its output from any real number > 3 till any finitely large number.

Thus, its range is (3, ∞) (it is an interval consisting of all the real numbers > 3)

This is the domain of its inverse function.

Thus, the domain of the inverse of the function f(x) = 5e^x + 3 is found being set of all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)

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Answer:

1/14

Step-by-step explanation:

The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14

Answer:

8.5

Step-by-step explanation:

To find the mean, you have to add the terms, and divide the sum by the number of terms.

7+8+9+10=34

34/4=8.5

-hope it helps

Answer:

<1+125=180°{linear pair}

<1=180-125

<1=55

Answer: kk

Step-by-step explanation:

Answer: C.0

x + 45 is the angle outside the circle of shield 2 arcs with measurements 55 and 145

=> x + 45 = 1/2.(145 - 55)

⇔ x + 45 = 1/2. 90

⇔ x + 45 = 45

⇔ x = 0

Step-by-step explanation:

\(\qquad \qquad \stackrel{indirect~\hfill }{\textit{inverse proportional variation}} \\\\ \textit{\underline{y} varies inversely with \underline{x} and \underline{z}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{xz}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\\\\\)

\(y = \cfrac{k}{xz}\qquad \textit{we also know} \begin{cases} x=3\\ y=24\\ z=15 \end{cases}\implies 24=\cfrac{k}{(3)(15)} \\\\\\ 24(3)(15)=k\implies 1080=k~\hspace{10em}\boxed{y=\cfrac{1080}{xz}}\)

Answer:

16/11

Step-by-step explanation:

Answer:

2*8/11 = x

x = 16/11

Step-by-step explanation:

Answer:

About 95% of individuals have IQ scores in the interval 100 ± 2 ( 15 ) = [ 70 , 130 ] .

Step-by-step explanation:

hope this helps

The number of exams that Gretchen has to take is 4 exams.

From the information illustrated, Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. The total hours that she used will be:

= 5.1 + 3 3/5 + 5 3/10

= 5.1 + 3.6 + 5.3

= 14 hours.

Since she spends 3/1/2 hours studying for each exam, the number of exams that she has to take will be:

= Number of hours / Hours used for each exam

= 14 / 3 1/2

= 4 exams

The number of exams are 4.

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Answer and Step-by-step explanation:

1/12 and 1/2 don't have common denominators. Change the 2 to 12 by multiplying by 6.

Then multiply 1 by 6, then 6+1 equals 7

7/12

Answer:

7/12

Step-by-step explanation:

Finding the LCD  on each would give you 12. Then multiplying what you multiplied on the denominator, you would get 1/12 + 6/12. Which would give you 7/12.

Hope this helped!

Have a good day!

The midpoint is 26.

Midpoint in this scenario = mean

(23+29)/2 = 26

Answer:

-6

Step-by-step explanation:

Proving  X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e".

Given :

If I can prove that X is c.e. and ω∖X is c.e. then I can prove that X is computable by the theorem "Let W⊆ω. Then W is computable if both W and ω∖W are c.e". But I'm not able to proceed on how should I do this.

Take a computable surjection :

f : ω → W.

Defined  G = { f ( x ) ∣ x ∈ ω and ∀y < x ( f ( y ) < f ( x ) ) }.

here clearly, G ⊆ W .

And G is infinite. For if f ( x ) ∈ G, take the smallest y such that f ( y ) > f ( x ); then f ( y ) ∈ V.

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The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

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

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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Answer:

?

Step-by-step explanation:

The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

-.4/.2

Step-by-step explanation:

take the points and divide them from 1/5

Dilation involves changing the size of triangle QRS

The coordinates of R' are (-2/5, 1/5)

The coordinate of R is given as:

\(\mathbf{R =(-2,1)}\)

The scale factor is given as 1/5; i.e.

\(\mathbf{k = \frac 15}\)

The dilation occurs through the origin,

So, the coordinates of R' is calculated using:

\(\mathbf{R' = k \times R}\)

This gives

\(\mathbf{R' = \frac 15 \times (-2,1)}\)

Multiply

\(\mathbf{R' = (-\frac 25,\frac 15)}\)

Hence, the coordinates of R' are (-2/5, 1/5)

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The distance between the points (−3, −5) and (−3, −7) is 2 units.

The distance formula gives the shortest distance between two points in a two-dimensional plane.

The distance formula is a useful tool for calculating the distance between two points.

Therefore,

d = √(x₂ - x₁)²+(y₂ - y₁)²

Let's find the distance between the points (−3, −5) and (−3, −7).

Hence,

x₁ = -3

x₂ = -3

y₁ = -5

y₂ = -7

d = √(-3 + 3)² + (-7 + 5)²

d = √(-2)²

d = √4

d = 2

Therefore, the distance between the point is 2 units.

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The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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