gabby has already knit 29 centimeters of scarf , and can knit 1 centimeter each night . After 18 nights of knitting , how many centimeters of scarf will gabby have knit in total ?

The pair of triangles that are similar to each other will be given below.

Triangle 1: 55°, 45° and Triangle 2: 55°, 80°.

Triangle 1: 105°, 23° and Triangle 2: 52°, 105°.

If any two angles of triangles are equal then the triangles are known as similar triangles.

The measures of two angles of pairs of triangles are given.

Triangle 1: 55° and 45°, then the third angle will be 80°.

Triangle 2: 55° and 80°, then the third angle will be 45°.

They are similar triangles.

Triangle 1: 105° and 23°, then the third angle will be 52°.

Triangle 2: 52° and 105°, then the third angle will be 23°.

They are similar triangles.

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Answer:

Triangle 1: 55° and 45°, then the third angle will be 80°.

Triangle 2: 55° and 80°, then the third angle will be 45°.

They are similar triangles.

Triangle 1: 105° and 23°, then the third angle will be 52°.

Triangle 2: 52° and 105°, then the third angle will be 23°.

The exponential distribution may be used to predict the failure rate of certain items over time. An LED light bulb has an expected lifetime of 25000 hours. Assuming that the lifetime of the LED light bulb follows the exponential distribution, the probability that it will last more than 3 years is closest to (C) 53%. Correct answer is option C

This is because the lifetime of an LED light bulb can be estimated using the following equation : P(x > 3 years) = 1 - P(x ≤ 3 years)where x is the lifetime of the LED light bulb.If we convert 3 years to hours, we get 3 * 365 * 24 = 26280 hours. As a result, P(x ≤ 3 years) = P(x ≤ 26280 hours)

Using the formula for exponential distribution, the probability of the LED light bulb failing after 26280 hours is : Probability = 1 - e^{-λx} Where λ is the failure rate per hour and x is the length of time in hours.We can now calculate the value of λ by dividing the expected lifetime of the bulb by the total number of hours.

 λ = 1/25000 hours  This implies that the probability of the LED light bulb failing after 26280 hours is : P (x ≤ 26280 hours)

Therefore, the probability that the LED light bulb will last more than 3 years is approximately 53 percent. The Correct answer is option C

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The true statements are:

GE ≅ AC

AW ≅ ER

RE ≅ WA

The false statements are:

∠GER ≅ ∠WAC

∠G ≅ ∠W

From the question, we are to determine which of the given statements are true or false.

From the given information,

Triangle GRE is congruent to triangle CWA

Given that a ΔABC and another ΔXYZ are congruent, then we can infer that

AB ≅ XY

BC ≅ YZ

CA ≅ ZX

∠ABC ≅ ∠XYZ

∠A ≅ ∠X

∠B ≅ ∠Y

∠C ≅ ∠Z and so on

Thus,

For the congruent triangles GRE and CWA, we can conclude that

GE ≅ AC

AW ≅ ER

RE ≅ WA

∠GER ≅ ∠CAW

∠G ≅ ∠C

Hence, the statements that are true are

GE ≅ AC

AW ≅ ER

RE ≅ WA

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Answer:

-3

Step-by-step explanation:

-5 1/2 + 6 3/4 - 4 1/4

= 1 1/4 - 4 1/4

= -3

Answer:

  (x, y) = (-1, 5)

Step-by-step explanation:

You want to solve this system of equations by substitution.

The idea of substitution means we want to replace an expression in one equation for an equivalent expression based on the other equation.

Here, the second equation gives an expression equivalent to "y", so we can use that expression in place of y in the first equation:

  5x +2(-2x +3) = 5 . . . . . . . . (-2x+3) substitutes for y

  x +6 = 5 . . . . . . . . . . simplify

  x = -1 . . . . . . . . . subtract 6

  y = -2(-1) +3 = 5 . . . . . use the second equation to find y

The solution is (x, y) = (-1, 5).

__

Additional comment

Choosing substitution as the solution method often works well if one of the equations gives an expression for one of the variables, or if it can be solved easily for one of the variables. The "y=" equation is a good candidate for providing an expression that can be substituted for y.

Any equation that has one of the variables with a coefficient of +1 or -1 is also a good candidate for providing a substitution expression.

  4x -y = 3   ⇒   y = 4x -3 . . . . . for example

The attached graph confirms the solution above.

Answer:

She got an equally good deal both times

Step-by-step explanation:

\(\frac{2}{20}\) can be simplified to make \(\frac{1}{5}\)

\(\frac{6}{30}\) can be simplified to make \(\frac{1}{5}\)

they are the same

To use Stokes' theorem to evaluate the given vector field, we need to find the curl of the vector field and calculate the surface integral over the cone.

First, let's find the curl of the vector field f(x, y, z) = arctan(x^2yz^2)i + x^2yj + x^2z^2k.

The curl of a vector field F = P i + Q j + R k is given by the following formula:
curl F = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, P = arctan(x^2yz^2), Q = x^2y, and R = x^2z^2.

Taking the partial derivatives, we get:
∂P/∂x = 0, ∂P/∂y = 2x^2z^2, ∂P/∂z = 2x^2yz^2
∂Q/∂x = 2xy, ∂Q/∂y = x^2, ∂Q/∂z = 0
∂R/∂x = 2xz^2, ∂R/∂y = 0, ∂R/∂z = 2x^2z

Now, substituting these values into the formula for the curl, we have:
curl f = (2x^2z^2 - 0)i + (0 - 2xz^2)j + (2xy - 2x^2yz^2)k
      = 2x^2z^2i - 2xz^2j + 2xyk

Next, we need to calculate the surface integral over the cone.

The surface integral can be evaluated using the formula:
∫∫S (curl f) · dS = ∫∫D (curl f) · (r_u × r_v) dA

Here, (r_u × r_v) is the cross product of the partial derivatives of the position vector r(u, v) with respect to the parameters u and v, and dA is the differential area element.

In this case, the cone is given by x = sqrt(y^2 + z^2), 0 <= x <= 2, and we can parameterize the surface as r(u, v) = u sqrt(1 + v^2) i + u v j + u sqrt(1 + v^2) k, where 0 <= u <= 2, -1 <= v <= 1.

Taking the partial derivatives of r with respect to u and v, we have:
r_u = sqrt(1 + v^2) i + v j + sqrt(1 + v^2) k
r_v = u v i + j + u v k

Now, calculating the cross product r_u × r_v, we get:
r_u × r_v = (v sqrt(1 + v^2) - u v sqrt(1 + v^2)) i - (sqrt(1 + v^2) - u v) j + (u v - v sqrt(1 + v^2)) k

Finally, substituting the values into the surface integral formula, we have:
∫∫S (curl f) · dS = ∫∫D (2x^2z^2i - 2xz^2j + 2xyk) · ((v sqrt(1 + v^2) - u v sqrt(1 + v^2)) i - (sqrt(1 + v^2) - u v) j + (u v - v sqrt(1 + v^2)) k) dA

Now, you can evaluate this surface integral to find the answer.

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The ratio of RMS speed of an ideal gas at 235K and 37K is 2.52011.

The equation V = √((3RT)/M), where R is the universal gas constant, T is the absolute (Kelvin) temperature, and M is the molecular mass, gives the root mean square (R.M.S.) speed V of the molecules of an ideal gas.

In the question, we are asked to find the ratio of the RMS speed of an ideal gas at 235K and 37K.

We are given two temperatures, T₁ = 235K and T₂ = 37K

We calculate the ratio V₁:V₂ in the following way:

V₁:V₂

= √((3RT₁)/M)/√((3RT₂)/M)

= √((3R(235))/M)/√((3R(37))/M)

= √(235/37) {Since, 3, R, and M, cancel off each other}

= √6.351 = 2.52011.

Thus, the ratio of RMS speed of an ideal gas at 235K and 37K is 2.52011.

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Jackson spent $6.20 and a pound of cherries more than Tim.

Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.

Given:

Two friends shop for fresh fruit.

Jackson buys a watermelon for ​$8.35 and 5 pounds of cherries.

Tim buys a pineapple for ​$2.15 and 4 pounds of cherries.

Let p be the variable that represents the​ price, in​ dollars, per pound of cherries.

For Jackson,

5p + 8.35

And for Tim,

4p +2.15

Jackson spent,

= 5p + 8.35 - 4p -2.15 = p + 6.20

Hence, p + 6.20 is the required expression.

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Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.

The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:

W = F * d

where:

W is the work done in joules

F is the force in newtons

d is the distance in meters

The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.

The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.

Plugging these values into the equation for work, we get:

W = 102.8 N * 4600 m = 472320 J

The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:

472320 J / 29 kJ/mol = 162.6 mol

To one decimal place, this is 0.23 moles of ATP.

Here are the assumptions that we made in this calculation:

No friction

No mass of the bike

A flat ride with no change in altitude

These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.

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The functions that are exponential are f(x) = 4(1/4)ˣ , g(x) = 14(4)ˣ and k(x) = 6(5.49)ˣ , the options that are correct are (a) , (b) and (e) .

In the question ,

five function are given ,

we need to select the functions that are exponential ,

We know that , Exponential function is a function whose value is a constant raised to power of a variable ,

For Example , f(x) = cˣ, where c is any constant value and x is a variable.

Part(a) ,

f(x) = 4(1/4)ˣ

Since , x is in the exponent , hence it is an exponential function .

Part(b) ,

g(x) = 14(4)ˣ

Since , x is in the exponent , hence it is an exponential function .

Part(c) ,

h(x) = 10x⁵

Since , x is present in the base , hence , it is not an exponential function .

Part(d) ,

j(x) = −9x⁴

Since , x is present in the base , hence ,it is not an exponential function .

Part(e) ,

k(x) = 6(5.49)ˣ

Since , x is in the exponent , hence it is an exponential function .

Therefore , The exponential functions are (a) f(x) = 4(1/4)ˣ  , (b) g(x) = 14(4)ˣ   and  (e) k(x) = 6(5.49)ˣ  .

The given question is incomplete , the complete question is

which of the following are exponential functions? select all correct answers.

(a) f(x) = 4(1/4)ˣ

(b) g(x) = 14(4)ˣ

(c) h(x) = 10x⁵

(d) j(x) = −9x⁴

(e) k(x) = 6(5.49)ˣ

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Answer:

8n+15p+11

Step-by-step explanation:

just combine like terms

Answer:

i dont now but i thin it is 5

Step-by-step explanation:

Answer:

r = 3.6 , a = 2

Step-by-step explanation:

given that r is inversely proportional to a then the equation relating them is

r = \(\frac{k}{a}\) ← k is the constant of proportion

to find k use the condition when r = 12 , a = 1.5

12 = \(\frac{k}{1.5}\) ( multiply both sides by 1.5 )

18 = k

r = \(\frac{18}{a}\) ← equation of proportion

when a = 5 , then

r = \(\frac{18}{5}\) = 3.6

when r = 9 , then

9 = \(\frac{18}{a}\) ( multiply both sides by a )

9a = 18 ( divide both sides by 9 )

a = 2

Answer:

a= (π/4) + (kπ/2)

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

9514 1404 393

Explanation:

This is an identity.

  cos²(A) +cos²(A)cot²(A) = cot²(A)

Transforming the left side, we have ...

  = cos²(A)(1 +cot²(A))

  = cos²(A)csc²(A)

  = (cos(A)/sin(A))²

  = cot²(A)

Explanation:

We assume the problem statement is telling us that the order of points on segment QR is Q, A, B, R, and that QA = AB = BR. This means that

  QB = QA +AB = 2BR

  BR = 1/2(QB)

The area of the triangles will be ...

  A = 1/2bh

For triangle PQB, the area is ...

  ar(PQB) = 1/2(QB)h . . . . . h is the perpendicular distance from QR to P

For triangle PBR, the area is ...

  ar(PBR) = 1/2(BR)h = 1/2(1/2QB)h . . . . h is the same as above

  ar(PBR) = 1/2ar(PQB)

__

Essentially, you're showing the base of the smaller triangle is 1/2 the base of the larger one and using that to show the area of the smaller triangle is 1/2 the area of the larger one. (Both have the same height.)

Answer:

the probability is 28.6% that you get both correct

Step-by-step explanation:

To find out how much juice each friend received, we need to divide the total amount of juice (5 liters) by the number of friends (12).

Each friend would receive 5/12 liters of juice. As for the croissants, we don't have enough information to determine how many croissants each friend received since the number of croissants in each tray is not specified. If Raven made 5 liters of fresh pineapple juice and shared it with 12 friends, we can calculate how much juice each friend received by dividing the total amount of juice by the number of friends.

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While guessing and checking is one way to do this problem, I will show you how to do it algebraically.

Let one side be A

Let the other side be B

2(A+B)=16

A*B=15

First equation because the perimeter is 16 and the second because the area is 15. Now solve the system of equations

A+B=8

A=8-B

Substitute into equation two

B(8-B)=15

-B^2+8b-15=0

B^2-8b+15=0

(B+3)(B+5)=0

B=3,5

A=5,3 respectively

From this we can see that one side is 5 meters long while the other side is three meters long.

Step-by-step explanation

Since we're looking at a rectangle, let's consider its perimeter and area formulas.

Perimeter: 2x + 2y (A rectangle has four sides, with two equal sides, so this is x + x + y + y simplified)

Area: (x)(y) (length x breadth so, x times y)

So we have two equations: 2x + 2y = 16 and x*y = 15. Solve simultaneously. Refer to the attached image.

speed = distance ÷ time = 30 ÷ 2.5 = 12 mph

Answer:  translation 8 units to the right

Step-by-step explanation:

An even function is a function such that:

h(x) = h(-x)

and the function is odd if:

h(-x) = -h(x)

Now, let's talk about transformations:

A) Reflection over the x-axis:

When we have a point (x,y) and we do a reflection over the x-axis, the reflected point will be:

(x, -y).

Then for the case of a function:

y = h(x).

then the reflection will be:

g(x) = - y = -h(x).

And if h(x) is even, -h(x) is also even, so this is not the correct option.

B) Vertical stretch by a factor of 7.

This is written as:

g(x) = 7*h(x).

then:

g(x) = 7*h(x)

g(-x) = 7*h(-x) = 7*h(x) = g(x)

the transformation is even.

C) Translation of 8 units to the right.

We can write this as:

g(x) = h(x - 8).

Then:

g(-x) = h(-x -8) = h(x + 8)

Then g(-x) is not equal to g(x)

and also g(-x) ≠ -g(x)

So in this case the transformation is neither odd or even.

C)  horizontal compression by a factor of One-half.

This transformation is written as:

g(x) = h( (1/2)*x)

And, similar as the case of the vertical compression, in this case the transformation is also even.

Answer: C

Step-by-step explanation:

Translation 8 units to the right

In order to determine the cost for 0.5 hours, Mohal would need to know the initial studio-use fee and the hourly fee charged by the studio.

It is not possible to determine the amount of money Mohal would need to pay in studio fees for 0.5 hours based on the information provided. The table shows a linear relationship between the number of hours in the studio (t) and the total amount of money paid (P), but it does not provide a mathematical equation that can be used to calculate the cost for any given number of hours. In order to determine the cost for 0.5 hours, Mohal would need to know the initial studio-use fee and the hourly fee charged by the studio.

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Answer:

f(0) =2

Step-by-step explanation:

f (x) = -x + 2

Let x = 0

f(0) = -0+2

f(0) = 2

Answer:

f(0) = 2

Step-by-step explanation:

Substitute x = 0 into f(x)

f(0) = - 0 + 2 = 0 + 2 = 2

Answer: DH and HF correspond.

Answer:

142

Step-by-step explanation:

x+38=180

x=142

Answer is 142

Answer:

very easy x=180-38= 142 is ans

Step-by-step explanation:

itis Because the sum of all side in triangle is 180 so 180-38=x