Write a division expression for each fraction 1/2

Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.

The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.

In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.

Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.

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Therefore, the AAA test of congruency demonstrated that ABE is Congruence to CDE.

Something that is "exactly equal" in terms of size and shape is referred to as congruent. No matter which way we spin, flip, or rotate the shapes, they remain accurate. For instance, you may draw two circles with the same radius, cut them out, and stack them.

In this case, we are aware that AB ll DC - GIVEN

In light of the characteristic of parallel lines,

Let's recall the property of parallel lines:-

"When the pair of alternating angles equals one another, two straight lines become parallel."

Alternate angles are angle ABE and angle CDB.

angle BAE ≅ angle DCE -{alternate angles}

E is a midway, given that.

According to the midpoint theorem, opposite angles are congruent when angle AES and angle CED are compared.

Here, we may see the congruency test from AAA.

Hence its proved that ∆ABE ≅ ∆CDE by AAA test of congruency.

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Answer:

y=16

Step-by-step explanation:

Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation

Answer:

See below in bold.

Step-by-step explanation:

The cost of what he wants to buy = 4.25 + 0.89 + 10.99

= $16.13

a) He does have enough to buy everything.

b) He has  20 - 16.13 = $3.87 left over.

The space inside the cylinder but outside the inscribed cone has a volume of 36π cubic centimeters.

Let's assume the radius of the cone is r and the height is h. Since the cone is inscribed in the cylinder, the base radius of the cone is equal to the radius of the cylinder, and the height of the cone is equal to the height of the cylinder.

The volume of a cylinder is given by V_cylinder = π\(r^2\)h, and in this case, we are given that the volume of the cylinder is 72π cubic centimeters.

72π = π\(r^2\)h

Simplifying the equation, we have:

\(r^2\)h = 72

Now, the volume of a cone is given by V_cone = (1/3)π\(r^2\)h. Since the cone is inscribed in the cylinder, its base radius and height are the same as that of the cylinder.

The volume of the space inside the cylinder but outside the cone is the difference between the volume of the cylinder and the volume of the cone:

V_space = V_cylinder - V_cone

Substituting the values, we have:

V_space = π\(r^2\)h - (1/3)π\(r^2\)h

Simplifying further, we get:

V_space = (2/3)π\(r^2\)h

Since \(r^2\)h = 72 from the earlier equation, we can substitute this value:

V_space = (2/3)π(72)

V_space = 48π

Therefore, the space inside the cylinder but outside the cone has a volume of 48π cubic centimeters, or 36π cubic centimeters after simplification.

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Answer: (m-3)(5m-2)

Step-by-step explanation:

5m^2-17m+6 factored is (m-3)(5m-2).

The value of dy f using the given values of x and dx is 0.01.

The differential dy of the given function y = \(e^{(x/10)}\) is

dy \(= (e^{(x/10)})/10\) dx.

Given that:

we get x = 0 and dx = 0.1.

Substituting these values in the differential expression,

we get:

dy\(=\)\((e^{(0/10)})/10 * 0.1 = 0.01\)

Thus, the differential dy of the given function is 0.01.

Substituting x = 0 in the function,

we get:

f(0) = \(e^{(0/10)}\) = 1

Now, we need to find the value of f'(x) at x = 0.

We have:

f(x) =\(e^{(x/10)}\)

Taking the derivative of f(x) with respect to x,

we get:

f'(x) = \((1/10)\) \(e^{(x/10)}\)

So, at x = 0,

we have:

f'(0) = \((1/10) e^{(0/10)}\) \(= 1/10\)

Thus, substituting the values of f'(0) and dx in the formula,

we get:

dy f = f'(0) dx\(= (1/10) * 0.1= 0.01\)

Therefore, the value of dy f using the given values of x and dx is 0.01.

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The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.

From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:

\(dv/dt = -k v^2\)

Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:

\(∫83^23 dv / v^2 = ∫0^1 -k dt\)

=> [1/83 - 1/23] = k

So the equation for the velocity of the boat as it coasts is:

\(dv/dt = -[(1/83 - 1/23)] v^2\)

The differential equation is separable:

\(dv/v^2 = -[(1/83 - 1/23)] dt\)

Integrating both sides, we get:

-1/v = [(1/83 - 1/23)] t + C

where C is an integration constant. Using the initial condition v(0) = 83, we get:

C = -1/83

Substituting this back, we have:

-1/v = [(1/83 - 1/23)] t - 1/83

Solving for v, we have:

v(t) = 83 / [1 + (83/23 - 1) t]

To find the distance traveled, we integrate v(t) from t = 0 to t = 120:

s =\(∫0^120 v(t) dt\)

Substituting v(t) and simplifying, we have:

s = 23 ln(1 + 3.6087t) + 60.391t + C

where C is another integration constant. Using the initial condition s(0) = 0, we get:

C = 0

Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:

s = 23 ln(1 + 3.6087t) + 60.391t

Evaluating this expression at t = 120 seconds, we get:

s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft

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The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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A good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up is count all the bytes of the data in the struct.

Rule:

In math rule refers a numerical pattern is a sequence of numbers that has been created based on a formula or rule called a pattern rule

Given,

Here we need to find a good rule of thumb for sizing a struct in c/c assuming that the struct is optimally set up.

According to the rule of thumb, the count all the bytes of the data in the struct.

and then we need to find the nearest power of 2, 4 or 8 based on the largest Data Type in your struct.

So, if the total number of bytes is larger than that power, then the struct will be the next power in size.

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Answer:

a = 1500

b = 0.97

Step-by-step explanation:

The equation we are modeling is ;

F(x) = ab^x

Now we have two parameters to fix.

These are the density and the annual percentage increase

We can substitute the value of 1500 for a and also make a corresponding substitution for b.

Now for b, the value to substitute is quite dicey.

3% = 3/100 = 0.03

To make any substitution, we need to subtract this value from 1 and that would be 0.97

So it is this 0.97 that we now raise x to for each of the number of years

Answer:

Step-by-step explanation:

The average age of 18 girls is 12.

Total age of girls:

The average age of 15 boys is 17

Total age of boys:

Total age of children:

Total number of children:

Average age of children:

The expected waiting time to get a court is 8(k + 1).

What is expected time?

The projected time is simply the time frame in which the Project is anticipated to be finished. When the parties to the project contract are signing it, they will either mutually agree upon this time or decide it together with the participation of all the stakeholders, contractors, and clients.

They need to wait for k+1 pairs to finish before they can start.

Since the exponential distribution is memoryless, the expected time for a given pair to finish once started is 40 minutes, and there are 5 courts,

the expected time for any of the 5 courts to finish is 40/5=8 minutes, and so their expected waiting time is 8(k+1) minutes.

Hence, the expected waiting time to get a court is 8(k + 1).

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Answer:

\(f(x)=-x^2 + 11x - 24\)

Step-by-step explanation:

Well for this problem, you want to start off by writing it in factored form.

In factored form, you can represent a quadratic as: \(f(x)=a(x-b)(x-c)\), where x=b, and x=c are zeroes of the function, since plugging them into the function makes one of the factors zero, and multiplying zero by the other factors will just give you zero.

The "a" in front of the two factors generally defines the stretch/compression of the function.

So let's start by plugging in the zeroes into the function, and then we can solve for "a" later: \(f(x) = a(x-3)(x-8)\)

Now let's use one point on the graph, which is not a root/zero to solve for "a". It's important to not use a zero/root since if we use that point the entire thing will be zero regardless of the value of "a"

Luckily we have one point provided that is not a zero and is: (4, 4)

So let's plug it in: \(4=a(4-3)(4-8)\\4=a(1)(-4)\\4=-4a\\a=-1\)

So now let's plug this into the factored form to get: \(f(x)=-(x-3)(x-8)\)

using foil to multiply these two factors you get: -[x^2 -8x - 3x + 24]

Now combine like terms

-[x^2 - 11x + 24]

distribute the negative sign

-x^2 + 11x - 24

\( \large \bf \implies{y = { - x}^{2} + 11x - 24}\)

Let standard form of quadratic equation be

If passes through (3,0) , (8,0) and (4,4)

The predicted leaf weight in the percent which is left after 80 days is equal to 67.03%.

Number of days after which predict the percent leaf weight left = 80 days

Experimentally determined k-value =  0.005,

Use the exponential decay model for leaf litter decomposition,

W(t) = W0 × e^(-kt)

where W(t) is the predicted percent leaf weight remaining at time t,

W0 is the initial percent leaf weight at time 0,

k is the decomposition rate constant,

And e is the mathematical constant approximately equal to 2.71828.

Using the given k-value of 0.005

And assuming an initial weight of 100%,

Plug in the values to get,

⇒ W(80) = 100 × e^(-0.005×80)

⇒ W(80) = 100 × e^(-0.4)

⇒ W(80) ≈ 67.03

Therefore, the predicted percent leaf weight left after 80 days is approximately 67.03%.

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Answer:

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Class 10

>>Maths

>>Areas Related to Circles

>>Area of Sector and Length of an Arc

>>Find the length of the arc in terms of p

Question

Bookmark

Find the length of the arc in terms of π that subtends an angle of 30

∘

at the centre of a circle of radius 4 cm.

Easy

Updated on : 2022-09-05

Solution

verified

Verified by Toppr

⇒ θ=30

o

and r=4cm

⇒ Length of an arc =

360

o

θ

(2πr)

Where, θ is angle subtended at a center.

2πr is circumference of a circle.

⇒ Length of an arc =

360

o

30

o

×2π×4

⇒ Length of an arc =

12

2π×4

∴ Length of an arc =

3

2π

Answer:

x = 135

Step-by-step explanation:

x = 9x15

= 135

x = 135

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Alternate interior angles are supplementary when transversal on parallel lines is perpendicular.

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles.

Given,

To prove alternate interior angles are supplementary.

In the figure

EF is a transversal intersecting the two line AB and CD at 90°.

AB||CD

∠3 and ∠6, ∠4 and ∠5 are alternate interior angles.

∵ EF⊥ AB and EF⊥CD

∴ ∠3 = ∠6 = ∠4 = ∠5 = 90°

Thus sum of alternate interior angles,

∠3 + ∠6 = 90° + 90° = 180°

∠4 + ∠5 = 90° + 90° = 180°

For supplementary angles sum of angles should be 180° .

Hence, when transversal is perpendicular to the parallel lines, the alternate interior angles are supplementary.

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Answer:

To solve for g in terms of T, L, we can manipulate the formula T = 2π √(L/g) as follows:

First, we divide both sides by 2π:

T/2π = √(L/g)

Then, we square both sides:

(T/2π)² = (L/g)

Then, we multiply both sides by g^2 :

(T^2/4π^2) = L

Finally, we divide both sides by L:

(T^2/4π^2 * L) = g

So the formula for g in terms of T, L is g = (T^2/4π^2 * L)

Please note that this formula is only valid for simple pendulum and not for any complex pendulum, and also the result is in terms of acceleration due to gravity g.

Answer:

4 duhh... Ur kidding me??

Answer:

22 because 2+2

Step-by-step explanation:

if we put 2 near 2 it will be 22 so the answer is 22

The roots of the equation is x = -20

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

Substituting the values in the equation , we get

The leading coefficient of the equation is -1

And , the constant term is -20

Now , according to rational root theorem ,

So , the equation is

-x - 20 = 0

Adding x on both sides of the equation , we get

x = -20

Therefore , the value of x is -20

Hence , the equation is x = -20

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point coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

Given that,

We have to find what are the endpoint coordinates for the middle portion of the parallel to PQ segment of the PQR.

We know that,

First we write the co-ordinates of the triangle in the given graph.

P is (-3,3)

Q is (2,1)

R is (-4,-2)

The triangle's midpoint, which is parallel to section PQ, must be located. As a result, we would need to locate the midpoints of the segments PR and QR before joining the points to obtain the mid segment.

Midpoint Formula is

(x₁+x₂/2, y₁+y₂/2)

So,

The midpoint of the side PR is

(-3+(-4)/2, 3+(-2)/2)

(-3-4/2, 3-2/2)

(-7/2,1/2)

So, S point is (-3.5, 0.5)

The midpoint of the side QR is

(2+(-4)/2, 1+(-2)/2)

(2-4/2, 1-2/2)

(-2/2,-1/2)

So, T point is (-1, -0.5)

Therefore, The endpoint coordinates for the mid segment of the parallel to PQ segment of the PQR is ST point is (-3.5, 0.5) and (-1, -0.5).

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A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

It is most commonly used to compare the sizes of two numbers on a number line.

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Answer:

f(x) = 2x³ - 6x² - 48x + 24

relative minimum: (4,-136)

relative maximum: (-2,80)

answer is the second option

Hey there! :)

Answer:

2nd option: (4, -136) is a relative minimum, (-2, 80) is a relative maximum.

Step-by-step explanation:

To begin, we can graph this equation (pictured on bottom of answer)

Relative minimums/maximums are the minimums and maximums of turning points of the graph. Observing the graph, we can see that:

(-2, 80) is a relative maximum because this is the maximum value at a turning point.

(4, -136) is a relative minimum because this is the minimum value at a turning point.

Answer:

Tammy

Step-by-step explanation:

Tammy read 7.75 hours last month. Kelley read 7.69 hours

Jim read 7.075 hours.

We would arrange the hours of reading from smallest to the highest

7.075, 7.69, 7.75

The person who spent the most time reading is the person with the highest number of hours that was spent reading. This person is Tammy.

Therefore, person who spent the most time reading is Tammy because she read for 7.75 hours.

The person who spent the most time reading is Tammy.

Therefore, from the decimals given, we can see that the highest is 7.75 hours that was used by Tammy.

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Answer:

16.5

Step-by-step explanation:

Break down the equation:

10*5=50

4 with an exponent of 2= 16

Then you have: 50+16 / 4

You can simplify it to 66/4

Finally, divide 66 by 4 which equals 16.5

Hope this helps!

To calculate the Loan to Value (LTV) ratio, we divide the loan amount by the purchase price of the property and express the result as a percentage. LTV = 80%

Given: Purchase price of the building: $8,000,000 Loan amount: $6,400,000 LTV = (Loan amount / Purchase price) * 100 LTV = ($6,400,000 / $8,000,000) * 100 LTV = 0.8 * 100 LTV = 80%

Therefore, the Loan to Value (LTV) ratio in this scenario is 80%. This means that the bank has provided a loan equivalent to 80% of the purchase price of the building.

The remaining 20% of the purchase price, which is $1,600,000 in this case, would be the down payment or equity contribution made by the borrower. Correct answer is 80%

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