Use a triple integral to find the volume of the given solid. the solid enclosed by the cylinder x2 + y2 = 9 and the planes y + z = 14 and z = 2.

Amount of last payment is approximately $497

Given that;

Number of year = 6 year

Annual deposit = $1,500

Annual rate = 8% = 0.08

Find:

Amount of last payment

Computation:

[tex]Future\ value = Annual\ deposit[(1+r)^n - 1]/r[/tex]

[tex]Future\ value\ of\ the\ 6\ annual\ deposits = 1500[\frac{(1+0.08)^6 - 1}{0.08}][/tex]

[tex]Future\ value\ of\ the\ 6\ annual\ deposits = 1500[(1.08)^6 - 1]/0.08\\\\Future value of the 6 annual deposits = 1500[0.58687]/0.08[/tex]

Future value of the 6 annual deposits = 11,003.25

Future value of the 6 annual deposits = $11,003 (Approx.)

Extra payment = 11,003 - 10,000

Extra payment = $1,003

So,

Amount of last payment = 1,500-1,003

Amount of last payment = $497

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Answer: Triple the height of the pyramid

Step-by-step explanation:

To triple the volume of a square pyramid, triple the height of the pyramid. Therefore, the option C is the correct answer.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

The volume of a square pyramid refers to the space enclosed between its five faces. The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height).

To triple the volume of a square pyramid, triple the height of the pyramid.

Therefore, the option C is the correct answer.

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I would say that the child is prepared for solid foods because it is capable of grasping things such as food. If the baby can gulp easily and sit up without adjustment solids are okay to switch the child on at this point. Also you can give a child solid food anywhere starting from 4-6 months old.

Supplementary breast milk is given to babies after babies 6 months of age and over with a gradual texture starting from fine, filtered porridge, pureed porridge, then solid food such as adult food. Complementary food for breast milk is better if it contains 4 stars namely carbohydrates, vegetable protein, animal protein, and vegetables.

When a baby enters the age of 6 months, he needs more calories than just the nutrition he gets through exclusive breastfeeding. At this age, you can introduce your baby's first solid food.

Feeding is not just filling the baby's stomach with nutritious food, but also provides education about pleasant interactions, stimulation of the sense of taste, fine motor training (moving hands and directing to the mouth that requires good coordination between hands, eyes, and of course, the brain), chewing and discipline.

8 Solid Foods for 6-Month-Old Babies

In addition to some of the foods above, introduce other solid foods as well. Of course, the texture must be adjusted to the stage of growth of the baby. Do not forget, introduce food one by one to see what foods cause allergies in children.

In general, the purpose of first feeding for babies from 6 months of age are:

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Grade: College

Subject: Health

Keyword: complementary, food, baby

Answer:

[tex]\frac{3}{8}[/tex] of the group

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] of a group of chickens tried to cross the road.

only [tex]\frac{3}{4}[/tex] of those chickens made it to the other side.

So  [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex]

= [tex]\frac{3}{8}[/tex]  of the group of chickens made it to the other side.

To find the probability of a unit ending up in rework in an assembly line process, you calculate the probabilities at each step of the process, including station defects, inspection, and rework.

To find the probability that a unit ends up in rework, we need to consider the probability at each step:

The probability of a defective unit at any station is 0.5% or 0.005.

The inspection catches 80% of defects, so the probability of defect detection at inspection is 0.8.

For the units that are sent to rework, the rework department fixes about 95% of the defects, making the probability of a defective unit passing rework 0.05.

Calculating the probability that a unit ends up in rework:

Multiplying the probabilities at each step: 0.005 (station) * 0.2 (not caught at inspection) * 0.95 (not fixed at rework) = 0.00095. Therefore, the probability that a unit ends up in rework is 0.00095 or 0.095% in decimal form.

Answer:

1.74 second long after it was thrown does it hit the ground.

Step-by-step explanation:

Given : A football is thrown with an initial upward velocity of 25 feet per second from a height of 5 feet above the ground. The equation [tex]h =-16t^2+25t+5[/tex] models the height in feet t seconds after it is thrown.

To find : How long after it was thrown does it hit the ground?

Solution :

The equation model is [tex]h(t)=-16t^2+25t+5[/tex]

After the ball passes its maximum height, it comes down and hits the ground.

i.e. h=0

So, [tex]-16t^2+25t+5=0[/tex]

Solve by quadratic formula of equation [tex]ax^2+bx+c=0[/tex] is [tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

Here, a=-16 , b=25 and c=5

[tex]t=\frac{-25 \pm \sqrt{(25)^2-4(-16)(5)}}{2(-16)}[/tex]

[tex]t=\frac{-25 \pm \sqrt{625+320}}{-32}[/tex]

[tex]t=\frac{-25 \pm \sqrt{945}}{-32}[/tex]

[tex]t=\frac{-25+\sqrt{945}}{-32},\frac{-25-\sqrt{945}}{-32}[/tex]

[tex]t=-0.179,1.741[/tex]

We reject t=-0.179.

Therefore, 1.74 second long after it was thrown does it hit the ground.

Answer:

Kayla will be able to cover the distance of 200 miles by riding bike for 11 days and by running for 15 days.

Step-by-step explanation:

Numbers of days Kayla's has to run be x

Numbers of days Kayla's has to ride bike be y

Speed while running = 6 miles/day

Distance covered by running in x days = 6miles/day × x

Speed while riding a bike = 10 mile/day

Distance covered by riding bike in y days = 10 miles/day × y

Distance desired by Kayla to cover = 200 miles

[tex]200miles=6 miles/day\times x+10 miles/day \times y[/tex]

At least 15 of the days running.Put  x = 15 days in above equation:

[tex]200miles=6 miles/day\times 15 days+10 miles/day \times y[/tex]

[tex]200 miles - 90 miles=10 miles/day \times y[/tex]

[tex]\frac{110 miles}{10 miles/day}=y[/tex]

y= 11 days

Kayla will be able to cover the distance of 200 miles by riding bike for 11 days and by running for 15 days.

There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year. You are assuming that 65 years is the length. We will find the number of seconds in 65 years.

60 x 60 x 24 x 365 x 65 = 2,049,840,000 seconds.
We should note that every 4 years there is an extra day, so if we find 65 % 4 or the modulus of 65 then we can add this. The modulus of this is 16.
60 x 60 x 24 x 16 x 65 = 89,856,000 seconds

2,139,696,000 seconds (when you add the two calculations together).

You are finding it "every 10 seconds" so divide this value by 10. Then divide by another 100 because you are only counting dollars and 100 pennies is equal to 1 dollar.
The answer is : $2,139,696

the difference between a full jug and a jug that is half full will give us the weight of the marbles only in a half full jug:
4 - 2.6 = 1.4 kg

In a half full jug that weighs 2.6 kg, the weight of the marbles is 1.4 kg 
the weight of the jug = 2.6 - 1.4 = 1.2 kg

Answer:

The jug weights empty 1.2 kg.

Step-by-step explanation:

In this case we can define two equations based on the description to find the weight of the empty jug, this is:

Eq. 1: [tex]Jug+\frac{1}{2} Marbles=2.6[/tex]

Eq. 2: [tex]Jug+Marbles=4[/tex]

Now putting the Eq. 2 in the Eq. 1 we have:

[tex]Jug+\frac{1}{2} (4-Jug)=2.6[/tex]

Clearing Jug:

[tex]\frac{1}{2}Jug=2.6-2[/tex]

[tex]Jug=0.6*2[/tex]

[tex]Jug=1.2[/tex]

The jug weights empty 1.2 kg.

Let us say that,

1 = smaller solid

2 = larger solid

We must remember that the surface area of an object is proportional to the square of their sides, therefore,

SA = k s^2

where k is the constant of proportionality.

By taking the ratio of the 2 similar solids:

SA2 / SA1 = k s2^2 / k s1^2

SA2 / SA1 = s2^2 / s1^2

sqrt (SA2 / SA1) = s2 / s1

s2 / s1 = sqrt (1158 / 340)

While the volume of an object is proportional to the cube of their sides, therefore:

V = k’ s^3
where k’ is the constant of proportionality.

By taking the ratio of the 2 similar solids:

V2 / V1 = k’ s2^3/ k’ s1^3

V2 / V1 = s2^3/ s1^3

1712 / V1 = [sqrt (1158 / 340)]^3

1712/V1 = 6.28556705

V1 = 272.37 yd^3

The inequality [tex]a^2 + b^2 > c^2[/tex] indicates that the triangle is not a right triangle and the angle theta is acute. The cosine of an acute angle theta will be positive, not negative.

When it is given that a triangle has sides a, b, and c, with c being the longest side, and the inequality [tex]a^2 + b^2 > c^2[/tex] holds, we can deduce certain characteristics of the triangle and angle theta, which is opposite to side c. This inequality indicates that the triangle is not a right triangle, because for a right triangle, according to the Pythagorean theorem, the relationship between the sides is [tex]a^2 + b^2 = c^2.[/tex]

Since [tex]a^2 + b^2 > c^2[/tex], we can infer that the angle opposite the longest side, theta, must be acute because the sum of the angles in any triangle equals two right angles. Therefore, if theta were obtuse, the sum of the angles would be greater than two right angles, which contradicts the basic properties of triangles.

The correct statements are that the triangle is not a right triangle and that theta is an acute angle.  cos(theta) is not necessarily < 0; for an acute angle, the cosine value will be positive. The first statement that the triangle is a right triangle is incorrect because it contradicts our given information and the Pythagorean theorem.

A figure with 5-part symmetry has 5 lines of symmetry.

A figure with 5-part symmetry has 5 lines of symmetry. This means that it can be divided into five equal parts by rotating it around these lines. Each line of symmetry divides the figure into two mirror-image halves.

The recursive formula for the sequence is an = an-1 + 2. The explicit formula is an = 9 + (n-1)(2). There are 31 seats in the 12th row.

a) Recursive formula: The difference between the numbers of seats in consecutive rows is always 2. So, the recursive formula can be written as: an = an-1 + 2. Here, an represents the number of seats in the nth row, and an-1 represents the number of seats in the (n-1)th row.

b) Explicit formula: The first term of the arithmetic sequence is 9, and the common difference is 2. The explicit formula can be written as: an = a1 + (n-1)d. Substituting the values, we get an = 9 + (n-1)(2).

c) Seats in the 12th row: Using the explicit formula, we can calculate the number of seats in the 12th row: a12 = 9 + (12-1)(2) = 9 + 22 = 31. So, there are 31 seats in the 12th row.

We are given the parametric equations:

x = 6 cos θ

y = 6 sin θ

We know that the derivative of cos a = - sin a and the derivative of sin a = cos a, therefore taking the 1st and 2nd derivates of x and y:

d x = 6 (-sin θ) = - 6 sin θ

d^2 x = -6 (cos θ) = - 6 cos θ

d y = 6 (cos θ) = 6 cos θ

d^2 y = 6 (-sin θ) = - 6 sin θ

Therefore the values we are asked to find are:

dy / dx = 6 cos θ / - 6 sin θ = - cos θ / sin θ = - cot θ

d^2 y / d^2 x = - 6 sin θ / - 6 cos θ = sin θ / tan θ = tan θ

We can find the value of the slope at θ = π/4 by using the dy/dx:

dy/dx = slope = - cot θ

dy/dx = - cot (π/4) = - 1 / tan (π/4)

dy/dx = -1 = slope

We can find the concavity at θ = π/4 by using the d^2 y/d^2 x:

d^2 y / d^2 x = tan θ

d^2 y / d^2 x = tan (π/4)

d^2 y / d^2 x = 1

Since the value of the 2nd derivative is positive, hence the concavity is going up or the function is concaved upward.

Summary of Answers:

dy/dx = - cot θ

d^2 y/d^2 x = tan θ

slope = -1

concaved upward

Final answer:

The quadratic equation 32x - 4 = 4x2 + 60 has real and equal solutions after rearranging to 4x2 - 32x + 64 = 0 and recognizing it as a perfect square.

Explanation:

To solve the equation 32x - 4 = 4x2 + 60, we first rearrange it into standard quadratic form ax2 + bx + c = 0.

We move all terms to one side: 4x2 - 32x + 64 = 0. Once in this form, we can use the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a), or factor if it is factorable, to find the solutions for x. After rearranging, we note that the quadratic is a perfect square, giving us (2x - 8)2 = 0, which means that the solution for x is 4, with multiplicity of two since it is a repeated root.

The description of the solutions would be that they are real and equal, since we have a repeated solution.

The lowest decimal number from 0.105, 0.501, 0.015, and 0.15 is 0.015. This is because when we compare the numbers from left to right, 0.015 has the smallest digit (0) at the second decimal place which is the hundredths place.

To determine which decimal number is the lowest, it's helpful to compare these numbers digit by digit from the left. The four numbers are 0.105, 0.501, 0.015, and 0.15. Each of them starts with 0. The second digit of 0.105, 0.501, and 0.15 is 1, but the second digit for 0.015 is 0. So, 0.015 is the lowest number because it has the smallest digit (0) in the second decimal place (hundredths place). Remember, these numbers are read as decimals and not as whole numbers, so the digit at each decimal place has a different significance.

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3 baseball + 9 football  9+3 = 12

3 out of 12 were base ball

3/12=0.25

60*0.25 = 15

 so there would be 15 baseball cards

Answer:

The answer is 15

Step-by-step explanation:

i took the test

Answer: $98 per day

Step-by-step explanation:

Let us calculate the amount he is paid per day.

Since Miguel works 5 days a week, we will divide his total pay per week by the number of days he works every week to get the amount of money he is paid daily.

Therefore, daily pay = 490/5

daily pay =$ 98.

Alternatively,

If 5 days ------> $490

1 day------->$x

Cross multiply and work out the value of x:

5x = 490

therefore, x= 490/5

x=$98 /day

Answer:

Failure of a Single Dell computer in terms of percentage=17%

It means you buy a computer, there is 17% chance that it will be bad Machine and (100-17)%=83% chance that, it will be a good machine.

Probability that if you buy four computers, atleast 1 will fail within a year

            [tex]=_{1}^{4}\textrm{P}\times [P(S)]^3\times P(F)+_{2}^{4}\textrm{P}\times [P(S)]^2\times [P(F)]^2+_{3}^{4}\textrm{P}\times P(S)\times [P(F)]^3+_{4}^{4}\textrm{P}\times [P(F)]^4\\\\=4 \times (0.83)^3\times (0.17)+6\times (0.83)^2\times (0.17)^2+4\times (0.83)\times (0.17)^3+1\times (0.17)^4\\\\=0.3881516+0.11945526+0.01631116+0.00083521\\\\=0.52475323[/tex]

=0.53(Approx)

=0.53 × 100

=53%

The GCF can be obtained by taking the prime factors of two numbers then multiplying the common prime factors. IF there are none, then the GCF is 1 and the numbers are called relatively prime.

There are a lot of relatively prime numbers. To name three sets:

3 and 19

7 and 20

15 and 28

For these sets, we see that there are no other common factors except 1. To illustrate the factors:

3 = 1, 3

19 = 1, 19

7 = 1, 7

20 = 1, 2, 2, 5

15 = 1, 3, 5

28 = 1, 2, 2, 7

So we see that only the number 1 is the factor in each set.

Final answer:

Three sets of relatively prime numbers are 9 and 16, 14 and 25, and 8 and 21, as they do not share any common prime factors other than 1.

Explanation:

If the Greatest Common Factor (GCF) of two numbers is 1, they are indeed referred to as relatively prime. To find sets of relatively prime numbers, we need to identify pairs of numbers that do not have any prime factors in common other than 1.

9 and 16: The prime factors of 9 are 3· 3, and the prime factors of 16 are 2· 2· 2· 2. They share no common prime factors, so they are relatively prime.

14 and 25: The prime factors of 14 are 2· 7, and the prime factors of 25 are 5· 5. Since they have no common factors, these numbers are also relatively prime.

8 and 21: The prime factors of 8 are 2· 2· 2, and the prime factors of 21 are 3· 7. With no prime factors in common, 8 and 21 are relatively prime.

Therefore, we have found three sets of relatively prime numbers: 9 and 16, 14 and 25, and 8 and 21.