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Two spheres of the same density have a ratio of 9 to 16 in surface area. If the small sphere weighs 15 kg, what does the large sphere weigh?

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15,500 tons because if u round it from the hundreds place then it rounds to 20,000 tons.

Study Solutions

Two spheres of the same density have a ratio of 9 to 16 in surface area. If the small sphere weighs 15 kg, what does the large sphere weigh?

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Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?

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We solve this problem by assuming that the relation is

linear. With that, the slope m must be constant with x = machine hours and y = average

maintenance costs, therefore

m = (13,000 – 8,000) / ($1.20 – $1.50) = (13,000 – 10,000)

/ ($1.20 – X)

($1.20 – X) = ($1.20 – $1.50) * (13,000 – 10,000) / (13,000

– 8,000)

$1.20 – X = – $0.30 * 3,000 / 5,000

$1.20 – X = – 0.18

X = $1.38

Therefore total expected maintenance cost is:

Total maintenance cost = $1.38 * 10,000

Total maintenance cost = $13,800

**Therefore the answer is closest to the value of $13,440.**

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Charlie had a waist circumference of 47 inches and a BMI of 29 this shows that she is overweight. **BMI** test level is high from normal ranges shows that she is at higher risk of **disease**. She should lose weight and concern to the doctor.

**Further Explanation:
**

Body mass index (BMI) is a measured value derived from the height of a person and mass.

BMI indicates whether the person is healthy or overweight mainly used by physicians.

• Range of BMI in a **normal person is 18.5-25**

• Range of BMI in** skinfold person is 25-30**

• Range of BMI in **underweight person is 15-18.5**

The skinfold measurement test is used to determine a person’s body fat percentage and body composition.

In this test, we are the proportion of body fat by determining skinfold thickness at pinches specific part of the body. The estimate of these folds is determined the fat beneath the skin, also called subcutaneous adipose tissue.

The tester pinches the skin at the site and drags the fold of skin away from the muscle so only the fat tissue and skin are being held. The skinfold thickness is measured by skinfold calipers in millimeters.

Skin test includes the seven locations of the body:

1. Triceps

2. Quadriceps

3. Suprailiac

4. Pectoral

5. Subscapular

6. Midaxilla

7. Abdomen

Charlie had a waist circumference of 47 inches and a BMI of 29 this shows that she is overweight. Females with waist size 47 inches have higher risk of having disease. BMI test level is high from normal ranges shows that she is at higher risk of disease.She should lose weight and concern to the doctor.

**Learn more:**

**1. **Learn more about carbohydrate monomer brainly.com/question/6947177

**2. **Learn more about core muscle stabilization brainly.com/question/1231927

**3. **Learn more about energy storagehttps://brainly.com/question/523624

**Answer Details:
**

**Grade: **High School

**Subject: **Health

**Chapter:** Physical Fitness

**Keywords:
**

Body index mass, weight, doctor, triceps, abdomen, midaxilla, Quadriceps, skinfold, mass, height, pectoral.

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Rex weighed 80 pounds a year ago. Now he weighs 92 pounds. What is the percent increase in his weight? (A)12% (B)13% (C)15% (D)16%

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**Answer: The answer is (C) Patricia is not correct because both 3 – 4i and -11+√2i must be roots.**

**Step-by-step explanation: **Given that (-11-√2i) , (3 + 4i), and 10 are the roots of the polynomial function f(x) that Patricia is studying.

**We know that the complex roots of a polynomial function always occur in pairs. That is, if (a + bi) is a root of a function, then (a – bi) will also be a root (one is the complex conjugate of the other).**

**The complex conjugate of (3 + 4i) is (3 – 4i) and the complex conjugate of (-11 – √2i) is (11 + √2i).**

**Therefore, (3 – 4i) and (-11 + √2i) both are the roots of f(x).**

Hence, since we have 5 roots, **so the degree of the polynomial function f(x) cannot be 4.**

Since Patricia concludes that the degree of f(x) is 4, so she is not correct because both (3 – 4i) and (-11+√2i) must be roots.

**Thus, option (C) is correct.**

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127=7 (mod n) means when 127 is divided by n, the division leaves a remainder of 7.

The statement is equivalent to

120=0 (mod n), meaning that n divides 120.

All divisors of 120 will satisfy the statement because 120 divided by a divisor (factor) will leave a remainder of 0.

Factors of 120 are:

n={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}, |n|=16.

You can count how many such values of n there are, and try to check that each one satisfies 127=7 mod n.

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The gravitational force Fg between two objects is given by the equation:

Fg=(G*m₁*m₂)/r₂, where G=6.67*10^-11 m³ kg⁻¹ s⁻² is the gravitational constant, m₁ and m₂ are the masses of the two bodies and r is the distance between those bodies.

Due to the gravitational attraction the pencil and the eraser will attract if we there is no friction on the surface.

m₁=10 g=0.01 kg is the mass of the pencil

m₂=20 g=0.02 kg is the mass of the eraser

r=2.5 cm = 0.025 m

First we calculate the Fg:

Fg={(6.67*10^-11)*0.01*0.02}/(0.025²)=2.1344*10^-11 N

To get the velocity v of the pencil:

v²=2as, where a is the acceleration of the pencil and s is the path. In our case s=r so we can write:

v²=2ar

a=Fg/m₁= 2.133*10^-9 m/s²

v²=2*(2.133*10^-9)*0.025=1.0665*10^-10

v=√(1.0665*10^-10)=1.0327*10^-5 m/s

We have the velocity and the acceleration, so we can calculate the time t with the equation:

t=v/a=(1.0327*10^-5)/(2.133*10^-9)=4841.6 s

1 hour has 3600 s so when we divide time t in seconds by 3600 we get time T in hours:

T=t/3600=4841.6/3600=1.3449 h.

So the time for the pencil and eraser to touch is T=1.3449 hours.

Also time T can be expressed like T= 1h and 20 mins and 41.64 s

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The weight of Anna is: 115 pounds

and the weight of Janet is: 135 pounds.

It is given that:

Janet weighs 20 pounds more than Anna.

This means if the weight of Anna is: x pounds

Then the age of Janet is: (x+20) pounds.

Also,

The sum of their weights is 250 pounds.

i.e.

x+x+20=250

i.e.

2x+20=250

On subtracting both side by 20 we have:

2x=250-20

i.e.

2x=230

On dividing both side by 2 we have:

x=115

Hence, the weight of Anna is:115 pounds.

and the weight of Janet is: 115+20=135 pounds.

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The point that lie on the line is:

** B. (1,1)**

We are given that a line passes through the point (0,-1) and has a slope of 2.

We know that the equation of a line passing through (a,b) and having slope m is given by:

Here we have: (a,b)=(0,-1) and m=2

This means that the equation of line is:

Now we will check which option is true.

**A)**

** (2,1)**

when x=2

we have:

Hence, option: A is** incorrect.**

**B)**

** (1,1)**

when x=1

we have:

** Hence, option: B is correct.**

**C)**

** (0,1)**

when x=0

we have:

Hence, option: C is** incorrect.**

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**Answer:**

a) The time the police officer required to reach the motorist was 15 s.

b) The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) The total distance traveled by the officer was 225 m.

**Explanation:**

The equations for the position and velocity of an object moving in a straight line are as follows:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

a)When the officer reaches the motorist, the position of the motorist is the same as the position of the officer:

x motorist = x officer

Using the equation for the position:

x motirist = x0 + v · t (since a = 0).

x officer = x0 + v0 · t + 1/2 · a · t²

Let´s place our frame of reference at the point where the officer starts following the motorist so that x0 = 0 for both:

x motorist = x officer

x0 + v · t = x0 + v0 · t + 1/2 · a · t² (the officer starts form rest, then, v0 = 0)

v · t = 1/2 · a · t²

Solving for t:

2 v/a = t

t = 2 · 15.0 m/s/ 2.00 m/s² = 15 s

The time the police officer required to reach the motorist was 15 s.

b) Now, we can calculate the speed of the officer using the time calculated in a) and the equation for velocity:

v = v0 + a · t

v = 0 m/s + 2.00 m/s² · 15 s

v = 30 m/s

The speed of the officer at the moment she overtakes the motorist is 30 m/s

c) Using the equation for the position, we can find the traveled distance in 15 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 1/2 · 2.00 m/s² · (15s)² = 225 m

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Say we have a cylinder

that has a height of dx, we see that the cylinder has a volume of:

Vcylinder = πr^2*h = π(5)^2(dx) = 25π dx

Then, the weight of oil in this cylinder is:

Fcylinder = 50 * Vcylinder = (50)(25π dx) = 1250π dx.

Then, since the oil x feet from the top of the tank needs to

travel x feet to get the top, we have:

Wcylinder = Force x Distance = (1250π dx)(x) = 1250π x dx.

Integrating from x1 to x2 ft gives the total work to be: (x1

= distance from top liquid level to ground level; x2 = distance from bottom

liquid level to ground level)

W = ∫ 1250π x dx

W = 1250π ∫ x dx

W = 625π * (x2 – x1)

x2 = 14 ft + 15 ft = 29 ft

x1 = 14 ft + 1 ft = 15

ft

W = 625π * (29^2 – 15^2) **W = 385,000π ft-lbs
= 1,209,513.17 ft-lbs**

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14. **E 2.0 m/s^2**

Initially, a 20 N force is applied to the block, so it has an acceleration of 3.9 m/s^2. According to Newton’s law, the mass of the block is:

In the second situation, a force of 10 N is applied to the block. Since the mass is still the same, the acceleration now is:

So, approximately 2.0 m/s^2.

**15. C. 866 N at 78.1° counterclockwise to the x-axis**

Resultant along the x- and y-axis:

Magnitude and direction of the resultant:

**16. D. 1720 N**

Since the sphere is suspended, it is in equilibrium, therefore the tension in the chain is equal to the weight of the sphere attached to it, therefore:

**17. C. A**

This arrangement generates the largest tension in the chain, because in all other arrangements the weight of the object is split between the two chains, while in this case all the weight is hold by one chain, therefore the tension in this case is larger.

**18. Straight path**

The gravity “holds” the planets keeping them in a circular orbit. If we remove gravity, the planets would continue in a straight path with constant speed, because now there are no more forces acting on it, so by inertia they will continue their uniform motion with constant speed.

**19. B. 1.6 × 104 N**

First we can find the deceleration of the car by using the SUVAT equation:

where v=0 m/s, u=2 m/s, and S=15 cm=0.15 m. Re-arranging, we have

And now we can calculate the average force exerted on the car, by using Newton’s second law:

(the negative sign means that the force’s direction is opposite to the motion of the car)

**20. A. magnetism**

Magnetism is part of the electromagnetic force, which is one of the fundamental forces which act also through empty space. All the other forces need some object in order to act.

**21. E. 45 N**

The magnitude of the force in link A is equal to the weight of the rod plus the weight of the lower block, therefore:

**22. C. on Earth at sea level**

The weight of the bowling ball is given by: , where m is the mass of the ball and g is the acceleration due to gravity. The value of g increases when moving from the Earth’s center to the Earth’s surface, then decreases when moving far from the surface, so the point where g is greatest is at sea level, where it is 9.81 m/s^2. On the surface of the Moon, g is much smaller (about 1/6 of the value on Earth).

**23. A. 0.5 m/s2**

The acceleration of the block is given by Newton’s second law:

**24. D. Both forces are equal in magnitude but opposite in direction.**

According to Newton’s third law: if an object A exerts a force on an object B, then object B exerts a force equal and opposite on object B. In this case, objects A and B are the bat and the baseball, therefore the two forces are equal in magnitude and opposite in direction.

**25. B. 2940 N**

The mass of the boulder is equal to its weight divided by the acceleration of gravity (9.81 m/s^2):

So now we can calculate the force needed to accelerate the boulder to 12.0 m/s^2:

**26. D. 32.2 N**

The weight of the object on Mercury is given by:

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The Right BMI is 17.62 which is B. and he is slightly in underweight

To calculate the BMI simply put the figures given in the statement in the given formulate

BMI = Weight (in pounds) × 703 / [Height (in inches)] ² = 130 × 703 / [72] ² Which will give us 17.62.

* The body mass index (BMI) is a tool to estimate a person’s body size. Invented by Adolphe Quételet, this index is also called the Quételet index.

* It is calculated according to the size and the body mass. It was originally designed for adults aged 18 to 65, but new patterns of growth have emerged in recent decades for children aged 0 to 18 years. In both cases, it is an indication and is involved in the calculation of the fat mass index (IMG).

* The values 18 and 25 are commonly accepted benchmarks for a normal BMI and therefore have a risk ratio deemed acceptable. Our patient is slight under 18 (17.62), so he need to gain some pounds.

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Recall your d = rt, distance = rate * time

let’s say the boat’s rate is “b” in still water, and the current’s rate is “c”

as the boat goes upstream, is not really going “b” fast, the water is not still anyway, is going much slower, is going ” b – c “, because the current’s rate is eroding speed because is going against the current.

as the boat goes downstream, is not going “b” fast either, is going faster, is going ” b + c ” fast, because is going downstream and thus with the current and the current is adding speed to it. notice, it takes longer going up, 5hrs, then coming down, 3hrs, same 150 on each way.

solve for “r”

what’s the boat’s rate? well, 30+r = b

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The options of the question are, A) by explaining that world leaders are doing all they can to tackle climate change now. B) by quoting Winston Churchill to show that he also believes that climate change is a serious issue. C) by comparing the inaction of the world leaders of today to the inaction of leaders in the past. D) by showing the differences in the effects of climate change and World War II.

**The correct answers are C) by comparing the inaction of the world leaders of today to the inaction of leaders in the past.
**

*The excerpt that develops Gore’s theme that climate change is a problem that must be addressed is “by comparing the inaction of the world leaders of today to the inaction of leaders in the past.”
*

Al Gore develops the urgency of attending the issues that climate change brings when in the excerpt he makes reference to the comparison made by Winston Churchill to Hitler’s threat: “They go on in strange paradox,, decided only to be undecided, resolved to be irresolute, adamant for drift, solid for fluidity, all-powerful to be impotent”. This way, Al Gore is comparing the inaction of the world leaders of today to the inaction of leaders in the past.

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15,500 tons because if u round it from the hundreds place then it rounds to 20,000 tons.

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To make an line perpendicular to another, you must take the slope of the first line and find its negative inverse to put in the second.

3y=x-6 –> y=(x-6)/3 –> y=1/3x-2

The slope of the first line is 1/3 so the slope of the second line will be -3.

Now you must use the point slope formula to find the actual equation of the second line.

y-y1=m(x-x1) –> y-(-7)=-3(x-4) –> y+7=-3x+12 –> y=-3x+5

Now you need to translate that to function notation, which is pretty easy. Simply remember f(x) = y. So…

f(x)=-3x+5, and that’s your answer.

Remember to check your answers using a graphing calculator. If you don’t have one, you can use one online. I recommend using https://www.desmos.com/calculator.

1, 5, 9, 13, 17, 21, 25, 29

You are adding 4 every time.

Points of intersection are (0,0),(0,8),(10,0),(4,6) plugging them into the equation you get 0,24,10,22. I don’t know if you’re looking for max value or min value.

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We are given function for area.

where x = width, gives you the area of the dog pen in square feet.

We need to find the width that gives the maximum area.

And maximum area of the rectangular dog pen.

The given function is a quadratic function.

And a quadratic function represents a parabolic shape on the graph.

**The highest point of the parabola is the vertex of the parabola.**

**So, we need to find the vertex of the parabola for the given function.**

A = 27x-x^2.

Formula for x-coordinate of the vertex is = -b/2a.

Plugging values of a and b in formula, we get

-27/ 2(-1) = -27/-2 = 13.5

Therefore, 13.5 feet width would give maximum area.

Let us find the maximum area now.

Plugging x=13.5 in given function, we get

=364.5 – 182.25

= 182.25 square feet ≈ 182.3

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**Answer:**

I option is right

**Step-by-step explanation:**

Given that there are 12 candidates. One has to be selected at random. FOr a fair choice of 1 among 12, we must have each one have the equal probability

i.e. prob of selecting any one = 1/12

This means sample space should consist of 12 events and one to be assigned for one.

In option i, we have coin toss has 2 outcomes, a die has 6 outcomes, together we have 12 equally likely outcomes thus making a fair choice.

Option II is incorrect because sample space consists of 5 numbers and 5 balls hence sample space would be 25 cannot give equal chances to 12.ption 3 is incorrect since when we flip a coin 4 times we have 16 different outcomes hence 12 assigning cannot be equaly likely.

When two dice of different colours are thrown, sample space is 36 and hence 12 cannot be assigned order in a fair manner.

So Option I is right

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**Answer:**

ounce or 0.0665 ounce

**Step-by-step explanation:**

The weight of ground nutmeg in a box = ounce

= ounce

If there are 20 teaspoons of nutmeg in the box.

The weight of one teaspoon of nutmeg = ÷ 20

= ×

=

= ounce

The weight of one teaspoon nutmeg would be ounce.

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**Answer:**

You are paid $11.75/hr. You work 40 hr/wk.

Weekly income is :

So, monthly income becomes :

Deductions are given as :

FICA (7.65%) =

Federal tax withholding (10.75%) =

State tax withholding (7.5%) =

**So, net income = = $1393.08**

2. 20 hours of overtime in next month at 1.5 times your regular rate, so rate is

So, overtime pay is =

And adding this to normal pay we get , 1880+352.50=$2232.50

Now deductions will be :

FICA at 7.65% =

Federal tax withholding at 10.75% =

State tax withholding at 7.5% =

Total deductions are = 170.786+239.993+167.437 = $578.216

So, net income becomes = 2232.50-578.216 = $1654.284

3. No discretionary expense is given in the question.

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