1. Find the volume for 5 different spheres by randomly choosing different radii.
Using the same radii values, find the volume of 5 cylinders where the height of the cylinder is the same as the diameter of the sphere.

Answer:

See picture

Step-by-step explanation:

The rule is ...

[tex]x^{m/n}=\sqrt[n]{x^m}[/tex]

The index of the surd becomes the denominator of the exponents inside.

Answer:

x^(5/3)*y^(1/3)

Step-by-step explanation:

note (a*b)^c = a^c*b^c

the given expression can be rewritten as (x^5*y)^1/3

=x^(5/3)*y^(1/3)

ans is the 2nd choice

Answer:

y= 35/2  when x=5

x=6 when y =21

Proportinal relatiionships:  y=−x ,  y=15x

Step-by-step explanation:

The formula for direct variation is

y= kx

If y=7 and x=2, we can solve for k

7 =k*2

Divide by 2

7/2 =k

y =7/2 x

Now if x=5

y =7/2 * 5

y =35/2

Now if y=21

21 =7/2 * x

Multiply by 2/7

21 * 2/7 = 7/2 * 2/7 x

6 =x

Which equation represents a proportional relationship?

y=−x

YES  k = -1   Some people debate about having a negative constant, but everything I have read and taught says you can have a negative constant.

y=−5(x+1)

This does not go through the origin so no

if x=0  y = -5

y = 5x + 1

if x = 0 y =1   so no

y=15x

YES  k = 15

Answer:

17.5

i just did it on my quiz and it was wrong(the other guy is wrong)

[tex]2a+b=\dfrac{2ab}{b}+\dfrac{bb}{b}=\dfrac{2ab}{b}+\dfrac{b^2}{b}=\boxed{\dfrac{2ab+b^2}{b}}[/tex]

For this case, we have that by definition:

Let "x" be an angle of any vertex of a right triangle.

[tex]tangent (x) = \frac {Cathet \ opposite} {Cathet \ adjacent}[/tex]

So, if we want to find the tangent of angle A:

[tex]tangent (A) = \frac {6} {8}[/tex]

Thus, the tangent of angle "A" is [tex]\frac {6} {8}[/tex]

Answer:

[tex]\frac {6} {8}[/tex]

Option b

Answer:

B) The maximum y-value of f(x) approaches 2

C) g(x) has the largest possible y-value

Step-by-step explanation:

f(x)=-5^x+2

f(x) is an exponential function.

Lim x→∞ f(x) = Lim x→∞ (-5^x+2) = -5^(∞)+2 = -∞+2→ Lim x→∞ f(x) = -∞

Lim x→ -∞ f(x) = Lim x→ -∞ (-5^x+2) = -5^(-∞)+2 = -1/5^∞+2 = -1/∞+2 = 0+2→

Lim x→ -∞ f(x) = 2

Then the maximun y-value of f(x) approaches 2

g(x)=-5x^2+2

g(x) is a quadratic function. The graph is a parabola

g(x)=ax^2+bx+c

a=-5<0, the parabola opens downward and has a maximum value at

x=-b/(2a)

b=0

c=2

x=-0/2(-5)

x=0/10

x=0

The maximum value is at x=0:

g(0)=-5(0)^2+2=-5(0)+2=0+2→g(0)=2

The maximum value of g(x) is 2

Answer:

2968.30 cm cube.

Step-by-step explanation:

Given is a cone and top of it is a hemisphere of radius 9 cm.

Cone has height as 17 and radius same 9 cm.

We have to find the volume of the compound shape

We find that the volume would be the sum of that of hemisphere of radius 9 cm and cone of height 17, and radius 9 cm.

Volume of compound shape = volume of cone+Volume of hemisphere

= [tex]\frac{1}{3} \pi r^{2} h+\frac{2}{3} \pi r^{3}[/tex]

substitute for h and r in the equation

Required volume =

[tex][tex]\frac{1}{3}\pi  r^{2} (h+2r) = \frac{1}{3}\pi  9^{2} (17+2(9))\\= 1441.99+1526.31\\=2968.30[/tex][/tex]

So answer is 2968.30 cm cube.

=

Total -

Right-handed: 214! Left-handed: 22!

Total of students: 236 students

I hope this helped! :D

Step-by-step explanation:

9th Grade: Right Handed: 111! Left Handed: 10!

10 Grade: Right Handed: 103! Left Handed: 22!

Add left handed for both grades. Add right handed for both grades. And add total numbers.

I hope this helped :D    

There are 121 students in 9th grade and 115 students in 10th grade at Jefferson High School.

This question involves counting and analyzing data about grade levels and handedness of students at Jefferson High School. To answer the question, we need to use the given information:

- There are 236 students in 9th and 10th grades combined.

- Out of these, 121 students are in 9th grade.

- Among the 214 right-handed students, 103 are in 10th grade.

We can use these numbers to find out how many students are in each grade level.

Let's denote the number of 9th-grade students as 'x' and 10th-grade students as 'y'.

From the given information:

x + y = 236 (total number of students)

x = 121 (number of 9th-grade students)

y = 103 (number of 10th-grade students)

To find the value of 'y', we can substitute the given value of 'x' into the first equation:

121 + y = 236

y = 236 - 121

y = 115

Therefore, there are 121 students in 9th grade and 115 students in 10th grade.

Answer:

1.4 × 10^-8

Step-by-step explanation:

The chip is 14  nanometers

14 * .000000001

.000000014

Move the decimal 8 places to the right, because we need 1 number in front of the decimal for scientific notation.  The exponent will be -8 because  we moved it 8 places to the right

1.4 × 10^-8

The thickness of the silicon chip in scientific notation is 1.4 x 10^-8 m.

To express the thickness of the silicon chip in scientific notation, we need to convert the given thickness of 14 nanometers to meters.

Since 1 nanometer (nm) is equal to 0.000000001 meters, we can convert 14 nanometers to meters by multiplying it by the conversion factor:

14 nm x 0.000000001 m/nm = 0.000000014 m

Now, we can express the thickness of the chip in scientific notation:

0.000000014 m = 1.4 x 10-8 m

half-turn

There is a point of rotational symmetry at the center of the pattern. Thus, turning it 180° (a half-turn) will map it to itself.

_____

Comment on other choices

Any sort of reflection will change it to bqbqbqbqbq. Translation puts its somewhere else, not on top of itself.

Answer:

A half turn reversal of direction (as in a staircase) either by one 180-degree turn or two right-angle turns

Step-by-step explanation:

Hope this helps :) -Mark Brainiest Please :)

f(x) factors as ...

... f(x) = (x² -4)(x² +3) = (x -2)(x +2)(x² +3)

The real roots are x = ±2.

The complex roots are x = ±i√3.

___

We don't know what "no real complex roots" means. We suspect your answer may be C. 2.

Answer:

I do believe the answer is C

Step-by-step explanation:

.004 / .0004 =

Answer:

c 10

Step-by-step explanation:

If we want to know how much bigger object A is than object B is we take object A and divide it by object B

object A        4 * 10^-3

-----------   = -------------

Object B        4 * 10 ^-4

When dividing exponents with the same base

We can subtract them.  The numbers out front get divided

4/4 * 10 ^ (-3- -4)

1 * 10 ^(-3+4)

1 * 10 ^1

10

Answer:

y = 1 + 1/((x -1)(x -4))

Step-by-step explanation:

To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.

To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.

Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.

... y = 1 + 1/((x -1)(x -4))

If you like, this can be "simplified" to ...

... y = (x² -5x +5)/(x² -5x +4)

_____

In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).

Answer:

Step-by-step explanation:

1. You can use a calculator if your knowledge of arithmetic fails you.

... 98 +17 +37 -176 = 152 -176 = -24

___

2. -37/8 = -(32 +5)/8 = -4 5/8 = -4.625

This number is on the left side of zero on the number line, but is slightly closer to zero than -4.63, so is "greater than" -4.63.

DAY 15: The measures of the angles in a certain triangle are in the ratio 1: 5: 6. Find the measure of the smallest angle.  

x +5x +6x=180  

12x =180  

x=15º  

DAY 16: In triangle ABC, the measure of angle A = 7x - 32, the measure of angle B = 3x + 4, and the exterior angle at C has measure 12 (x - 5). Find the value of x.  

exterior angle = sum of two remote (other) interiors  

7x -32 +3x+4 =12(x-5)  

10x -28 =12x -60  

32-2x  

x=16  

DAY 17: Find the slope of the line perpendicular to the line through the points (21, 11) and (-4, -12).  

11 - -12 / 21 - -4 =23/25  

slope of perpendicular line is negative reciprocal =  

-25/23 ( no 17!)  

DAY 18: In a certain triangle, the largest angle is 6 times the smallest. The third angle is 18 less than 4 times the smallest. What is the measure of the smallest angle?  

x= smallest  

6x =largest  

third angle =4x-18  

x+6x +4x-18 =180  

11x =198  

x=18º

Answer:

8 gallons have to be evaporated to have a 20% salt solution.

hope this helped :)

Step-by-step explanation:

.10*20=2 gallons of salt.

That leaves 18 gallons of water.

.2x=2

x=2/.2

x=10 gallons after evaporation.

18-10=8

To obtain a 20% salt solution from a 10% salt solution, 20 gallons of water must be evaporated.

To obtain a 20% salt solution from a 10% salt solution, the amount of water that needs to be evaporated can be calculated using a proportion. First, convert the percentages to decimals by dividing them by 100. Let x be the amount of water to be evaporated. The amount of salt in the initial solution is 10% of 20 gallons, or 0.10 * 20 = 2 gallons. The resulting solution will have 20% salt in a total volume of 20 - x gallons. Set up a proportion:

(2 gallons)/(20 gallons) = (0.20 * (20 - x) gallons)/(20 - x gallons)

Cross multiply and solve for x:

2(20 - x) = 0.20(20 - x)

Now solve the equation:

40 - 2x = 4 - 0.20x

2x - 0.20x = 40 - 4

1.8x = 36

x = 36/1.8

x = 20

Therefore, 20 gallons of water must be evaporated from the initial 20-gallon solution to obtain a 20% salt solution.

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The mean age decreased.

I find it convenient to look at the additions with respect to the current mean age.

The current total age is 14×34. We have added members with ages (34 -10) and (34 +2), so the new total age is ...

... (34×14) + (34 -10) + (34 +2) = (16×34) - 8

Dividing this total by 16 will give the new mean age. (We already know it is less than 34.)

... ((16×34) -8)/16 = 34 - 1/2 = 33 1/2 . . . new mean age; a decrease

Another equation that shares the same solutions as x²-16x+12=0 is 2x² - 32x + 24 = 0. This equation is the initial equation multiplied by 2 and thus would produce the same solutions when the quadratic formula is applied.

The equation given is a quadratic equation, which is in the form ax²+bx+c = 0. The solutions of a quadratic equation are given by the formula: -b ± √b² - 4ac / 2a. This formula can be used to find the solutions of any other quadratic equation. For the given equation, x²-16x+12=0, the values of a, b, and c are 1, -16, and 12 respectively. So, another equation with the same solutions could be 2x² - 32x + 24 = 0. This equation has the same solutions because it's simply the initial equation multiplied by 2, so this doesn't change the results of the quadratic formula.

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Answer:

$9275

Step-by-step explanation:

Selma earns 5% on the first $40,000, which is $2000.

She earns 5.5% on the next $35,000, which is $1925.

She earns 6% on the next $25,000, which is $1500.

And she earns 7% on the last $55,000 (the amount over 100,000), which is $3850.

Altogether, Selma's commission is ...

... $2000 +1925 +1500 +3850 = $9275.

_____

Comment on the sliding scale

Each of the segments of this sliding scale could be rewritten to simplify its computation. For example, for amounts above $100,000, the formula could be either of ...

Answer:

6 2/3 hours

Step-by-step explanation:

We assume the time of interest is the total time spent on the main road and side road.

In each case, ...

... time = distance/speed

On the main road, ...

... tmain = s/v

On the side road, ...

... tside = (2s)/(v -2)

Then the total time spent is ...

... ttotal = tmain + tside

... = s/v + (2s)/(v -2)

For s=10 and v=6, this is ...

... ttotal = 10/6 + 2·10/(6 -2) = 5/3 + 20/4 = 5/3 + 5 . . . . hours

... ttotal = 6 2/3 hours

Answer:

6 hr 40 min

Step-by-step explanation:

Answer:

Second Option is the correct answer 3/2

Step-by-step explanation:

Tangent of an angle in a triangle is given by Perpendicular of that triangle / Base of that triangle , with resoect to angle in consideration.

Tangent Ratio for angle B = Perpendicular / Base

Tangent Ratio for angle B = AC / BC

Tangent Ratio for angle B = 3/2

Hope it helps.

Thank you.

y = 10(√3)/3

unnamed side = 5(√3)/3

Side ratios in a 30°-60°-90° triangle are 1 : √3 : 2.

Multiplying these by 5/√3 gives ...

... unnamed side : 5 : y = 5/√3 : 5 : 10/√3

Then ...

... unnamed side = 5/√3 = 5(√3)/3

... y = 10/√3 = 10(√3)/3

5.51 seconds

y = 0 when the stone hits the ground. At that point, t can be found from ...

... 0 = -16t^2 +486

... 0 = t^2 -30.375 . . . . divide by -16

... 30.375 = t^2 . . . . . . add the opposite of the constant

Take the square root to get ...

... √30.375 = t ≈ 5.51 . . . . seconds

You are given the length of every side, except for two, that can be easily derived from the others:

The sum of all sides, including these two, will give you the perimeter of the polygon.

The perimeter of the polygon is determined as P = 210 feet.

Given data:

The polygon of the perimeter is the total side length of all the sides of the polygon.

Let the perimeter be represented as P.

From the attached figure of the polygon:

P = ( 15 + 22 + 10 + 18 + 10 + 14 + 5 + 16 + ( 15 + 5 + 5 ) + 16 + 5 + ( 14 + 18 + 22 )

On simplifying the equation:

P = 210 feet

So, the value of P is 210 feet.

Hence, the perimeter is 210 feet.

To learn more about perimeter of rectangle:

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Answer:

A

Step-by-step explanation:

First discount is the original price reduced by 35% prior to the annual clearance.

So, 35% of 1325 = 0.35 × 1325 = 463.75.

After the discount of $463.75, the price that remains =  1,325 -  463.75 = $861.25.

Then, additional disount of 10%.

10% of $1,325. = 0.10  × 1,325. = 132.50

The final price after discount of 10% = 861.25 - 132.50. =  728.75.

Round to the nearest cent, we get 728.75.

Therefore, you would pay $ 728.75 after applying the discounts.

Answer:

B. 775.13

Step-by-step explanation:

Edge says A was wrong.

A. {(5,  5), (6,  −6), (8,  7), (−9,  9)}

Compare the table contents to the ordered pairs in each relation. The first pair of table values, (5, 5) matches relations A and B, but not C or D.

The second pair of table values (8, 7), matches relation A, but not B. Since all pairs of table values show up in relation A, and we have rejected relations B, C, and D as inappropriate choices, the answer is A.

Answer:

Step-by-step explanation:

1. First differences in the y-values are ...

... -5-0 = -5; -8-(-5) = -3; -9-(-8) = -1; -8-(-9) = 1; -5-(-8) = 3; 0-(-5) = 5

Second differences are ...

... -3-(-5) = 2; -1-(-3) = 2; 1-(-1) = 2; 3-1 = 2; 5-3 = 2

These 2nd differences are constant, so the points can be described by a 2nd-degree polynomial.

2. Values on the graph range from 0 to a low of -9 and back up to 0. There is a minimum at (1, -9).

3. The value at x=-1 is -5; at x=1, it is -9, which is less than -5. The function is decreasing on the interval -1 to 1.

Answer:

B. side-angle-side

Step-by-step explanation:

You are given that side SR matches its counterpart; angle SRT matches its counterpart; and you know side ST matches its counterpart, because they are the same segment.

Hence, you have two matching sides and the angle between them. This set of side-angle-side lets you invoke the theorem that matches that name.

Numerical Reasoning

Consider a set of prints that consists of 2 small prints and one large print (that is, twice as many small prints as large). The value of that set will be ...

... 2×$20 +45 = $85

To have revenue of at least $510, the studio must sell ...

... $510/$85 = 6

sets of prints. That is, the studio needs to sell at least 6 large prints and 12 small ones.

_____

With an equation

Let x represent the number of large prints the studio needs to sell. Then 2x will represent the number of small prints. Total sales will be ...

... 20·2x +45·x ≥ 510

... 85x ≥ 510

... x ≥ 510/85

... x ≥ 6

The studio needs to sell at least 6 large prints and 12 small prints.