In a circle with radius 2, an angle
intercepts an arc of length 7 π/2. Find the angle in radians in simplest form.

Answer:

  132175.2 cm³

Step-by-step explanation:

You want the volume of a sphere with radius 31.6 cm.

The volume of a sphere is given by the formula ...

  V = 4/3πr³

For a radius of 31.6 cm, we find the volume to be ...

  V = 4/3π(31.6 cm)³ ≈ 132,175.2 cm³

The volume of the sphere is about 132,175.2 cm³.

The corresponding height of similar rectangular prism m is 9 centimeter.

Given that, the volume of rectangular prism m is 17 cm³ and the volume of rectangular prism n is 136 cm³.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

The height of n is 18 cm.

Here, m³/n³ = 17/136

m³/18³ = 17/136

m³/18³ = 17/136

(m/18)³ = 1/8

(m/18)³ = (1/2)³

m/18 = 1/2

m=9 cm

Therefore, the corresponding height of similar rectangular prism m is 9 centimeter.

Learn more about the similar figure here:

brainly.com/question/20368229.

#SPJ1

The values of x, y and z in the given simultaneous equation is:

x = 4

y = 6

z = -3

The 3 simultaneous equations are given as:

x + 7y - z = 49

2x - 5y + 2z = -28

x - 6y=-32

Rearranging the first equation  gives:

x = 49 - 7y + z

2x - 5y + 2z = -28

x - 6y = -32

Substitute 49 - 7y + z into equations 2 and 3 to get:

2(49 - 7y + z) - 5y + 2z = -28

49 - 7y + z - 6y = -32

Convert the equation in terms of u and solving simultaneously gives:

y = 6 and z = -3

Thus:

x = 49 - 7(6) + (-3)

x = 4

Read more about Simultaneous Equations at: https://brainly.com/question/148035

#SPJ1

B) gas mileage decreases with increase of car weight.

Answer:non linear

Step-by-step explanation: since the exponent is greater than 1

Answer:

rectangular pyramid has 8 edges

The volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm is equal to 76.10 cubic centimeters.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 2.5/2 = 1.25 cm.

By substituting the parameters, we have:

Volume of cylinder, V = 3.142 × 1.25² × 15.5

Volume of cylinder, V = 76.10 cubic centimeters.

Read more on cylinder here: brainly.com/question/14060443

#SPJ1

Complete Question:

Calculate the volume of a cylinder whose diameter measures 2.5 cm and has a height of 15.5 cm.

The equation has a slope of 2/3 and the y-intercept is -1. The graph is aatched with the answer below.

An equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of all the points on a straight line. It takes the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). This equation allows us to easily calculate the y-coordinate of any point on the line, given its x-coordinate.

A linear graph, also known as a straight-line graph, is a graph that represents a linear equation. The x and y coordinates of each point on the line are plotted on a graph, with the x values on the horizontal axis and the y values on the vertical axis.

The resulting graph is a straight line that passes through the y-intercept (the point where the line intersects the y-axis) and has a slope equal to the coefficient of x in the equation.

Linear graphs are useful in many fields, including mathematics, science, engineering, economics, and business, as they allow us to visualize and analyze relationships between two variables that are directly proportional to each other.

To know more about graphs of linear equations follow

https://brainly.com/question/14488816

#SPJ1

The fraction of the cookies that are peanut butter cookies is 1/5

From the question, we have the following parameters that can be used in our computation:

Total = 10

Peanut butter = 2

using the above as a guide, we have the following:

Fraction = Peanut butter /Total

So, we have

Fraction = 2/10

Evaluate

Fraction = 1/5

Hence, the fraction is 1/5

Read more about proportions at

https://brainly.com/question/870035

#SPJ1

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Learn more about Edouard Manet's painting here:

https://brainly.com/question/26188885

#SPJ1

Proposition 3.9 means that if there is a third subgroup that contains the first two subgroups in group G, then when the subgroups are unified, they would still be a subgroup of G.

Put simply, a subgroup collection of Group G is directed if it contains any two subgroups that have a third subgroup containing them both. The subgroup union of this sorted collection is also a subgroup of G.

This definite conclusion occurs because the subgroup criterion states that if any small two subgroups of G are part of a union, then that union is also a subgroup of G. Additionally, a directed subgroup family can be perceived as a series of successive subgroups, with each subgroup being enclosed within the following one.

Find out more on subgroups at https://brainly.com/question/31611800

#SPJ1

The measure of v is 61 degree.

We have,

Interior angle = (v - 19) or v

Exterior angle = v + 42

Using exterior Angle Property

Exterior angle= Sum of opposite interior angle

v + 42 = v - 19 + v

v + 42 = 2v - 19

v - 2v = -19 - 42

-v = -61

v= 61

Thus, the value of v is 61.

Learn more about Exterior Angle Theorem here:

https://brainly.com/question/956912

#SPJ1

Answer:

22

Step-by-step explanation:

4

Answer:

[tex](x-6)^2+(y+7)^2=4[/tex]

Step-by-step explanation:

The formula for the equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where:

From inspection of the given graphed circle, we can see that the coordinates of its center are (6, -7), and its radius is 2 units. Therefore:

To determine the equation of the graphed circle, substitute these values into the equation of a circle formula:

[tex]\implies (x-6)^2+(y-(-7))^2=2^2[/tex]

[tex]\implies (x-6)^2+(y+7)^2=4[/tex]

Therefore, the equation of the graphed circle is:

[tex]\boxed{(x-6)^2+(y+7)^2=4}[/tex]

Result:

The probability of getting a sum greater than 25 = 1/9.

The answer is not among the given options.

To find the probability, we would need to consider the possible combinations of the spinner and number cube that result in a sum greater than 25.

First, note that the highest possible sum we can get is 12 (that is 6 from the spinner and 6 from the number cube). Therefore, we can remove all combinations that result in a sum of 24 or less.

Next, we can consider the combinations that result in a sum of 25 like this:

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 4

Finally, we can consider the combinations that result in a sum greater than 25:

Spinner lands on 5, number cube lands on 5

Spinner lands on 6, number cube lands on 5

Spinner lands on 5, number cube lands on 6

Spinner lands on 6, number cube lands on 6

Here, 4 possible combinations can result in a sum greater than 25 from a total of 6 x 6 = 36 possible outcomes.

So, the probability of getting a sum greater than 25 is 4/36 = 1/9.

Therefore, none of the given answer choices matches this result.

Learn more about probability at brainly.com/question/13604758

#SPJ1

The volume of 8 rectangular prism stacked base to base is 2560 in³.

Volume is a measure of three-dimensional space.

To calculate the volume of 8 rectangular prism stacked base to base, we use the formula below

Formula:

Where:

From the question,

Given:

We find the value of h using the formula for the surface area of a prism

Given:

Substitute these values into equation 2

Finally, we subtitute into equation 1

Hence the volume is 2560 in³.

Learn more about volume here: https://brainly.com/question/1972490

#SPJ1

Answer:

Kenneth's average stacking time is less than 8.2 seconds.

Brainly wouldn't allow me to give an explanation because apparently, it contains inappropriate words..? How odd.

Answer:

The data does not provide sufficient evidence to conclude that Kenneth's mean stacking time is is less than 8.2 seconds

Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level.

Step-by-step explanation:

Null hypothesis (H0): mu = 8.2 seconds

Alternate hypothesis (Ha): mu < 8.2 seconds

Significance level = 0.04

p-value = 0.0401

Using the p-value approach for testing hypothesis, do not reject H0 because the p-value 0.0401 is greater than the significance level 0.04.

There is not sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds.

The probability of drawing 2 blue marbles in a row is 9/64

From the question, we have the following parameters that can be used in our computation:

Marbles = 1 + 3 + 4 = 8

Blue = 3

Selecting the first marble we have

P(Blue) = 3/8

The marble is returned

So, we have the probablility of the second to be

P(Blue) = 3/8

The probability of drawing two blue marbles is

P = 3/8 * 3/8

Evaluate

P = 9/64

Hence, the probability is 9/64

Read more about probability at

brainly.com/question/24756209

#SPJ1

Answer:

Since the first blue marble is replaced before the second draw, the probability of drawing a blue marble on the second draw is still 3/8, the same as the probability of drawing a blue marble on the first draw.

To find the probability of both events occurring, we can multiply the probabilities of each event:

P(drawing two blue marbles in a row) = P(drawing a blue marble on first draw) x P(drawing a blue marble on second draw)

P(drawing two blue marbles in a row) = (3/8) x (3/8)

P(drawing two blue marbles in a row) = 9/64

Therefore, the probability of drawing two blue marbles in a row is 9/64.

Step-by-step explanation:

The measure of the arc length AB is [tex]\frac{16\pi }{15}[/tex] centimeters.

An arc length is simply the distance between two points along a section of a curve.

The arc length is expressed as:

s = 2πr × (θ/360°)

Where s is the arc length, r is the radius, θ is the angle and π is constant pi.

Given that:

Plug the values into the above formula

s = 2πr × (θ/360°)

s = 2 × π × 3cm × ( 64°/360°)

[tex]s = \frac{16\pi }{15} cm[/tex]

Therefore, the arc length is [tex]\frac{16\pi }{15}[/tex] cm.

Learn more about arc length here: https://brainly.com/question/16403495

#SPJ1

Answer:

Step-by-step explanation:

You want to know the number of hours Liz worked at each job, when the total pay for a total of 28 hours work was $175.80. Job A paid $6 per hour, and job B paid $6.60 per hour.

We can let 'b' represent the number of hours worked at job B. Then (28-b) is the number of hours worked at job A. Liz's total pay was ...

  6(28 -b) +6.60(b) = 175.80

Simplifying the equation gives ...

  0.60b +168.00 = 175.80

  0.60b = 7.80 . . . . . . . . . . . subtract 168

  b = 13 . . . . . . . . . . . . . . divide by 0.6

  28-b = 28-13 = 15 . . . hours at Job A

Liz worked 15 hours at Job A, and 13 hours at Job B.

__

Additional comment

Here, we used one equation. If you use two equations, you can get this same equation by substituting for the variable representing hours at Job A. Letting the variable represent hours at the higher-paying job generally results in arithmetic using positive numbers. If you write the equation for the hours at Job A, negative numbers will usually be involved. Though it shouldn't, sometimes that causes confusion.

A graphing calculator may offer two or three ways (or more) you use to can solve the equations. One of them is illustrated in the attachment. It solves the equations ...

1. The Height of the stone after 5s is 490feet

2. The time it will reach the ground 8.98s

3. The velocity of the stone when it hits the ground is 287.33 feet/s

Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity.

The equation of motion under gravity is given as;

H = ut ± 1/2gt²

v² = u²±2gh

v = u ± gt

1. The height = 18 × 5 -1/2 ( -32) 5²

h = 90+ 400

h = 490 feet

2. The time to reach the ground is calculated as;

h = ut + 1/2gt²

at max height u = 0

total height = 490+800

= 1290m

1290 = 1/2 × 32t²

2580 = 32t²

t² = 80.6

t = √80.6

t = 8.98s

3. The velocity when it reach the ground is

v² = u²+ 2gh

v² = 2× 32 × 1290

v ² = 82560

v = √82560

v = 287.33feet/s

learn more about motion under gravity from

https://brainly.com/question/28554700

#SPJ1

Answer:

The 80.6 square foot roll is less expensive per square foot since it costs $0.03/square foot compared to the other which costs $0.02/square foot

Step-by-step explanation:

Because the question asks which of the two paper towel rolls is less expensive per square foot, we must find the unit rate of both rolls (specifically, cost per 1 square foot)

We can find the unit rate using a proportion:

53.7 square foot roll

[tex]\frac{1.49}{53.7}=\frac{x}{1} \\1.49=53.7x\\0.0277=x\\0.03=x[/tex]

80.6 square foot roll

[tex]\frac{1.89}{80.6}=\frac{x}{1} \\1.89=80.6x\\0.0234=x\\0.02=x[/tex]

Thus, per square foot, the 80.6 square foot roll is less expensive than the 53.7 square foot roll

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

9 divided by 11.91 rounded to the nearest hundredth is: 0.76

To show that two numbers are divided, we can add a division sign '÷' between them. So, for example, if we have to show 36 divided by 6, we can write it as 36 ÷ 6. We can also show it in a fraction form as 36/6.

We want to find 9 divided by 11.91 . Thus, this can be expressed as:

9/11.91

where:

9 is the dividend

11.91 is the divisor

Using calculator, we have:

9/11.91 = 0.76

Read more about Number Division at: https://brainly.com/question/11418015

#SPJ1

The circle with a chord are those that have a line joining two points on the circumferences

Recall that a chord a chord of a circle is a line segment that joins any two points on the circumference of the circle

From question number 1,  the chords are circles 1, 2 and 5.  This is because each of the circles has a line joining two points

2)  From question 2 all the chords intercepted each other.  This is because an intercept is a point where two straight lines meet. or you can say that An intercept in mathematics is a point on the y-axis through which the slope of a line passes

Learn more about circle theorem on https://brainly.com/question/29159533

#SPJ1

The length of Tim's deck is 1/15th of the length of Al's deck.

Finding the expressions for the length of each deck.

For Al's deck:

Area of a rectangle = length × width

60x + 40 = length × 4

length = (60x + 40) / 4

length = 15x + 10 ft

For Tim's deck:

Area of a rectangle = length × width

21x + 14 = length × 7

length = (21x + 14) / 7

length = 3x + 2 ft

Now we can find no. of times the length of Tim's deck is Al's deck by dividing the length of Al's deck by the length of Tim's deck:

(15x + 10) / (3x + 2)

Simplifying this expression:

(3(5x + 3) + 1) / (3x + 2)

(3(5x + 3) / (3x + 2)) + (1 / (3x + 2))

15 + (1 / (3x + 2))

Therefore, the length of Tim's deck is 1/15th of the length of Al's deck.

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ1

La madre canguro saltó una distancia total de 6 millas para llegar al lago.  .

The value of the missing lengths are;

a. b =  17. 32, c = 20

b. x = 8. 49, y = 8.49

Note that the different trigonometric identities are;

These identities have their ratios written as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the diagram shown, we have;

tan 30 = 10/b

cross multiply the values

b = 17. 32

Also, we have;

sin 30 = 10/c

cross multiply the values

c = 20

b. Using the sine identity

sin 45 = x/12

cross multiply the values

x = 8. 49

Also,

cos 45 = y/12

cross multiply

y = 8. 49

Learn more about trigonometric identities at: https://brainly.com/question/22591162

#SPJ1