What is the volume of the above figure ?

Answer:

D

Step-by-step explanation:

To find the center and radius of a circle given its equation, we need to rewrite the equation in the standard form (x - a)^2 + (y - b)^2 = r^2, where (a,b) are the coordinates of the center and r is the radius.

So, let's complete square for x and y terms:

x^2 + 14x + y^2 + 2y + 14 = 0

x^2 + 14x + 49 - 49 + y^2 + 2y + 1 - 1 + 14 = 0

(x + 7)^2 + (y + 1)^2 = 36

Comparing this equation with the standard equation, we get the center at (-7, -1) and radius as sqrt(36) = 6 units.

So, the correct answer is option D: (-7, -1), 6 units.

Answer:

1.a.SAS axiom

b. ASA axiom

Step-by-step explanation:

There are five basic conditions for triangles to be congruent:

For Question:

1.

a. InΔABC and ΔBCD

AB=CD opposite sides of the parallel line are equal Side

∡BAC=∡BDA Given Angle

BC=BC Same side Side

It fulfills the condition of the SAS axiom,

InΔABC ≅ ΔBCD by SAS axiom

b. InΔABC and ΔCDE

∡ACB=∡DCE Vertically opposite angle Angle

BC=CD given Side

∡ABC=∡CDE right angle Angle

It fulfills the condition of the ASA axiom,

InΔABC ≅ ΔCDE by ASA axiom It may be R.H.S. axiom too.

Answer:

  B.  (4, 8)

Step-by-step explanation:

You want the coordinates of R(1, 5) after translation by (1, -1) and dilation by a factor of 2.

Applying the given transformation, you have ...

  (x, y) ⇒ (x +1, y -1)

  R(1, 5) ⇒ R'(1 +1, 5 -1) = R'(2, 4)

The dilation multiplies each coordinate value by the dilation factor, 2.

  (x, y) ⇒ (2x, 2y)

  R'(2, 4) ⇒ R''(2·2, 2·4)  = R''(4, 8)

The coordinates after translation and dilation are (4, 8).

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The volume of this rectangular prism given the base area and height is 385 cubic inches.

Volume of the rectangular prism = Base area × height

Base area = 35 square inches

h = 11 inches

Volume of the rectangular prism = Bh

= 35 square inches × 11 inches

= 385 cubic inches

Hence, 385 cubic inches is the volume of the rectangular prism.

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Answer:

-5

Step-by-step explanation:

Arranging the numbers

-4 (n+8) = -12

n+8 = -12/-4

n+8 = 3

n = 3-8

n = -5

The quadratic equation with roots a - 2 and b - 2 is x² + 9x + 22 = 0

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 5x + 8 = 0

On simplifying , we get

From the given quadratic equation x² + 5x + 8 = 0, we can identify that a = 1, b = 5, and c = 8.

So, the sum of the roots a and ß is -b/a = -5/1 = -5, and the product of the roots is a x b = c/a = 8/1 = 8.

Now, we need to find the quadratic equation with roots a - 2 and ß - 2.

By using the sum and product of the roots, we can write:

Sum of roots = (a - 2) + (b - 2) = a + b - 4

Product of roots = (a - 2) x (b - 2) = ab - 2a - 2ß + 4

From the given quadratic equation x² + 5x + 8 = 0, we know that:

a + b = -5

ab = 8

Substituting these values in the above equations, we get:

Sum of roots = -5 - 4 = -9

Product of roots = 8 - 2a - 2b + 4 = 12 - 2(a + b) = 22

So , the quadratic equation is given as x² + 9x + 22 = 0

Hence , the equation is x² + 9x + 22 = 0

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5/2 pounds is equal to 40 ounces.

We have to find the 5/2 pounds to ounces

1 pound is equal to 16 ounces.

To convert 5/2 pounds to ounces, we can multiply by 16:

5/2 pounds × 16 ounces/pound = 40 ounces

Therefore, 5/2 pounds is equal to 40 ounces.

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The option that makes the function, f(x) = P·(a)ˣ, an exponential growth function is the option B

B. P = 1/9; a = 12

An exponential function is a function of the form; Y = a·bˣ

Where;

a = The y-intercept, (a, 0)

b = The growth or decay factor

x = The exponent

The function can be expressed as follows;

f(x) = P·(a)ˣ

An exponential growth function is one that increases in value as the value of the input variable increases, in which the growth or decay factor is a > 1

The option that therefore yields an exponential growth is one in which the value of the variable a is larger than 1.

The correct option is therefore, option B.

B. P = 1/9; a = 12

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Step-by-step explanation:

14 10 is 90 less than the mean 1500

   z score =  - 90 / 75 =  -  1.200

    from a z-score table this represents  .1151  

       or  11.51 % will last LESS than 1410 hrs

Bernie drove 1.125 times as fast as Janelle.

To determine who drove faster, we can calculate the average speed (in km/h) of each driver using the formula:

average speed = distance / time

For Janelle:

average speed = 60 km / (5/6 hours) = (60 km) x (6/5 hours) = 72 km/h

For Bernie:

average speed = 54 km / (2/3 hours) = (54 km) x (3/2 hours) = 81 km/h

Therefore, Bernie drove faster than Janelle. To determine how many times as fast, we can divide Bernie's average speed by Janelle's average speed:

81 km/h / 72 km/h = 1.125

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The expression a² - 16a - 12 when factored is a(a - 16) - 12

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

a² - 16a - 12

The above expression is a quadratic expression

It cannot be completely factored

This is because the roots of the expressions are irrational numbers

To partially factor the expression, we have

a² - 16a - 12 = a(a - 16) - 12

Hence, the expression a² - 16a - 12 when factored is a(a - 16) - 12

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it is 19 because maths says that 9+10 is 19

Answer:

the answer is 19......

Step-by-step explanation:

The range of the given function y = |x| is [0, ∞).

As per the question, consider that the absolute value of any real number x is always non-negative.

Therefore, the output of the function y = |x| is always non-negative as well.

Furthermore, for any non-negative real number y, there are two possible inputs x that will produce that value of y: x and -x. For example, if y = 2, then x could be either 2 or -2.

Thus, every non-negative real number is in the range of y = |x|, and no negative numbers are in the range.

Therefore, the range of y = |x| is [0, ∞).

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The sentence that uses active voice is: "My friend invited his whole class to Saturday's soccer championship."

Now, let's examine the sentences you provided:

Passive voice: The subject ("the winning homerun") is being acted upon by the action (hit by the worst player).

Active voice: The subject ("my friend") is performing the action (inviting his whole class).

Passive voice: The subject ("the children") is being acted upon by the action (taken to the circus by their doting grandfather).

Passive voice: The subject ("some cookies") is being acted upon by the action (baked by the baker).

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Step-by-step explanation:

All of the sides are equal so find 'x'

6x -10 =  4x + 5

2x = 15

x = 7.5

as a check : the the sides are     6(7.5) - 10 = 35 cm

                                                      4 ( 7.5) + 5 = 35

                                                      10 ( 7.5 - 4 = 35 cm

three sides of 35 cm =   3 x 35 = 105 cm = 1.05 m

    so YES the perimeter is greater than one meter

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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Answer:

  8 m

Step-by-step explanation:

You want the length x that gives a triangle area of 26 m² when the angle between side x and side 13 m is 30°.

The area formula is ...

  A = 1/2ab·sin(C)

  26 = 1/2(13)(x)·sin(30°) = 13/4x . . . . . use given values

  x = (4/13)(26) = 8 . . . . . . divide by the coefficient of x

The length x in the triangle is 8 m.

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Answer:

--------------------

The scale factor is the ratio of corresponding sides.

Find the scale factor k for the pictured triangles:

Answer:

The set of ordered pairs that represents g¹(x) can be found by reversing the order of each pair in the original function g(x) and then solving for x. Therefore, g¹(x) would be:

{(-14, -9), (40, 18), (10, 3), (-26, -15)} with the x-coordinates being -9, 18, 3, and -15 respectively.

Step-by-step explanation:

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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We can say that a chip can hold 1 billion transistors in the year 2007.

To solve for the year when a chip can hold 1 billion transistors, we need to set the function f(x) equal to 1000 (since 1 billion is 1000 million).

So,[tex]42(1.41)^x = 1000[/tex]

Divide both sides by 42:

[tex](1.41)^x = 23.81[/tex]

Take the logarithm of both sides (with base 1.41):

x = log(23.81)

Using a calculator, we find that x is approximately 5.98.

Since X represents the number of years since 2000, we add 5.98 to 2000 to get the year when a chip can hold 1 billion transistors:

2000 + 5.98 = 2006.98

Rounding to the nearest year, we can say that a chip can hold 1 billion transistors in the year 2007.

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The solution is, the solution is x > −1.

This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1.

This means that any value of x greater than −1 satisfies x + 3 > 2.

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The perimeters and areas of the rectangles are listed below:

Case 1: p = 54 yd, A = 170 yd²

Case 2: p = 46 m, A = 120 m²

Case 3: p = 44 mm, A = 72 mm²

Case 4: p = 60 in, A = 209 in²

Cases 5 / 6: p = 32 mi, A = 55 mi

Case 7: p = 66 m, A = 242 m²

Case 8: p = 94 yd, A = 550 yd²

Case 9: p = 72 km, A = 320 km²

In this problem we must determine the perimeter and the area of eight rectangles, whose formulae are introduced below:

Perimeter

p = 2 · (w + h)

Area

A = w · h

Where:

Now we determine the perimeter and the area for each case:

Case 1

p = 2 · (17 yd + 10 yd)

p = 54 yd

A = (17 yd) · (10 yd)

A = 170 yd²

Case 2

p = 2 · (15 m + 8 m)

p = 46 m

A = (15 m) · (8 m)

A = 120 m²

Case 3

p = 2 · (18 mm + 4 mm)

p = 44 mm

A = (18 mm) · (4 mm)

A = 72 mm²

Case 4

p = 2 · (11 in + 19 in)

p = 60 in

A = (11 in) · (19 in)

A = 209 in²

Cases 5 and 6

p = 2 · (5 mi + 11 mi)

p = 32 mi

A = (5 mi) · (11 mi)

A = 55 mi

Case 7

p = 2 · (22 m + 11 m)

p = 66 m

A = (22 m) · (11 m)

A = 242 m²

Case 8

p = 2 · (22 yd + 25 yd)

p = 94 yd

A = (22 yd) · (25 yd)

A = 550 yd²

Case 9

p = 2 · (16 km + 20 km)

p = 72 km

A = (16 km) · (20 km)

A = 320 km²

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Hello!

the equation of the blue line is 3y + 0.5x

The probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.

We have,

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

The conditional probability is the happening of an event, when the probability of occurring of other event is given. The probability of event A, given that the event B is occurred.

Students of high school who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. In this,

74% likely to tryout for softball;

27% likely to tryout for volleyball;

42% likely to tryout for tennis;  

88% likely to tryout for swimming.

Let the tryout for volleyball is event A and tryout for swimming is event B. Thus,

P(A)=0.27

P(B)=0.88

Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

Thus, probability of the union of trying out for either volleyball or swimming

P(A or B)=P(A)+P(B)-P(A and B)

P(A or B)=0.27+0.88-P(A)*P(B)

P(A or B)=0.27+0.88-0.27×0.88

P(A or B)=0.9

Hence, the probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.

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complete question:

The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the union of trying out for either volleyball or swimming?

a. 1. 15

b. 0. 61

c. 0. 91

d. 0. 24

The solution to the system is 6 and 11.

We have,

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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation.

Given equation:

y=2x-1 .....(1)

y=x+5....(2)

Now solving equation 1 and 2, we get

2x -1 = x + 5

2x - x= 5 +1

x = 6

and, y= 2x-1

y= 2(6)-1

y= 12 -1

y= 11

Hence, the value of x is 6 and y is 11.

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complete question:

On a piece of paper, graph the system of equations. Find the solution to the system. y=2x-1 y=x+5

The first statement, "if 1 + 1 = 2, then 2 + 2 = 1 + 1," is true due to the associative property of addition, which allows us to group the numbers in any order we want.

The first statement, "if 1 + 1 = 2, then 2 + 2 = 1 + 1," is true due to the associative property of addition, which allows us to group the numbers in any order we want.

The second statement, "If 2 + 1 = 21, then everything else must equal 21," is false. If we assume that 2 + 1 = 21, we must know the specific mathematical system being used to determine if everything else equals 21.

Without additional information or constraints, the equation "[tex]3 + y^3 + z^3 = k[/tex] cannot be solved. It is a three-variable equation with only one equation, which means there are an infinite number of solutions depending on the values of y, z, and k.

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A regression through the origin is a linear regression model where the intercept time period is assumed to be 0, meaning the regression line passes through the starting place.

This version is also referred to as zero-intercept regression or homogeneous regression.

It's far frequently used whilst there's a theoretical foundation to agree with that the relationship among the dependent and unbiased variable passes via the foundation or whilst the information propose that the intercept ought to be 0.

The slope coefficient represents the change within the structured variable for a one-unit increase inside the unbiased variable.

However, this kind of regression may not be appropriate in all cases, and a general linear regression version with an intercept term can be greater suitable.

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The absolute value equation that has these minimum and maximum heights as its solutions is 9=|x−45|

We have,

"The min is simply the lowest observation, while the max is the highest observation. Obviously, it is easiest to determine the min and max if the data are ordered from lowest to highest."

First, find the difference of both solutions.

54 - 36 = 18

Than, divide it by 2

18/2 = 9

9 = | x − 54+9 |

Either way:       9 =|x−45|

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compplete question:

For the Pony Ride, the minimum height is 36 inches and the maximum height is 54 inches. Write and solve an absolute value equation that has these minimum and maximum heights as its solutions.​