The density of water is 1 gram per cubic centimeter. An object floats in the water if its density is less than water's density, and it sinks if its density is great than water's.

Suppose a ball with mass 90 grams is in the shape of a sphere with radius 4 centimeters. Will the ball sink or float in the water?


ROUND YOUR ANSWERS TO THE NEAREST HUNDRETH AND USE THE π BUTTON WHEN CALCULATING.​

We can see here that matching the letters to the correct terms, we have:

C - 3. y-intercept.

D - 2. vertex

A - 1. axis of symmetry

B - 4. x-intercept

A vertex is a location where two or more lines, curves, or edges cross in mathematics. In computer science, graph theory, and geometry, the word "vertex" is frequently used to refer to an object's corners or points.

When two or more line segments, rays, or lines come together to make an angle, they form a vertex in geometry. Each of the three spots where the three sides of a triangle intersect is known as a vertex. In a similar way, each of a cube's eight corners is a vertex.

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The x1 is\(\frac{9}{5}\) and the x2 is \(\frac{12}{5}\) and the x3 is \(\frac{16}{5}\) using Pythagoras's theorem.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC2 = AB2 + AC2 is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.

The given triangle is a right angled triangle so applying Pythagoras's theorem for ABC triangle we get x1+x2 as \(\sqrt{3^{2}+ 4^{2} } = 5\)

The area of ΔABC is \(\frac{1}{2}\)×b×h = \(\frac{1}{2}\)×3×4=6

Now taking CD as height and AB as base we get   \(\frac{1}{2}\)×5× x2 = 6 ⇒ x2 = \(\frac{12}{5}\).

Now applying Pythagoras's theorem to triangle ACD we get x1 as \(\sqrt{3^{2}-\frac{9}{5} ^{2} } = \frac{9}{5}\)

Now substituting x1 in x1 + x3 = 5 we get x3 as \(\frac{16}{5}\).

The x1 is \(\frac{9}{5}\) and the x2 is \(\frac{12}{5}\) and the x3 is \(\frac{16}{5}\) using Pythagoras's theorem.

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These are answers of asked question.

A. To factor out the Greatest Common Factor (GCF) of the expression 3t^4 - 6t^3 - 9t + 12, we need to identify the highest power of t that can be factored out. In this case, the GCF is 3t. So we can rewrite the expression as follows:

3t^4 - 6t^3 - 9t + 12 = 3t(t^3 - 2t^2 - 3) + 3t(4)

The GCF, 3t, is factored out from the first two terms, leaving us with t^3 - 2t^2 - 3. The last term, 12, is divisible by 3t, so it becomes +3t(4). Therefore, the factored form of the expression is:

3t(t^3 - 2t^2 - 3) + 3t(4)

B. To factor the expression g^2 - 5g - 14 using the Distributive Method, we look for two numbers whose product is -14 and whose sum is -5 (the coefficient of the middle term). In this case, -7 and +2 satisfy these conditions. So we can rewrite the expression as follows:

g^2 - 5g - 14 = (g - 7)(g + 2)

Using the Distributive Property, we multiply (g - 7) by (g + 2) to verify the factoring:

(g - 7)(g + 2) = g(g) + g(2) - 7(g) - 7(2) = g^2 + 2g - 7g - 14 = g^2 - 5g - 14

Therefore, the factored form of the expression is:

(g - 7)(g + 2)

C. To factor the expression r^2 - 64, we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = r and b = 8, since 8^2 = 64. So we can rewrite the expression as follows:

r^2 - 64 = (r + 8)(r - 8)

Using the difference of squares formula, we can multiply (r + 8) by (r - 8) to verify the factoring:

(r + 8)(r - 8) = r(r) - r(8) + 8(r) - 8(8) = r^2 - 8r + 8r - 64 = r^2 - 64

Therefore, the factored form of the expression is:

(r + 8)(r - 8)

D. To factor the expression 9p^2 - 42p + 49, we look for two numbers whose product is 49 and whose sum is -42 (the coefficient of the middle term). In this case, -7 and -7 satisfy these conditions. So we can rewrite the expression as follows:

9p^2 - 42p + 49 = (3p - 7)(3p - 7)

Using the Distributive Property, we multiply (3p - 7) by (3p - 7) to verify the factoring:

(3p - 7)(3p - 7) = 3p(3p) - 3p(7) - 7(3p) - 7(7) = 9p^2 - 21p - 21p +

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Answer:

X = -2.5

See the photo for detailed answer

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

Answer:

$4870

Step-by-step explanation:

The goal is $7,000.

They already had $1,750 saved, and the students brought another $380.

1750+380=2130

7000-2130=4870

You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.

A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.

The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.

The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.

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(a) a = 1.

(b) To sketch the piece-wise linear graph, we plot the two linear graphs on the same axis and join the end of the first graph to the start of the second graph as follows: graph\({x+1 [-10, 10, -5, 5, 1/2, 1/4] 2x+1 [-10, 10, -5, 5, 1/2, 1/4] 4x-1 [-10, 10, -5, 5, 1/2, 1/4]}\)

(a) To find the point of intersection of the linear graphs and hence state the value of a, we can equate the equations for the two linear graphs as follows:

\(2x + 1 = 4x - 1\\= > 2x - 4x = - 1 - 1\\= > - 2x = - 2\\= > x = 1\)

Therefore, the point of intersection is (1, 3).

To find the value of a, we substitute x = a in the second equation and equate to the first equation as follows:

\(2a + 1 = 4a - 1\\= > 2a - 4a = - 1 - 1\\= > - 2a = - 2\\= > a = 1\)

Therefore, a = 1.

(b) To sketch the piece-wise linear graph, we plot the two linear graphs on the same axis and join the end of the first graph to the start of the second graph as follows:

\(graph{x+1 [-10, 10, -5, 5, 1/2, 1/4] 2x+1 [-10, 10, -5, 5, 1/2, 1/4] 4x-1 [-10, 10, -5, 5, 1/2, 1/4]}\)

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Answer:

then he'll get a bagel 2 pieced sanwich with a side of E

Step-by-step explanation:

Answer:

Decimal Form: 1.375   Fraction Form: 1 3/8 or 11/8

Step-by-step explanation:

:)

Answer:

2) x/ 2y^2

Explanation:

1) reduce the fraction:

27x^3 -----> x^3

216y^6----> 8y^6

2) evaluate the cube root

x

------

2y^2

Answer:

x/2y²

Step-by-step explanation:

What is the cube root of 27?

3. because 3x3x3 = 27.

What is the cube root of 216?

6. because 6x6x6 = 216.

For the 3 on the right side, since it's a power or an exponent, we just divide by 3. Same thing for the 6 in the right.

Now, we have 3x/6y².

We need to simplify.

The GCF of 3 and 6 is 3, because 3 is the highest number that can be divided by both 3 and 6 while the results are whole numbers.

3/3 = 1

6/3 = 2

x/2y² is the answer.

The equation only has 1 solution, which is x = 5.

There is a 1 in 36 chance of getting every question correct, if you just guess randomly

The requried, given system of equations y=x+3 and 3x-3y=9 has no common solution.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,

From the first equation, we can solve for y:

y = x + 3

Substitute y = x + 3 into the second equation:

3x - 3(x + 3) = 9

Simplify the right side:

3x - 3x - 9 = 9

-9 = 9 (inconsistent)

Since the equation -9 = 9 is inconsistent, the system of equations has no solution, which means that there are no values of x and y that make both equations true at the same time. It implies the system of equations has no solution.

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Answer:

61 degrees

Step-by-step explanation:

TRUST ME I JUST DID THE IMAGINE MATH LESSON. !!!!

The measure of ∠XYZ in right triangle is 90 degrees.

It has two equal sides, and those two equal sides make 90 degrees (right angle) internally. An isosceles triangle has two of its side length of same measure.

Let the considered isosceles triangle has two same lengthed sides of 'a' units.

Let its third side be of 'b' units.

Then, if we drop a perpendicular from the vertex joining similar sides to the opposite side, the opposite side is cut in half, each of length b/2 units.

We are given that;

A right triangle △WXY and △WZY

Now,

Let's label ∠WZY as α, so we have:

∠WZY = α

∠WYZ = α

Since the sum of the angles in a triangle is 180 degrees, we can find ∠WYX of △WXY:

∠WYX = 90 - ∠WXY

Now, we can use the fact that ∠WXY and ∠XYZ are complementary angles of a right triangle, so:

∠WXY + ∠XYZ = 90

Substituting ∠WYX for ∠WXY, we get:

∠WYX + ∠XYZ = 90

90 - ∠WXY + ∠XYZ = 90

∠XYZ = ∠WXY

Therefore, we can conclude that ∠XYZ is equal to ∠WYX, which is the angle opposite to the hypotenuse in a right triangle. So, we have:

∠XYZ = 90 degrees

Hence, in the given right triangle answer will be 90 degrees.

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To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.

Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k

Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.

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Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we can use either sine or cosine

\( \sin(30) = \frac{5}{x} \\ x \sin(30) = 5 \\ x = \frac{5}{ \sin(30) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

\( \cos(60) = \frac{5}{x} \\ x \cos(60) = 5 \\ x = \frac{5}{ \cos(60) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

Hope this helps you

Answer:

21,42/2,-(42/-2)

Step-by-step explanation:

please mark me as brainlest

The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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Yes, Elena purchase 1.5 pounds of dried chili peppers and 3 pounds of corn husks and spend less than $50.

For the given question;

The equation becomes;

16.95 d + 6.49 h

16.95 (1.5) + 6.49 (3)

  25.425 + 19.47

        44.895 < $50

Thus, Elena purchase 1.5 pounds of dried chili peppers and 3 pounds of corn husks and spend less than $50.

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Answer:

answer it yourself

Step-by-step explanation:

Chris cut a length of rope that was 12 feet long. Dayna cut a rope 4 times as long as Chris's rope. Benita cut a rope 1/4 as long as Chris's rope.

3. How long is Dayna's rope?

Dayana= 12 x 4 =48 ft

4. How long is Benita's rope?

The expression that means the same as “a number plus 14” is “14 more than a number”.

In mathematical terms, when we say “a number plus 14”, we are essentially talking about adding 14 to an unknown number.

The word “plus” is used to indicate the operation of addition.
Similarly, when we say “14 more than a number”, we are also talking about the same operation of addition. Here, we are adding 14 to an unknown number.

However,

The words used to describe the operation are different.
Both expressions essentially convey the same mathematical idea, which is adding 14 to an unknown quantity. Depending on the context and the problem at hand, either expression can be used interchangeably.
It is important to note that in mathematics, expressions can be written in different forms while still conveying the same meaning.

This flexibility in writing expressions allows for more efficient and effective communication in problem-solving.

The expression that means the same as "a number plus 14" can be written in algebraic form as x + 14, where x represents any number.

In this expression, the variable x can be replaced by any number, and when we add 14 to that number, we get the result of "a number plus 14".

For example,

If we substitute x with 7, we get 7 + 14 = 21, which means "a number plus 14" is equal to 21.

The algebraic expression x + 14 means the same as "a number plus 14".

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As the degrees of freedom increase, the Student's t distribution becomes more like the standard normal (z) distribution. Correct option is C.

The Student's t distribution is a probability distribution that is used to estimate the mean of a population when the sample size is small or when the population standard deviation is unknown. It is similar to the standard normal distribution, but it has heavier tails and more spread out.

As the degrees of freedom increase, the t-distribution approaches the normal distribution because the shape of the t-distribution becomes more and more similar to the normal distribution.

This is due to the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches the normal distribution.

When the degrees of freedom is large, the t-distribution becomes less variable, and the tails become less heavy, approaching the normal distribution. Therefore, the standard normal (z) distribution is the limiting distribution of the Student's t distribution as the degrees of freedom increase.

Therefore, Correct option is C.

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complete question is:

As the degrees of freedom increase, what distribution does the student's t distribution become more like?

a) uniform

b) chi-square

c) standard normal (z)

d) binomial

Answer:

I believe the answer is 5/6

Step-by-step explanation:

3  

2

1

​

−2  

3

2

​

Multiply 3 and 2 to get 6.

2

6+1

​

−  

3

2×3+2

​

Add 6 and 1 to get 7.

2

7

​

−  

3

2×3+2

​

Multiply 2 and 3 to get 6.

2

7

​

−  

3

6+2

​

Add 6 and 2 to get 8.

2

7

​

−  

3

8

​

Least common multiple of 2 and 3 is 6. Convert  

2

7

​

 and  

3

8

​

 to fractions with denominator 6.

6

21

​

−  

6

16

​

Since  

6

21

​

 and  

6

16

​

 have the same denominator, subtract them by subtracting their numerators.

6

21−16

​

Subtract 16 from 21 to get 5.

6

5

​

To determine the probability that a bottle has a flaw and fails the inspection, we need to consider both the probability of a bottle having a flaw and the probability of it failing the inspection.

Given that the proportion of bottles with flaws is 0.0002, the probability of a bottle having a flaw is 0.0002.

Now, if a bottle has a flaw, the probability that it fails the inspection is 0.995. On the other hand, if a bottle does not have a flaw, the probability that it passes the inspection is 0.99.

To find the probability that a bottle has a flaw and fails the inspection, we multiply the probability of a bottle having a flaw (0.0002) by the probability of it failing the inspection given that it has a flaw (0.995). This gives us: 0.0002 * 0.995 = 0.000199.

Therefore, the probability that a bottle has a flaw and fails the inspection is approximately 0.000199.

To summarize:
- Proportion of bottles with flaws: 0.0002
- Probability of a bottle having a flaw: 0.0002
- Probability of a bottle failing the inspection given that it has a flaw: 0.995
- Probability of a bottle passing the inspection given that it does not have a flaw: 0.99
- Probability of a bottle having a flaw and failing the inspection: 0.0002 * 0.995 = 0.000199

In summary, the main answer to the question is that the probability that a bottle has a flaw and fails the inspection is approximately 0.000199.

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Answer:

The most common measure of an angle is in degrees. Here is a brief introduction to the four types of angles: Right angle. With this angle, you can never go wrong. The right angle is one of the most easily recognizable angles. It’s in the form of the letter L, and it makes a square corner (see Figure 2). It has a measure of 90 degrees.

Step-by-step explanation: