A bag contains 4 red, 3 yellow, 3 blue, and 2 white marbles, for a total of 12 marbles. If Lucia randomly picks two marbles from the bag without putting the first marble back, what is the probability that the first marble is red and the second is white?

Algebraic expression can be used to express the statement one less than x squared is option (B) [tex]x^{2} -1[/tex]

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

Given,

one less than x squared is

[tex]x^{2} -1[/tex]

Hence, the algebraic expression can be used to express the statement one less than x squared is option (B) [tex]x^{2} -1[/tex]

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The answer is 6. I'm just adding this to help anyone else struggling with this quiz.

Final answer:

Set up a proportion where 10% of the total number of cups equals 200 green cups, then calculate to find that there are 2000 cups in the entire package.

Explanation:

To find the total number of cups in the package when 200 green cups represent 10% of the total, we can set up a simple proportion. Here, 10% corresponds to the number of green cups we know about. We need to find 100% to discover the total number of cups in the package.

The proportion we'll set up is:

10% / 200 cups = 100% / x cups

To solve for x (the total number of cups), we will divide 200 cups by 10% to find the value of 1% and then multiply by 100%:

1% of total = 200 cups / 10

x (total cups) = (200 cups / 10) × 100

Perform the calculation:

x = 20 cups × 100

x = 2000 cups

So, there are 2000 cups in the total package.

Answer:

67.50%

Step-by-step explanation:

We can prove that the answer is correct by taking 67.50 percent of 80 to get 54:

(80 x 67.50)/100 = 54

Note that our calculator rounds the answers up to two decimals if necessary. Once again, the answer is as follows:

67.50%

Final answer:

The true statement given that quadrilateral ACEG is congruent to quadrilateral NMRP is D: CE≡NP, which matches the corresponding sides based on the order of the vertices in the name of each quadrilateral following CPCTC.

Explanation:

If quadrilateral ACEG is congruent to quadrilateral NMRP, then corresponding parts of congruent polygons are congruent as well. This principle is often abbreviated as CPCTC (Corresponding Parts of Congruent Triangles are Congruent). Applying this rule, we need to match each vertex of quadrilateral ACEG to the corresponding vertex of quadrilateral NMRP.

To determine which statement is true, we need to compare the corresponding parts:

Hence, the correct statement based on the information given and the application of CPCTC is D: CE≡NP.

Answer:

The number of ounces in each glass is [tex]12.2\ ounces[/tex]

Step-by-step explanation:

Let

s-------> the number of ounces in each glass

we know that

To get the number of ounces in each glass, subtract the amount of tea left in the pitcher from the total amount of tea and divide the result by the number of glasses.

so

The equation that represent the situation is

[tex]s=(64-3)/5[/tex]

[tex]s=(61)/5=12.2\ ounces[/tex]

Answer:

Step-by-step explanation:

Answer:

282.6

Step-by-step explanation:

Answer:

Rs.833.94

Step-by-step explanation:

To solve for the sum of money or principal, we use the formula:

[tex]P=\dfrac{A}{1+rt}[/tex]

The current variables we have are:

A = Rs.1,155

r = 11% or 0.11

t = 3.5

Now let's plug the variables into the formula.

[tex]P=\dfrac{A}{1+rt}[/tex]

[tex]P=\dfrac{1,155}{1+(0.11)(3.5)}[/tex]

[tex]P=\dfrac{1,155}{1+0.385}[/tex]

[tex]P=\dfrac{1,155}{1.385}[/tex]

[tex]P=Rs.833.94[/tex]

The correct net of the prism is net A and the surface area of the prism is 510 square inches

To calculate the area of the triangular prism, we make use of the net A

Start by calculating the area of the rectangle.

The dimension of the rectangle is (5 + 12 + 13) by 15

So, the area of the rectangle is:

[tex]Area = (5 + 12 + 13) * 15[/tex]

[tex]Area = 450[/tex]

Next, calculate the area of the two congruent triangles of base 5 and height 12

[tex]Area = 2 * 0.5 * (5 * 12)[/tex]

[tex]Area = 60[/tex]

Sum both areas

[tex]Total = 450 + 60[/tex]

[tex]Total = 510[/tex]

Hence, the surface area of the prism is 510 square inches

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Answer:

It would be 157/200

Step-by-step explanation:

The gent in the comments

Answer:

Translation from (0,0) to (3,-3), 3 units down, and 3 units to the right.

Step-by-step explanation:

The Geometric Transformation called Translation of this parabola f(x)=x² is obtained, firstly by shifting it down 3 units simply adding -3 units as the independent term.

The Translation of the Parabola is counted by its vertex. y=x² (0,0) to y=x²-6x+6 (3,-3).

Algebraically:

So, f(x)=x² -3

Looking at g(x)=x²-6x+6, we still need to make it down after the curve intercept y-axis. b<0

Then, let's shift it three units to the right so its vertex hit the point 6, as y-coordinate, we have to add -3. If we want to add to the right sum negative value, then square it:

y= (x-3)²-3

y=x²-6x+9-3

y=x²-6x+6

Answer:

A is true

B = SSS OR RHS

Step-by-step explanation:

bcoz both can be applied here

Jeremy's statement that triangle ABD is congruent to triangle CBD by the SAS congruence postulate is incorrect.

If we are also given that AD is congruent to CD, then we can use the SSS congruence postulate to prove that triangle ABD is congruent to triangle CBD.

Answer to part (a)

I disagree with Jeremy's statement that triangle ABD is congruent to triangle CBD by the SAS congruence postulate.

The SAS congruence postulate states that two triangles are congruent if they have two pairs of corresponding sides congruent and the included angle congruent.

In this case, we have two pairs of corresponding sides congruent (AB = BC and AD = CD, since B is the midpoint of AC). However, we are not given that the included angle (angle ABD) is congruent to angle CBD.

Therefore, we cannot use the SAS congruence postulate to prove that triangle ABD is congruent to triangle CBD.

Answer to part (b)

If we are also given that AD is congruent to CD, then we can use the SSS congruence postulate to prove that triangle ABD is congruent to triangle CBD.

The SSS congruence postulate states that two triangles are congruent if they have three pairs of corresponding sides congruent.

In this case, we have three pairs of corresponding sides congruent (AB = BC, AD = CD, and BD = BD). Therefore, we can use the SSS congruence postulate to prove that triangle ABD is congruent to triangle CBD.

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The plane in question is approximately 23 degrees off course. This calculation is derived from the tangent function in trigonometry based on the distances given.

From the question, we understand that the plane is creating a right triangle due to its off-course direction. Using the Pythagorean theorem, the length of the hypotenuse, or the distance that the plane will travel, is 325 miles. The difference between the direct route (300 miles) and the off-course southern distance (125 miles) forms the two other sides of the triangle.

However, we're looking for the angle, not the sides. This is where trigonometry comes in. Specifically, the tangent function will be valuable here as it involves the opposite and adjacent sides of a right triangle (the off-course southern distance and the direct route distance). If we let the 'off-course' angle be θ, then we have:

Tan(θ) = (distance south / direct distance) = (125 miles / 300 miles)

In order to find the angle θ from this equation, we'll need to use the inverse tangent function.

θ = atan(125/300) = 22.61986495 degrees.

Therefore, to the nearest degree, the plane is approximately 23 degrees off course.

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