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A group of children are asked whether they prefer vanilla or chocolate ice cream. The data are collected in the table.

Answer:

Temperature t > -15 degrees.

Step-by-step explanation:

Let t denote the temperature.

The inequality sign for above or greater is >. The inequality sign for less than is <.

It is given temperature stayed above -15 degrees.

This can be written in inequality form as t> -15 °(degrees)

The inequality to represent the temperature is t > -15°C

Given data:

To represent the situation where the temperature stayed above -15 degrees, the inequality symbol used is ">".

In an inequality, the ">" symbol means "greater than." By using this symbol,  the temperature needs to be greater than -15 degrees.

The inequality representing this situation is:

Temperature > -15°C

So, t > -15°C

If the temperature is higher than -15 degrees, the inequality is true.

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Carla paid $34.13 as interest for the $1,400 loan at 9.75% for three months that is option A is the correct answer.

The interest Carla paid for the loan is $34.13.

Calculate the interest using the formula: Interest = Principal x Rate x Time.

Substitute the values for Principal, Rate, and Time into the formula to find the interest amount.

For Carla's loan ($1,400 at 9.75% for three months), the interest is calculated to be $34.13.

Answer:

[tex]\frac{2\sqrt a}{a}[/tex]

Step-by-step explanation:

The given equation is  [tex]2a^{-1/2}[/tex]

The exponent rule: [tex]x^{-a}=\frac{1}{x^a}[/tex]

Using this rule, we get

[tex]2a^{-1/2}\\\\=\frac{2}{a^1/2}[/tex]

We can rewrite this in radical form as

[tex]\frac{2}{\sqrt a}[/tex]

Rationalize the denominator by multiplying numerator and denominator by [tex]\sqrt a[/tex]

[tex]\frac{2}{\sqrt a}\cdot \frac{\sqrt a}{\sqrt a}[/tex]

On simplifying

[tex]\frac{2\sqrt a}{a}[/tex]

Answer:  The correct answer is 3

Step-by-step explanation:

C = 3

AC = 3/3 = 1

BD = 4 - 3 = 1

The length of each diagonal is 12/5. This demonstrates that in a rectangle, the diagonals are always equal in length.

In a rectangle, the diagonals are equal in length. Therefore, we can equate [tex]\(AC\) and \(BD\)[/tex].

Given [tex]\(AC = \frac{C}{3}\) and \(BD = 4 - C\)[/tex], we set them equal: [tex]\(\frac{C}{3} = 4 - C\)[/tex]. Solving for \(C\) yields [tex]\(C = \frac{12}{5}\)[/tex].

Substituting this value back into either [tex]\(AC\) or \(BD\)[/tex] gives us the length of the diagonals.

Thus, the length of each diagonal is [tex]\(AC = BD = \frac{12}{5}\)[/tex]. This demonstrates that in a rectangle, the diagonals are always equal in length.

Answer:

It is a rhombus.

Step-by-step explanation:

To identify the type of polygon, we will first determine if the opposite sides are parallel.  To do this, we find the slope of each line segment.  (Parallel lines have the same slope.)

For WX, m = (5-2)/(1-5) = 3/-4 = -3/4

For XY, m = (2--1)/(5-1) = 3/4

For ZY, m = (2--1)/(-3-1) = 3/-4 = -3/4

For ZW, m = (2-5)/(-3-1) = -3/-4 = 3/4

Since the slopes of WX and ZY are the same, these two sides are parallel.  Since the slopes of XY and ZW are the same, these two sides are parallel.  Since opposite sides are parallel, the figure is a parallelogram.

In order to be a rectangle, the angles would have to be right angles.  Since perpendicular lines have slopes that are negative reciprocals of each other, the slopes of adjoining sides would have to be opposite signs and flipped.  This is not the case, so the angles are not right; this means it is not a rectangle.

The only other option for a parallelogram without right angles would be a rhombus.  This is the case if the length of each side is the same.  We will use the distance formula for this:

[tex]WX=\sqrt{(5-2)^2+(1-5)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\XY=\sqrt{(2--1)^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\\\\YZ=\sqrt{(2--1)^2+(-3-1)^2}=\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5\\\\ZW=\sqrt{(2-5)^2+(-3-1)^2}=\sqrt{(-3)^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]

Since the length of each side is the same, this figure is a rhombus.

By using the tangent function and the angles of depression given, we can calculate the distances from the boat to the lighthouse when it was first spotted and when it stopped. Subtracting the second distance from the first gives us the distance the boat traveled.

This is a question about Trigonometry, involving the concepts of angles of depression and distances. In the situation presented, we are given the height of the lighthouse (200 feet), and two angles of depression - 17°31' when the boat was first noticed and 46°41' when the boat stopped. We can use the tangent function to calculate the distance from the lighthouse to the boat at these two points, then subtract these distances to find how far the boat traveled.

The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. Therefore, when the angle of depression was 17°31', we can use the equation tan(17°31') = 200/distance1 to solve for the first distance. Similarly, for the angle of depression 46°41', we use the equation tan(46°41') = 200/distance2.

Solving these two equations separately will give us the distances from the boat to the lighthouse at these two moments. Then we subtract distance2 from distance1 to get the distance the boat traveled.

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[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

Step-by-step explanation:

Given :

[tex]\dfrac {c-4}{c-2} = \dfrac {c-2}{c+2} - \dfrac{1}{2-c}[/tex]                   --------- (1)

Calculation :

[tex]\dfrac {c-4}{c-2} = \dfrac {(c-2)^2+(c+2)}{(c+2)(c-2)}[/tex]

[tex]c-4 = \dfrac {(c^2-4c+4)+(c+2)}{(c+2)}[/tex]

[tex](c-4)(c+2) = (c^2-3c+6)[/tex]

[tex](c^2-2c-8) = (c^2-3c+6)[/tex]

[tex]c=14[/tex]

There is no extraneous solution because as we put the value of c in equation (1), it does not make the equation (1) not define.

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Answer:

14 and Zero

Step-by-step explanation:

Final answer:

To find the probability of selecting 3 green marbles out of 10, use the combinations formula. The calculation involves 455 * 6435 divided by 1027227812 to determine the probability.

Explanation:

To calculate the probability of choosing exactly 3 green marbles out of 10 selected, we use the concept of combinations. The formula for combinations is nCr = n! / r!(n-r)!. In this case, the calculation would be 15C3 * 35C7 / 50C10, which simplifies to 455 * 6435 / 1027227812, resulting in the probability of choosing exactly 3 green marbles out of 10 selected.

General Idea:

There are few exponent rules that need to be used to simplify the rational exponent to get to the answer.

Exponent rules:

[tex] Rule\; 1: a \cdot a \cdot a \cdot a =a^4\\ \\ Rule\; 2: (a^m)^n=a^{m \times n} [/tex]

Applying the concept:

Rewriting 81 as a number with an exponent using prime factorization.

[tex] 81=3 \times 3 \times 3 \times 3 = 3^4\\ \\ Applying \; Rule \; 1, \; we\; get\; \\\\81^{\frac{3}{4}}=(3^4)^{\frac{3}{4}} \\ \\ Applying \; Rule \; 2,\; we\; get\\ \\ 3^{4 \times\frac{3}{4} } = 3^{\frac{12}{4} }=3^3=3 \times 3 \times 3 = 27 [/tex]

Conclusion:

The above explanation explains why [tex] 81^{\frac{3}{4}} =27 [/tex]

Answer:

if your asking for plato it will be B

Step-by-step explanation:

got it correct just now

Follow below steps:

To determine the number of packs Jessica needs for 54 cupcakes:

Divide the total number of cupcakes by the number of cupcakes in each pack: 54 ÷ 10 = 5.4

Since Jessica cannot buy a fraction of a pack, she needs to round up to the nearest whole number. Therefore, Jessica needs 6 packs of cupcakes.

Answer:

B

Step-by-step explanation:

The graph of G(x) = F(x - 8) is the graph of F(x) shifted 8 units to the right, option A.

When comparing the graph of G(x) = F(x - 8) with the graph of F(x), we note that there is a horizontal shift involved. Following the rules for transformations, subtracting a positive constant from the independent variable x results in shifting the graph to the right by that constant. Therefore, the statement that best compares the graph of G(x) with the graph of F(x) is: The graph of G(x) is the graph of F(x) shifted 8 units to the right, option A.

This is similar to the effect observed when comparing the functions f(x) and f(x - 2), where the latter's graph is a rightward shift of the former's graph by 2 units.

Answer:

$76.16

Step-by-step explanation:

$76.16