Kevin rolled two number cubes each numbered 1 to 6.

what is the probability that both number cubes land on 3?

Answer: 50t+75g=1,500

Answer:

Time taken to reach the ball to the ground is 21 seconds.                  

Step-by-step explanation:

Given : A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’s height h at time t seconds is [tex]h = -16t^2 + 272t + 1344[/tex].

To find : When will the ball strike the ground?

Solution :

The equation for the ball's height 'h' at time 't' is given by,

[tex]h(t)= -16t^2 + 272t + 1344[/tex]

When the ball strike the ground the height of the ball became zero.

Substitute h=0 in the given equation,

[tex]-16t^2 + 272t + 1344=0[/tex]

Taking 16 common,

[tex]16(-t^2 + 17t + 84)=0[/tex]

or [tex]t^2-17t-84=0[/tex]

Solve by middle term split,

[tex]t^2-21+4t-84=0[/tex]

[tex]t(t-21)+4(t-21)=0[/tex]

[tex](t-21)(t+4)=0[/tex]

[tex]t=21,-4=0[/tex]

Reject t=-4 as time can never be negative.

Therefore, Time taken to reach the ball to the ground is 21 seconds.

Answer:

We should add 9 on the both sides of the given equation.

Step-by-step explanation:

Since, for making a perfect square on the left side of a quadratic equation,

We add the square of the half of the coefficient of x on both sides,

The given equation,

[tex]x^2-6x = 5[/tex]

Here, the coefficient of x is 6,

Half of 6 = 3

Square of 3 = 9,

Thus, we should add 9 on the both sides of the given equation.

Verification :

[tex]x^2 - 6x + 9 = 5 + 9[/tex]

[tex](x-3)^2 = 14[/tex]

<R angle of RST has the smallest measure.

The correct option is C.

We have,

RS=11 ,RT=9 and ST=6

Now, from the given lengths it can be seen that the length of ST is shortest and length of RS is longest.

By the definition which states that,

The angle opposite to longest side is largest and the angle oppsite to shortest side is smallest.

From given, <R is opposite to shortest side ST.

Thus, the smallest angle is R.

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Final answer:

The inequality for Sam's expenditures on grapes and carrots, with grapes costing $4 and carrots costing $2 per pound, is 4 + 2c <= d.

Explanation:

The inequality that represents Sam's spending on grapes and carrots, given that he has d dollars to spend, is 4 + 2c ≤ d. This inequality is derived from the cost of one bag of grapes, which is $4, and the cost of carrots, which is $2 per pound. The variable c represents the number of pounds of carrots Sam wants to buy. The total cost of grapes and carrots must be less than or equal to the amount of money Sam has, which is d dollars.

Final answer:

The equation to represent the total cost c that Tiffany pays for p pounds of chocolate, when a pound costs 7 dollars, is c = 7 × p. This is a simple linear equation with 7 as the price per pound.

Explanation:

The question asks to write an equation to represent the total cost c that Tiffany pays for p pounds of chocolate, with the knowledge that a pound of chocolate costs 7 dollars.

To find the total cost c, we simply need to multiply the cost per pound of chocolate by the number of pounds Tiffany buys. If each pound costs $7, then the equation showing the total cost for p pounds would be:

c = 7 × p

Where:

c represents the total cost

p represents the number of pounds of chocolate

This is a straightforward linear equation with the coefficient 7 representing the price per pound of chocolate.

Milt used a total of 9 unit cubes to build his prism. This was calculated by multiplying the quantity of unit cubes in each layer (3 cubes) by the total number of layers (3).

This is a Mathematics question about the concept of volume in prisms, specifically a cube. Milt starts by building a prism using 3 unit cubes and then adds 2 more layers of 3 unit cubes each. This means he has 3 layers of 3 cubes each.

We can calculate the total number of unit cubes used by multiplying the number of cubes in each layer by the number of layers. Here's the step-by-step calculation:

Start with quantity in a single layer: 3 unit cubes.

Multiply by the total number of layers to get the total quantity: 3 layers * 3 cubes/layer = 9 unit cubes.

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If [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.

In the linear equation [tex]\(y = 2x + 1\)[/tex], the coefficient of [tex]\(x\)[/tex] is 2. This means that the slope of the line is 2, and for every one unit increase in [tex]\(x\), \(y\)[/tex] will increase by 2 units.

Given that [tex]\(x\)[/tex] increases by 4 points, the corresponding increase in [tex]\(y\)[/tex] can be found by multiplying the change in [tex]\(x\)[/tex] by the slope:

[tex]\[\Delta y = \text{Slope} \times \Delta x\][/tex]

[tex]\[ \Delta y = 2 \times 4 = 8\][/tex]

Therefore, if [tex]\(x\)[/tex] increases by 4 points, [tex]\(y\)[/tex] will increase by 8 units.

Example:

Let's use the given linear equation [tex]\(y = 2x + 1\)[/tex] and demonstrate how an increase in [tex]\(x\)[/tex] by 4 points results in an increase in [tex]\(y\)[/tex] by 8 units.

Given Linear Equation:

[tex]\[y = 2x + 1\][/tex]

Let's consider an initial point on the line where [tex]\(x = 3\)[/tex]. Find the corresponding [tex]\(y\)[/tex]:

[tex]\[y = 2(3) + 1 = 7\][/tex]

So, when [tex]\(x = 3\), \(y = 7\)[/tex].

Now, if [tex]\(x\)[/tex] increases by 4 points, new [tex]\(x\)[/tex] value will be [tex]\(3 + 4 = 7\)[/tex].

Using the same linear equation to find the new [tex]\(y\)[/tex]:

[tex]\[y_{\text{new}} = 2(7) + 1 = 15\][/tex]

Now, calculate the increase in [tex]\(y\)[/tex]:

[tex]\[\Delta y = y_{\text{new}} - y_{\text{initial}} = 15 - 7 = 8\][/tex]

So, in this example, when [tex]\(x\)[/tex] increases by 4 points (from 3 to 7), [tex]\(y\)[/tex] increases by 8 units (from 7 to 15), confirming that the increase in [tex]\(y\)[/tex] is proportional to the increase in [tex]\(x\)[/tex] with a slope of 2.

The option c is correct

A rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

According to the question,

The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.

Hence, option c is correct for given condition.

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Answer:

Bracken has incurred a loss of $37,500

Step-by-step explanation:

People who have registered with Bracken insurance company pays premium of $100. 1,000 people in total have registered with Bracken. In 5 years Bracken would have earned an income of $500,000 [tex]\left ( $100\times1,000\times5)\right[/tex].

25 among the 1,000 registered have undergone surgery. Average surgery expense is $25,000. $3,500 is deductible.  So Bracken's total expense per client is $21,500 (25,000 - 3,500). For 25 patients, it will be $537,500 [tex]($21,500\times25)[/tex].

Since expenses of $537,500 is more than income of $500,000, Bracken incurs a loss of $37,500 (500,000 - 537,500) over 5 years.

Therefore, Bracken's loss over 5 years is $37,500

The variance of a discrete random variable calculation involves working out (x-µ)^2 * p(x) for each x value and summing them up. Using given data and mean as 20.59, variance ≈ 27.89 (options a and b).

To calculate the variance of a discrete random variable, we use the formula: Variance = Σ[(x-µ)^2 * p(x)] where 'x' is each value of the variable, 'µ' is the mean and 'p(x)' is the probability of 'x'

Given that the mean µ is 20.59 we perform the calculation, (x-µ)^2 * p(x) for each value of 'x' and sum them all up:

So, the correct answer is 27.89, which corresponds to option a and b.

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the correct answer is the expression with parentheses