The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation could be used to find the base (b) of the sign?

The answer is 4.6, confirming the other answerers.

Hope this helps, Kam

The probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.

Probability is the branch of mathematics that deals with the study of random events or phenomena. It involves the quantification of uncertainty and the measurement of the likelihood of occurrence of an event.

The average number of dots on a fair die is

= (1+2+3+4+5+6)/6

= 3.5.

We can model the sum of the numbers on the 30 dice as a normal distribution with mean

= (30)(3.5) = 105

and, standard deviation √(30)(35/12) ≈ 9.13.

Let X be the sum of the numbers on the 30 dice, and let Y be the average number of dots. Then Y = X/30.

We want to find P(2 ≤ Y ≤ 4). This is equivalent to P(60 ≤ X ≤ 120), since Y = X/30.

Using the normal distribution, we can standardize X to get:

Z = (X - 105) / 9.13

Then we can compute the probability as:

P(60 ≤ X ≤ 120)

= P[(60 - 105) / 9.13 ≤ Z ≤ (120 - 105) / 9.13]

≈ P(-4.93 ≤ Z ≤ 1.64)

Using a standard normal distribution table or calculator, we can find that P(-4.93 ≤ Z ≤ 1.64) ≈ 0.9441.

Therefore, the approximate probability that the average number of dots is between 2 and 4 when rolling 30 fair dice is 0.9441.

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Answer:

Option A. 8 cubes

Step-by-step explanation:

In the given structure we can count the cubes by dividing the figure in three sub parts.

Two in L shape and one below on L shape figure.

Two L shape figure contains 2×3 = 6 cubes

Cubes hidden under one L shape = 2

Then total cubes = 6 + 2 = 8

Option A. 8 cubes is the answer.

Answer:

3 in

Step-by-step explanation:

The area of a 2D form is the amount of space within its perimeter. The area of the given parallelogram is 812 in².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The given figure is a parallelogram, and the area of the parallelogram is given by the formula,

Area of parallelogram = Base × Altitude

                                     = 29 in × 28 in

                                     = 812 in²

Hence, the area of the given parallelogram is 812 in².

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The zeros of a function are also known as the roots of the function

The correct option for  the zeros of f(x) = x² - 10·x + 25 is the option D.

D. x = 5 only

The reasons why the selected option is correct are given as follows:

The given equation is presented as follows;

f(x) = x² - 10·x + 25

Solution:

The zeros are the values of x when the equation is equal to zero which is given as follows;

x² - 10·x + 25 = 0

By observation, we have;

Given that the coefficient of x² is one, and we have that 25 = (-5) × (-5), and -10 = -5 + (-5), therefore, we can write;

Therefore, the zeros of the function is 5 only, and the correct option is option D.

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The length of a rectangle can be found by dividing the area of the rectangle by its height if the area is known. Without the area, additional information is necessary to calculate the length.

To find the length of a rectangle when given the height, we typically need additional information such as the area or the aspect ratio of the rectangle. However, without that information, directly calculating the length is not possible. Let's explore a scenario where we have the area of the rectangle. In such a case, if we are given the area (A) of the rectangle and the height (h), we can use the formula for the area of a rectangle which is A = length times height. Solving for the length (l), we rearrange the formula to get l = A/h. For instance, if the area of the rectangle is 150 square centimetres and the height is 10 centimetres, the length would be 150 cm2 / 10 cm = 15 cm. It's also important to consider proportions when scaling shapes.

The correct option is A.

Vanessa can borrow approximately $6255.57, represented by option A: [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex].

To determine the value of the most money Vanessa can borrow with a monthly payment of $1405 for a 20-year house loan with an APR of 4.8%, compounded monthly, we can use the formula for the monthly payment of a mortgage:

[tex]\[P = \frac{M}{\frac{r}{12} \left(1 - \left(1 + \frac{r}{12}\right)^{-nt}\right)}\][/tex]

Where:

P = Principal amount (the amount she can borrow)

M = Monthly payment ($1405)

r = Monthly interest rate (APR divided by 12, or 0.048/12)

n = Number of times the interest is compounded per year (12 for monthly)

t = Number of years (20)

Now, let's plug in the values and solve for P:

[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1 + \frac{0.004}{12}\right)^{-12*20}\right)}\][/tex]

Let's calculate the exponent and simplify:

[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1 + \frac{0.004}{12}\right)^{-240}\right)}\][/tex]

Now, we can simplify the monthly interest rate:

[tex]\[P = \frac{1405}{\frac{0.004}{12} \left(1 - \left(1.000333333\right)^{-240}\right)}\][/tex]

[tex]\[P = \frac{1405}{0.333333 \left(1 - 0.328624967\right)}\][/tex]

Now, let's calculate the value inside the parentheses:

[tex]\[P = \frac{1405}{0.333333 \times 0.671375033}\][/tex]

[tex]\[P \approx \frac{1405}{0.22487499}\][/tex]

Now, calculate P:

P ≈ 6255.57

So, Vanessa can borrow approximately $6255.57.

The correct expression that represents the value of the most money she can borrow is:

A. [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]

The complete question is here:

Vanessa can afford a [tex]$\$ 1405$[/tex]-per-month house loan payment. If she is being offered a 20-year house loan with an APR of [tex]$4.8 \%$[/tex], compounded monthly, which of these expressions represents the value of the most money she can borrow?

A. [tex]$\frac{(\$ 1405)\left((1+0.004)^{240}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]

B. [tex]$\frac{(\$ 1405)\left((1-0.048)^{240}-1\right.}{(0.048)(1+0.048)^{249}}$[/tex]

C. [tex]$\frac{(\$ 1405)\left((1-0.004)^{200}-1\right)}{(0.004)(1+0.004)^{240}}$[/tex]

D. [tex]$\frac{(51405)\left((1+0.048)^{200}-1\right)}{(0.048)(1+0.048)^{240}}$[/tex].

Using the formula for monthly loan payment, we find Vanessa can borrow up to $220,000 with a 20-year loan at 4.8% APR.

To find the maximum amount Vanessa can borrow, we can use the formula for the monthly payment of a loan:

[tex]\[ P = \frac{A \times r}{1 - (1 + r)^{-n}} \][/tex]

Where:

-  P  = monthly payment

-  A = loan amount (the value we want to find)

-  r  = monthly interest rate (APR divided by 12)

-  n  = total number of payments (number of years multiplied by 12)

Given:

- Monthly payment ( P) = $1405

- APR ( r ) = 4.8% = 0.048

- Loan term = 20 years

First, we calculate r :

[tex]\[ r = \frac{4.8}{100 \times 12} = 0.004 \][/tex]

Then, calculate n:

[tex]\[ n = 20 \times 12 = 240 \][/tex]

Now, plug the values into the formula and solve for A:

[tex]\[ 1405 = \frac{A \times 0.004}{1 - (1 + 0.004)^{-240}} \][/tex]

Solve for A:

[tex]\[ A = \frac{1405 \times (1 - (1 + 0.004)^{-240})}{0.004} \][/tex]

[tex]\[ A \approx \$220,000 \][/tex]

So, Vanessa can borrow a maximum of $220,000.

The question probable maybe:

Vanessa can afford a $1405-per-month house loan payment. If she is being offered a 20-year house loan with an APR of 4.8%, compounded monthly, What is the value of  the most money she can borrow?

Answer:

The polynomial 3x2 is a  

monomial

with a degree of  

2

.

The polynomial x2y + 3xy2 + 1 is a  

trinomial

with a degree of  

✔ 3

.

Step-by-step explanation:

this the answer on the edge

Answer:

1.8

Step-by-step explanation:

Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

We have to find the error which is done by Beth to eliminate the parameter. So, we will take the first equation and do all the steps to find the error and get the desired result.

Given that, x=t²+3 and y=4t

Try find the expression of "t" in terms of "x". We will use equation (1) and we have

x-3=t²

t=√(x-3)

Thus, Beth says that she can write that she should have taken both the positive and negative square root to eliminate the parameter. Therefore, option (c) is correct.

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Answer: B

Step-by-step explanation:

The slope of the cost function for Michelle’s new store is 10.25.

This is because this equation is in slope-intercept form, y=mx + b, where m is the slope and b is the y intercept. Despite the different variables in the above equation, the idea remains the same. The slope is the coefficient on the variable n, which represents the rate of change of this function.

Hope this helps!