How to explain what comes next 1,2,2,3,3,3,4,4,4,4 for third graders?

Find the surface area of the figure below.

gayaneshka [121]

Answer:

261 cm²

Step-by-step explanation:

To find the surface area of a square pyramid, you must first recognize all of the shapes.

There are four triangles and one square.

To find the area of a square, multiply the side by itself twice.
To find the area of a triangle, multiply the base and the height, then multiply the product by 1/2.

The triangles have a base of 9 and a height of 10.

$9*10=90$

Multiply the product by 1/2.

$90*1/2 = 45$

There are four triangles.

$45*4=180$

The area of all three triangles is 180 centimeters; the area of a single triangle is 45 centimeters.

There square has sides of 9 centimeters.

$9*9=81$

The area of the square is 81 centimeters.

Lastly, we add the areas of the shapes.

$45+45+45+45+81 = 261.$

Therefore, the surface area of this square prism is 261 cm².

You can use this layout to find the surface area of a square pyramid.

6 0

3 years ago

Predict how much money can be saved without having a negative actual net income.

satela [25.4K]

$170 can be saved resulting in an actual net income of $0.

6 0

4 years ago

Sam Sounds received a $290 discount loan to purchase a stereo. The loan was offered at 16% for 90 days. Find the interest in dol

garri49 [273]

I = Adt; where p = $290 is the Amount of the loan, d = 16% = 0.16 is the discount rate and t = 90days = 90/365 = 18/73 is the period.

I = 290 x 0.16 x 18/73 = 11.44
Interest = $11.44

Proceed = Amount - Interest = 290 - 11.44 = $278.56

6 0

3 years ago

Read 2 more answers

In each box is a step in the process of solving a max/min problem like the one in Question 8. Number these steps in order (1-8)

Dmitriy789 [7]

Answer:

The steps are numbered below

Step-by-step explanation:

To solve a maximum/minimum problem, the steps are as follows.

1. Make a drawing.

2. Assign variables to quantities that change.

3. Identify and write down a formula for the quantity that is being optimized.

4. Identify the endpoints, that is, the domain of the function being optimized.

5. Identify the constraint equation.

6. Use the constraint equation to write a new formula for the quantity being optimized that is a function of one variable.

7. Find the derivative and then the critical points of the function being optimized.

8. Evaluate the y-values of the critical points and endpoints by plugging them into the function being optimized. The largest y- value is the global maximum, and the smallest y-value is the global minimum.

8 0

3 years ago

The life of a red bulb used in a traffic signal can be modeled using an exponential distribution with an average life of 24 mont

BartSMP [9]

Answer:

See steps below

Step-by-step explanation:

Let X be the random variable that measures the lifespan of a bulb.

If the random variable X is exponentially distributed and X has an average value of 24 month, then its probability density function is

$\bf f(x)=\frac{1}{24}e^{-x/24}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/24}$

• What is probability that the red bulb will need to be replaced at the first inspection?

The probability that the bulb fails the first year is

$\bf P(X\leq 12)=1-e^{-12/24}=1-e^{-0.5}=0.39347$

• If the bulb is in good condition at the end of 18 months, what is the probability that the bulb will be in good condition at the end of 24 months?

Let A and B be the events,

A = “The bulb will last at least 24 months”

B = “The bulb will last at least 18 months”

We want to find P(A | B).

By definition P(A | B) = P(A∩B)P(B)

but B⊂A, so A∩B = B and

$\bf P(A | B) = P(B)P(B) = (P(B))^2$

We have

$\bf P(B)=P(X>18)=1-P(X\leq 18)=1-(1-e^{-18/24})=e^{-3/4}=0.47237$

hence,

$\bf P(A | B)=(P(B))^2=(0.47237)^2=0.22313$

• If the signal has six red bulbs, what is the probability that at least one of them needs replacement at the first inspection? Assume distribution of lifetime of each bulb is independent

If the distribution of lifetime of each bulb is independent, then we have here a binomial distribution of six trials with probability of “success” (one bulb needs replacement at the first inspection) p = 0.39347

Now the probability that exactly k bulbs need replacement is

$\bf \binom{6}{k}(0.39347)^k(1-0.39347)^{6-k}$

<em>Probability that at least one of them needs replacement at the first inspection = 1- probability that none of them needs replacement at the first inspection. </em>

This means that,

<em>Probability that at least one of them needs replacement at the first inspection = </em>

$\bf 1-\binom{6}{0}(0.39347)^0(1-0.39347)^{6}=1-(0.60653)^6=0.95021$

5 0

3 years ago