MATHEMATICS HIGH SCHOOL

Tickets to the spring festival are being sold online. the ticket price is $8 per person. the expression 8t + 2 represents the total cost for t tickets, including a $2 service fee.mr mathes purchases 4 tickets for his family. find the value if the expression when t= 4.

8t + 2 = 8(. ? ) + 2

Answers

Answer 1

Answer:

Answer: 4

Step-by-step explanation:

Answer 2

Answer:

Answer:

32 because 8×4=32 that's why 33is the answer

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Using your calculator, find the proportion of observations from a standard normal distribution that satisfies the following statement. Sketch the normal curve and shade the area under the curve that is the answer to the question: Z < –1.5.

Answers

Final answer:

The proportion of observations from a standard normal distribution that satisfies the statement Z < -1.5 is approximately 0.0668. To depict this, one can sketch a normal curve with the mean at the center and shade the area to the left of -1.5 under the curve.

Explanation:

To find the proportion of observations from a standard normal distribution that satisfies the statement Z < -1.5, we need to find the area to the left of -1.5 on the standard normal distribution curve. This area represents the proportion of observations that have a z-score less than -1.5.

Using a calculator or a z-table, we can find that the area to the left of -1.5 is approximately 0.0668, which is the proportion of observations that satisfy the given statement. To sketch the normal curve and shade the area under the curve, we would draw a standard normal distribution curve with the mean at the center, and then shade the area to the left of -1.5 under the curve.

Learn more about Proportion of observations in a standard normal distribution here:

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A right cylinder has a diameter of 40 mm and a height of 30 mm, as shown. Semester Test, Part 1 What is the volume of the cylinder?a. 37,680 mm3
b. 1256 mm3
c. 150,720 mm3
d. 12,000 mm3

Answers

Answer: a. $37,680\ mm^3$

Step-by-step explanation:

We know that the volume of a cylinder is given by :-

$V=\pi r^2 h$ , where r is radius and h is height of the cylinder.

Given: The diameter of cylinder = 40 mm

The radius of cylinder = $r=(40)/(2)=20\ mm$

The height of cylinder = 30 mm

Then , the volume of the cylinder will be :-

$V=(3.14) (20)^2 (30)=37680\ mm^3$

Hence, the volume of the cylinder = $V=37680\ mm^3$

Volume = Area * height
= (pi/4)*D^2 * h
= (pi/4)*(40)^2 * 30
= 37,680 mm3
so, the answer is (a)

My grandparents have four grandchildren. The product of the ages of the four grandchildren is 67 184. The youngest grandchild is younger than 10, and is also 30 years younger than the oldest grandchild.Determine all possibilities for the ages of my grandparents’ grandchildren.

Answers

Answer:

The possible ages of the four grandchildren are a = 4, b = 19, c = 26, and d = 34

Step-by-step explanation:

The given parameters are;

The number of grandchildren in the family = 4

The product of the ages of the four grand children = 67184

The age of the youngest grandchild < 10

The age of the oldest grandchild = 30 + The age of the youngest grandchild

Let a represent the age of the youngest grandchild, and let b, and c represent the ages of the other two intermediate grandchild

Therefore, we have;

a < 10

The age of the oldest grandchild = a + 30 < 10 + 30

∴ The age of the oldest grandchild < 40

The product of the ages of the four grandchildren = a × b × c × (a + 30) = 67184

The factors of 67184 that are between 1 and 40 are;

1, 2, 4, 8, 13, 16, 17, 19, 26, 34, 38

Taking a = 8, we have;

The age of the oldest grandchild × The age of the youngest grandchild = a × (a + 30) = 8 × 38 = 342

Therefore. a × b = 67184/(a × (a + 30) = 196.44

Therefore, a ≠ 8

For a = 4, we have the age of the oldest grandchild = a + 30 = 4 + 30 = 34

The age of the oldest grandchild × The age of the youngest grandchild = a × (a + 30) = 4 × 34 = 136

Therefore. a × b = 67184/(a × (a + 30) = 494

We find that the other factors of 67184, which are 19 and 26 have a product of 494

Therefore, the possible ages of the four grandchildren are a = 4, b = 19, c = 26, and d = 34

To give, 4 × 19 × 26 × 34 = 67,184.

For fun questionfind the formula for how many items are in a 2 deimentional pyramid (each row is 1 more than previous row like in attachment) when you have n number of rows

n=number of rows
n,x means when you have n rows, you have x items in pyramid

n=1, 1
n=2, 3
n=3, 6
n=4, 10
n=5, 15

find the number of items when you have n number of rows
f(n)=something

SHOW ALL WORK AND LOGIC
NO GOOGLING TO FIND ANSWER OR JUST PUTTING THE ANSWER

Answers

We have an arithmetic progression:
an=number of item at row n

an=a₁+(n-1)d

d=common difference=an-a(n-1)=a₂-a₁=2-1=1
n=number of row

In this case:

an=1+(n-1)*1=n

The sum of an arithmetic serie is:
Sn=(a₁+an)n / 2

In this case:
a₁=1 (number of itms in the first row)
an=n (we have to calculate this before)

Sn=(1+n)n /2=(n+n²)/2

Therefore:
f(n)=Sn=number of items when we have n number of rows

f(n)=(n+n²)/2

Answer: f(n)=(n+n²)/2

To chek:

f(1)=(1+1²)/2=1
f(2)=(2+2²)/2=6/2=3
f(3)=(3+3²)/2=(3+9)/2=12/2=6
....

Factor completely. n ^4 - 1