What is the lateral area of the pyramid
Answer:
43.75 ft²
Step-by-step explanation:
[tex]s_l[/tex] = (l√(w/2)² + h²) + (w√(l/2)² + h²)
l & w become 3.5, and h becomes 6.
[tex]s_l[/tex] = (3.5√(3.5/2)² + 6²) + (3.5√(3.5/2)² + 6²)
Step 1:Because this is a square pyramid, what you see above essentially becomes what you see below.
[tex]s_l[/tex] = 2(3.5√(3.5/2)² + 6²)
Step 2: Divide 3.5 by 2 to get 1.75.
[tex]s_l[/tex] = 2(3.5√1.75² + 6²)
Step 3: Square both 1.75 and 6 to get 3.0625 and 36 respectively.
[tex]s_l[/tex] = 2(3.5√3.0625 + 36)
Step 4: Add 3.0625 and 36 to get 39.0625.
[tex]s_l[/tex] = 2(3.5√39.0625)
Step 5: The square root of 39.0625 is 6.25.
[tex]s_l[/tex] = 2(3.5 * 6.25)
Step 6: Multiply 3.5 by 6.25 to get 21.875.
[tex]s_l[/tex] = 2(21.875)
Step 7: Multiply 2 by 21.875 to get 43.75.
[tex]s_l[/tex] = 43.75 ft²
The lateral area of this pyramid is 43.75 ft².
Suppose that $10,083 is invested at an interest rate of 6.8% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
Answer:
a) The exponential function is [tex]A(t) = 10083(1.068)^t[/tex]
b)
The balance after 1 year is of $10,768.644
The balance after 2 years is of $11,500.91
The balance after 5 years is of $14,010.25.
The balance after 10 years is of $19,467.15
c)
The doubling time is of 10.54 years.
Step-by-step explanation:
Continuously compounded interest:
The amount of money earning after t years, with interest compounded continuously, is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the amount of the initial investment and r is the growth rate, as a decimal.
a) Find the exponential function that describes the amount in the account after time t, in years.
Suppose that $10,083 is invested at an interest rate of 6.8% per year
This means, respectively, that [tex]A(0) = 10083, r = 0.068[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = 10083(1+0.068)^t[/tex]
[tex]A(t) = 10083(1.068)^t[/tex]
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
After 1 year:
[tex]A(1) = 10083(1.068)^{1} = 10,768.644[/tex]
The balance after 1 year is of $10,768.644
After 2 years:
[tex]A(2) = 10083(1.068)^{2} = 11,500.91[/tex]
The balance after 2 years is of $11,500.91.
After 5 years:
[tex]A(5) = 10083(1.068)^{5} = 14,010.25[/tex]
The balance after 5 years is of $14,010.25.
After 10 years:
[tex]A(10) = 10083(1.068)^{10} = 19,467.15[/tex]
The balance after 10 years is of $19,467.15.
c) What is the doubling time?
This is t for which [tex]A(t) = 2A(0)[/tex]. So
[tex]A(t) = A(0)(1.068)^t[/tex]
[tex](1.068)^t = 2[/tex]
[tex]\log{(1.068)^t} = \log{2}[/tex]
[tex]t\log{1.068} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.068}}[/tex]
[tex]t = 10.54[/tex]
The doubling time is of 10.54 years.
A family spends 1/10 of it's annual income for housing 1/4 for food and clothing 1/5 for general expenses and 2/15 for entertainment what fractional part of their income is spent on these items altogether.
Answer:
The family spends 41/60 of its income on these items altogether.
Step-by-step explanation:
Given that a family spends 1/10 of it's annual income for housing, 1/4 for food and clothing, 1/5 for general expenses and 2/15 for entertainment, to determine what fractional part of their income is spent on these items altogether the following calculation must be performed:
10, 4, 5, and 15 have a common least multiple at 60.
1/10 = 6/60
1/4 = 15/60
1/5 = 12/60
2/15 = 8/60
6 + 15 + 12 + 8 = 41
Therefore, the family spends 41/60 of its income on these items altogether.
A picture is to be printed onto a sheet of paper with dimensions of 81/2 x 11 inches, A margin of 1 1/2 inches is to be left on all sides of the picture. What is the area of the printed picture?
Answer:
The area of the printed picture is 172.5 square inches.
Step-by-step explanation:
Since a picture is to be printed onto a sheet of paper with dimensions of 81/2 x 11 inches, and a margin of 1 1/2 inches is to be left on all sides of the picture, to determine what is the area of the printed picture the following calculation must be carried out, knowing that the area of a rectangle is equal to the base multiplied by the height:
81/2 = 40.5
1/2 = 0.5
40.5 - 1.5 x 4 = 34.5
11 - 1.5 x 4 = 5
34.5 x 5 = 172.5
Therefore, the area of the printed picture is 172.5 square inches.
What is one-fifth of a number, x, increased by 24 is equal to eight tenths of the same number, x.
Answer:
x = 40
Step-by-step explanation:
(x × [tex]\frac{1}{5}[/tex] )+ 24 = [tex]\frac{8}{10}[/tex] × x
0.2x + 24 = 0.8x
0.2x - 0.2x + 24 = 0.8x - 0.2x
24 = 0.6x
0.6x = 24
0.6x × [tex]1\frac{2}{3}[/tex] = 24 × [tex]1\frac{2}{3}[/tex]
x = 40
Answer:
x=40
Step-by-step explanation:
1/5x+24=8/10x
give like denominators
2/10x+24=8/10x
subtract 2/10x on both sides
24=6/10x
divide 24 by 6/10, or multiply by 10/6
x=240/6
refine/simplify
x=40
The length of a rectangular swimming pool is exactly three times as long
as its width. If the pool has a perimeter of 472m find the width of the pool
Answer:
59m
Step-by-step explanation:
Length= 3 × ( width)
But perimeter= 2width + 2 Lenght= 472
Let length= X
Width= Y
X= 3Y.........eqn(1)
2X + 2Y= 472........eqn(2)
Substitute X= 3Y in eqn(2)
2(3Y) + 2Y = 472
6Y + 2Y= 472
8Y= 472
Y= 59 m
Hence, the width of the pool is 59 m
Wayne Gretsky scored a Poisson mean six number of points per game. sixty percent of these were goals and forty percent were assists (each is worth one point). Suppose he is paid a bonus of 3K for a goal and 1K for an assist. (a) Find the mean and standard deviation for the total revenue he earns per game. (b) What is the probability that he has four goals and two assists in one game
Answer:
a) The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.
b) 0.05 = 5% probability that he has four goals and two assists in one game
Step-by-step explanation:
In hockey, a point is counted for each goal or assist of the player.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval. The standard deviation is the square root of the mean.
(a) Find the mean and standard deviation for the total revenue he earns per game.
60% of six are goals, which means that 60% of the time he earned 3K.
40% of six are goals, which means that 40% of the time he earned 1K.
The mean is:
[tex]\mu = 6*0.6*3 + 6*0.4*1 = 13.2[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\mu} = \sqrt{13.2} = 3.63[/tex]
The mean for the total revenue he earns per game is of 13.2K while the standard deviation is of 3.63K.
(b) What is the probability that he has four goals and two assists in one game
Goals and assists are independent of each other, which means that we find the probability P(A) of scoring four goals, the probability P(B) of getting two assists, and multiply them.
Probability of four goals:
60% of 6 are goals, which means that:
[tex]\mu = 6*0.6 = 3.6[/tex]
The probability of scoring four goals is:
[tex]P(A) = P(X = 4) = \frac{e^{-3.6}*(3.6)^{4}}{(4)!} = 0.19122[/tex]
Probability of two assists:
40% of 2 are assists, which means that:
[tex]\mu = 6*0.4 = 2.4[/tex]
The probability of getting two assists is:
[tex]P(B) = P(X = 2) = \frac{e^{-2.4}*(2.4)^{2}}{(2)!} = 0.26127[/tex]
Probability of four goals and two assists:
[tex]P(A \cap B) = P(A)*P(B) = 0.19122*0.26127 = 0.05[/tex]
0.05 = 5% probability that he has four goals and two assists in one game
The area of a. square field is 100m square. what is the perimeter of the field?
answer:the Perimeter is 40m
look at pic 10 pts will mark brainilest
Answer:
A) The width is 12 cm; the average time is 3 minutes
Step-by-step explanation:
[tex]\frac{5}{3}= \frac{20}{y}[/tex]
Cross multiply.
5 × y = 3 × 20
5y = 60
5y ÷ 5 = 60 ÷ 5
y = 12
The width is 12 cm. Moving onto the time.
[tex]\frac{12}{4} =\frac{y}{1}[/tex]
Cross multiply.
4 × y = 12 × 1
4y = 12
4y ÷ 4 = 12 ÷ 4
y = 3
The time is 3 minutes.
Answer:
answer is d sorry if I'm wrong
is 1 5/6 a rational number or a iraarational
Answer: rational number
Step-by-step explanation:
Mixed numbers are all rational numbers because they can be expressed as a fraction. To be a rational number, a number must be able to be written
PLEASE HELP!!
What value if m makes the equation true??
m+2m-6 =-12+2m
m=?????
How do you know if a number is rational irrational or not real number
Answer:
A rational number can expressed as a whole number, integer, square root, fraction, and more as long as it's not imaginary. However, the number has to be clean like 1/2=0.5, 1/3=0.333, -1, 200. If it is a number that goes on forever and is not repeated like 1.22222, then it's an irrational number like pie-3.14159..., 5/0, 2.201845. If you have an imaginary number- 6i, then this would be considered as non real numbers like x+2, red, wind, and y/7.
Step-by-step explanation:
I hope this helped you!
Don uses a funnel to pour oil into his car engine. The funnel has a radius of 6 cm and a slant height of 10 cm. How much oil, to the nearest cubic centimeter, will the funnel hold.
A mans basic wage for a 40 hour week is 160 . He is paid 5 per hour for overtime .If he fors for 6.5 hours overtime in a certain week , his wages for that week is
Answer: $192.50
Step-by-step explanation:
wages for 40 hrs + wages for overtime work
$160.00 + 6hrs × $5.00 + $2.50 (1/2 hrs)
$192.50
Credit: anjalijalan3126
Find the volume of the following figure using unit cubes.
Answer:
Volume : 94
Step-by-step explanation:
2(4 x 5) = 40
2(3 x 5) = 30
2(3 x 4) = 24
------------------
40 + 30 + 24 = 94
Can someone please help me with Systems of Equation. If so please comment here and friend me at fmilluzionz#1521. I am in 8th grade math
Answer:
The FitnessGram PACER Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The test is used to measure a student's aerobic capacity as part of the FitnessGram assessment. Students run back and forth as many times as they can, each lap signaled by a beep sound.
Step-by-step explanation:
what is the product of 4/5 and 6/7
What is 0.0475 converted to a percentage
Answer:
0.0475 = 4.75%
Step-by-step explanation:
Answer:
4.75%
Step-by-step explanation:
Look at the decimal number 0.0475 as 0.0475 out of one. Furthermore, percent means per hundred. So the task is to convert 0.0475 out of one to 0.0475 out of one hundred.
The equation to solve the problem is displayed below where x is the 0.0475 as a percentage.
[tex]\frac{0.0475}{1}[/tex]=[tex]\frac{x}{100}[/tex]
We solve the equation for x above by first multiplying each side by one and then multiplying each side by one hundred. Thus, the answer to 0.0475 as a percentage is: 4.75%
Joseph is planning to meet up with his friend Naomi. Joseph jogs from his house traveling at a rate of 4
miles per hour. Naomi is initially 27 miles from Joseph's house and travels towards Joseph at 5 miles per
hour.
a) Show your solution graphically.
b) How many hours went by before they met?
hours
c) How many miles were they from Joseph's house when they met?
miles
30
25
Joseph
Answer:
It took 3 hours for the two to meet, and they were 12 miles from Joseph's home when they met.
Step-by-step explanation:
Since Joseph is planning to meet up with his friend Naomi, and Joseph jogs from his house traveling at a rate of 4 miles per hour, while Naomi is initially 27 miles from Joseph's house and travels towards Joseph at 5 miles per hour, for To determine how many hours went by before they met and how many miles were they from Joseph's house when they met, the following calculations should be performed:
27 - (4 + 5) = 27 - 9 = 18
27 - (4 + 5) x 3 = 0
Therefore, it took 3 hours for the two to meet.
4 x 3 = 12
Thus, they were 12 miles from Joseph's home when they met.
PLEASE HELP!! ....................... URGENT
Answer:
I got an F- on math soo i cannot help i am sorry
Step-by-step explanation:
.-.
Please help, test due in 2 hours! Will give good review and brainliest. :)
Answer:
224in³
Step-by-step explanation:
Find the volume of the rectangular prism, then subtract the volume of the pyramid from it.
Volume of rectangular prism= (length)(width)height)
=(14)(4)(10)=560in³
Volume of pyramid=((length)(width)height))/3
=((14)(4)(6))=336in³
560in³-336in³=224in³
1.11. There are 37 girls and 39 boys going on a field trip with the drama club. At least 1 adult for
every 6 students will also go on the trip. Which correctly explains how to find the number of
adults needed for the trip?
(
Answer:
C
I have done the math on a calculator. :p
Answer:
C
Step-by-step explanation:
First you Just Divide
and the remainder
will be R4 and it's 76÷6
the function f(x) = -x^2 + 44x -384 models the daily profit in dollars that a shop makes
Find the value of x in the triangle shown below.
1
13
2
12
Choose 1 answers
Answer:
x = 5
Step-by-step explanation:
a² + b² = c²
x² + 12² = 13²
x² + 144 = 169
x² = 169 - 144
x² = 25
[tex]\sqrt{x^2} =\sqrt{25}[/tex]
x = 5
A jewerler had a fixed amount of gold
Answer:
ohhhhh and who is the jeweler
Seamus draws a triangle with angles of measures 40°, 60°, and 80°. Edwina draws a triangle with these same three angle measures. Which statement must be true?
A Edwina's triangle is the same size as Seamus's triangle.
B Edwina's triangle is the same shape as Seamus's triangle.
C The perimeter of Seamus's triangle is greater than the perimeter of Edwina's triangle.
D The area of Edwina's triangle is less than the area of Seamus's triangle.
Answer:
It may be D or A hopeit helps
Step-by-step explanation:
WHATS THE LENGTH ROUND TO THE NEAREST 10th if NEEDED
Answer: 8.6
Step-by-step explanation:
Using pythagorean theorem, c²=a²+b² you can find the distance between AB.
c²=7²+5²
c²=74
√c²=√74
c=8.6
Find the range of the data
5,9,13,6,4,5,8,12,12,6
Answer:
9
Step-by-step explanation:
highest value: 13
lowest value: 4
13-4= 9 which is the range
Answer: 9
Step-by-step explanation: 13-4=9
For every four female students in a training class, there are two men. There are seven male students. What is the total number of students in cass?
Answer:
it may be 19 or 20 but I may be wrong
Step-by-step explanation:
sorry if I'm wrong
The circumference of a circle is 23 pi M what is the area in square meters express your answer in terms of pie
Answer:132.25π m²
Step-by-step explanation:The circumference of a circle is 23π
On the other hand, The circumference of a circle = 2×π×r ; where r is the radius. Then by equating the last two expressions we get: 23π = 2πr then r = 23/2 then the area = π × r² = (23/2)²×π = (132.25)×π
