Answer:
[tex]\large \boxed{2}[/tex]
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.
[tex]\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}[/tex]
Check:
[tex]\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}[/tex]
It checks.
the mustard factory has 20,000 ounces of mustard to put into small packets.uf each packets holds 1/4 ounce,how many packets can be filled
EXPLAIN what equivalent fractions are and give an example. PLEASE answer me.
Answer: Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.
Step-by-step explanation : For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100
Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.
Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number ! Again, hoped this helped. If you do used, don't word for copy. Make it into your own words.
Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.
For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100
Find the 88th term of the arithmetic sequence 4,-1,-6
Answer:
an = a1 + d(n - 1)
a88 = 4 + (-5)(88 - 1)
a88 = 4 + (-5)(87)
a88 = 4 - 435
a88 = -431
So, the 88th term of the arithmetic sequence is -431.
The 88th term of the given arithmetic sequence is equal to -431.
Given the following data:
First (1st) term = 4Second term = -1To calculate the 88th term of the given arithmetic sequence:
Mathematically, the nth term of an arithmetic sequence is given by the formula:
[tex]a_n = a_1 + d(n - 1)[/tex] ...equation 1.
Where:
d is the common difference.[tex]a_1[/tex] is the first term of an arithmetic sequence.First of all, we would determine the common difference as follows:
[tex]d = a_2 - a_1\\\\d=-1-4[/tex]
d = -5
Substituting the values into eqn. 1, we have:
[tex]a_{88} = 4 + [-5](88 - 1)\\\\a_{88} = 4 -5(87)\\\\a_{88} = 4 -435\\\\a_{88} = -431[/tex]
Read more on arithmetic sequence: https://brainly.com/question/12630565
What is 32+8(y-6) simplified
Answer:
8y - 16
Step-by-step explanation:
Step 1: Distribute
32 + 8(y - 6)
32 + 8y - 48
8y - 16
Answer: 8y - 16
If needed solve for y:
8y - 16 + 16 = 0 + 16
8y / 8 = 16 / 8
y = 2
Answer:
8y - 16
Step-by-step explanation:
82 children had to learn the one line of fun song. The fun song has 47 lines. How many lines did they learn altogether
Answer:
3,854
Step-by-step explanation:
There’s 82 kids each learned 47 lines you would multiply
The children learned a total of 3854 lines of the song. This is found by multiplying the number of children by the number of lines in the song.
Explanation:This problem involves simple multiplication. Since each child needs to learn one line of the song, and the fun song has 47 lines, to find the total number of lines the children learned altogether, you simply multiply the number of children by the number of lines in the song. Therefore, 82 (number of children) x 47 (number of lines in the song) equals 3854. So, the children learned 3854 lines in total.
Learn more about Multiplication here:https://brainly.com/question/5992872
#SPJ12
I need the answer to y=2x+7 in a graph and passes through (3,3)
I need the given, parallel, slope intercept form
The slope-intercept form is y = 2x-3.
Step-by-step explanation:
Given,
The equation of the line is y=2x+7.The general equation of the line is in the form y= mx+c.where 'm' represents the slope of the line.Comparing the given equation with general equation, it can be determined that :
m = 2 and c = 7 (y-intercept).
The given line passes through the point (3,3) which is equal to (x1,y1)
Therefore, x1=3 and y1=3.
Substitute m=2 and the values of (x1,y1) in the slope-intercept form,
The slope-intercept form is (y-y1) = m (x-x1)
(y-3) = 2(x-3)
y = 2x-6+3
y = 2x-3
Ms G has 16 hw papers and 14 quiz and MS M has 64 hw papers and 60 quiz to return. What tge ratio to represent the number of he papers to quiz that have to be returned.
The two teachers have 16 and 64 homework papers to return, totalling in 80.
They also have 14 and 60 quizzes to return, totalling in 74.
The ratio of homework papers to quizzes that need to be returned is 80:74
In total, there are 80 homework papers and 74 quizzes to be returned. The ratio for the total would be 80 : 74 (or 80/74), and 40 : 37 (or 40/37) simplified.
For Ms. G alone, the ratio would be 16 : 14 (or 16/14), and 8 : 7 (or 8/7) simplified.
For Ms. M alone, the ratio would be 64 : 60 (or 64/60), and 16 : 15 (or 16/15) simplified.
Hope this helps!! :)
Em certa adição de três números naturais consecutivos,o menor deles é 49.Qual deve ser a soma?
The question means in Portuguese: In a certain addition of three consecutive natural numbers, the smallest is 49. What should the sum be?
English: Since 49 is the smallest number, the next number up and the next number up give us the 3 consecutive numbers. So 49+50+51 is 150.
Portuguese: Como 49 é o menor número, o próximo número acima e o próximo número acima nos dão os 3 números consecutivos. Então 49 + 50 + 51 é 150.
For a game, Tony has a rectangle drawn on a piece of paper that has an area of 18 in.^2. What should he do to the dimensions in order to have a similar rectangle that's area is only 2 in.^2?
options:
Divide them by nine.
Divide them by six.
Divide them by three.
Multiply them by three.
We have to divide the dimensions by 9 to get a similar rectangle that's area is only 2 in.^2
Solution:
Given that,
For a game, Tony has a rectangle drawn on a piece of paper that has an area of 18 in.^2
In order to have a similar rectangle that's area is only 2 in.^2
Thus, we need to find the scale factor
Let "c" be the scale factor
Let "x" be the area of original rectangle
Let "y" be the area of dilated rectangle
Therefore,
[tex]c = \frac{y}{x}\\\\c = \frac{2}{18}\\\\c = \frac{1}{9}[/tex]
Therefore, we have to divide the dimensions by 9 to get a similar rectangle that's area is only 2 in.^2
Answer:
Divide them by three.
A city has a population of 300000 people. Suppose that each year the population grows by 8.5%. What will the population be after 15 years? Use the calculator provided round your answer to the nearest whole number.
Answer:
682,500 people
Step-by-step explanation:
so just find how many people per year it grows by then add that number 15 times to 300,000
so 8.5% of 300,000 is 25,500 people
now multiply that by 15 to get 382,500
add that to 300,000
Final answer:
Using the exponential growth formula, the population of a city with an initial population of 300,000 and an annual growth rate of 8.5% will be approximately 962,100 after 15 years.
Explanation:
To calculate the future population of a city with an initial population of 300,000 people and an annual growth rate of 8.5% over 15 years, we use the formula for exponential growth:
P = P_0 (1 + r)[tex]^{t}[/tex]
where:
P is the future population,
P_0 is the initial population (300,000),
r is the annual growth rate (expressed as a decimal, so 8.5% becomes 0.085), and
t is the number of years (15).
Substituting the values we get:
P = 300,000 (1 + 0.085)¹⁵
Calculating this, we find:
P = 300,000 (1.085)¹⁵
P = 300,000 (3.207)
P ≈ 962,100
Therefore, after 15 years, the population is expected to be approximately 962,100, rounding to the nearest whole number.
What is the slope of (12, 51) and (4, 17)?
Answer:
Slope=4.25
Step-by-step explanation:
Formula for slope is y2-y1/x2-x1
Y1=51,y2=17,x1=12,x2=4
Input this values into the above formula
17-51/4-12
Slope=-34/-8
Divide both numerator and denominator by -2
Slope=17/4
Slope=4.25
What is the measure of angle CAB in circle O? 24 48 72 96
Answer: 24
Step-by-step explanation:
Based on the inscribed angle theorem, the measure of angle CAB in circle (O) is: A. 24 degrees.
The inscribed angle theorem.According to the inscribed angle theorem, the measure of an inscribed angle whose vertex lies on a circle is always half the measure of the intercepted arc that is subtended at a point on the circle.
Given the following data:
Inscribed angle = ∠CABIntercepted arc = 48°Based on the inscribed angle theorem, we have:
∠CAB = ∡CB/2
∠CAB = 48/2
∠CAB = 24 degrees.
Learn more about inscribed angle here: https://brainly.com/question/15852619
i need help I don't understand this question
14a+7
Answer:
7*(2a-1)
Step-by-step explanation:
Answer:
7*(2a+1) / 2*(7a+1)
Step-by-step explanation:
Please help me I’m terrible at algebra
Answer:
10[tex]\leq[/tex]D+R
D[tex]\geq[/tex]R/3 (or 3D[tex]\geq[/tex]R)
Step-by-step explanation:
Say that D = Decaf and R = Regular
10[tex]\leq[/tex]D+R
D[tex]\geq[/tex]R/3 (or 3D[tex]\geq[/tex]R)
What's the supplimentary angle ?
Answer:
Step-by-step explanation:
A supplementary angle is equal to 180 degrees. So subtract 96.7 degrees from 180. 180-96.7= 83.3 degrees
Your answer is 83.3 degrees.
Answer: 83.7 is supplimentary
Step-by-step explanation: 180 - 96.7 = 83.7
The cuboid ABCDEFGH has sides AB = 3 cm, BC = 4 cm and CG = 5 cm.
What is the length AG? Give your answer in cm correct to 3 significant figures.
Answer:
7.071 cm
Step-by-step explanation:
Final answer:
To find the length AG in the cuboid ABCDEFGH, use the three-dimensional Pythagorean theorem twice. First finding the diagonal AC (which is equal to 5 cm), and then using it to find AG. The length AG, to three significant figures, is approximately 7.07 cm.
Explanation:
The length AG of a cuboid ABCDEFGH can be found by using the Pythagorean theorem in three dimensions. This theorem is an extension of the traditional Pythagorean theorem used in two dimensions. For the given cuboid, we start by using the Pythagorean theorem on triangle ABC to find the diagonal AC. The formula for the Pythagorean theorem is:
c2 = a2 + b2
Where c is the diagonal and a and b are the sides of the right triangle:
AC2 = AB2 + BC2
Plugging in the given values, we have:
AC2 = 32 + 42 = 9 + 16 = 25
So, AC = 5 cm.
Now, to find AG, we use the diagonal AC and side CG in another application of the Pythagorean theorem for the right triangle ACG:
AG2 = AC2 + CG2
AG2 = 52 + 52 = 25 + 25 = 50
AG = √50 ≈ 7.071 approximately.
Therefore, the length AG, expressed to three significant figures, is approximately 7.07 cm.
I will mark brainliest if correct please answer fast I will give 10 points to the first person who answers
.answer:
120
step-by-step explanation:
10+10+10+10=40
8+8+8+8. =32
12+12+12+12=48
add everything up (the numbers that we got) and you would get 120cm
Answer:
960
Step-by-step explanation:
You multiply the base x height x width. So you do 10 x 8 x 12 = 960 cm.
Name the three dimensional figure that is formed by folding the net
Answer:
cube
Step-by-step explanation:
the four cubes in the middle make a square and the two other ones fill in the sides of the cube
Help please! Find the Surface area. Whoever gets it right ill give Brainliest!
Answer:
284.6 square yards
284.6 yd^2
Step-by-step explanation:
Base: 7 × 13 = 91
Rectangle Sides: 6.1 × 13 = 79.3 (x2 = 158.6)
Triangle Sides: 5 × 7 = 35 (÷2 ×2 = 35)
Add: 91 + 158.6 + 35 = 284.6
can you expand 8(3x-y) please
Answer:
24x − 8y
Step-by-step explanation:
8(3x-y)
apply distributive property;
1. 8 (3x) + 8 (−y)
multiply 3 by 8 ;
2. 24x + 8 (-y)
multiply -1 by 8;
3. 24x - 8y
Regroup terms ;
4. 24x − 8y
Today is your friend's birthday. She is y years
old. Her brother is 5 years younger.
pls help me find out the answer for number 12 please and thank you
Answer:
D:step 4
Step-by-step explanation:
Maria put trim around a banner that is the shape of a triangle. Each side is 22 inches long. Maria has 1/2foot of trim left. What was the length of the trim when she started? Write your answer in yards
Maria had 2 yards of trim when she started.
Step-by-step explanation:
Step 1:
All of the sides of the triangle is 22 inches long each.
The total length of the sides of the triangle [tex]= 3(22) = 66.[/tex]
So the total length of the trim for the banner is 66 inches long.
If Maria still has [tex]\frac{1}{2}[/tex] a foot of trim left, she had 6 inches of the trim left.
The length of the trim when she started[tex]=66 +6 = 72[/tex] inches.
Step 2:
Now we need to convert the 72 inches into yards.
We have 1 inch = 0.0277778 yards.
So 72 inches [tex]= 0.0277778(72) = 2.[/tex]
So Maria had 2 yards of trim when she started.
the lengths of the sides of a triangle are shown. 8.73, 12.4, and 10.075. what is the perimeter of the triangle
Answer:
31.205
Step-by-step explanation:
The perimeter is the sum of the side lengths:
8.73 +12.4 +10.075 = 31.205
_____
If you're after an answer that has the appropriate precision (assuming these are measured values), that would be one that is rounded to 1 decimal place: 31.2.
pls help . super confused .. question worth 20. I’m going to ask ., if your not here to help, don’t answer. & if you r pls show your work, thank you.
Answer: 1) 1 1/2, 2 1/4, and 4
Step-by-step explanation: 1) We know that the equation would be the cups of flour being multiplied by the batches. Like, 5 times 3/4 would equal 15/4 which would simplify to 3 3/4.
So, to find the first missing number, we do 2 x 3/4, which equals 6/4( 1 1/2).
The next missing number would be 3, because we're going in order-- like 1, 2, 3, 4. So we do 3 x 3/4.
We then don't have a number for batches this time. So we still do, 3/4 x 3 but this time we cross out both the 3 on the top and we're left with 4, our answer.
The equation for this is 3/4 x b. (Did this help..?)
What is the x value for the solution -x+2y=6
6y =x+18
For the given set of equations, x = 0 and y = 3.
Step-by-step explanation:
Step 1:
From the question,
[tex]-x + 2y = 6[/tex], take this as equation 1,
[tex]6y =x+18, x - 6y = -18[/tex], take this as equation 2.
Step 2:
When we add equation 1 and equation 2, the x variable is canceled out and y can be calculated.
[tex]-4y = -12, y = \frac{-12}{-4}, y = 3.[/tex]
Step 3:
Substituting this value of y in any of the previous equations we will get x's value.
Here this value of y i.e y = 3 is substituted in equation 1.
[tex]-x + 6 = 6, -x = 6 -6, -x=0, x=0.[/tex]
So we have x = 0 and y = 3.
1. A firefighter is called to rescue a cat caught in a tree. If the firefighter is standing 30
m from the base of the tree and if the angle to the cat is 20'. How high in the tree is
the cat?
Answer:
10.92m
Step-by-step explanation:
See attached picture for more illustration
Using SOH CAH TOA,
Tan 20° = opposite / adjacent
Tan 20° = x / 30
x = 30 * tan20
x = 10.919m = 10.92m
The height of the tree is 10.92m
Final answer:
The height of the cat in the tree is 10.44m
Explanation:
The question involves finding the height of a cat caught in a tree using trigonometry, specifically the tangent function. If the firefighter is standing 30m from the base of the tree and the angle to the cat is 20 minutes (which should be converted to degrees for typical trigonometric calculations), we can calculate the height of the cat in the tree. First, we need to convert the angle from minutes to degrees. Since 1 degree = 60 minutes, 20 minutes is equal to 20/60 degrees or approximately 0.33 degrees.
To find the height of the cat, we can use the tangent function (tan) in trigonometry, which is the ratio of the opposite side (the height of the cat in the tree, which we're trying to find) to the adjacent side (the distance from the firefighter to the base of the tree). Thus, the formula becomes height = tan(angle) × distance.
Using the formula:
distance = 30m
angle = 0.33 degrees
height = tan(0.33 degrees) × 30
Tan(20') x Distance
Calculating: Height = Tan(20') x 30m = 10.44m
Graph f(x)=(x−2)(x−6) .
Use the parabola tool then choose the vertex followed by one point on the parabola.
Here is the graph for the equation
Given function to be graphed is,
f(x) = (x - 2)(x - 6)
We will convert the equation of the function into the vertex form,
(x - 2)(x - 6) = x(x - 6) - 2(x - 6)
= x² - 6x - 2x + 12
= x² - 8x + 12
= x² - 2(4x) + 16 - 4
f(x) = (x - 4)²- 4
By comparing this equation with the vertex form of the equation of a parabola,
g(x) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola.
Therefore, vertex of the function 'f' will be (4, 4).
Now we will find the x-intercepts and y-intercept of the function.
For x-intercept, put f(x) = 0
0 = (x - 4)²- 4
(x - 4) = ±2
x = 4 ± 2
x = 2, 6
Therefore, x-intercepts of the function are (2, 0) and (6, 0).
For y-intercept, put x = 0
f(0) = (0 - 2)(0 - 6)
f(0) = 12
Therefore, y-intercept of the function is (0, 12).
By plotting these ordered pairs and joining them by a curve we can get the graph of the parabola.
Learn more how to graph a curve,
https://brainly.com/question/16180199
Answer pleas I’ll give 20 points
PLLLSSS HURRRYYY
The Problem:
Mrs. Ashe is planning to take her study group on a field trip to an amusement park. The regular cost is $55 per person. There is a party special that costs $46 per person with an additional $45 fee for a private room where students can eat lunch. Mrs. Ashe is trying to decide if she should use the regular price or the party special.
Part 1:
A) Write an equation in slope-intercept form (y=mx+b) to show the total cost of the regular price with x people, where x = number of students in the study group and y = the total cost. (50 points)
B) Write an equation in slope-intercept form (y=mx+b) to show the total cost of the party special with x people, where x = number of students in the study group and y = the total cost. (50 points)
Answer:
y = 55xy = 46x +45Step-by-step explanation:
A. The regular cost is 55 per person. Using the given variable definitions, that cost can be expressed as ...
y = 55x
__
B. The party special cost is 46 per person, with an added fee of 45. That cost can be expressed as ...
y = 46x +45
_____
As you know, the cost of a purchase is the product of the cost of an item and the number of items. Here, the cost of entry is the cost of the item of interest, and the number of persons needing entry is the number of items. The party special has the addition item of a private room, so its cost is added to the total for the party special.