The geometric series an = 400(1.05)^(n-1) has a common ratio and an initial term
The first four terms are a1 = 400; a2 = 420; a3 = 441 and a4 = 463.05
How to determine the first four terms?The geometric series is given as:
an = 400(1.05)^(n-1)
Substitute 1 for n
a1 = 400 * (1.05)^(1-1)
Evaluate the product
a1 = 400
Substitute 2 for n
a2 = 400 * (1.05)^(2-1)
Evaluate the product
a2 = 420
Substitute 3 for n
a3 = 400 * (1.05)^(3-1)
Evaluate the product
a3 = 441
Substitute 4 for n
a4 = 400 * (1.05)^(4-1)
Evaluate the product
a4 = 463.05
Hence, the first four terms are
a1 = 400; a2 = 420; a3 = 441 and a4 = 463.05
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Answer:
a1 = 400
a2 = 420
a3 = 441
a4 = 463
C
Step-by-step explanation:
Many manufacturers reduce the size of their products to appear to reduce their prices.
The amount of cereal in a particular brand box was reduced by 2.1 ounces. This is a 14% reduction from the original amount. What was the original amount?
The original amount was
ounces.
Answer:
2.44 ounces
Step-by-step explanation:
100% - 14% = 86%
2.1 ÷ 0.86 = 2.44
Where is the blue dot on the number line?
the blue dot on the number of line is -11.3
Answer:
-11.3
Step-by-step explanation:
Each jump/line is 0.1
As we can see the blue dot is 3 lines from -11 and 2 lines from -11.5 so our answer will be -11 + -0.3 and -11.5 - (-0.2)
-11 + -0.3 = -11.3
-11.5 - (-0.2) = -11.5 + 0.2 = -11.3
Hope this helps and brainliest please
Find the length of h. Round to the nearest hundreth.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{h}{0.3}~~ = ~~\cfrac{0.4}{0.5}\implies \cfrac{h}{~~ \frac{3}{10}~~}~~ = ~~\cfrac{~~ \frac{4}{10}~~}{\frac{5}{10}}\implies \cfrac{10h}{3}~~ = ~~\cfrac{4}{5} \\\\\\ 50h=12\implies h=\cfrac{12}{50}\implies h=\cfrac{6}{25}\implies h=0.24[/tex]
A triangle has a base of x^1/2 m and a height if x^3/4 m. If the area of the triangle is 16m^2, what are the base and height of the triangle?
Answer:
Base = 4 m
Height = 8 m
Step-by-step explanation:
For triangle:
[tex]Base\: (b) = x^{\frac{1}{2}}\: m\\\\Height \:(h) = x^{\frac{3}{4}}\: m\\\\ A(\triangle)= 16\:m^2\\\\A(\triangle)= {\frac{1}{2}}(b)(h)\\\\\implies 16=\frac{1}{2}(x^{\frac{1}{2}})(x^{\frac{3}{4}})\\\\\implies 32= (x^{\frac{2}{4}})(x^{\frac{3}{4}})\\\\\implies 2^5=x^{\frac{3+2}{4}}\\\\\implies 2^5=x^{\frac{5}{4}}\\\\\implies 2=x^{\frac{1}{4}}\\\\\implies 2^4=x\\\\\implies x=16\:m[/tex]
[tex]Base\: (b) = x^{\frac{1}{2}}={16}^{\frac{1}{2}}={(4^2)}^{\frac{1}{2}}=4\: m[/tex]
[tex] Height\: (h) = x^{\frac{3}{4}}={16}^{\frac{3}{4}}={(2^4)}^{\frac{3}{4}}=(2)^3=8\: m[/tex]
Which Line is Perpendicular to y= -1/4x - 8?
A) y=-4x+5
B) y=-1/4x-3
C) y=1/4x
D) y=4x+2
Answer:
D
Step-by-step explanation:
For two lines to be perpendicular, their gradients must have a product of -1The only one that fits this is DAnswer:
D
Step-by-step explanation:
The product of the slope of the perpendicular lines are -1
y = -1/4x - 8
Slope = -1/4
D) y = 4x + 2
Slope = 4
[tex]4 * \dfrac{-1}{4}=-1[/tex]
What is the area of the following triangle?
Answer:
150in²
Step-by-step explanation:
area of traingle = (base x height)/2
here base = 25in and height = 12in
therefore area = (25 x 12)/2
150in²
Answer:
150in2
Step-by-step explanation:
The Formula is A= 1/2 bh
You multiply 25 x 12
300
Then you divide it by 2
how do geometric functions differ from algebraic functions?
Answer:
happy to explain
Step-by-step explanation:
Algebra is an area in mathematics that uses variables, in the forms of letters and symbols, to act as numbers or quantities in equations and formulas. Geometry is an area in mathematics that studies points, lines, varied-dimensional objects and shapes, surfaces, and solids
Four friends each flipped a coin different numbers of times. Alice got heads 75% of time.Mary got heads 8 out of 10 times. Sarah got heads 17 out of 20 times. Ellen got heads 3 5 of the time.
who had the greatest percentage of heads?
I FARTED HEHE
Step-by-step explanation:
IM 54
What is the simplified expression for
44.4°?
49
40
41
42
43
Answer:
[tex]4^2[/tex]
Step-by-step explanation:
[tex]\dfrac{4^4 \cdot 4^3}{4^5}\\\\\\=\dfrac{4^{4+3}}{4^5}\\\\\\=\dfrac{4^{7}}{4^5}\\\\\\=4^{7-5}\\\\\\=4^2[/tex]
Answer:
4^2
Step-by-step explanation:
4^4*4^3=4^7
4^7/4^5=4^2
If x = 10, which equation is true?
A 3 ( 20 - x) = 44
B3 ( 12 - x ) = 6
C2 x + 3 = 25
D2 x - 3 = 22
Answer:
B
Step-by-step explanation:
[tex]3(12-10)=3\cdot 2 = 6[/tex]
Which will have a negative number?
A)
(-3)(-9)
B)
(-6)(4)
C
-4 --5
D)
-7+9
Answer:
B
Step-by-step explanation:
A: 27
C: 1
D: 2
B: -24
anytime you multiply two negative numbers it makes the product positive
22
Liam is trying to remember a 3-digit code.
He knows the rule that
the first digit is a cube number
the second digit is a factor of 16
the third digit is an odd number.
Liam tries at random a code that matches the rule.
Work out the probability that this is the correct code.
[4 marks]
The first digit may be 1 or 8.
The second digit may be 1, 2, 4, 8.
The third digit may be 1, 3, 5, 7, 9.
There are [tex]2\times4\times5=40\:variants[/tex]
The probability that this is the correct code is [tex]\frac{1}{40}[/tex]
1/40 is the probability that this is the correct code.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Liam is trying to remember a 3-digit code.
the first digit is a cube number so the first digit may be 1 or 8.
the second digit is a factor of 16.
The factor of 16 are 1, 2, 4 , 8.
Third digit is an odd number so the third digit may be 1, 3, 5, 7, 9.
There are 2×4×5 possibilities of Liam code.
40 possibilities
the probability that this is the correct code is 1/40
Hence, 1/40 is the probability that this is the correct code.
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PLEASE HELP NEED NOW!!
Jayden has a bag that contains pineapple chews, strawberry chews, and lime chews.
He performs an experiment. Jayden randomly removes a chew from the bag, records
the result, and returns the chew to the bag. Jayden performs the experiment 41 times.
The results are shown below:
A pineapple chew was selected 31 times.
A strawberry chew was selected 4 times.
A lime chew was selected 6 times.
Based on these results, express the probability that the next chew Jayden removes
from the bag will be strawberry chew as a fraction in simplest form.
Answer:
Submit Answer
attempt 2 out of 2
Answer:
4/41
Step-by-step explanation:
The circumference of a circle is 20pi in. What is the area, in square inches? Express
your answer in terms of Pi
Answer:
10.14π
Step-by-step explanation:
First we have to work backwards. We know the forumla for circumference is pi x diameter. So we have to work backwards. 20 divided by pi is 6.37. So thats our diameter. Now that we that we can put it into our forumla for area. A= π x R^2.
The raidus is half of the diamater so 6.37/2. Which equals 3.185. Now we that into our formula. A= π x 3.185^2. Now we keep simplyifying the equation. 3.185^2=10.14. So now we have A=10.14π
The history museum is hosting a special exhibition on history of flight. The admission ticket for each adult costs $7 and the admission
ticket for each child costs $2. On the opening day of the exhibition, 40 tickets were sold for a total of $180. How many adults visited the
special exhibition?
Answer:
Use simultaneous equation for this problem
y= number of adults
x = number of children
3y + 2x = 160
y + x = 60
then we double the second equation
3y + 2x = 160
2y + 2x = 120
we cancel x by elimination
3y - 2y = 160 - 120
y = 40
Step-by-step explanation:
hope this helps
Your medical research team is investigating the standard deviation of the cost of a 30-day-supply of a certain heart medication. A pharmaceutical company thinks that the standard deviation of the cost is less than $23. You want to support this claim. How would you write the null and alternative hypothesis?
Considering the situation described, the hypothesis tested are given as follows:
The null hypothesis is [tex]H_0: \sigma \geq 23[/tex]The alternative hypothesis is [tex]H_1: \sigma < 23[/tex]What are the hypothesis tested?At the null hypothesis, it is tested if the standard deviation is not less than $23, that is:
[tex]H_0: \sigma \geq 23[/tex]
At the alternative hypothesis, it is tested if there is significant evidence t conclude that the standard deviation is less than $23, that is:
[tex]H_1: \sigma < 23[/tex]
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If 10^2y = 25, then 10^-y equals:
(a) -1/5,
(b) 1/625,
(c) 1/50,
(d) 1/25,
(e) 1/5
[tex] {10}^{2y} = 25[/tex]
[tex] {(10)}^{y2} = {5}^{2} [/tex]
[tex] {10}^{y} = 5[/tex]
[tex] \frac{1}{10 {y} } = \frac{1}{5} [/tex]
[tex] {10}^{ - y} = \frac{1}{5} [/tex]
answer= option e.
11 Describe how the numbers-7-and-7 would be positioned relative to each
other on a horizontal number line.
Select one answer.
A The number-7 would be positioned to the left of -7 on a horizontal
number line because -7<-7.
B The number - 7 would be positioned to the left of -7 on a horizontal
number line because
use -7/>-7.
C The number - 7 would be positioned to the right of -7 on a horizontal
number line because -2
-7/1/2<-7.
D The number - 7 would be positioned to the right of -7 on a horizontal
number line because -7> -7.
Step-by-step explanation:
you have to be careful with the precise notation of terms and expressions.
you keep using only -7 for everything.
i suspect you mean 7 and -7, right ?
if that is correct, then just remember this :
on a number line the positive values are on the right, and the negative values on the left.
in fact, the further right you go, the larger the number gets. and the further left you go, the smaller (or lower) the number gets.
e.g. -7 is smaller than -6.
and so, -7 would be to the left of 7, because -7 < 7.
or vice versa :
7 would be to the right of -7, because 7 > -7
If y varies directly with x and y is 12 when x is 9, what is x when y is 4?
Answer:
3
Step-by-step explanation:
y/x=12/9=4/3
when y is 4 x is 3
Which shape will result from taking a cross section of the tetrahedron through the points shown?
triangle
square
trapezoid
pentagon
Answer:
the anwer is a triangle as it is shown below.
10( 7+6s) its distributing
Answer:
10(7 + 6s) = 70 + 60s
Step-by-step explanation:
10(7 + 6s)
Distribute the 10 in the parenthesis. When distributing, multiply the number by every term in the parenthesis.
10 * 7 + 10 * 6s
Multiply.
70 + 60s
Answer:
10(7)+10(6s) which equals 70+60s
How can you find the maximum or minimum value of the quadratic function?
A. Evaluate the function for x = 0. The resulting value is the maximum or the minimum value.
B. Find the vertex. The y-coordinate of the vertex is the minimum or the maximum value of the parabola.
C. Find the y-intercept. The y-intercept is the maximum or the minimum value of the parabola.
D. Find the vertex. The x-coordinate of the vertex is the minimum or the maximum value of the parabola
Answer:
B
Step-by-step explanation:
the y-coordinate of the vertex will be the max or min value of the quadratic function
hope this helps!
Please help. Will mark brainlyest!
Answer:
last one
Step-by-step explanation:
Answer:
(-3,-2)
Step-by-step explanation:
(x,y)
Which value is not a solution of the inequality 2 - 4 > 2?
Ox= 10
x = 6
o
Ox=4
O2 = 14
21
The inequality x -4 > 2 uses a greater than symbol
All numbers lesser or equal to 6 are not a solution of the inequality x -4 > 2
How to determine the value not in the solution?The inequality is given as:
x -4 > 2
Add 4 to both sides of the inequality
x - 4 + 4 > 2 + 4
Evaluate the sum
x > 6
The above means that only numbers greater than 6 are in the solution of the inequality.
Since the options are not given, I will give a general solution that all numbers lesser or equal to 6 are not a solution of the inequality x -4 > 2
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How do I convert the letter in an answered equation into a number, for example the answer 8.50246E6
Answer:
1Step-by-step explanation:
1 + IS 1 AND ITS 1
Answer:
See below
Step-by-step explanation:
E means exponent of 10
8.50246E6 means 8.50246 x 10^6 = 8502460
Which relation is a function?
Answer:
The bottom left one
Step-by-step explanation:
They are the only graph that has one output for each x value
Haha please help i don't know what I'm doing
Answer:
(5x+1)(x+7)
Step-by-step explanation:
4x^2+26x+6+x^2+10x
5x^2+36x+7
(5x+1)(x+7)
Prove
5x*x + 5x*7 + 1*x + 1*7
= 5x^2 + 35x + x + 7
= 5x^2 + 36x + 7
I NEED HELP ON THESE QUESTIONS QUICKLY PLEASE!!!!
1. Maximize Z=2x+3y subject to the constraints:
3x+2y≤15
4x+y≤0
x≥0
y≥0
On the attachments I need questions 7,21,22.23and 25 answered and it has to be in the next 2 hours please this is very Important
1
The objective function Z = 2x + 3y cannot be maximized, while the maximum value of the objective function Z = 2x + 5y is 19
Part A (Question 1): Maximize ZThe objective function is given as:
Z = 2x + 3y
The constraints are given as:
3x+2y≤15
4x+y≤0
x≥0; y≥0
See attachment for the graph of the constraints
From the attached graph, we have the optimal solution to be:
(x,y) = (-3,12)
Because x≥0 & y≥0, and x is negative in (-3,12), then
The function cannot be maximized.
Part B (Question 7): Maximize ZThe objective function is given as:
Z = 2x + 5y
The constraints are given as:
x + y ≤ 5
y - x ≤ 1
x≥0; y≥0
See attachment for the graph of the constraints
From the attached graph, we have the optimal solution to be:
(x,y) = (2,3)
Substitute 2 and 3 for x and y in the objective function.
Z = 2 * 2 + 5 * 3
Evaluate
Z = 19
Hence, the maximum value of the objective function is 19
The questions 21, 22, 23 and 25 are not included in the attachment
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HERES A HARD ONE, is Annie ok?
Answer:
Her mistake is that she should plot the point (0, 5) first, not (1, -3)
Step-by-step explanation:
First I simplified the equation given.
y - 3 = 2 (x + 1)
y - 3 = 2x + 2
+3 +3
y = 2x + 5
Since 5 is our y-intercept we would want to graph that first, which would be (0, 5) as a point.
Hope this helps!
which situation is the best for the equation 3x=288
Answer:
The situation best for the equation 3x=288 Is by dividing both sides by the coefficient of x to single out the variable
Step-by-step explanation:
=> 3x/3=288/3
=> x = 96
Step-by-step explanation:
Step 1: Determine a situation best for the equation
We walk into the store and see an amazing drone and the store has 3 of them. The total price for them is 288 dollars. Determine the individual price of each drone.
Hope this helps!