The sequence has the 10th term of 15625000
How to find the 10th term for the arithmetic sequence?The sequence is given as:
8,40,200,...
The above sequence has the following parameters
First term, a = 8
Common ratio, r = 5 i.e. 40/8 = 5
Number of terms , n = 10
This means that the sequence is a geometric sequence
The nth term of an geometric sequence is calculated as
f(n) = ar^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(10) = 8 * 5^(10 - 1)
Evaluate
f(10) = 15625000
Hence, the 10th term for the sequence is 15625000
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Highest common factor of 32 , 48 and 72
Answer:
8
Step-by-step explanation:
4*8=32
6*8=48
9*8=72
They are all multiples of 8
Answer: 8
Step-by-step explanation: You can factor out 32, 48, and 72 by using prime factorization which is listing all of the PRIME factors for each number
32: 2 x 2 x 2 x 2 x 2
48: 3 x 2 x 2 x 2 x 2
72: 3 x 3 x 2 x 2 x 2
If you look at all the prime factors, 2 appears in every number 3 times, so you do 2x2x2 to get the final answer, which is 8.
Express your answer as a polynomial in standard form.
f(x)=
f(x)=
\,\,-3x+5
−3x+5
g(x)=
g(x)=
\,\,x^2+2x+15
x
2
+2x+15
\text{Find: }(g\circ f)(x)
Find: (g∘f)(x)
The function (g∘f)(x) expressed as a polynomial in standard form is 9x² - 36x + 40
What is a function?A function can be defined as an equation, a rule or a law that shows or rather explain the relationship between two variables in an equation.
The variables are known as;
The independent variableThe dependent variableWe have the function given;
fx) = - 3x + 5g(x) = x² + 2x + 15To determine the composite function (g ∘f)(x), we have to substitute the value of x as fx) in the function g(x), we have;
(g∘f)(x) = (- 3x + 5)² + 2( -3x + 5) + 5
expand the bracket
(g∘f)(x) = 9x² - 15x - 15x + 25 - 6x + 10 + 5
Now, collect like terms, we get;
(g∘f)(x) = 9x² - 15x - 15x - 6x + 25 + 10 + 5
Add or subtract the like terms, we get;
(g∘f)(x) = 9x² - 36x + 40
The polynomial is written as; 9x² - 36x + 40
Hence, the value is 9x² - 36x + 40
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The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?
Answer: 4.5m
Step-by-step explanation:
because 12.5 can - by 2.5
then 9.0=9 -5.5=4.5
how do I solve this?
Answer:
7
Step-by-step explanation: -13(-1) + 36 + 42(-1)
Step 1: -13(-1)= 13
Step 2: 13 + 36= 49
Step 3: 49 + 42(-1)= 49 + (-42)= 7
Solution: 7
9. (-1kw-1z-2)-3
- (-1)-³³₂
11, 9-648
h2
These are the questions here is the photo
Using the simplification of power, [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex] and [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex].
In the given question,
We have to simplify the given expression.
Before simplifying the expression we first learn that the negative power can be positive after changing their position from numerator to denominator.
We use the method of adding the power of expression to solve the expression.
(1) The given expression is [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}[/tex].
We firstly simplifying the power after the bracket by multiplying the power to each variable.
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-\frac{1}{4})^{-3}(w^{-1})^{-3}(z^{-2})^{-3}[/tex]
Simplifying the expression.
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1)^{-3}(\frac{1}{4})^{-3}(w^{-3})(z^{6})[/tex]
Now we make the power positive by changing their position
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1){4}^{3}(w^{-3})(z^{6})[/tex]
Simplifying
[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex]
(2) The given expression is [tex]\frac{g^{-6}h^8}{h^2}[/tex].
Simplifying the expression.
As we know that the power with same base get subtracted when they are in division.
So [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{8-2}[/tex]
[tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex]
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help meeeeeeeeeeeeeeeeee please
Answer:
t=0
Step-by-step explanation:
Your equation would be 324=-16t^2+324 since 370-46 is 324. subtract each side by 324 and you get 0=-16t^2. t=0
In a certain skyscraper, the elevators whisk you to a restaurant in the skyscraper at a speed of 800 feet
in 10 seconds. If the restaurant is 300 feet up, how long will it take you to reach the restaurant by
elevator?
Answer:
[tex]3\frac{3}{4}[/tex] seconds
Step-by-step explanation:
So you travel 800 feet in 10 seconds. If you divide that by 2, then you travel 400 feet in 5 seconds, or 100 feet in 5/4 seconds. Multiply by 3 to get 300 feet in 15/4 seconds, or 15 feet in [tex]3\frac{3}{4}[/tex] seconds.
a principal orders t-shirts and wants to check some of them to make sure they were printed properly. she randomly selects 222 of the 101010 boxes of shirts and checks every shirt in those 222 boxes. what type of sample is this?
This is an example of Cluster random sampling.
Cluster sampling refers to probability sampling when the population is divided into multiple smaller groups, also called clusters, and then further sampling is performed to check the data.
Here we can see that the principal had selected 222 boxes randomly over here. This implies that she had taken a group of boxes randomly. Then she proceeded to check every t-shirt in this box.
Therefore here we see that the population i.e the boxes were divided into smaller groups. The 222 boxes are the clusters here. Therefore we can conclude that the principal uses the cluster random sampling method.
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Scores for a common standardized college aptitude test
are normally distributed with a mean of 507 and a
standard deviation of 104. Randomly selected students
are given a Test Preparation Course before taking this
test. Assume, for sake of argument, that the
preparation course has no effect.
If 1 student is randomly selected, find the probability
that their score is at least 555.3.
P(X> 555.3) =
The probability that their score is at least P(X> 555.3) = 0.8275
What is a normal distribution?
A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.
Here, we have
Let x denotes the score of a man.
standard deviation (σ) = 104
mean (μ) = 507
If 1 of the men is randomly selected, find the probability that his score is at least 553.5 will be :-
P(X > 553.5) = 1 - P(X ≤ x)
= 1 - P{((x - μ)/σ) ≤ (553.5 - 507/104)}
= 1 - P(z ≤ 0.447)
= 1 - 0.1725
= 0.8275
Hence, the probability that their score is at least P(X> 555.3) = 0.8275
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4) Simplify the expression and identify any restrictions on x.
Answer:
6X/X^2-2X+1
Step-by-step explanation:
x
2
−3x+2
9x
2
+18x
÷
2x−4
3x
2
+3x−6
Divide
x
2
−3x+2
9x
2
+18x
by
2x−4
3x
2
+3x−6
by multiplying
x
2
−3x+2
9x
2
+18x
by the reciprocal of
2x−4
3x
2
+3x−6
.
(x
2
−3x+2)(3x
2
+3x−6)
(9x
2
+18x)(2x−4)
Factor the expressions that are not already factored.
3(x−2)(x+2)(x−1)
2
2×9x(x−2)(x+2)
Cancel out 3(x−2)(x+2) in both numerator and denominator.
(x−1)
2
2×3x
Expand the expression.
x
2
−2x+1
6x
Can anyone write the equation of the graph?
The absolute value function y = |x - 3| + 5 generates the representation set on Cartesian plane.
What equation is behind a given graph?
In this question we need to determine the equation behind a representation set on a Cartesian plane. After a quick inspection, we find that the representation shows an absolute value function of the form:
y = |x - a| + b
Where:
a - Horizontal translation factor.b - Vertical translation factor.Based on all the given facts, the primitive absolute value function (f'(x) = |x|) is translated horizontally 3 units in the +x direction and vertically 5 units in the +y direction. If we know that a = 3 and b = 5, then we find the absolute value function y = |x - 3| + 5, whose representation is shown below.
In a nutshell, the representation comes from the absolute value function y = |x - 3| + 5.
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0.000007328 rounded to the nearest millioneth,the numbers is about
When the numerical data (number) 0.000007328 is rounded to the nearest millionth, the number is about 0.000007.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Hundred of thousands.Millions.Tens of millions.Hundreds of millions.Billions.Based on the numerical data (number) provided above, the place value of seven (7) is millionth and it would be rounded up as seven (7) because the next number on its right (3) is less than five (5) and as such, it can seven (7) rounded up to eight (8).
In this context, we can reasonably infer and logically deduce that 0.000007 is a numerical data (number) that represents millionth based on the place value of seven (7).
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a certain insecticide kills 60% of all insects in laboratory experiments. a sample of 9 insects is exposed to the insecticide in a particular experiment. what is the probability that exactly one insect will die? round your answer to four decimal places.
The probability that exactly one insect will die is 142.611.
Define probability.The subject of a random event is covered in the mathematical field of probability. For instance, if a coin is flung into the air, it could land on its Head or Tail. Probability is equal to the number of favorable outcomes (Total number of outcomes) P = n (E) / n (S) (S) E is the event, P is the probability, and S is the sample area.
Given,
P( an insect will die) = 0.60
q = 1 - p
q = 1 - 0.60
q = 0.40
Sample size,
n = 9
Binomial distribution:
P(X) = ⁿCₓ pˣ qⁿ⁻ˣ
Probability that exactly one insect will die = P(X = 1)
= ⁹C₁ × 0.6¹ × 0.4⁸
= 362880 × 0.6 × 0.000655
= 142.611
The probability that exactly one insect will die is 142.611.
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4. A triangle has two sides measuring 8 cm and 15 cm. Write an inequality to represent the possible lengths of the third side.
Answer:
7 < x < 23
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the interval
difference of 2 sides < x < sum of 2 sides , that is
15 - 8 < x < 15 + 8
7 < x < 23
1 can go on saturday and 14 can go on sunday; some of them can go on both days. how many people can only go to the game on saturday? 6
Answer:
No solution
Step-by-step explanation:
The reason why I say this problem has no solution is due to the fact that it says only one person may go on Saturday yet some fraction of the people between the numbers 1 - 14 can go. We have no idea what this fraction is, leading to a paradox of multiple equations and guesses desperately trying to figure out the number. Thus, the problem has no solution.
Hope this helps.
Micah is making salsa at a factory using tomatoes
and onions in the ratio of 5:2. If the total volume
of salsa Micah makes is 147 cups, find the volume
of the tomatoes Micah uses.
Answer: 21 Tomatoes
Step-by-step explanation:
5 + 2 = 7
147 / 7 = 21
21 Tomatoes
How to find correlation coefficient? I'm stuck pls help me
(0,1132), (1,1107), (2,1000), (3,1019)
The correlation coefficient of the data (0,1132), (1,1107), (2,1000), (3,1019) is -0.89
How to determine the correlation coefficient?Correlation coefficients are used to measure how strong a relationship is between two variables
Given: (0,1132), (1,1107), (2,1000), (3,1019)
x >>>> y >>>> x² >>>> y² >>>> xy
0 1132 0 1281424 0
1 1107 1 1225449 1107
2 1000 4 1000000 2000
3 1019 9 1038361 3057
................................................................................................
6 4258 14 4545234 6164
.................................................................................................
The formula for the correlation coefficient is:
r = ( n∑xy -(∑x)(∑y) ) / ( √(n∑x² - (∑x)²) .√(n∑y² - (∑y)²) )
From the table:
∑x = 6, ∑y = 4258, ∑x² = 14, ∑y² = 4545234 and ∑xy = 6164
n = 4 (number of data points)
Substituting the values into the formula will give:
r = ( 4×6164 -(6)(4258) ) / ( √(4×14 - (6)²) .√(4×4545234 - (4258²) )
r = 24656-25548 / √(20).√(50372)
r = -892/√(1007440)
r = -0.89
Therefore, the correlation coefficient is -0.89
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[24+9-(5x3)+10]÷2
what is the value of the following the expression
Answer:
14
Step-by-step explanation:
[tex](33 - (15) + 10) \div 2 \\ 33 - 15 + 10 \div 2 \\ 18 + 10 \div 2 \\ 28 \div 2 \\ = 14[/tex]
Answer:14
Step-by-step explanation:1/2 (24+9- 5 x 3 + 10
write an equation of the line in slope intercept form
The equation of the line in slope intercept form is y = (-4/3)x .
In the question ,
a line graph is given ,
we need to find the equation of that line .
the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,
the equation of the line passing from the points (x₁ , y₁) with slope m in the slope intercept form is given by
(y - y₁) = m(x - x₁) .
we first need to find the slope .
So , m = (0 - 4)/(0 + 3)
m = -4/3
The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is
(y - 4) = (-4/3)(x -(-3))
y - 4 = (-4/3)(x + 3)
y - 4 = (-4/3)x - 4
y = (-4/3)x - 4 + 4
y = (-4/3)x
Therefore , The equation of the line in slope intercept form is y = (-4/3)x .
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Which of the following is true about the constant of proportionality? Select all that apply. Multiple select questions. cross out
A) The constant of proportionality is also the unit rate. cross out
B) The constant of proportionality is always equal to 1. cross out
C) The constant of proportionality is always equal to 0. cross out
D) There is no constant of proportionality in a nonproportional relationship. cross out
E) If two quantities are proportional, the constant of proportionality is the constant ratio between them.
Answer:
D
Step-by-step explanation:
The magnitude, M, of an earthquake is represented by the equation M=23log(EE0) where E is the amount of energy released by the earthquake in joules and E0=104.4 is the assigned minimal measure released by an earthquake. To the nearest tenth, what would be the magnitude of an earthquake releasing 3.4⋅1014 joules of energy?
Magnitude of an earthquake releasing 3.4*10^14 joules of energy is M ≈ 6.754.
Given:
The magnitude, M, of an earthquake is represented by the equation M=2/3log(E/E0) where E is the amount of energy released by the earthquake in joules and E0=10^4.4 .
E = 3.4*10^14
M = 2/3*log(3.4*10^14 / 10^4.4)
= 2/3*log(13535643798.8)
= 2/3*10.1314
= 20.2628 / 3
M = 6.754
Therefore Magnitude of an earthquake releasing 3.4⋅1014 joules of energy is M ≈ 6.754.
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Pls solve this problem
Answer: -22/5 or -4.4
Step-by-step explanation:
Simplify so 2(22/7*10)(10+h)=352
Distribute so (2*22/7*10)(10) + (2*22/7*10)(h) = 352
Which would equal 4400/7 +440/7h=352
Subtract 4400/7 to both sides
That equals 440/7h=-1396/7
Multiply both sides by 7/440
h=-22/5
suppose you paid $4 for a bet on a horse and, as a result, you will win $110 if your horse wins a given race. find the expected value of the bet (in $) if the odds that the horse will win are 3 to 12.
The expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8
What is expected value?
Expected value is the predictive value of all the possibilities that occur by multiplying the value by the probability.
Winning probability = odds / total outcomes
= 3 / (3 + 12)
= 3 / 15
= 0.2
Now, we need to calculate expected value.
= winning probability x amount won - losing probability x amount lost
= 0.2 x 110 - (1 - 0.2) x 4
= 22 - 3.2
= 18.8
Thus, the expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8
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please I am begging you, answer this TODAY and show your work.
Answer:
1) t = -2
2) t = 8
3) t = -2
4) t = 1
5)t = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
1)-22t+6 = 11t + 72
-33t = 66
t = -2
2) 3t + 4t - 20 = t + 28
6t = 48
t = 8
3) -8 -10t - 6t = 3t + 30
-19t = 38
t = -2
4) 12t - 6t + 24 = 12t + 12 +6
-6t = -6
t = 1
5) -12-21t-3t=48t-36
-24t - 48t = 12 - 36
-72t = -24
t = [tex]\frac{1}{3}[/tex]
How can you write the equation of the
line?
(: before the lady in the video shows
you :)
y 5x = 3
y = 3x - 5
y = -5x + 3
y + 3 = -5x
what is the value of X
-9(x+6)=-207
Answer:
x=17
It just is. I don't know how to explain it.
Find x
35°
100°
X
algebra 1
Answer:
X would be 135 degrees
Step-by-step explanation:
35 is a vertical angle
180-(100+35) = 45
By supplements, 180-45 = 135 which would be your answer
hope this helps
the value o f x is 135, it mean x=135°
scores on a standard iq test for people aged 20 to 34 are normally distributed with mean 110 and standard deviation 25. what is the probability that a randomly selected young adult will score between 85 and 160 on this iq test? round your answer to four decimal places.
The probability that a young adult chosen at random will achieve an IQ between 85 and 160 is 0.8185.
The problem states that;
A typical IQ test result for individuals between the ages of 20 and 34 has a mean of 110 and a standard deviation of 25, and the values are regularly distributed.
To get the probability that a randomly selected young adult will score between 85 and 160 on this IQ test.
Let,
P(85 < x < 160) = P[ (85 - 110)/ 25) < (x - μ) / σ < (160 - 110) / 25) ]
= P(-1 < z < 2)
= P(z < 2) - P(z < -1)
= 0.9772 - 0.1587
= 0.8185
Therefore, the probability that a randomly selected young adult will score between 85 and 160 on this IQ test is 0.8185.
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everyone can someone help me here please (complete solution and graph)
Answer:
1: x^2+y^2-6x-4y-3=0
2: x^2+y^2-10x+4y=0
3: x^2+y^2-10x+2y+1=0
Quadrilateral ABCD has vertices A(9, 9), B(—7, 9),
C(-8,-5), and D(4,-5). In terms of units, what is the
perimeter of quadrilateral ABCD?
Round your answer to the nearest tenth.
Answer:get a tutor
Step-by-step explanation:
its free
