Find a8 when a1= 9, d = 4 of the arithmetic sequence whose first term is a1 and common difference is d.
General Arithmetic Terms
[tex] \displaystyle \large{a_n = a_1 + (n - 1)d}[/tex]
We want to find a8; we know:
a1 = 9d = 4Substitute in the formula.
[tex] \displaystyle \large{a_n = 9 + (n - 1)4} \\ \displaystyle \large{a_n = 9 + 4n - 4} \\ \displaystyle \large{a_n = 4n + 5}[/tex]
To find a8, substitute n = 8
[tex] \displaystyle \large{a_8= 4(8) + 5} \\ \displaystyle \large{a_8= 32 + 5} \\ \displaystyle \large{a_8= 37}[/tex]
Hence, the 8th term of sequence is 37
b^3-21/5b+9 when b = 3
Answer:
-21b + 180 / 5
Step-by-step explanation:
Hey there!
b^3 - 21/5b + 9
= 3^3 - 21/5(3) + 9
= 27 - 63/5 + 9
= 72/5 + 9
= 117/5
Answer: 117/5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What is the following difference?
230 192ab -5 V81365
PLEASE ANSWER QUICK 70 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1 to Line 2:______________
Line 2 to Line 3:_______________
Answer:
The answer above me is correct!
Step-by-step explanation:
Give them BRAINLIEST! have a good day<3 :)
work ou the value of 19+7÷2-5
helllppp pls
Answer:
17 1/2
Step-by-step explanation:
19+7÷2-5
Solve using PEMDAS
Divide first
19 + 7/2 -5
Then add and subtract from left to right
Getting a common denominator
38/2 + 7/2 - 10/2
45/2 - 10/2
35/2
17 1/2
The winning team's score in 5 high school basketball games was recorded. If the sample mean is 62.3 points and the sample standard deviation is 11.0 points, find the
98% confidence interval of the true mean.
A) 57.4 < µ < 67.2 B) 50.8 < µ < 73.8
C) 25.4 < µ < 99.2 D) 43.9 < µ < 80.7
Answer:
This is 3.747*11/sqrt(5)=18.4
the interval is (49.9,86.7), the SE added to and subtracted from the mean.
It is B
Thank You
4x-2=18x+5
Show ur work
Step-by-step explanation:
[tex]4x - 2 = 18x + 5[/tex]
Collect like terms and simplify
[tex] - 2 - 5 = 18x - 4x \\ - 7 = 14x[/tex]
Divide both sides of the equation by 14
[tex] \frac{ - 7}{14} = \frac{14x}{14} \\ - \frac{1}{2} = x[/tex]
Answer:
x = -1/2
Step-by-step explanation:
4x-2=18x+5
-2-5=18x-4x
-7=14x
-7/14=14/14x
-1/2=x
0.189 divided by 1.75=
Explain your answer
Answer:
0.189x1000=189
1.75x1000=1750
189÷1750 = 0.108
Evaluate:
[tex] \int \limits^{2}_{1} { \sin }^{3} x. \cos(2x) dx[/tex]
hello, anyone can help me if you don't mind, I am getting confused.
Thanks, I really appreciate
Recall some identities:
sin²(x) + cos²(x) = 1
cos(2x) = cos²(x) - sin²(x)
and from the first identity, you can establish that
cos(2x) = 2 cos²(x) - 1
So, rewrite the integrand as much as possible in terms of cos(x) :
[tex]\sin^3(x) \cos(2x) = \sin(x) \sin^2(x) (\cos^2(x)-\sin^2(x)) \\\\ \sin^3(x) \cos(2x) = \sin(x) (1-\cos^2(x)) (2\cos^2(x) - 1)[/tex]
Then in the integral, substitute u = cos(x) and du = -sin(x) dx. With some rewriting, you end up with
[tex]\displaystyle \int_1^2 \sin^3(x) \cos(2x) \,\mathrm dx = -\int_{x=1}^{x=2} (1-\cos^2(x))(2\cos^2(x)-1) (-\sin(x)\,\mathrm dx) \\\\ = -\int_{u=\cos(1)}^{u=\cos(2)} (1-u^2)(2u^2-1)\,\mathrm du \\\\ = \int_{\cos(1)}^{\cos(2)} (1-3u^2+2u^4) \,\mathrm du \\\\ = \left(u-u^3+\frac25u^5\right)\bigg|_{\cos(1)}^{\cos(2)} \\\\ = \left(\cos(2)-\cos^3(2)+\frac25\cos^5(2)\right) - \left(\cos(1)-\cos^3(1)+\frac25\cos^5(1)\right) \\\\ = \boxed{\cos(2) - \cos^3(2) + \frac 25 \cos^5(2) - \cos(1) + \cos^3(1) - \frac25 \cos^5(1)}[/tex]
Multiply.
(b - 7)(2b +9)
(b - 7)(2b +9)=(Simplify your answer.)
Answer:
[tex]2 {b}^{2} - 5b - 63[/tex]
Step-by-step explanation:
[tex](b - 7) \times (2b + 9)[/tex]
[tex]b \times 2b + 9b - 7 \times 2b - 7 \times 9[/tex]
[tex]2 {b}^{2} + 9b - 14b - 63[/tex]
[tex]2 {b}^{2} - 5b - 63[/tex]
1.) A six-sided number cube is rolled, and the spinner
below is spun. Determine the probability of rolling a 3 and
spinning blue. (B=blue, R=red) Express your answer as a
fraction, a decimal, and a %.
Answer:
Step-by-step explanation:
The question is not totally clear. I will assume that the spinner has 2 colors, red and blue.
Your chances of rolling a 3 are 1 in 6 = 1/6
Your chance of getting blue is 1/2
Your chances are 1/2 * 1/6 = 1/12
As a decimal that is 0.0833333
As a % it is 8.3333 %
A garden table and a bench cost $853 combined. The garden table costs $47 less than the bench. What is the cost of the bench?
Answer:
the cost of the bench is $806
Step-by-step explanation:
853 minus 47 is 806
is 9.407 a natrual number?
Answer:
Sorry about that, I did not see the decimal. As liamly said, it is positive but is not a natural number because of the decimal.
Step-by-step explanation:
Alguien me ayuda con esto?
Answer:
x=10
Step-by-step explanation:
10 a 8 son dos, entonces 14 ax es 4
Answer:
La explicación sería:
//////////////////////////
=> 9 * 2 + 4/2 = 20
=> 18 +2 =20
=> 20 =20
//////////////////////////
=> 5*2 + 8/2 = 14
=> 10 +4 =14
=> 14 =14
//////////////////////////
=> 3*2 + 10/2 = x
=> 6 + 5 = x
=> 11 = x
help me do this plz brainiest to whoever right
Answer:
3.16 miles
Step-by-step explanation:
Hi there!
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
We're given that the campsite is located at (1,7) and the checkpoint station is located at (4,6). We must calculate the distance between them. Plug these points into the formula:
[tex]d=\sqrt{(x_2-1)^2+(y_2-7)^2}\\d=\sqrt{(4-1)^2+(6-7)^2}\\d=\sqrt{(3)^2+(-1)^2}\\d=\sqrt{9+1}\\d=\sqrt{10}\\d\approx3.16[/tex]
Therefore, the distance between the campsite and the checkpoint is 3.16 miles when rounded to the nearest hundredth.
I hope this helps!
Find the volume of the cylinder.
Either enter an exact answer in terms of it or use 3.14 for T.
Answer:
188 units cubed
Step-by-step explanation:
Calculate the area of this figure. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
The figure is divided into a rectangle and a right-triangle.
The area of the figure is the sum of the individual areas of the rectangle and triangle
Area of rectangle = Length x Width = 10 ft x 8 ft = 80 ft²
Area of triangle = 1/2 x Base X Height = 1/2 x 6 ft x 8 ft =24ft²
Hence, the area of the figure is:
80 ft²+ 24ft² = 104 ft²
Answer:
104 ft^2
Step-by-step explanation:
The figure consist a rectangle and a triangle
to calculate triangle's area we multiply height and base then divide it by two
the height of the triangle is 8 ft (the given is a special right triangle)
8*6/2 = 24 ft^2
to calculate the area of the rectangle we multiply width and length
8*10 = 80 ft^2 the total area of the figure is :
24 + 80 = 104 ft^2
LOUNGE SUITE FOR SALE Selling Price-R15 000 Deposit -15% of selling price Monthly Payments - R800 Repayment period 24 months calculate the loan amount
Answer:
610023626728387383838
What is the value of (x – 3) if – 5(3x – 9) = -15?
The value of the required expression (x- 3 ) using the given equation -5(3x - 9) = -15 is equal to 1.
Let's solve for the value of "x" in the given equation:
-5(3x - 9) = -15
First, distribute the -5 on the left side of the equation:
-15x + 45 = -15
Now, subtract 45 from both sides to isolate the term with "x":
-15x = -60
Divide both sides by -15 to solve for "x":
x = 4
Now that we have the value of "x," we can find the value of (x - 3):
x - 3
= 4 - 3
= 1
Therefore, the value of (x - 3) is 1.
learn more about value here
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What is the volume of the following rectangular prism?
Answer:
[tex]volume \: of \: rectangular \: prism = base \: area \: \times height \\ \\ = length \times width \times height[/tex]
Simplify (3xy)^5/x^3
Answer:
[tex]243 {x}^{2} {y}^{5} [/tex]
Step-by-step explanation:
[tex] \frac{(3xy {)}^{5} }{ {x}^{3} } [/tex]
[tex] \frac{243 {x}^{5} {y}^{5} }{ {x}^{3} } [/tex]
simplify:
[tex]243 {x}^{2} {y}^{5} [/tex] ✅
Approximately 54% of mathematics students do their homework on time. In a class of 250 students, what is the mean, variance, and standard deviation if we assume normality and use the normal distribution as an approximation of the binomial distribution
Answer:
135
Step-by-step explanation:
250 x 54%=135
solve the equation 6 = 5 x -2
Answer:
8/5 = x
Step-by-step explanation:
6 = 5x - 2
~Add 2 to both sides
8 = 5x
~Divide 5 to both sides
8/5 = x
Best of Luck!
2x + 3y = 6
The equation x + 2y = 16 is in standard form.
What is the slope of the line?
3y = -2x + 6
X-2
6
3
-1
y y=-3x +
y= - +
O
-0.5
+2
O
0.5
9514 1404 393
Answer:
(c) -0.5
Step-by-step explanation:
Starting from standard form ...
ax +by = c
and solving for y, we get the slope-intercept form ...
y = (-a/b)x +c/b
The coefficient of x is the slope: -a/b.
For your equation x+2y=16, the slope is -1/2 = -0.5.
6 less than 8 times a number (x) is equal to 14
Answer:
8x-6=14
Step-by-step explanation:
Whenever you see less next to a number, you know it's gonna be -6. If it said 6 minus 8x though, then you would do 6-8x etc. Hope this helped.
The sixth grade teachers bought food for a reward party. They purchased 64 bags of chips and 80 bottles of water . What is the largest number of students that can be invited to the party so they each get the same amount of chips and water?
Answer:
64
Step-by-step explanation:
Since each student must get the same amount of chips and water, the ratio of the number of chips to water received by each student is 1:1.
Hence, a maximum of 64 students can be invited to the party, as the bags of chips is lower than that of the number of bottles of water, and we take it as a 64.
someone to help me complete this and explain how to do it, please
42x2 y4 − 41xyz3
Answer:
use cymath
Step-by-step explanation:
Darnelle works for a real estate agent. She receives a basic wage of $250 per week plus commission on sales. The rate of commission is variable. For houses up to $300,000 the commission is 0.5%. For houses over $300,000, the commission is an additional 0.25% on the amount over $300 000. How much pay did she receive in the week she sold a house for
a. $280 000
b. $428 000
Answer:
For option A she would receive $1,690. For house B, she would receive $2,070 for a weeks worth of pay.
Step-by-step explanation:
Please mark Brainliest if this helped :)
evaluate the expression when x=3
Answer:
3. 15
6. 4
Step-by-step explanation:
Put 3 instead of x
3. 5x
= 5 × 3
= 15
6. 12 ÷ x
= 12 ÷ 3
= 4
Answer:
When X is 3 it will be
5(3)=15
Then for the second one it will be 12/3
The answer is 4
Hope I helped
Can a set of data having two modes have two points of central tendency
Answer:
The Measure of Central Tendency are
1. Mean
2. Median and Quartiles
3. Mode
4. Geometric Mean
5. Harmonic Mean
→When all the five Measure of Dispersion are Same, it means the two data sets have Identical Variate.
→Now consider the two data sets,
A=3,4,4,5
B=1,4,4,7
Both the Data set have , same mean, median, and Mode,which is equal to 4.
→When you will consider, First three as Measure of central tendency ,then it becomes incorrect statement ,that Data Set are same.
Step-by-step explanation:
A measure of central tendency is a descriptive statistic
The correct response to the question is as follows;
Yes; A data having two modes can have two points of central tendency
The reason a dataset having two modes can have two points of central tendency is as follows:
A dataset having two modes is said to be bimodal
A dataset having three modes is said to be trimodal
A dataset having more than three modes is said to be multimodal
A measure of central tendency is a type of summary statistics that is a
single value representing the center point, or average of a set of data
thereby providing a description of the data by telling the middle value, the
average or the most common value which is the mode
As can be seen from the given example, by having two modes, a bimodal
data set describes a data that has two points of central tendency, thereby
giving a description of the data type, which for example may a collection
of the height of individuals, male and female, that have two most common
height values for each gender
Therefore, the correct response is yes, a dataset having two modes can
have two points of central tendency because the mode is a measure of
central tendency which is a descriptive statistics
Learn more about the measures of central tendency here:
https://brainly.com/question/17762288
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