Answer:
[tex]S_{15}= 50[/tex]
Step-by-step explanation:
Given
[tex]a_7 = \frac{14}{3}[/tex]
[tex]d = -\frac{4}{3}[/tex]
[tex]n = 15[/tex]
Required
The sum of n terms
First, we calculate the first term using:
[tex]a_n = a + (n - 1)d[/tex]
Let [tex]n = 7[/tex]
So, we have:
[tex]a_7 = a + (7 - 1)d[/tex]
[tex]a_7 = a + 6d[/tex]
Substitute [tex]a_7 = \frac{14}{3}[/tex] and [tex]d = -\frac{4}{3}[/tex]
[tex]\frac{14}{3} = a + 6*\frac{-4}{3}[/tex]
[tex]\frac{14}{3} = a -8[/tex]
Collect like terms
[tex]a =\frac{14}{3} +8[/tex]
Take LCM and solve
[tex]a =\frac{14+24}{3}[/tex]
[tex]a =\frac{38}{3}[/tex]
The sum of n terms is then calculated as:
[tex]S_n = \frac{n}{2}(2a + (n - 1)d)[/tex]
Where: [tex]n = 15[/tex]
So, we have:
[tex]S_n = \frac{15}{2}(2*\frac{38}{3} + (15 - 1)*\frac{-4}{3})[/tex]
[tex]S_n = \frac{15}{2}(2*\frac{38}{3} + 14 *\frac{-4}{3})[/tex]
[tex]S_n = \frac{15}{2}(2*\frac{38}{3} - 14 *\frac{4}{3})[/tex]
[tex]S_n = \frac{15}{2}(\frac{2*38}{3} - \frac{14 *4}{3})[/tex]
Take LCM
[tex]S_n = \frac{15}{2}(\frac{2*38-14 *4}{3})[/tex]
[tex]S_n = \frac{15}{2}(\frac{20}{3})[/tex]
Open bracket
[tex]S_n = \frac{15*20}{2*3}[/tex]
[tex]S_n = \frac{300}{6}[/tex]
[tex]S_n = 50[/tex]
Hence,
[tex]S_{15}= 50[/tex]
point a is at (-7 5) and point c is at (5 -1). find the coordinates of point b on line ab such that ab is 5 times as long as bc
Step-by-step explanation:
Let the coordinates of point b be (x,y).
Given the coordinates of a (-7,5) and c(5,-1)
Now according to question
ab = 5bc
using distance formula
[tex]\sqrt{(x+7)^2+(y-5)^2} =5\sqrt{(5-x)^2+(-1-y)^2}[/tex]
Solving we can get
[tex]x=-\frac{-11+\sqrt{-4y^2-10y+25}}{2},\:x=\frac{\sqrt{-4y^2-10y+25}+11}{2}[/tex]'
However, we do need either x or y coordinate of point b to find the other.
Solve the system of equations using the substitution method.
{2x+8y=4x=−3y+5
Enter your answers in the boxes.
x=
y=
Answer:
[tex]x = 14[/tex]
[tex]y = -3[/tex]
Step-by-step explanation:
Given
[tex]2x + 8y =4[/tex]
[tex]x = -3y + 5[/tex]
Required
Solve
Substitute [tex]x = -3y + 5[/tex] in [tex]2x + 8y =4[/tex]
[tex]2(-3y + 5) + 8y =4[/tex]
Open bracket
[tex]-6y + 10 + 8y =4[/tex]
Collect like terms
[tex]-6y + 8y =4-10[/tex]
[tex]2y =-6[/tex]
Divide both sides by 2
[tex]y = -3[/tex]
Substitute [tex]y = -3[/tex] in [tex]x = -3y + 5[/tex]
[tex]x = -3 * -3 + 5[/tex]
[tex]x = 9+ 5[/tex]
[tex]x = 14[/tex]
If v=9i + 12j , find |v|
Answer:
=12j + 9i
Step-by-step explanation:
quickly answer or ill take this question down
PLEASE HELP
A bag hes 10 red marbles, 3 green marbles,
7 yelow marbles, and 5 blue merbles. What is
the probability of crowing a red marble and
then g, blue, marble without replacing the first?
Answer:
[tex]\frac{3}{5}[/tex]
Step-by-step explanation:
Probability is the chance of an event happening. One finds the probability of an event by using the following general formula,
[tex]\frac{desired}{total}[/tex]
In this case, the desired outcome is pulling whether a red or blue marble from the bag, the desired equals the sum of the number of red and blue marbles.
(red) + (blue)
= 10 + 5
= 15
The total number of marbles is the sum of all the number of marbles in the bag.
(red) + green) + (yellow) + (blue)
= 10 + 3 + 7 + 5
= 25
Now substitute these values into the formula to find the probability, then simplify,
[tex]\frac{15}{25}[/tex]
Divide both the numerator and denominator by (5),
[tex]\frac{3}{5}[/tex]
What is the missing number?
The possible answers are -19, 19, 24 and -15
Answer:
15 because it says -(-2) so that means it is negative in something so your answer will be 15
Step-by-step explanation:
If you know how to solve this, Please answer it. Thank You
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
Step-by-step explanation:
f[g(X)]
=f(X+5)
=(x+3)+5
=x+8
Ans: fg(x)=x+8
Step-by-step explanation:
If you know how to solve this, Please answer it. Thank You
The first one to answer the question right, will get Brainlist!
I PROMISE!!!!!
. If you roll two dice, what is the probability of rolling a not rolling a
double with a sum greater than 7? Give answer as a fraction in simplest
form. *
which of the following is not a solution of -2 is less than or equal to x less than 5
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]-2 \le x < 5[/tex]
Required
Which is not a solution
The options are not given. So, I will list out the solutions, instead.
We have:
[tex]-2 \le x < 5[/tex]
This implies that: x starts from -2 and ends at 4
[tex]x = \{-2,-1,0,1,2,3,4\}[/tex]
Any number outside the above is not a solution of [tex]-2 \le x < 5[/tex]
Can someone please help, ty!
Will mark brainliest!
Answer:
I think it is -31
Step-by-step explanation:
-4(5) -11 = -31
Answer:
-31
Step-by-step explanation:
First you substitute in 5 for all of the x in the equation, making
f(5) = -4(5) - 11
Then you just have to simplify from there.
f(5) = -20 - 11
f(5) = -31
Need help with the answer??
angle B is teh answer
100% sure !
Plz mark me brainliest
10 m
10 m
Please help quick :(
I guess you need to find the area :
Area of the figure = Square area + half of
circle area
A = ( length )^2 + 1/2 × pie × ( radius)^2
A = ( 10 )^2 + 1/2 × pie × ( 10/2 )^2
A = 100 + 1/2 × pie × 25
A = 100 + 12.5 pie
____________________________
If pie = 3 : | If pie = 3.14 :
|
A = 100 + 12.5 × 3 | A = 100 + 12.5 × 3.14
|
A = 100 + 37.5 | A = 100 + 39.25
|
A = 137.5 m^2 | A = 139.25 m^2
The table represents the balance of Fernando’s loan, y, over a period several months, x. He used technology to create the scatter plot shown and determine the best fit equation to model the data: y = -440.91x + 22,060.70. Determine how long it will take to reach the given balances.
Answer:
The balance of the loan will be approximately $15,000. - Month 16
The balance of the loan will reach $0. - Month 50
some please help i’ll give brainliest
Answer:
Statement Reason
∠1 = ∠2 Given
AP = BP Given
∠APD = ∠BPC Vertical angles
Therefore, by ASA , ΔAPD ≅ ΔBPC
WILL GIVE BRAINLIST
MATH
CONVERT EACH MEASUREMENT
25FT TO YARDS
SHOW STEPS ALL HOW YOU GOT THE ANSWER
Answer:
8.333... Yards.
Step-by-step explanation:
To convert feet to yards, divide the feet by 3.
[tex]\frac{25}{3} = \frac{25}{3}/8.333...[/tex]
To check work
Multiply 8.333... by 3.
8.333 · 3 = 24.999...
It Is Not Exactly 25 Because The 3 Is Infinite But It Is Enough To Prove Your Answer.
TT is an unending decimal. Find the
circumference of the circle below using
exact TT.
C = [?]TT
8
c=
2r
Answer:
C = 16 pi
Step-by-step explanation:
The circumference is given by
C = 2*pi*r
C = 2* pi*8
C = 16 pi
Answer:
Solution given:
radius [r]=8
Now
we have
circumference of circle=2πr=2*8*π=16π
16 is a required answer.
There are 6 shipping boxes that each ocontain 36 lbs of merchandise from a toy store.
Before the boxes are loaded onto a delivery truck, the same amount of additional
merchandise is added to each box. The total weight of all of the boxes is 258 pounds.
How much additional weight was added to each box?
Answer:
7kg
Step-by-step explanation:
258 / 36 = 7.16
the nearest ten, 7.20
Mark me brianest
Thare are 2 yellow 3 pink and 5 blue. What is the possibility of drawing two pink marbles if the first one is placed back in the bag before the second draw?
Answer:
3/10
Step-by-step explanation:
find the radian measure of the angle 55°
Answer:
[tex]55 degree= \frac{\pi }{180}\times55=\frac{11\pi }{36} =0.9599 radians[/tex]
Step-by-step explanation:
[tex]180 degree= \pi radian\\1 degree= \frac{\pi }{180}\\55 degree= \frac{\pi }{180}\times55=\frac{11\pi }{36} =0.9599 radians[/tex]
Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Assume that the distributions for each state are normal and that all variances are equal.
Arkansas 4.8 4.9 5.0 5.4 5.4 5.4 5.6 5.6 5.6 5.9 6.0 6.1
California. 1.5 3.7 4.0 4.5 4.9 5.1 5.3 5.4 5.4 5.5 5.6 5.6
Texas. 5.6 5.8 6.6 6.9. 6.9 6.9 7.1 7.3 7.5 7.6 7.7 7.7
Answer:
Texas Texas Texas is I think right
No, the claim that the three samples are from populations with the same mean is not correct and this can be determined by using the given data.
Given :
The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level.The Hypothesis test is given below:
Null Hypothesis: [tex]H_0:\mu_1=\mu_2=\mu_3[/tex]
Alternative Hypothesis: [tex]H_a:\mu_1\neq \mu_2\neq \mu_3[/tex]
For the F-test, the test statistics is given by:
[tex]F = \dfrac{MS_{\rm{between}}}{MS_{\rm{within}}}[/tex]
Now, substitute the values of known terms in the above expression.
[tex]F = \dfrac{15.8252}{0.6896}[/tex]
[tex]F = 22.95[/tex]
So, the p-value regarding the value of F is:
[tex]P-value=P(F>22.95)[/tex]
[tex]P-value = 1.0.9999[/tex]
[tex]P-value = 0.0001[/tex]
The Null Hypothesis is rejected because P-value is less than the significance value.
For more information, refer to the link given below:
https://brainly.com/question/10758924
solve and explain your reasoning (x+3)=-6
Answer:
(x+3)=-6
x=-6-3
x=-9
Step-by-step explanation:
Hope it helps!
When side changes positive changes into negative.
how many different California license plates can be made if there has to be one number followed by three letters followed by three more numbers
Answer:
175,760,000 different California license plates can be made.
Step-by-step explanation:
Possible outcomes for each number of letter:
10 numbers(from 0 to 9) and 26 letters.
Format of the plate:
Number - letter - letter - letter - number - number - number
The numbers of possible outcomes are:
10 - 26 - 26 - 26 - 10 - 10 -10
How many different plates?
We multiply these values. So
10*26*26*26*10*10*10 = 175,760,000
175,760,000 different California license plates can be made.
What is the distance between (-9, -6) and (-2,-2)?
Choose 1 answer:
I NEED HELP I DONT UNDERSTAND!!
Answer:
Step-by-step explanation:
there is a formula for finding distance,
distance = sqrt [ ( x2-x1)^2 + (y2-y1)^2 ]
where point P1 = (-9.-6)
in the form of (x1,y1)
and point P2 = (-2,-2)
in the form of (x2,y2)
then
distance = sqrt [ (-2-(-9))^2 + (-2-(-6))^2 ]
distance = sqrt [ (-2+9)^2 + (-2+6)^2 ]
distance = sqrt [ [tex]7^{2}[/tex] + [tex]4^{2}[/tex] ]
distance = [tex]\sqrt{65}[/tex]
you can leave it in the form of [tex]\sqrt{65}[/tex] because that's the most accurate , but also can make a close approximation with 8.062257748
That's all the places my calculators goes out to, the numbers continue thou.
PLEASE HELP Which is the least common multiple of 18, 36, and 45 A 90 B 180 C 450 D 900
Find the equilibrium solutions. Enter your answer as a list of ordered pairs (A,L), where A is the number of aphids and L the number of ladybugs. For example, if you found three equilibrium solutions, one with 100 aphids and 10 ladybugs, one with 200 aphids and 20 ladybugs, and one with 300 aphids and 30 ladybugs, you would enter (100,10),(200,20),(300,30). Do not round fractional answers to the nearest integer.
The Required equilibrium solution are (400, 40) (500, 50) (600,60).
To find the equilibrium solutions and to enter answer as a list of ordered pairs (A,L), where A is the number of aphids and L the number of ladybugs.
equation is the relationship between variable and represented as y =ax+b is example of polynomial equation.
since the equilibrium solution given by the expression
L = 10A
where A is the number of aphids and L the number of ladybugs.
And ordered pairs with equilibrium solution of one with 400 aphids and 40 ladybugs, one with 500 aphids and 60 ladybugs and one with 600 aphids and 60 ladybugs are (400, 40) (500, 50) (600,60).
Thus, The Required equilibrium solution are (400, 40) (500, 50) (600,60).
Learn more about equation here:
brainly.com/question/10413253
#SPJ2
4 1/2 divied 1 5/8 please help
Answer:
36/13 (2 10/13)
Step-by-step explanation:
Convert 4 1/2 into an improper fraction: 4 1/2 = 9/2
Convert 1 5/8 to an improper fraction : 1 5/8 = 13/8
Divide: Dividing 2 fractions is the same as multiplying the first fraction by the reciprocal of the second value (the numerator becomes the denominator and the denominator becomes the numerator). 13/8 is 8/13 as a reciprocal. Next multiply the 2 numerators. 9 x 8 = 72. Then multiply the denominators. 2 x 13 = 26. Which gives 72/26. Divide both numbers by 2 which gives 36/13. 36/13 as a mixed number is 2 10/13
Answer:
36/13 (2 10/13)
Step-by-step explanation:
:)
Juan drank 3 quarts of water. Alfred drank 8 quarts. How many cups of water did they drink altogether?(no links will get brainliest)
Answer: 44 Us Cups
Step-by-step explanation:
In a survey based on a random sample of high school seniors at Roosevelt High School,
60% of those surveyed said they do more than 2.5 hours of homework per day. Based on this
data which of the following conclusions are valid? (Choose 2)
A) Less than 60% of all seniors at Roosevelt do more than 2.5 hours of homework per day.
B) About 60% of seniors at Roosevelt do more than 2.5 hours of homework per day.
C) About 40% of all seniors at Roosevelt do less than 2.5 hours of homework per day.
D) 40% of seniors at Whitney do no homework.
Which type of car had the largest range in monthly sales? Explain how you came up with your answer.
Answer:
Can you please attach a picture of the question so I can help?
Step-by-step explanation:
Someone please Help!