Answer:
B
Step-by-step explanation:
before finding the sum we require to find first term and common difference.
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₀ = - 5 and a₁₅ = - 7 [tex]\frac{1}{2}[/tex] = - 7.5 then
a₁ + 9d = - 5 → (1)
a₁ + 14d = - 7.5 → (2)
subtract (1) from (2) term by term to eliminate a₁
0 + 5d = - 2.5
5d = - 2.5 ( divide both sides by 5 )
d = - 0.5
substitute d = - 0.5 into (1) and solve for a₁
a₁ + 9(- 0.5) = - 5
a₁ - 4.5 = - 5 ( add 4.5 to both sides )
a₁ = - 0.5
the sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
here a₁ = - 0.5 and d = - 0.5 , then
S₂₀ = [tex]\frac{20}{2}[/tex] [ (2 × - 0.5) + (19 × - 0.5) ]
= 10 (- 1 -9.5)
= 10 × - 10.5
= - 105
Hi! So I am stuck on three problems right now, can you Please help me?number 1, says "What is the cosine ratio of
The cosine ratio is given by the following formula:
[tex]\cos (Z)=\frac{\text{adjacent leg}}{hypotenuse}[/tex]The adjacent leg of angle Z is side ZY=12 and the hypotenuse of the triangle is the side XZ=20, thus the cosine ratio of Z is:
[tex]\cos (Z)=\frac{12}{20}[/tex]Evaluate: -6 × (-4)
= Enter your next step here
() TO
Answer:
24
Step-by-step explanation:
-6*(-4)
The negative signs cancel:
6*4
24
Convert 450 liters into fluid ounces. Round your answer to the nearest whole number.
Answer:15216.31 Fluid Ounces
Step-by-step explanation:
a list of 1111 positive integers has a mean of 1010, a median of 99 and a unique mode of 88 what is the largest possible value of an integer in the list?
The largest possible value in the list is 35.
What is mean, median and mode?
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.
Given: There is a list of 11 positive integers.
Has a mean of 10, a median of 9 and a unique mode of 8.
Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).
If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.
The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.
The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.
Therefore, the largest possible value of an integer in the list is, 35.
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535(-8) ??? What is the answer
Answer: the answer is -4280
Step-by-step explanation:
Solve 4(3m + 1) − 2m = −16. m = −0.83 m equals negative 20 over 12 m equals negative 17 over 10 m = −2.
The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2
How to determine the solution to the equation?The equation is given as
4(3m + 1) − 2m = −16
Open the brackets in the above equation
So, we have
12m + 4 − 2m = −16
Collect the like terms in the above equation
So, we have the following equation
12m − 2m = −16 -4
Evaluate the like terms in the above equation
So, we have the following equation
10m = −20
Divide both sides by 10
m = -2
Hence, the soluton is m = -2
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what is the correct ascending order for these numbers1.525/848%
Given the set of numbers:
[tex]\text{ 1.52, 5/8 and 48\%}[/tex]To be able to determine their correct ascending order, we must first make all the numbers into similar forms.
Let's convert a
find the remainder when 2 to the 100th power is divided by 5. explain your work
When 2 to the power of hundred is divided by 5 it show s remainder of 1
How to calculate the value of 2 to the 100th power divided by 52 to the 100th power is solved as follows
2 ^ 100 = 1.2676506 * 10^30
This is solved using a calculator and the solution means that
2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2 (2 multiplying itself till the number of 2's are up to 100)
This gives the value = 1.2676506 * 10^30
Division of the 2^100, by 5
2^100 / 5
2^1 / 5 remainder =2
2^2 / 5 remainder = 4
2^3 / 5 remainder = 3
2^4 / 5 remainder = 1
2^5 / 5 remainder = 2
2^6 / 5 remainder = 4
2^7 / 5 remainder = 3
2^8 / 5 remainder = 1
2^9 / 5 remainder = 2
2^10 / 5 remainder = 4
2^11 / 5 remainder = 3
It can be seen that it generates a pattern which is
1243The pattern counts in 4's. If we follow the pattern and count to 2^30
= 100 / 4
= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1
This is to say
2^97 / 5 remainder = 2
2^98 / 5 remainder = 4
2^99 / 5 remainder = 3
2^100 / 5 remainder = 1
Hence 2^100 divided by 5 will give a remainder of 1
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gmm
2
#x²
13
O
1
2
ABC
3
5x+2
3x + 40
Find the measure of angle 2.
label optional
1
2 3 4
5 6 78 9
XY Z<
7
VI
Xi
+
8
=
V
Answer: [tex]\angle 2=83^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]5x+2=3x+40\\\\2x=38\\\\x=19[/tex]
This means that [tex]5x+2=3x+40=97[/tex].
Since [tex]\angle 2[/tex] and the [tex]97^{\circ}[/tex] form a linear pair, they add to 180 degrees. So, [tex]\angle 2=83^{\circ}[/tex]
The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011$5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year (d) Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of P0 and d to the nearest dollar.Pt= (e) Using the regression model, predict the cost of insurance in 2030.$ (f) According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year
Part (a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).
we have the ordered pairs
(1999, 2,196) -------> (0,2,196)
(2019,7,186) -------> (20,7,196)
Find out the slope
where
t -----> is the number of years since 1999
P ----> the cost
m=(7,196-2,196)/(20-0)
m=5,000/20
m=250
Find the equation of the linear model in slope-intercept form
P=mt+b
we have
m=250
point (0,2,196)
substitute and solve for b
2,196=250(0)+b
b=2,196
therefore
P=250t+2,196
Part b
Using this linear model, predict the cost of insurance in 2030
For t=2030=2030-1999=31 years
substitute
P=250(31)+2,196
P=$9,946
Part c
According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute in the linear model
12,000=250t+2,196
250t=12,000-2,196
250t=9,804
t=39 years
therefore
1999+39=year 2038
Part d
Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of
P0 and d to the nearest dollar
using a regression calculator
the equation is
ŷ = 239.15065X + 2406.39827
y=239x+2,406
Part e
Using the regression model, predict the cost of insurance in 2030
For t=2030-1999=31 years
P=239(31)+2,406
P=$9,815
Part f
According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute
12,000=239x+2,406
239x=12,000-2,406
239x=9,594
t=40 years
year=1999+40=2039
The relationship between time and the number of laps is not proportional across all swimmers. which two swimmers swam at the same rate (had time and laps in the same proportion)?
Answer: Undefined
Step-by-step explanation:
There is not enough information to complete the task.
Answer:
Jonathan and Seth
Step-by-step explanation:
multiple the laps by 2 youll get the minutes
A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
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In the diagram shown, lines MN and PQ intersect at R. If ZNRS is a right angle and the measure of ZMRQ is 1420, then what is the measure of ZPRS? Show or explain how you arrive at your answer.
The measure of the angle PRS is given as follows:
m<PRS = 45º.
Measure of angle PRSAs stated in this problem, these following angles are given:
<MRQ = 142º.m<NRS = 90º.MRQ and and QRN form a ray, hence they are supplementary angles.
For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:
142 + x = 180
x = 180 - 142
x = 38º.
The entire diagram forms an angle of 360º, hence:
142 + 38 + 90 + m<MRS = 360º.
270 + m<MRS = 360º
m<MRS = 90º.
The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:
The diagram is given by the image at the end of the answer.
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In 3 hours, 5 people can paint a hall with the area of 750 ft 2. How long would it take for 2 people to paint the hall with the same rate of speed?
ANSWER:
STEP-BY-STEP EXPLANATION:
In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people
[tex]\frac{5}{3}=\frac{2}{x}[/tex]solving for x:
[tex]undefined[/tex]Assume that blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8 if 100 people are randomly selected find the probability that their mean blood pressure will be less than 127
According to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.
Given :
Blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8.
The formula of z-score is used to determine the probability that their mean blood pressure will be less than 127. The formula of z score is given by:
[tex]z = \frac{\frac{x - m}{\alpha } }{\sqrt{n} }[/tex]
Now, substitute the values of known terms in the above equation.
[tex]z = \frac{\frac{127 - 125}{8} }{\sqrt{100} }[/tex]
[tex]z = \frac{\frac{2}{8} }{10} }[/tex]
Further, simplify the above expression.
z = 2.5
P(z < 2.5) = 0.9938
So, the probability is 99.38%.
Therefore, according to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.
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Use the information provided to answer questions 2 - 5. Leah would like to earn at least $ 120 per month. She babysits for $ 5 per hour and works at an ice cream shop for $ 8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;
[tex]\begin{gathered} 5x+8y\ge120---(1) \\ x+y\leq20---(2) \\ Solve\text{ these on a graph and you'll have;} \end{gathered}[/tex]The red graph represents x + y =<20
The blue graph represents 5x +8y =>120
Observe that the region where the blue and red are "mixed" together represent the solution region.
Option A (4, 15)
Option B (5, 12) and
Option C (10, 9) are possible solutions
which classification describes the following system of equations x=5 y=6 -x-y+z=0
?
A. inconsistent and dependent
B. consistent and dependent
C. consistent and independent
D. inconsistent and independent
The system of equations has one solution, so it is consistent and independent, the correct option is C.
What is the classification of the system of equations?
Here we have the system of equations:
x = 5
y = 6
-x - y + z = 0
By replacing the first and second equations into the third one, we get:
-5 - 6 + z = 0
-11 + z = 0
z = 11
So the solution is (5, 6, 11)
So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).
Then the correct option is C.
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Shannon started a savings account by putting
in $25. On the 1st week she deposited $15
and plans to continue depositing $15 each
week.
Given the graph, description or sequence values create an explicit equation
Which angle pair is NOT an example of Corresponding Angles?
angle 2 and angle 10
angle 1 and angle 11
angle 13 and angle 15
angle 8 and angle 16
Answer:
Step-by-step explanation:
So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!
A circle passes through (-2, 6) , (2, 8) , and (5, -1) Using the general form of a circle and the points above, fill in missing numbers to create the system of equations. (-2, 6) creates D + E + 1F = (2, 8) creates D + E + 1F = (5, -1) creates D + E + 1F = Solve the system of equations that you created, and write the equation for the circle by filling in the values for D, E, and F.
The equation of the circle passing through points (-2, 6) , (2, 8) , and (5, -1) is given as follows:
(x - 2)² + (y - 3)² = 25.
Equation of a circleThe equation of a circle with center (x*, y*) and radius r is given according to the following rule:
(x - x*)² + (y - y*)² = r².
The circle passes through point (-2,6), hence the first equation of the system is given as follows:
(-2 - x*) + (6 - y*)² = r².
r² = x*² + 4x* + 4 + y*² - 12y* + 36.
The circle also passes through point (2,8), hence the second equation of the system is given as follows:
(2 - x*) + (8 - y*)² = r².
r² = x*² - 4x* + 4 + y*² - 16y* + 64.
The final point is point (5,-1), meaning that the third equation is:
(5 - x*) + (-1 - y*)² = r².
r² = x*² - 10x* + 25 + y*² + 2y* + 1.
The system of equations to find the coordinates of the center and the radius is given as follows:
x*² + y*² + 4x* - 12y* + 40 - r² = 0.x*² + y*² - 4x* - 16y* + 68 - r² = 0.x*² + y*² - 10x* + 2y* + 26 - r² = 0.The solution to the system is given as follows:
x* = 2, y* = 3, r² = 25.
Hence the equation of the circle is:
(x - 2)² + (y - 3)² = 25.
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A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total.What do x and y represent?
Answer:
x = no of people in a small car
y = number of people in a van
Explanation:
The relevant information in the problem is that the total number of people is 27 and that the small car costs $10 and the large van $15.
If we call x the number of people in a small car, and y the number in the large van then the following equations can be obtained
[tex]\begin{gathered} x+y=27 \\ 10x+15y=80 \end{gathered}[/tex]The first equation simply says that the total number of people is 27 and the second equation says that the total cost of the trip is $80.
Hence,
x = no of people in a small car
y = number of people in a van
Simplify: 2.4 x 10−4 0.00024 0.000024 −0.000024 −2.4000
Answer:
0.00067
Step-by-step explanation:
You always want the period to the right of the first number meaning you’ll start from there counting backwards because it is negative.
How many solutions does the following system of equations have?
2x - Y=3
-4x + 2y=5
Answer:
no solutions
Step-by-step explanation:
2x - y = 3 → (1)
- 4x + 2y = 5 → (2)
multiply (1) by 2 and add to (2)
4x - 2y = 6 → (3)
add (2) and (3) term by term
0 + 0 = 11
0 = 11 ← not possible
this indicates the system has no solution
Michael thinks of a number she multiplies the number by 100÷8 then add six. 50 the answer is 1206.5 what was the starting number
The starting number of Michael's thought is 96
How to determine the starting number?From the question, the given parameters are:
Multiplies a number by 100÷8Add 6.50 The answer is 1206.5The above sequence of statements can be represented as
x * (100÷8) + 6.50 = 1206.5
Where x represents the number
So, we have
x * (100÷8) + 6.50 = 1206.5
Evaluate the quotient
x * 12.5 + 6.50 = 1206.5
Subtract 6.50 from both sides
x * 12.5 = 1200
Divide both sides by 12.5
x = 96
Hence, the initial number is 96
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A secant line intersects the curve g(x)=-x² +8 at x = 1 and x = 1+h. What expression is equal to the slope of this secant?
The slope of the line secant to the curve g(x) = - x² + 8 is equal to m = - (2 + h).
How to derive the equation of the slope of a line secant to a curve
A secant line is a line that passes through a curve in two places, the formula for the slope of the secant line is described below:
m = [f(a + h) - f(a)] / [(a + h) - a]
m = [f(a + h) - f(a)] / h
If we know that f(x) = - x² + 8 and a = 1, then the equation for the slope of the secant line is:
m = {[- (1 + h)² + 8] - (-1² + 8)} / h
m = (- 1² - 2 · h - h² + 8 + 1² - 8) / h
m = (- 2 · h - h²) / h
m = - 2 - h
m = - (2 + h)
The slope of the line is equal to m = - (2 + h).
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I need help figuring out the answer, I’m very much confused
My first step is to draw a picture
We know that the length is 2 times the width
L = 2w
We are given a width of 4.6 yards
L = 2(4.6) = 9.2 yards
We can find the area by using the formula
A = l*w
A = 9.2 * 4.6
A =42.32 yd^2
At a restaurant, Elena wants to leave a tip that is 15% of the bill B plus $1. Which linear model best describes the total T?
Answer:
The total T can be described as
[tex]T = (B+(B*.15))+1[/tex]
The sum of the angle measures of a polygon with s sides is 2,340 degrees. Find s.thank you ! :)
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The sum of interior angles of a polygon is:
[tex]\begin{gathered} (s\text{ -2 \rparen x 180}^0=\text{ 2340}^0\text{ , where s = number of sides} \\ Divide\text{ both sides by 180}^0,\text{ we have that:} \\ s\text{ - 2 = 13} \\ s\text{ = 13 + 2} \\ s\text{ = 15} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]s\text{ = 15}[/tex]solve 2/3x + 4 = 5/6x by eliminating the fraction.
The value of x in the given equation is 24.
Given equation:
(2/3)x + 4 = (5/6)x
We have to find the value of x by eliminating the fraction.
Fraction
Fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
LCM (3,6) = 6
Multiplying the whole equation by 6, we get:-
(2/3)x*6 + 4*6 = (5/6)x*6
4x + 24 = 5x
5x - 4x = 24
x = 24
Hence, the value of x is 24.
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The question is in the image. Answer question 13 only.
We need to convert 40 degrees to radians:
Then, we need to use the next equation:
[tex]40\ast\frac{\pi}{180}[/tex]Solve it:
[tex]40\ast\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Hence, 40 degrees is equal to 2/9π radians.