Answer:
532
Step-by-step explanation:
Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac{n}{2}(a_1+a_n)}[/tex]
Where:
aₙ is the nth term.a₁ is the first term.n is the position of the term.Given terms:
[tex]a_1=12[/tex][tex]a_n=64[/tex]Substitute the given terms into the formula to create an equation for the nth term:
[tex]\implies S_n=\dfrac{n}{2}(12+64)[/tex]
[tex]\implies S_n=\dfrac{n}{2}(76)[/tex]
[tex]\implies S_n=38n[/tex]
To find S₁₄, substitute n = 14 into the found equation:
[tex]\begin{aligned}n=14 \implies S_{14}&=38(14)\\ & = 532\end{aligned}[/tex]
v=u+ at
u= 2 a=-5
Work out the value of v.
Substitution
Tynel
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Answer:
v=-0.5
Step-by-step explanation:
v=2+(-5×0.5)
v=2-2.5
v=-0.5
place the numbers in order from least to greatest…PLS HELP!
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
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Step-by-step explanation:
Milly and Lotte are knitting scarves. For every 6 cm that Milly knits, Lotte knits 11 cm. If Milly knits a scarf that is 1.2 m long, how long will Lotte's scarf be in metres?
If Milly knits a scarf that is 1.2 m long then Lotte's scarf be 2.20 in metres.
We will use unitary method to solve this problem.
We know, Milly and Lotte are knitting scarves.
For every 6 cm that Milly knits, Lotte knits 11 cm. This can also be written as,
6 cm Milly knits ----------------> 11 cm Lotte knits
1 cm Milly knits ----------------> (11/6 ) cm Lotte knits
We know, 1m = 100cm. So, we can write
120 cm Milly knits ----------------> ( 11/6 ) × 120 cm Lotte knits
120 cm Milly knits ----------------> 220 cm Lotte knits
120 cm Milly knits ----------------> 2.20 m Lotte knits
Thus, we can conclude that if Milly knits a scarf that is 1.2 m long then Lotte knits 2.20 metres scarf .
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A building company employs 3 labourers 12 joiners 8 electrician 4 plumbers. For a job, the company needs one of each type of worker in how may ways can the company choose four workers
The number of ways that the company can choose four workers is 40920 ways.
How to calculate the number?From the information, the building company employs 3 laborers 12 joiners 8 electrician 4 plumbers. The total number of workers will be:
= 3 + 12 + 8 + 4
= 27 workers
It should be noted that combination will be used to choose the 4 workers. This is illustrated as
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
where n = 33
r = 4
ⁿCr = n! / ((n – r)! r!)
³³C₄ = 33! / (33 - 4)! 4!
= 33! / 29! 4!
= 33 × 32 × 31 × 30 / 4 × 3 × 2
= 40920 ways
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The diagram shows a rhombus inside a regular pentagon.
Work out the size of angle x.
The size of the angle x in the pentagon is 36 degrees.
How to find the angles in a pentagon?A regular pentagon is a polygon with five sides. The angles of a regular polygon is equal to each other.
Therefore,
the sum of angles in a regular pentagon = 540 degrees.
Each angle in a regular pentagon is 540 / 5 = 108 degrees.
The rhombus is inside the pentagon. Opposite angles in a rhombus are equal.
Therefore, the sum of interior angles of a rhombus adds up to 360 degrees
Hence,
108 + 108 + 2y = 360
where
y is the angle of the rhombus on the x variable.
Therefore,
2y = 360 - 216
2y = 144
y = 144 / 2
y = 72°
Therefore,
x = 108 - 72
x = 36 degrees
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I really need help on this, tyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:3
Step-by-step explanation: 105 divided by 3 is 35 there are 3 groups so 1 ten would go in each group.
The value of [tex]\tan 1^{\circ}\tan 2^{\circ}+\tan 2^{\circ}\tan 3^{\circ}+\tan 3^{\circ}\tan 4^{\circ}+\cdots+\tan 88^{\circ}\tan 89^{\circ}[/tex] can be expressed in the form [tex]\cot^2 1^{\circ}-n[/tex]. What is the value of [tex]n[/tex]?
Answer:
n = 89Step-by-step explanation:
Use of identitiestan (x - y) = (tan x - tan y)/(tan x tan y + 1) 1/tan x = cot xtan (90 - x) = cot xtan (- x) = - tan xConvert the first one above:
tan x tan y = (tan x - tan y) / tan (x - y) - 1Apply this to each term of the given expression to get:
tan1°tan2° + tan2°tan3° + ... + tan88°tan89° = (tan1° - tan2°)/(tan-1°) - 1 + (tan2° - tan3°)/(tan-1°) - 1 + ... + (tan88° - tan89°)/(tan-1°) - 1 = (tan1° - tan2° + tan2° - tan3° + ... + tan88° - tan89°)/(tan-1°) - 88 = (tan1° - tan89°)/(tan-1°) - 88 = tan1°/ (tan-1°) - tan89°/tan-1° - 88 = - 1 - cot1*(- cot1°) - 88 = cot² 1° - 89The value of n is 89.
Answer:
n = 89
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]
Rewrite the tan double angle identity to isolate tanAtanB:
[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]
[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]
Therefore:
[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]
[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]
[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]
[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]
[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]
[tex]\implies \cot^21^{\circ}-89[/tex]
Therefore, n = 89.
Given the function f(x)=x^2+7x+6f(x)=x
2 +7x+6, determine the average rate of change of the function over the interval −4≤x≤−1.
The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2
What is the average rate of change the function?The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.
It is expressed as;
Given the data in the question;
f( x ) = x² + 7x + 6Interval: −4 ≤ x ≤ −1 ⇒ [-4.-1]Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )
Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )
Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )
Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )
Average rate of change = ( 0 + 6 ) / ( 3 )
Average rate of change = 6 / 3
Average rate of change = 2
Therefore, the average rate of change of the function is 2.
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ad and solve the problems.
Dan builds identical model cars and sells them
online. He records the number of models he
completes every couple of hours. The graph shows
Dan's data. Choose two pairs of points on the line
and calculate the slopes between them. Is Dan's
productivity constant? Explain.
The slope between the two pair of points is 3/2. Yes, Dan's productivity is constant.
Number of model are represented on y axis and the hours are represent on x axis.
As we can observe,
One pair of points on the graph is (4,6) and (2,3) and the other pair of points is (6,9) and (0,0)
The slope m between any two points (a,b) and (c,d) can be calculated as,
m = (d-b)/(c-a)
The two points we have are (4,6) and (2,3), so the slope M between them is,
M = (3-6)/(2-4)
M = -3/-2
M = 3/2.
And the slope M' between other two point (6,9) and (0,0) is,
M' = (9-0)/(6-0)
M' = 9/6
M' = 3/2.
As we can see, the slope is same. The slope represents the ratio of number of models and hours. We can conclude that Dan's productivity is constant.
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Solve this inequality
-3 < x + 5 < 10
Answer:
-8 < x < 5
Step-by-step explanation:
-3 < x + 5 < 10
=> Minus 5 in all sides
=> -8 < x < 5
7+4x= -5 helppppppppppppp
what is the answer to the absolute value equation? |5x-3|=-2
Answer:
No answer
Step-by-step explanation:
An absolute cannot equal a negative number
Given: <1 and <2 are complementary; <1=<4 prove: <3 and <4 are complementary
Statements:
1. <1 and <2 are complementary
2. m<1 + m<2= 90°
3. <1=~<4
4. m<1 = m<4
5. <2 =~<3
6. m<2 = m<3
7. m<4 + m<3 = 90°
8. <3 and <4 are complementary
Please list reasons (geometry)
Answer:
<3 and <4 are complementary
4(a-c)+2(a-b)
x(x-y)+y(y-x)
Answer:
hi how are you . i cant find the answer youre looking for
Answer:
1) 6 ( a - b )
2) x² - 2xy + y²
Step-by-step explanation:
1) 4 ( a - c ) + 2 ( a - b )
First, solve the brackets.
4a - 4c + 2a - 2b
Combine like terms.
6a - 6b
Take the common factor out.
6 ( a - b )
2) x ( x - y ) + y ( y - x )
First, solve the brackets
x² - xy + y² - xy
Combine like terms.
x² - 2xy + y²
C(0)=0
Let c(t) be the number of customers in a restaurant t hours after 8am Explain the meaning of each statement please help
The meaning of each statement is shown below.
Step-by-step explanation:
Assume that the given statements are
(a) c(0)=0
(b) c(3)=c(8)
(c) c(n)=29
(d) c(13)<c(12)
Let c(t) be the number of customers in a restaurant t hours after 8 A.M.
We need to find the meaning of each given statement.
(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.
(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).
(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.
(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.)
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HELP PLEASEEEE
Suppose that y varies directly with x and that y=84
when x=7
. What is the value of x when y=108
?
Suppose that y varies directly with x and that y=84 when x=7. What is the value of x when y=108?
when y=84 and when x=7, x to y in proportion is 1:12. Keeping the ratio of x to y at 1 to 12, when y = 108, x = 9.
-|4-7|+3 whats the answer to this question?
The answer to the question -|4-7|+3 is 0 .
The Absolute Value of x denoted by |x| is the non negative value of , without regarding its sign .
For example the absolute value of -3 will be |-3| = 3 .
and absolute value of |-2| = 2 .
In the question ,
it is given that
the question is -|4-7|+3 .
and we have to find the answer of -|4-7|+3 .
let the answer be "y"
So , y = -|4-7|+3
= -|-3| + 3
On further simplification ,
we get ,
= -(3) + 3 because |-3| = 3
= -3 +3
= 0
Therefore , The answer to -|4-7|+3 is 0 .
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An angle measures 4pi/5 radians. What is this angle's measure in degrees?
4π/ 5 radians = ?
Then if
π radians= 180°
(4/5)•π radians = 180• 4/5
. = 144
Answer is
4pi/5 radians = 144 degrees
jeremy sells strawberries 5 pounds for $7.50. what is the cost for 1 pound of strawberries?
The average U.S. home uses about 11,000 kilowatt-hours (kWh) of electricity per year. Appliances and refrigeration account for about 17% of this total. If electricity costs $0.16 per kWh in a particular area, how much would the average U.S. homeowner pay annually to run appliances and refrigeration?
First we need to find the 17% of 11,000
solve for p 3w+4pw=a
if l //m and m<4=5x-42 and m<5=-x+82, what is the m<5
The measure of <5 is 47
what is parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance away from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
m<4=5x-42
and m<5=-x+82
as, <4 and <5 are in co- interior angle
<4 + <5 = 180
5x - 42 + (-x + 82) = 180
5x -42 - x + 82= 180
4x +40 = 180
4x = 140
x= 140/4
x= 35
Hence, the measure of <5 = -x+ 82 = -35 + 82 = 47
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À La Mode Ice Cream Parlor uses the function f(x) to calculate its profits. When the parlor sells x cones, it makes f(x) dollars in profit. What does f(50)=85 tell you?
f is the given profit function whose input is number of cones and output is profit, f(50)=80 tells that $80 profit is made by selling 50 cones of ice cream.
What is function?A function is a relation that assigns each element of a set a unique element of another set.
f(x) denotes that function f works on the input values x and give output f(x).
If f is a function and f(x) = x+2, then if we have to check x= 1 , then
f(1) = 1+2 = 3 is the value of the function f at x=1
A La Mode Ice Cream Parlor uses a function f as profit function
The input x is the number of cones it sells and output is profit
f(50) = 85
⇒x = 50 and f(50) = 85
It means that when the parlor sells x = 50 cones , it makes profit $ f(50) = 85
or On selling 50 cones the profit made is $80
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The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sells a certain washer with an outside circumference of 4 centimeters. The company has decided that a washer whose actual circumference is in the interval 3.9≤C≤4.1 centimeters is acceptable. Use a compound inequality and find the corresponding interval for diameters of these washers.
1.242 ≤ d ≤ 1.305 is the corresponding interval for the diameter of the washer.
Given that,
Company A makes and sells a washer having a 4-centimeter outer radius. The corporation has decided on a washer with an actual radius in the range of 3.9 ≤ C ≤ 4.1.
Inequality is defined as the connection of an equation having the symbol ( ≤, ≥, <, >) in place of the assignment operator.
Here,
C = 3.14d
Given inequality,
3.9 ≤ C ≤ 4.1
3.9 ≤ 3.14d ≤ 4.1
dividing both sides of the inequality by 3.14,
1.242 ≤ d ≤ 1.305
As a result, the needed matching spacing for the washer's diameter is 1.242 ≤ d ≤ 1.305.
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if apples cost $3 per pound and bananas cost $5 per pound, how many whole pounds of apples should bill buy if he wants to maximize his utility and he has $31 to spend?
I f Bill wants to maximize his utility while spending $31 on apple. Bill van buy 10 whole pounds of Apples
How to find the number of whole pounds of apples bill can buy if he has $31 to spendgiven data
Apples cost $3 per pound
Bananas cost $5 per pound
amount Bill has to spend $31
The number of whole apple Bill can buy
Using $31 the number of whole apples this can buy is gotten dividing the the total amount by the price of apple per pound.
= amount Bill has to spend $31 / Apples cost $3 per pound
= 31 / 3
= 10.33
Since we are solving for whole pounds of apple Bill can buy 10 whole pounds of apples
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ben is making a dessert that requires 212 lb of strawberries and 112 lb of blueberries. strawberries cost $1 less per pound than blueberries. ben spent a total of $9.50 on the fruit. what is the price per pound of each type of fruit?
Answer:
Step-by-step explanation:Price per pound of strawberries is $-0.31635 and blueberries is $0.6836.
Explanation :
Given data ;
Weight of strawberries required for dessert = 212 lb
Weight of blueberries required for dessert = 112 lb
Total cost spent = $9.50
Let,
Cost of blueberries per pound =x
Cost of strawberries per pound = (x-1)
We know that,
Cost of blueberries for overall weight + Cost of strawberries for overall weight = Total cost spent on fruits.
x(112) + (x-1)212 = 9.50
112x + 212x – 212 = 9.50
324x = 221.5
X = 221.5/324
X = $0.6836
So, (x-1) = $-0.31635
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Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794
Given that ;
Ben is making a dessert that requires 212 lbs of strawberries and 112 lbs of blueberries. Strawberries cost $1 less per pound than blueberries. Ben spent a total of $9.50 on the fruit.
So according to the question get the price per pound of each type of fruit;
Let ' x ' be the price per pound of strawberries and ' y ' be the price per pound of blueberries.
By assuming the following equations;
212x - 112y = 1 → ( I )
212x + 112y = 9.5 → ( II )
By solving above equations ( I ) ( II ) we get;
424x = 10.5
x = 10.5/424
x = 0.02476
224y = 8.5
y = 8.5/224
y = 0.03794
Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794
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Need help with this, if you can edit it and send back,, that’ll help, thank you<3
The quotient of the triangle side lengths are same as below for different triangle ( please refer attached image for better understanding)-
For ABC - 9/4 or 2.25, 9/6 or 1.5, 6/4 or 1.5
For DEF - 18/8 or 2.25, 18/12 or 1.5, 12/8 or 1.5
For GHI - 27/12 or 2.25, 27/18 or 1.5, 18/12 or 1.5
For JKL - 4.5/2 or 2.25, 4.5/3 or 1.5, 3/2 or 1.5
Quotient in mathematics, can be defined as the result of the division of a number by any divisor.
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2. Write an equation in slope-intercept form of the line that passes through the point (-5, 7) and is perpendicular to the line y = 5x-1.
The general slope intercept form equation of a line is as stated below;
[tex]y=mx+b[/tex]where m is the slope and b is the intercept.
If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.
The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;
So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);
Remember, the point slope form equation of a line is given as;
[tex]y-y_1=m(x-x_{1)}[/tex]Substituting the above values, we'll have
[tex]y-7=-\frac{1}{5}(x+5)[/tex]Let's open up the parenthesis first, we'll have;
[tex]\begin{gathered} y-7=-\frac{1}{5}x-\frac{5}{5} \\ y-7=-\frac{1}{5}x-1 \end{gathered}[/tex]Let's isolate y by adding 7 to both sides of the equation;
[tex]y=-\frac{1}{5}x+6[/tex]The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).
the null and alternative hypotheses are given. determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. what parameter is being tested? 105
The hypothesis test is a Left-tailed test and the parameter being tested is known as a Population mean.
What is a null and alternative hypotheses?
A null hypothesis predicts no effect between variables while an alternative hypothesis predict an effect or relationship between variables of the study.
What is the given hypothesis test?
In the question, the given hypothesis test includes "H0: σ=110" and "H1: σ<110"
Hence, based on the test above, the hypothesis test is a Left-tailed test and the parameter being tested is known as a Population mean.
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Find the value of x to the nearest tenth.