The first five term of the sequence are 42, 35, 28, 21 and 14.
According to the given question.
We have a rule for finding the terms of a sequence i.e. [tex]a_{n} = a_{n-1} -7[/tex].
Also, the first term of the sequence is a1 = 42
Therefore,
The second term of the sequence is given by
Second term [tex]a_{2}[/tex] = [tex]a_{1}[/tex] - 7
⇒ Second term = 42 - 7 = 35
Similarly,
The third term of the sequence, [tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 7 = 35 - 7 = 28
Fourth term of the sequence = 28 - 7 = 21
Fifth term of the sequence = 21 - 7 = 14
Hence, the first five term of the sequence are 42, 35, 28, 21 and 14.
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Pleae help me with this problem.
Answer:
11) KI = 28
12) PR = 22
Step-by-step explanation:
You want the base segment lengths KI and PR, given relations between those segments and the corresponding midsegment of the triangle.
MidsegmentA midsegment is a line segment that joins midpoints of other line segments, usually the midpoints of triangle sides or opposite sides of a quadrilateral. In the case of a triangle, the midsegment is parallel to the third side, and half its length. This relation is used to solve these problems.
11)KI = 2·AB
(x +37) = 2(x +23) . . . . substitute given expressions
x +37 = 2x +46 . . . . . . eliminate parentheses
37 = x +46 . . . . . . . . . . subtract x
28 = x +37 . . . . . . . . . . subtract 9
The length of KI is 28 units.
12)PR = 2·HG
(x +30) = 2(19 +x) . . . . substitute given expressions
x +30 = 38 +2x . . . . . eliminate parentheses
22 = x +30 . . . . . . . . subtract (x+8)
The length of PR is 22 units.
__
Additional comment
As you can see here, there is no real reason to find the value of x, then substitute it back into the expression for the segment of interest. We can, and did, solve directly for the value of that expression.
As with any algebraic manipulation, any operation performed on one side of the equal sign must also be performed on the other side of the equal sign. When we say "subtract ()", we mean "subtract () from both sides of the equation."
In problem 11, x=-9. In problem 12, x=-8. Negative values of x work just fine, as long as the resulting segment lengths are positive.
an online retailer is shipping a shower curtain pole that is 13 feet long. their largest box is in the shape of a rectangular prism that is 10 ft × 9 ft × 8 ft. will the pole fit in the box?
Yes, the pole will fit in the box when kept diagonally.
In order to fit the pole in rectangular prism or cuboid, it has to be kept diagonally. Now, we need to calculate the length of body diagonal of cuboid. The length of body diagonal of cuboid should be greater than pole to fit it.
The length of body diagonal of cuboid can be calculated by the formula -
Diagonal = √(l² + b² + h²)
Keep the values in formula to find the diagonal of rectangular prism
Diagonal = √(10² + 9² + 8²)
Taking square of the three numbers to find the diagonal of rectangular prism
Diagonal = √100 + 81 + 64
Taking sum of numbers present on Right Hand Side of the equation
Diagonal = √245
Taking square root of the number
Diagonal = 15.65 feet
Hence, as the diagonal of rectangular prism is greater than shower curtain pole, it will definitely fit.
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Need help with this question ASAP please and youu??
Answer: (8, 8)
Step-by-step explanation:
y>x-7, y<=2x-8
1: 5>12-7
5>5 ==> Not true
2: 3>12-7
3>5 ==> Not true
3: -10>-6-7
-10>-13
-10<=2(-6)-8
-10<=-12-8
-10<=-20 ==> Not true
4: 8>8-7
8>1 ==> True
8<=2(8)-8
8<=16-8
8<=8 ==> True ==> (8, 8)
a researcher records the repair cost for 1313 randomly selected stereos. a sample mean of $85.52$85.52 and standard deviation of $10.81$10.81 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the stereos. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
The mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
We have been given that a researcher records the repair cost for 13 randomly selected stereos. a sample mean of $85.52 and a standard deviation of $10.81 are subsequently computed.
Since we don't know the population standard deviation, we used t statistics to create the 90% confidence interval in this case.
So, the 90% confidence interval for the true mean repair cost, μ is ;
⇒ P(-2.015 < t₅ < 2.015) = 0.90
{As the critical value of t at 5 degrees of freedom are -2.015 & 2.015 with P = 5%}
⇒ P(-2.015 < (x-μ)/(s/√n) < 2.015) = 0.90
⇒ P(-2.015×(s/√n) < (x-μ) < 2.015×(s/√n)) = 0.90
⇒ P(x - 2.015×(s/√n) < μ < x + 2.015×(s/√n)) = 0.90
90% confidence interval for
⇒ μ = (x - 2.015×(s/√n) , x + 2.015×(s/√n))
Here, x = $85.52, s = $10.81, and n = 13
⇒ μ = (85.52 - 2.015×(10.81/√13) , 85.52 + 2.015×(10.81/√13))
⇒ μ = (79.47, 91.56)
Hence, the mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.
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A tv show had 3.6 x 104 viewers in the first week and 4.1 x 104 viewers in the second week. determine the average number of viewers over the two weeks and write the final answer in scientific notation.
The computation shows that the average number of viewers over the two weeks will be 3.85 × 10⁴.
How to compute the value?From the information given, the tv show had 3.6 x 10⁴ viewers in the first week and 4.1 x 10⁴ viewers in the second week.
Therefore, the average number of viewers over the two weeks will be:
= (3.6 × 10⁴ + 4.1 × 10⁴)/2
= 7.7 × 10⁴/2
= 3.85 × 10⁴
Therefore, the average is 3.85 × 10⁴
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In which number does the digit 6 have that is 10 times as great as the value of the digit 6 in 283,691
Answer:
486,732 hope this helps
Please solve the problem in the image!!!!!
Answer:
455 is the answer of your question
You find a job that pays $14.25/hr working 25 hours per
week. How much will you make in 4 weeks?
Answer:
$1425
Step-by-step explanation:
To find how much money you would make, we would first have to multiply the number of weeks worked by how many hours you work per week.
4 · 25 = 100
What this tells us is that in 4 weeks, you worked 100 hours in total. Now we can multiply total hours worked by how much you are paid per hour to get our answer.
14.25 · 100 = 1425
A restaurant manger surveyed a random sample of costumers to determine which drink they prefer. Fourteen chose tea and 36 chose soda. Based on the results ,how many of the 275 customers can be expected to prefer soda?
198 of the 275 customers can be expected to prefer soda
A restaurant manger surveyed a random sample of costumers to determine which drink they prefer. Fourteen chose tea and 36 chose soda.
Based on the results , we have to find how many of the 275 customers can be expected to prefer soda?
total customers x = 275
customers chose soda y= 36
customers chose tea z= 14
therefore out of 275 customer who prefer soda = (x * y)/(y+z)
Based on the given conditions, formulate: [tex]: \frac{275 * 36}{14+36} \\\\[/tex]
Calculate the product or quotient:[tex]\frac{9900}{14+36}[/tex]
Calculate the sum or difference:[tex]\frac{9900}{50}[/tex]
Cross out the common factor: [tex]198[/tex]
Hence ,198 of the 275 customers can be expected to prefer soda
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find equations of the tangent line and of the normal line to the curve at the point . write the equations of the lines in the form .
The equations of the lines in the form y=mx+b are-
Tangent line: y = 240x - 215994Normal line: y = - 0.00417x + 9.75What is slope?A line's slope is described like the change in y coordinate to the change in x coordinate. The net y coordinate change is y, whereas the net x coordinate change is x.
Therefore the variation in y coordinate in relation to the variation in x coordinate is written as, dy/dx.
Now, as per the given conditions;
The equation of the line is y = (6 + 4x)²
Simplifying the equation;
y = (6 + 4x)²
= 36 + 48x + 16x²
y = 16x² + 48x + 36
Now, differentiate the equation to find the tangent slope;
dy/dx = 32x + 48
At the point (6,900),
dy/dx = 32(6) + 48 = 240
Let equation of the tangent at point (a,b) is;
(y - b) = m(x - a)
a = 6, b = 900, m = 240
y - 6 = 240(x - 900)
Write this in y = mx + b form,
y - 6 = 240x - 216000
y = 240x - 215994 (Equation of Tangent line)
The slope of the normal line = -(1/slope of the tangent line) (since they're both perpendicular to each other)
Slope of the normal line = -1/240
The, equation of the normal will become;
y - 6 = (-1/240)(x - 900)
y - 6 = (-x/240) + 3.75
y = (-1/240)x + 9.75
y = - 0.00417x + 9.75 (Equation of Normal line)
Thus, the equation for the normal and tangent has be found.
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The complete question is-
Find the equation of the tangent line and normal line to the curve y = (6 + 4x)² at the point (6,900). Write the equations of the lines in the form y=mx+b. Tangent line: y=
Normal line: y=
Please Help:
Here are the statistics for the high temperatures in a city during October:
mean of 65.3 degrees Fahrenheit
median of 63.5 degrees Fahrenheit
standard deviation of 9.3 degrees Fahrenheit
IQR of 7.1 degrees Fahrenheit
Recall that the temperature C, measured in degrees Celsius, is related to the temperature F, measured in degrees Fahrenheit, by C=5/9(F−32).
a. Describe how the value of each statistic changes when 32 is subtracted from the temperature in degrees Fahrenheit.
b. Describe how the value of each statistic further changes when the new values are multiplied by 5/9.
c. Describe how to find the value of each statistic when the temperature is measured in degrees Celsius.
Answer:
a. Describe how the value of each statistic changes when 32 is subtracted from the temperature in degrees Fahrenheit.
a) The mean will change and other quantities remain same.
b) The mean, standard deviation and IQR change.
c) The standard deviation and IQR change.
a. When 32 is subtracted from the temperature in degrees Fahrenheit:
The mean would change by subtracting 32 from the original mean of 65.3.The median would remain the same since subtracting a constant value does not affect the relative order of the data points.The standard deviation would remain the same since it is a measure of dispersion and does not depend on the shift of the data.The IQR would remain the same since it is based on the order statistics (including the median) and is not affected by a constant shift.b. When the new values (obtained after subtracting 32) are multiplied by 5/9:
The mean would change by multiplying the new mean by 5/9.The median would remain the same since scaling by a constant value does not affect the relative order of the data points.The standard deviation would change by multiplying the new standard deviation by 5/9 since it is a measure of dispersion and scales with the data.The IQR would change by multiplying the new IQR by 5/9 since it is based on the order statistics and scales with the data.c. To find the value of each statistic when the temperature is measured in degrees Celsius:
The mean and median would remain the same since the Celsius scale and Fahrenheit scale have a linear relationship, and shifting or scaling the data does not affect their relative values.The standard deviation would change by multiplying the new standard deviation by 5/9 since it scales with the data.The IQR would change by multiplying the new IQR by 5/9 since it scales with the data.Learn more about IQR here:
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What two numbers are missing from this factor tree for the prime factorization of 252
Answer:
the prime factorization of 252 is. 252 = 2 × 2 × 3 × 3 × 7 = 22 × 32 × 7.
The 2 missing numbers are not given, so I'm unsure about the 2 missing numbers.
Step-by-step explanation:
hope this helps :)
Answer:
Step-by-step explanation:
Definitions
Prime number: A whole number greater than 1 that cannot be made by multiplying other whole numbers.
Prime Factorization: Prime numbers that multiply together to make the original number.
The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, ...
To find which prime numbers multiply together to make 252, begin by dividing 252 by the first prime number, 2:
⇒ 252 ÷ 2 = 126
As 126 is not a prime number, we need to divide again.
⇒ 126 ÷ 2 = 63
As 63 is not a prime number, and 63 is not divisible by 2, try dividing it by the next prime number, 3:
⇒ 63 ÷ 3 = 21
As 63 is not a prime number, divide again.
⇒ 21 ÷ 3 = 7
As 7 is a prime number, we can stop.
Therefore, 252 is the product of:
⇒ 252 = 2 × 2 × 3 × 3 × 7
As 2 and 3 appear twice, we can write these using exponents:
⇒ 252 = 2² × 3² × 7
a. show one pair of corresponding points and two pairs of corresponding sides in the original and it’s copy.
b.what scale factor takes the original polygon to its smaller copy?
Answer:
1/4
Step-by-step explanation:
Let x = the scale factor
4x = 1 Divide both sides by 4
x = 1/4
Find the equation of the line that is parallel to y=-2/3x and contains the point (4,-8)
Answer:
y = (-2/3)x + 16/3
Step-by-step explanation:
Any line parallel to y = (-2/3)x has the same slope: (-2/3).
Then, in this pattern, y = (-2/3)x + c, where c is the y-intercept.
If (4, -8) lives on this new line, then:
-8 = (-2/3)(4) + c, and
-8 = -8/3 + c
This last equation is equivalent to -24/3 + 8/3 + c => -16/3 = -c.
Therefore the y-intercept is 16/3 = c, and the desired equation is
y = (-2/3)x + 16/3
a hotel chain charges $90 each night for the first two nights and $50 for each additional night's stay. the total cost t is a function of the number of nights x that a guest stays.
The total cost is T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}
What is algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/).
Given:
T(x)={a if x≤2, b if x > 2}
let us take
a= 90x, 0≤x≤2
and, b = 180 + 50x for x>2
Hence. the total cost be T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}
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Can somebody help me find this missing angle please.
Answer:
x = 96 degrees
Step-by-step explanation:
49 + 35 + x = 180
84 + x = 180
x = 180 - 84
x = 96 degrees
Order the values from least to greatest.88, 8 tens, 8*1/100
The order of the values from least to greatest is 8*1/ 100, 8 tens, 88
How to determine the orderTo determine the order of the values from least to greatest is to outline or arrange the value on the basis of the sizes or according to their magnitude
Given the values as;
888 tens8/ 100Note that 8 ten is simply written as
= 8 × 10 = 80
= 8/ 100 = 0. 8
= 88
From the number system, the values can be arranged as;
0. 8, 80 , 88
Thus, the order of the values from least to greatest is 8*1/ 100, 8 tens, 88
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1. Is there a triangle with two right angles?
Answer:
A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible.
Answer:
No, it is not possible for a triangle to have two right angles because a triangle's angles add up to 180 degrees, and two right angles add up to 180. A triangle also has three angles, so the third angle cannot be 0 degrees.
Solve the equation by graphing. If the exact roots cannot be found, state the consecutive integers between which the roots are located. If there are no roots, state no real solution. List all roots or consecutive integers in order from least to greatest. 2 x^ 2 + x = 11
The roots of the quadratic equation represented by the graph are; x = -2.5 and x = 2.5.
What is the Solution of the Quadratic Equation?
The solutions to the equation 2x² + x = 11 will be given by the points at which the graph intercepts the x-axis.
By looking at the graph, we can clearly see that the graph intercepts the x-axis at x = -2.5 and x = 2.5.
The roots are located between -3 and 3.
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SOMEONE PLEASE HELP ME I REALLY NEED HELP ON THIS
The volume of the square frustrum is 1018791.667 cubic feet, the volume of the pyramid is 22019.625 cubic feet and the volume of the Washington Monument is 1040811.292 cubic feet.
What is the volume of the Washington Monument?
The Washington Monument is an obelisc and the volume of the obelisc is the sum of the volumes of the square frustrum and the pyramid, that is:
V = V' + V'' (1)
V' = (1 / 3) · (a² + a · b + b²) · h (2)
V'' = (1 / 3) · b² · h' (3)
Where:
V' - Volume of the square frustrum, in cubic feet.V'' - Volume of the pyramid, in cubic feet.a - Length of the side of the lower base, in feet.b - Length of the side of the upper base, in feet. h - Height of the square frustrum, in feet.h' - Height of the pyramid, in feet.If we know that a = 55 ft, b = 34.5 ft, h = 500 ft and h' = 55.5 ft, then the volume of the Washington monumement is:
V' = (1 / 3) · (55² + 55 · 34.5 + 34.5²) · 500
V' = 1018791.667 ft³
V'' = (1 / 3) · 34.5² · 55.5
V'' = 22019.625 ft³
V = 1040811.292 ft³
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HELP ASAP!!!
Solve for m in the following equation.
4m/3= 8
m= 10
m= 6
m= 2
m= 96
You buy three more than twice as many pounds of apples as bananas. If you bought seven pounds of apples, how many pounds of bananas did you buy?
What is the correct equation and solution for this problem?
3p – 2 = 7; p = 3 pounds
2p – 3 = 7; p = 5 pounds
3p + 2 = 7; p = 3 pounds
2p + 3 = 7; p = 2 pounds
Thank you!!
The value of the unknown variable, m in the equation 4m / 3 = 8 is 6. option B
How to solve for unknown in an equation?4m / 3 = 8
cross product4m = 8 × 3
4m = 24
divide both sides by 4m = 24/4
m = 6
let
pounds of apple = apounds of bananas = bthree more than twice as many pounds of apples as bananas.
a = 2b + 3
If you bought seven pounds of apples, how many pounds of bananas did you buy?
b = 7 pounds
a = 2b + 3
7 = 2b + 3
7 - 3 = 2b
4 = 2b
b = 4/2
b = 2 pounds
So therefore, the correct equation and solution for this problem is 2p + 3 = 7; p = 2 pounds. option D
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I need help. Please
a team can row 40km in 2 hours when rowing with the current, but only 16km in 2 hours when rowing against the current. determine the teams rowing speed when there is no current
Based on the rowing speed of the team when rowing with the current and when rowing against, the team rowing speed when there is no current is 14 km/h.
What is the rowing speed without current?Assuming that x is the rowing rate and y is the rate of the current, the equations needed will be:
2 (x + y) = 40
2 (x - y) = 16
We can add the x-values of the equation to find the value of x which will be the rowing speed without current:
2x + 2x = 40 + 16
4x = 56
x = 56 / 4
x = 14 km /h
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Sandra's bicycle is old and rusty. Her parents won't buy her a new one unless she does more chores around the house. Sandra's dad said he will buy a new bicycle if Sandra mows the lawn, rakes the leaves, and washes the windows every weekend for 16 weeks in a row. Sandra is very motivated and does her chores for 3 weeks straight.
Which equation can Sandra use to find how many more weeks w she needs to do her chores before her parents will buy her a new bicycle?
Answer:W=16-3
Step-by-step explanation:
W is how many more weeks she has to work
she needs to work a total of 16 weeks and she has worked for 3 so far to find the total number of weeks she still needs to work she would take 16-3=13 13=W
please help math 30 points
Answer:
144.288
Step-by-step explanation:
yes because I just took the tes
Solve the following equation for aa. Be sure to take into account whether a letter is capitalized or not.
d=
d=
\,\,Ma-N^3a
Ma−N
3
a
Answer:
a = [tex]\frac{d}{M-N^3}[/tex]
Step-by-step explanation:
d = Ma - N³a ← factor out a from each term on the right side
d = a(M - N³) ← isolate a by dividing both sides by M - N³ )
[tex]\frac{d}{M-N^3}[/tex] = a
Write an absolute value equation that has the solutions x=-6 and x=10.
Answer:
[tex]r \times \cos( 0) = - 6 \\ r = - \frac{6}{ \cos(0) } \\ r = - 6 \sec(0) \\ \\ r \times \cos(0) = 10 \\ r = \frac{10}{ \cos(0) } \\ r = 10 \sec(0) [/tex]
Which expression is equivalent to the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power?
The equivalent expression is 5^(4) * 3^(-10)
What is an equivalent expression?Equivalent expressions are expressions having the same solution but different arrangement
Two expressions are said to be equivalent if they have the same value of solution irrespective of the variable(s) in them.
Now, let's represent the expression;
( 5^-2 × 3^5 )^-2
We simply by multiply the exponential value by the
5^-2(-2) × 3^5(-2)
5^4 × 3^- 10
Hence, the equivalent expression is 5^(4) * 3^(-10)
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Helpp
Question 3 (Essay Worth 2 points)
(01.02 HC)
Is the expression x3 x3 x3 equivalent to x3 3.3? Why or why not? Explain your reasoning.
No the expression x³.x³.x³ is not equivalent to expression x³ˣ³ˣ³.
Given the expression:
x³.x³.x³
here we apply the law of exponent that, when bases are same powers are added.
Two exponential terms with the same base are multiplied, and while the base doesn't change, their powers are added. On the other hand, their powers are removed when two exponential expressions with the same base are split.
therefore, x³.x³.x³ = x ³⁺³⁺³
= x⁹
and in the second expression x³ˣ³ˣ³.
In this expression powers are multiplied.
= x³ˣ³ˣ³.
= x²⁷
therefore both expressions are not equivalent.
Hence the expressions are not equivalent.
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A grocery store sells a bag for six oranges for 2.34 is mav spent 1.95 on oranges how many did she buy
Answer:
Mav bought 5 oranges.
Step-by-step explanation:
$2.34 ÷ 6 oranges = $0.39 ( Price per orange)
$0.39 x 5 oranges = $1.95