Answers
Answer:
47, 40, 33, 26 are the first four terms of the sequence.
Step-by-step explanation:
Expression representing the sequence is,
[tex]a_n=46-7(n-1)[/tex]
where n = number of term in the sequence
For n = 1,
[tex]a_1=47-7(1-1)[/tex]
= 47
For n = 2,
[tex]a_2=47-7(2-1)[/tex]
= 47 - 7
= 40
For n = 3,
[tex]a_3[/tex] = 47 - 7(3 -1)
= 47 - 14
= 33
For n = 4,
[tex]a_4=47-7(4-1)[/tex]
= 47 - 21
= 26
Therefore, first four terms of the sequence are 47, 40, 33 and 26.
Related Questions
5/12 +( 5/12 + 3/4 ) =
Answers
Answer:
Proper: 15/4
Improper: 3 3/4
Step-by-step explanation:
Well to solve the following question,
5/12 + (5/12 + 3/4)
We solve the part in the parenthesis first,
5/12 + 3/4 = 14/4
Simplified -> 7/2
5/12 + 7/2
= 45/12
Simplified -> 15/4
Thus,
the answer is 15/4 or 3 3/4.
Hope this helps :)
Answer:
19/12= [tex]1 \frac{7}{12}[/tex]Step-by-step explanation:
[tex]\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\\\\=\frac{5}{12}+\frac{5}{12}+\frac{3}{4}\\\\\mathrm{Add\:similar\:elements:}\:\frac{5}{12}+\frac{5}{12}=2\times \frac{5}{12}\\=2\times \frac{5}{12}+\frac{3}{4}\\\\=\frac{5\times \:2}{12}\\\\=\frac{10}{12}\\\\=\frac{10}{12}\\\\=\frac{5}{6}+\frac{3}{4}\\L.C.M =12\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{5}{6}=\frac{5\cdot \:2}{6\times \:2}=\frac{10}{12}\\\\\frac{3}{4}=\frac{3\times \:3}{4\times \:3}=\frac{9}{12}\\[/tex]
[tex]\\=\frac{10}{12}+\frac{9}{12}\\\mathrm{Since\:the\:denominators\:are\:equal\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{10+9}{12}\\\\=\frac{19}{12}[/tex]
Which One Doesn't Belong? Why?
There are multiple reasons that each one of these 4 could be different than the others.
I just need an answer from one of these 4.
Answers
The number of times a player has golfed in one's
lifetime is compared to the number of strokes it takes
the player to complete 18 holes. The correlation
coefficient relating the two variables is 0.26.
Which best describes the strength of the correlation,
and what is true about the causation between the
variables?
It is a weak negative correlation, and it is not likely
causal.
O It is a weak negative correlation, and it is likely
causal.
O It is a strong negative correlation, and it is not likely
causal.
O It is a strong negative correlation, and it is likely
causal.
Answers
Answer:
It is a weak negative correlation, and it is likely causal.
Step-by-step explanation:
Correlation coefficient can be said to be a statistical value that shows the relationship between two variables.
Here, the correlation coefficient is 0.26 which means that the magnitude of correlation is low and it causes a weak correlation.
Here, since one variable increases as the other variable decreases, the correlation is said to be negative and weak. We can see that the more a player golf's, the lower the number to required strokes. This would result in a negative slope.
Therefore, It is a weak negative correlation, and it is likely
causal.
Answer:
The correct answer is B on edge 2020.
Step-by-step explanation:
select the fraction equivalent of 0.06. reduce to the lowest terms
Answers
Answer: 3/50
Step-by-step explanation:
0.06 = 6/100 , 100 would be the denominator because we have two figures after the decimal point. Each figures can also be represented by 10,
Again,
0.06 = 6 × 10-²
Now 0.06 = 6/100
= 3/50.
Therefore, the fractional form = 3/50 in its lowest term.
Please help!! Need help with Geometry! Would really appreciate it!!
Answers
Answer:
The answer is the first one
Step-by-step explanation:
The rays are: XW, ZY
The lines are: XZ
Rays are with one endpoint and one side that goes forever (aka and arrow).
A line has no endpoint going on forever in both directions.
Answer:
The first one
Step-by-step explanation:
Since a line is an infinite object, with no starting or ending point we symbolize it by an arrow over two points that belong to this line:
[tex]\line{XY}[/tex]
A ray, on the other hand has a starting point and no ending point.
So, in the picture we have a pair of rays, with common points to the line XY
Namely:
XW e ZY
Find the Perimeter of the polygon if angle B= angle D Please Help Trying to graduate.
Answers
Answer:
P = 60 cm
Step-by-step explanation:
To solve this question we will use the property of the tangents drawn from a point to a circle.
"Length of tangents drawn from a point to a circle are equal in measure."
By this property,
Therefore, BG ≅ FB ≅ 7.5 cm
AG ≅ AH ≅ 6.5 cm
CF ≅ EC ≅ 8.5 cm
Since m∠B ≅ m∠D
Therefore, length of tangents FB ≅ GB ≅ DE ≅ DH ≅ 7.5 cm
Since, Perimeter of ABCD = AB + BC + CD + DA
AB = 7.5 + 6.5 = 14 cm
BC = 7.5 + 8.5 = 16 cm
CD = 8.5 + 7.5 = 16 cm
DA = 7.5 + 6.5 = 14 cm
Now Perimeter = 16 + 16 + 14 + 14 = 60 cm
Therefore, P = 60 cm will be the answer.
Joey borrows 2000 from his grandfather and pays the money back in monthly payments of 200.
1. Write a lineat function that represents the remaining money owed L(x) after x months.
2. Evaluate L(10) and interpret the meaning in the context of this problem.
A. L(x) - 200x + 2,400; L(10) = 4,400, This represents the amount Joey has paid his grandfather after 10 months.
B. L(x) = 200x + 2,400; L(10) - 4,400, This represents the amount Joey still owes his grandfather after 10 months.
C. L(x) = -200x + 2,400; L(10) = 400, This represents the amount Joey has paid his grandfather after 10 months.
D. L(x) = -200x + 2,400; L(10) = 400, This represents the amount Joey still owes his grandfather after 10 months.
Answers
The correct question is;
Joey borrows $2400 from his grandfather and pays the money back in monthly payments of $200.
a. Write a linear function that represents the remaining money owed L(x) after x months.
b. Evaluate L(10) and interpret the meaning in the context of this problem.
A) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey still owes his
grandfather after 10 months.
B) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey has paid his
grandfather after 10 months.
C) L(x) = 200x + 2400; L(10) = 4400, This represents the amount Joey has paid his
grandfather after 10 months.
D) L(x) = -200x + 2400; L(10) = 400, This represents the amount Joey still owes his
grandfather after 10 months.
Answer:
A) L(x) = 2400 - 200x
B) Option D is correct
Step-by-step explanation:
A) We are told that Joey borrowed 2400.
Now he pays back in installments of 200 every month.
Thus for x number of months he would have paid 200x.
Thus,the linear function that represents the remaining money owed is;
L(x) = 2400 - 200x
B) L(10) = 2400 - (200 * 10)
L(10) = 2400 - 2000
L(10) = 400
Thus, after 10 months, Joey is owing 400.
So, looking at the given options, the correct one is option D.
A compressive uniform stress distributed on a rectangular areas of sides. located on the two opposite vertical/radial faces of step. If Force = 1.87kN and stress = 0.987MPa calculate the h * t in m^2
Answers
Answer:
Area = 0.019 m²
Step-by-step explanation:
stess = applied Force over Area
since stress = 0.987 MPa
and the force = 1.87 Kn
then Area = h * t
Q = F / (h * t)
0.987 mPa = 1.87 kN / (h* t)
since h * t = Area then 1.87 / 0.987
Area = 1.89 x 0.01 =
Area = 0.019 m²
Which of the following shows the graph of y = –(2)x – 1? On a coordinate plane, a curve is level at y = 0 in quadrant 2 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 0.5). On a coordinate plane, a curve is level at y = negative 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, negative 2). On a coordinate plane, a curve is level at y = 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, 0).
Answers
Answer:
On a coordinate plane, a curve is level at y = -1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).
Step-by-step explanation:
y = -2 ^x -1
On a coordinate plane, a curve is level at y = – 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2). Option C is correct.
What is Cartesian coordinate plane?The Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure can be drawn. A location is assigned to each point on a Cartesian plane.
On a coordinate plane, a curve is level at y = – 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).
Hence, option C is correct.
To learn more about the Cartesian plane, refer;
https://brainly.com/question/27538987
#SPJ2
n ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how long will it be (in cm)?
Answers
Answer:
48.28 cmStep-by-step explanation:
Since the shape is a cube of side 20cm, then all the side of the cube will be 20cm since all the side of a cube are all equal.
The shortest path the ant can be take is to first travel along the diagonal of the square from point A to the other edge on the front face and then move to point B on its adjacent side on a straight line.
To get the total distance he will take, we will first calcuate the value of the diagonal distance of the square face using pythagoras theorem as shown.
hypotenuse² = opposite² + adjacent²
The opposite = adjacent = 20cm
The hypotenuse is the length of the diagonal that we need.
hyp² = 20²+20²
hyp² = 400+400
hyp² = 800
hyp = √800
hyp = 28.28 cm
The length of the diagonal is 28.28 cm.
Afterwards, the ant will move 20cm to point B from the stopping point.
Total distance will be 28.28 + 20 = 48.28 cm
Use Bayes' theorem to find the indicated probability 5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
a. 0.905
b. 0.585
c. 0.038
d. 0.475
Answers
Answer:
b. 0.585
Step-by-step explanation:
According to Bayes' theorem:
[tex]P(A|B)=\frac{P(B|A)*P(A)}{P(B)}[/tex]
Let A = Person is infected, and B = Person tested positive. Then:
P(B|A) = 93.9%
P(A) = 5.8%
P(B) = P(infected and positive) + P(not infected and positive)
[tex]P(B) = 0.058*0.939+(1-0.058)*0.041\\P(B)=0.09308[/tex]
Therefore, the probability that a person has the disease given that the test result is positive, P(A|B), is:
[tex]P(A|B)=\frac{0.939*0.058}{0.09308}\\P(A|B)=0.585[/tex]
The probability is 0.585.
A customer gave her hair dresser a 20% tip, which amounted to $7. What was the price before the tip?
Answers
Answer:
The price before tip was 35
Step-by-step explanation:
Let x = original amount
x * 20% = 7
Change to decimal form
x * .20 = 7
Divide each side by .20
x*.20/.20 = 7/.20
x =35
Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval.
Answers
Answer:
Step-by-step explanation:
Complete Question
The complete question is shown on the first uploaded image
Answer:
The area is [tex]A =8 sq\cdot unit[/tex]
Step-by-step explanation:
From the question we are told that
The first equation is [tex]f(x) = x^2 + x \ \ \ x< 1[/tex]
[tex]on[ -2 , 3 ][/tex]
The second equation is [tex]f(x) = 2 x \ \ \ x \ge 1[/tex]
This means that the limit of the area under the enclosed region is limited between -2 to 1 on the x- axis for first equation and 1 to 3 for second equation
Now the area under the region is evaluated as
[tex]A = \int\limits^1_{-2}{x^2 + x } \, dx + \int\limits^3_{1}{2x } \, dx[/tex]
[tex]A ={ \frac{x^3}{3} + \frac{x^2}{2} + c } | \left \ 1 } \atop {-2}} \right. + {\frac{2x^2}{2} }| \left \ 3} \atop {1}} \right.[/tex]
[tex]A =9 + c - 1 -c[/tex]
[tex]A =8 sq\cdot unit[/tex]
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to:
Answers
Answer:
[tex]Mean = 344[/tex]
Step-by-step explanation:
Given
[tex]Population = 1013[/tex]
Let p represents the proportion of those who worry about identity theft;
[tex]p = 66\%[/tex]
Required
Mean of those who do not worry about identity theft
First, the proportion of those who do not worry, has to be calculated;
Represent this with q
In probability;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute [tex]p = 66\%[/tex]
[tex]q = 1 - 66\%[/tex]
Convert percentage to fraction
[tex]q = 1 - 0.66[/tex]
[tex]q = 0.34[/tex]
Now, the mean can be calculated using:
[tex]Mean = nq[/tex]
Where n represents the population
[tex]Mean = 1013 * 0.34[/tex]
[tex]Mean = 344.42[/tex]
[tex]Mean = 344[/tex] (Approximated)
Find the common ratio of the following geometric sequence:
11,55, 275, 1375, ....
Answers
Answer:
Hey there!
The common ratio is 5, because you multiply by 5 to get from one term to the next.
Hope this helps :)
Answer:
5
Step-by-step explanation:
To find the common ratio take the second term and divide by the first term
55/11 = 5
The common ratio would be 5
Please solve this problem in a statement reason setup.
Answers
Step-by-step explanation:
Statement: ∠O ≅ ∠O
Reason: Reflexive property
Statement: m∠OKW = 90° − m∠O
Reason: Complementary angles
Statement: m∠OJP = 90° − m∠O
Reason: Complementary angles
Statement: m∠OKW = m∠OJP
Reason: Substitution
Statement: ∠OKW ≅ ∠OJP
Reason: Definition of congruent angles
Statement: ΔOKW ~ ΔOJP
Reason: AA similarity
The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.
Answers
Answer:
A= 35°
b= 55°
Step-by-step explanation:
Let's take the small angles of the right angle triangle to be and b
a+b +90= 180....(sum of angles in a right angle triangle)
The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle
2a-15= b
a+2a -15 +90= 180
3a = 180-75
3a= 105
a= 105/3
a= 35°
a+b +90= 180.
35+b+90= 180
b = 180-90-35
b = 55°
Answer:
x = 35°; y = 55°
Step-by-step explanation:
Let x = one of the angles
and y = the other angle. Then
2x = twice the measure of x and
2x - 15 = 15 less than twice the measure of x
You have two conditions
(1) y = 2x - 15
(2) x+ y = 90
Calculations:
[tex]\begin{array}{lrcll}(1) & y & = & 2x - 15\\(2)& x + y & =&90\\(3)& x + 2x - 15 & =&90&\text{Substituted (1) into (2)}\\& 3x- 15 & = & 90&\text{Simplified}\\&3x & = & 105&\text{Added 15 to each side}\\ (4)& x & = & \mathbf{35}&\text{Divided each side by 3}\\& y & = & 2(35) - 15&\text{Substituted (4) into (1)}\\& & = & 70 - 15&\text{Simplified}\\&&=&\mathbf{55}&\end{array}\\[/tex]
x = 35°; y = 55°
Check:
[tex]\begin{array}{ccc}55 = 2(35) - 15 & \qquad & 35 + 55 = 90\\55 = 70 - 15 & \qquad & 90 = 90\\55 = 55 && \\\end{array}[/tex]
It checks.
verify sin(360 - etheta = -sin etheta
Answers
Answer:
see explanation
Step-by-step explanation:
Using the subtraction identity for sine
sin(a + b) = sinacosb - cosasinb
Given
sin(360 - Θ)°
= sin360°cosΘ° - cos360°sinΘ°
= (0 × cosΘ ) - (1 × sinΘ)
= 0 - sinΘ
= - sinΘ ← as required
Show that between any two terminating decimals ,there is another terminating decimal
Answers
Answer:
1.5+1.7/2=1.6
Step-by-step explanation:
What is x in this Math problem 2/3x=27
Answers
Answer: x = 40.5
Step-by-step explanation:
Simply divide 27/(2/3) to get 40.5
Hope it helps <3
Answer:
x= 40.5
Step-by-step explanation:
We want to find out what x is. Therefore, we must get x by itself on one side of the equation.
2/3x= 27
2/3 and x are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 2/3.
2/3x / 2/3 = 27/ 2/3
When dividing by a fraction, you can also multiply by the reciprocal of the fraction.
To find the reciprocal, flip the numerator (top number) and denominator( bottom number)
2/3 —> 3/2
Multiply both sides of the equation by 3/2
2/3x *3/2 = 27*3/2
x= 27*3/2
x= 27/1*3/2
x= (27*3)/(1*2)
x= 81/2
x= 40.5
John needs to produce a scale diagram of a bedroom using a scale of 1:40. The length of the room is 3.4 metres. What is the length on the diagram? _____ cm
Answers
Answer:
8.5cm
Step-by-step explanation:
convert 3.4metres to cm that is by multiplying by 100
3.4×100=340cm
1rep 40
?rep 340
that is 340/40
=8.5cm
Answer:
8.5 cm
Step-by-step explanation:
Scale = 1:40
Length of the room = 3.4 meters
3.4 meters =3.4 X 100 =340 cm
Since 1 unit on the diagram represents 40 units
The length of the diagram
[tex]=\dfrac{340}{40}\\\\=8.5$ cm[/tex]
The length of the room on the diagram is 8.5 cm.
PLEASE HELP!!! Find the area of the shaded polygon:
Answers
Answer:
147
Step-by-step explanation:
Suppose that the local sales tax rate is 6% and you purchase a computer for $1260.
a. How much tax is paid?
b. What is the computer’s total cost?
Answers
Answer:
a. $75.60
b. $1335.60
Step-by-step explanation:
A. First convert the percentage to a decimal.
6% = 0.06
Multiply the cost of the computer by the decimal to find the tax paid.
$1260 × 0.06 = $75.60
B. To find the total cost, add the cost of the computer with the tax.
$1260 + $75.60 = $1335.60
B: $1335.60
The answer choices below represent different hypothesis tests. Which of the choices are one-tailed tests? Select all correct answers. Select all that apply: H0:p=0.46, Ha:p<0.46 H0:p=0.34, Ha:p≠0.34 H0:p=0.63, Ha:p≠0.63 H0:p=0.35, Ha:p≠0.35 H0:p=0.39, Ha:p<0.39
Answers
Answer:
H0:p=0.46, Ha:p<0.46
H0:p=0.39, Ha:p<0.39
Step-by-step explanation:
A one tailed test occurs in such a way that the value/results gotten is one sided and can either be lesser or greater than the particular given value but cannot be both.
Thus, in this case a one sided test includes
H0:p=0.46, Ha:p<0.46
H0:p=0.39, Ha:p<0.39
Degree Of Length Degree Of Width Degree Of Height Degree Of Volume
Answers
Answer: length = 1, width = 1, height = 3, volume = 5
Step-by-step explanation:
Degree is the biggest exponent for the variables in the expression
Length = 4x - 1. The exponent for x is 1 --> degree = 1
Width = x The exponent for x is 1 --> degree = 1
Height = x³ The exponent for x³ is 3 --> degree = 3
Volume = 4x⁵ - x⁴. The biggest exponent for x is 5 --> degree = 5
Answer:
- First answer: 1
- Second answer: 1
- Third answer: 3
- Last answer: 5
Step-by-step explanation:
Correct on E2020
Help ASAP!!!
Find the given angle, to the nearest degree.
Answers
Answer:
[tex]\boxed{\mathrm{x = 43.8 \ degrees}}[/tex]
Step-by-step explanation:
Let the angle be x
Tan x = [tex]\frac{opposite}{adjacent}[/tex]
Where opposite = 48, Adjacent = 50
Tan x = [tex]\frac{48}{50}[/tex]
Tan x = 0.96
x = [tex]Tan ^{-1}0.96[/tex]
x = 43.8 degrees
Answer:
[tex]\boxed{43.8 \°}[/tex]
Step-by-step explanation:
Use tangent since hypotenuse length is not given.
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
[tex]tan(x)=\frac{48}{50}[/tex]
[tex]x=tan^{-1}(\frac{48}{50} )[/tex]
[tex]x=43.8[/tex]
In △ABC, GF=17 in. What is the length of CF¯¯¯¯¯? Enter your answer in the box.
Answers
Answer:
51 inches
Step-by-step explanation:
The centroid G divides each median into the ratio 2:1, so GF is 1/3 of CF. That is, ...
CF = 3(GF) = 3(17 in)
CF = 51 in
What might be done to make the ratio from the coin flipping exercise become more similar to the ratio from question
Answers
Answer:
When a coin is tossed, we have possibilities of a head, a tail, a head-head, a tail-tail, a head-tail, a tail-head. Similarly, question ratio can be in 1/4, 1/2, 1
Step-by-step explanation:
Ratio of obtaining a head is 0.5 ≡ 50%
Ratio of obtaining a tail is 0.5 ≡ 50%
Ratio of obtaining a head or tail is 0.25 ≡ 25%
Ratio of obtaining a tail or head is 0.25 ≡ 25%
Ratio of obtaining a head is 0.5 ≡ 50%
Ratio of obtaining a tail is 0.5 ≡ 50%
Ratio of obtaining a head or tail is 0.25 ≡ 25%
Ratio of obtaining a tail and head is 0.0625=6.25%
Ratio of obtaining a head and tail is 0.0625=6.25%
Similarly, question ratio can be in 1/4, 1/2, 1
Joylin’s work to solve a math problem is shown below. Problem: Manny walked StartFraction 5 Over 16 EndFraction of the distance to the library in One-third of an hour. If he walks at a constant rate, what is the total amount of time he will spend walking to the library? Step 1: StartFraction 5 Over 16 EndFraction divided by one-third = h Step 2: StartFraction 16 Over 5 EndFraction times StartFraction 3 Over 1 EndFraction = h Step 3: StartFraction 48 Over 5 EndFraction = h Answer: 9 and three-fifths = h What was Joylin’s first error? She switched the divisor and the dividend when creating an equation to model the problem in step 1. She replaced both the divisor and the dividend with their reciprocals when changing division to multiplication in step 2. She multiplied the two numerators and the two denominators to generate her product in step 3. She reduced the improper fraction incorrectly when getting her final answer.
Answers
Answer: She replaced both the divisor and the dividend with their reciprocals when changing division to multiplication in step 2
Step-by-step explanation:
Answer:
She replaced both the divisor and the dividend with their reciprocals when changing division to multiplication in step 2.
Step-by-step explanation:
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
Answers
Answer:
14 Quarters and 28 dimes
Step-by-step explanation: 14 quarters $3.50
28 dimes is $2.80 total is $6.30