Answers
Given data:
The given pattern is shown.
The expression for the dot pattern is,
[tex]a_n=n^2+1_{}[/tex]For step 10 subtitute 10 for n in the above expression.
[tex]\begin{gathered} a_{10}=10^2+1 \\ =101 \end{gathered}[/tex]Thus, the numbers of dots in step 10 are 101.
Related Questions
what is the explicit formula for this sequence-15, -18, -21, -24,...
Answers
Answer: The explicit formula for the following sequence is:
[tex]-15,-18,-21,-24[/tex]According to the pattern in the sequence, the explicit formula is as follows:
[tex]\begin{gathered} a_n=-15-3(n-1) \\ \\ a_n=-15-3n+3 \\ \\ a_n=-12-3n \\ \\ \therefore\rightarrow \\ \\ a_n=-12-3n=-15+(n-1)(-3) \\ \\ a_n=-15+(n-1)(-3) \end{gathered}[/tex]Therefore the answer is Option(2).
-7+×=-2 what's the answer
Answers
Answer:
The value of x is;
[tex]x=5[/tex]Explanation:
Given the equation;
[tex]-7+x=-2[/tex]To solve, let's add 7 to both sides;
[tex]\begin{gathered} -7+7+x=-2+7 \\ x=-2+7 \\ x=5 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=5[/tex]car averages 15 miles per gallon of gas in city driving and 20 miles per gallon in highway driving. At these rates, how many gallons of gas will the car use on a 600 mile trip if 4/5 of the trip is highway driving and the rest is city driving
Answers
We have the average rate of fuel consumption for both city and highway.
Driving in the city, the car can travel 15 miles per gallon, while on highway it can travel 20 miles per gallon.
Alternatively, we can say that driving in the city, the car consumes 1/15 gallons per each mile traveled, while on highway it consumes 1/20 gallons per each mile travelled:
[tex]\begin{gathered} \text{Fuel consumption:} \\ \text{City: }\frac{1}{15}\text{gal}/\text{mile} \\ \text{Highway: }\frac{1}{20}\text{gal}/\text{mile} \end{gathered}[/tex]Expressing the fuel consumption that way will allow us to calculate easier the total amount of fuel consumed later.
The car will travel 600 miles. 4/5 of that trip will be on highway, therefore the remaining 1/5 will be in the city.
With this information, we can calculate exactly how many miles are traveled on highway and how many in the city:
[tex]\text{Miles on highway}=\frac{4}{5}\cdot600=\frac{2400}{5}=480\text{miles}[/tex][tex]\text{Miles on city}=\frac{1}{5}\cdot600=\frac{600}{5}=120\text{miles}[/tex]Then, from those 600 miles traveled, 480 will be on highway while 120 will be on city.
If the travels 120 miles on the city, and it consumes 1/15 gallons per each mile travelled, we can calculate the amount of fuel used in the city as follows:
[tex]120\text{miles}\cdot\frac{1}{15}\frac{\text{gallons}}{\text{mile}}=8\text{gallons}[/tex]While travelling 120 miles in the city, the car will consume 8 gallons.
Similarly, for the amount of fuel used while on the highway:
[tex]480\text{miles}\cdot\frac{1}{20}\frac{\text{gallons}}{\text{mile}}=24\text{gallons}[/tex]While travelling 480 miles in the city, the car will consume 24 gallons.
Now we know the number of gallons the car used each part of the trip. The total amount used for the whole trip is just the sum of them:
[tex]\text{Total fuel consumed}=8\text{gallons}+24\text{gallons}=32\text{gallons}[/tex]The car will use 32 gallons on its 600-mile trip.
what is the area of a circle with the radius 11cm
Answers
The area of a circle is calculated as follows:
[tex]A=\pi r^2[/tex]where r is the radius of the circle.
Substituting with r = 11 cm, we get:
[tex]\begin{gathered} A=\pi\cdot11^2 \\ A=\pi\cdot121 \\ A\approx380.1\operatorname{cm}^2 \end{gathered}[/tex]A standard number cube is tossed. Find the probability of getting P(greater than 2 or less than 4).1/215/66
Answers
The probability of getting P(greater than 2 or less than 4) is given by
[tex]\begin{gathered} P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(greater than 2 AND less than 4)} \\ \text{which is equal to} \\ P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(3)} \end{gathered}[/tex]because the a number greater than 2 and less than 4 is 3.
Since the cube has 6 faces, the probability of getting one face is 1/6, then we have
[tex]\begin{gathered} \text{P(greater than 2)}=P(3)+P(4)+P(5)+P(6) \\ \text{P(greater than 2)}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ \text{P(greater than 2)}=\frac{4}{6} \end{gathered}[/tex]Similarly,
[tex]\begin{gathered} P(\text{less than 4)}=P(3)+P(2)+P(1) \\ P(\text{less than 4)}=\frac{1}{6}+\frac{1}{6}+\frac{1}{6} \\ P(\text{less than 4)}=\frac{3}{6} \end{gathered}[/tex]since P(3)= 1/6, we have
[tex]\begin{gathered} P(\text{greater than 2 OR less than 4)=P(greater than 2)}+P(\text{less than 4)-P(3)} \\ P(\text{greater than 2 OR less than 4)=}\frac{4}{6}+\frac{3}{6}-\frac{1}{6} \end{gathered}[/tex]which gives
[tex]P(\text{greater than 2 OR less than 4)=}\frac{7-1}{6}=\frac{6}{6}=1[/tex]Therefore, the answer is 1.
Find the value of k in the data set so that f (x) is a linear function.
Answers
The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]so
step 1
Find out the slope m
we take two points from the table
(2,3) and (5,9)
[tex]\begin{gathered} m=\frac{9-3}{5-2} \\ \\ m=\frac{6}{3} \\ \\ m=2 \end{gathered}[/tex]step 2
Find out the value of b
we have
m=2
point (2,3)
substitute and solve for b
[tex]\begin{gathered} 3=2(2)+b \\ 3=4+b \\ b=-1 \end{gathered}[/tex]The linear equation is
[tex]f(x)=2x-1[/tex]step 3
Find out the value of k
For x=-2
[tex]\begin{gathered} f(x)=2(-2)-1 \\ f(x)=-4-1 \\ f(x)=-5 \end{gathered}[/tex]therefore
The value of k=-5Help these are all parts of one question just find the answers for them and in your answer label it like part A part B part C part D please and thank you. 1. The 30% discount on a $49 dollhouse2.the 20% tip on a $8 sandwich3. the total cost of a $112.75 meal with a 20% tip4. the price paid for a $15 shirt after a 45% discount
Answers
The 30% discount refers to 30% of 49 less. So, let's find 30% of 49.
[tex]0.30\cdot49=14.7[/tex]The discount is $14.7. To find the final price, we subtract
[tex]49-14.7=34.30[/tex]The final price, after the discount, is $34.30.
PART B.20% tip on an $8 sandwich means we have to find 20% of 8.
[tex]0.20\cdot8=1.6[/tex]The tip is $1.6.
PART C.First, we find the 20% of 112.75.
[tex]0.20\cdot112.75=22.55[/tex]Then, we add the tip to the cost.
[tex]112.75+22.55=135.30[/tex]The final price is $135.30.
PART D.First, we find 45% of 15.
[tex]0.45\cdot15=6.75[/tex]Then, we subtract the discount from the price
[tex]15-6.75=8.25[/tex]The price paid was $8.25.
A website recorded the numbery of referrals it received from social media websitesover a 10-year period. The results can be modeled byy = 2500(1.50)', where t is the year and O S + < 9.Interpret the values of a and b in this situation. Whatis the annual percent increase? Explain.
Answers
Exponential Growth Model
The function that models an exponential growth of some variable is:
[tex]y=a\cdot b^t[/tex]Where a is the initial amount of the variable and b is the base of the exponential function: b = 1 + r and r is the growth rate. We can express the model as:
[tex]y=a\cdot(1+r)^t[/tex]We are given the model as:
[tex]y=2500\cdot(1.50)^t[/tex]We can get the values of a and b by comparing them with the general model:
a = 2500, b = 1.50
We can also find r by solving 1 + r = 1.50 => r = 0.50 = 50%
These values can be interpreted as follows:
There were initially 2500 referrals for the website. It increases by a factor of 1.5 every year, which means the annual percent increase is 50%,
Find the area of the shaded region given the radius of each circle is 4. Answer in exact form is preferred.
Answers
In each circle, we have a sector that subtends an angle of 270 deg at the center, with a radius of 4
We can obtain the area of each sector as :
[tex]\begin{gathered} \text{Area of sector = }\frac{\theta}{360^0}\text{ }\times\text{ }\pi r^2 \\ =\text{ }\frac{270^0}{360^0}\text{ }\times\text{ }\pi\text{ }\times4^2 \\ =\text{ 37.7 square units} \end{gathered}[/tex]Given that there are 4 of such sectors, we have:
[tex]\begin{gathered} \text{Area of shaded region = 4 }\times\text{ 37.7} \\ =\text{ }150.8\text{ square units} \\ =\text{ 151 square units} \end{gathered}[/tex]Answer = 151 square units
Consider the following graph of two functions.(8.9(-2)Step 3 of 4: Find (8 (-2)Enable Zoom/Pan8(x) = 3x - 1101MA10-510-5f(x) = x + 3
Answers
Given:
Two functions are given
[tex]\begin{gathered} f(x)=x+3 \\ g(x)=-3x-1 \end{gathered}[/tex]Required:
We have to find (g.f)(-2)
Explanation:
to find (g.f)(-2) first we have to find the (g.f)(x)
to find (g.f)(x) we have to put value of f(x) as x in g
[tex]g(f)(x)=-3(x+3)-1=-3x-9-1=-3x-10[/tex]now put the value of x-2
[tex]g(f)(-2)=-3(-2)-10=6-10=-4[/tex]Final answer:
[tex](g.f)(-2)=-4[/tex]for given equations
The cost of 10 kg weight is Rs 225, the cost of 8 kg of wheat is?
Answers
ANSWER
[tex]\begin{equation*} Rs180 \end{equation*}[/tex]EXPLANATION
To find the cost of 8kg of wheat, we have to apply proportions.
Let the cost of 8 kg of wheat be x.
We can write that:
[tex]\begin{gathered} 10kg=Rs225 \\ 8kg=x \end{gathered}[/tex]To solve for x, cross-multiply:
[tex]\begin{gathered} x*10=8*225 \\ x=\frac{8*225}{10} \\ x=Rs180 \end{gathered}[/tex]That is the cost of 8 kg of wheat.
Find the value of Q in the following system so that the solution to the system is {(x,y) : x-3y=4}
Answers
We have a pair of equations and we are told that the solution to this system is the equation:
[tex]x-3y=4[/tex]This implies that the system has infinite solutions so one of the equations must be a multiple of the other. We are going to take the first equation and multiply both of its sides by a number k and then compare the result with the second equation:
[tex]\begin{gathered} k\cdot(x-3y)=k\cdot4 \\ kx-3ky=4k\leftrightarrow2x-6y=Q \end{gathered}[/tex]Now let's compare the left sides of this equations. If k=2 then the teo left sides are the same expression. So the second equation must be the first equation multiplied by 2. Then the value of Q is:
[tex]\begin{gathered} Q=4k=4\cdot2 \\ Q=8 \end{gathered}[/tex]So with Q=8 the second equation is a multiple of the first and the solution of the system is the one requested.
AnswerThen the answer is 8.
Answer:
x-3y=4
Step-by-step explanation:
Find the value of each variable in the circle to the right . The dot represents the center of the circle . a= (Simplify your answer . Do not include the degree symbol in your answer .)
Answers
Given that the triangle is formed by the diameter of the triangle, we can deduct that angle b is 90°.
[tex]b=90[/tex]Then, we use the inscribed angle theorem to get
[tex]a=\frac{1}{2}\cdot109=54.5[/tex]Then, we use the interior angles theorem (triangle) to find the third acute angle
[tex]\begin{gathered} a+b+x=180 \\ 54.5+90+x=180 \\ x=180-90-54.5 \\ x=35.5 \end{gathered}[/tex]Now, we find arc c
[tex]\begin{gathered} x=\frac{1}{2}\cdot c \\ 35.5=\frac{1}{2}\cdot c \\ c=2\cdot35.5 \\ c=71 \end{gathered}[/tex]Hence, a = 54.5, b = 90, and c = 71.In 2019, there were 143 teen drivers killed; total fatalities (deaths) were 3,754. What is the % of teen driver deaths?
Answers
3.81%
1) Since the total number of casualties was 3,754 we can find the percentage of 143 teens setting a proportion
3754 -------- 100%
143 ------------ x
Cross multiplying we have
3754x = 14300
x=14300/3754
x=3.809
x≈ 3.81%
2) So the percentage of teen driver deaths was in 2019, 3.81% of all fatalities.
Given sine of theta equals square root of three/ two determine three possible angles for theta on the domain of [0, infinity)
Answers
Answer:
60°, 120°, and 420°.
Explanation:
Given:
[tex]\sin\theta=\frac{\sqrt{3}}{2}[/tex]Take the arcsin of both sides:
[tex]\begin{gathered} \theta=\arcsin(\frac{\sqrt{3}}{2}) \\ \theta=60\degree+360(n)\text{ or }\theta=120\degree+360(n),\theta\in[0,\infty) \end{gathered}[/tex]Therefore, three possible angles for θ on the domain of [0, ∞) are:
[tex]\begin{gathered} \theta=60\degree \\ \theta=120\operatorname{\degree} \\ \theta=60\operatorname{\degree}+360\degree=420\degree \end{gathered}[/tex]Three possible angles are 60°, 120°, and 420°.
What is the possible postulate or theorem to be used?
Answers
Solution
For this case we need to select the possible postulate inorder that the two triangles are similar so we can use:
d. AAS
Since we have two congruent angles and one equivalent side
Hancox Homes is a popular construction company that builds affordable housing. When the company first started, they sold 1 home the first month, 3 homes the second month, 9 homes the third month, and 27 homes the fourth month. DESCRIBE THE PATTERN THEN REPRESENT THE SEQUENCE AS A NUMERIC SEQUENCE AND A TABLE OF VALUE
Answers
The pattern is given below
1, 3, 9, 27
We can clearly see that the terms are indeed the powers of 3
i.e
[tex]\begin{gathered} 3^0\text{ = 1} \\ 3^1\text{ = 3} \\ 3^2\text{ = 9} \\ 3^3\text{ =27} \end{gathered}[/tex]looking closely at the sequence generated, we can show that it follows the geometric sequence as
[tex]r\text{ = }\frac{T_2}{T_1}\text{ = }\frac{T_3}{T_2}\text{ = }\frac{T_{n+1}}{T_n}[/tex]Thus, the common ratio r equals
[tex]r\text{ = }\frac{3}{1}\text{ = }\frac{9}{3}\text{ = }\frac{27}{9}\text{ = 3}[/tex]for any two consecutive numbers in the sequence
Hence, we can express the sequence as a numeric sequence thus:
[tex]\begin{gathered} \text{Recall that T}_n=ar^{n-1} \\ T_n=(1)(3)^{n-1} \\ T_n=3^{n-1} \end{gathered}[/tex]We can also create a table of values to show that this sequence follows the geometric sequence
The function is decreasing on the interval (-0, 0)and increasing on the interval (0, 0).The function is increasing on the interval (-0,0)and decreasing on the interval (0, ).The function is increasing on the interval (-00, 0).The function is decreasing on the interval(-0, 0).
Answers
D; The function is decreasing in the interval;
[tex](-\infty,\infty)[/tex]Here, we want to interpret the given rate of change of the function
From what we have, coming from negative infinity, we can see that there is a decrease in the rate of change of the function. As we move closer to zero, we can see a decrease in the range value of the function
Now, moving away from zero, we can see that there is a continuous decrease as we move towards positive infinity. We can therefore conclude that there is a continuous decrease from the point x = 0 towards the point x = positive infinity
So, the correct choice here is that the function is decreasing in the interval negative infinity to positive infinity
Is it necessary to perform the horizontal line test when finding the inverse of every function? Why or why not?
Answers
The function has an inverse if it is a one-to-one function
We use the horizontal line test to check if the function is a one-to-one function or not
Then it is necessary to use the horizontal line test because if the function is not a one-to-one function there is no inverse to it
The answer is
Yes it is necessary
hello I seem to be having some difficulty with this problem and need some help thank you
Answers
Solution
Given that
The Parker's are saving up to go for a family vacation in 3 years
Number of year, n, is 3 years.
They invested $3100 into an account
Principal, P, is $3100
Annual interest rate of 1.36% compounded monthly
a) To find the amount, A, the Parker's account after 3 years, the formula is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where
[tex]\begin{gathered} r=\frac{1.36}{100}=0.0136 \\ t=12 \end{gathered}[/tex]Substitute the variables into the formula above
[tex]\begin{gathered} A=3100(1+\frac{0.0136}{12})^{3\times12} \\ A=3100(1+\frac{0.0136}{12})^{36}=\text{ \$3229.02} \\ A=\text{ \$3229.02 \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the amount in the Parker's account after 3 years is $3,229.02 (nearest cent)
b) To find the interest, I, earned on the Parker's investment, the formula is
[tex]I=A-P[/tex]Where
[tex]\begin{gathered} A=\text{ \$3229.02} \\ P=\text{ \$3100} \end{gathered}[/tex]Substitute the values into the formula to find the interest above
[tex]\begin{gathered} I=A-P \\ I=3229.02-3100=\text{ \$129.02} \\ I=\text{ \$129.02} \end{gathered}[/tex]Hence, the interest, I, earned on the Parker's investment is $129.02 (nearest cent)
Please solve this question for me Note: the value of p=2
Answers
Given:
[tex]\sum_{n\mathop{=}1}^{\infty}\frac{(np)^{-2}}{\frac{2}{n^2}+\frac{3}{n}+1}[/tex]Find-:
Find the formula for n partial sum, and determine whether the series converges or diverges.
Explanation-:
The value is:
[tex]\begin{gathered} =\sum_{n\mathop{=}1}^{\infty}\frac{(np)^{-2}}{\frac{2}{n^2}+\frac{3}{n}+1} \\ \\ =\sum_{n\mathop{=}1}^{\infty}\frac{1}{n^2p^2(\frac{1}{n^2}+\frac{3}{n}+1)} \\ \\ =\sum_{n\mathop{=}1}^{\infty}\frac{1}{p^2(\frac{n^2}{n^2}+\frac{3n^2}{n}+n^2)} \\ \\ =\sum_{n\mathop{=}1}^{\infty}\frac{1}{p^2(1+3n+n^2)} \end{gathered}[/tex]So, the value is,
[tex]=\frac{1}{p^2}\sum_{n\mathop{=}1}^{\infty}\frac{1}{n^2+3n+1}[/tex]Apply telescoping series
[tex]\sum_{n\mathop{=}1}^{\infty}\frac{1}{n^2+3n+1}=\frac{1}{2}[/tex]The value is:
[tex]\begin{gathered} =\frac{1}{p^2}\times\frac{1}{2} \\ \\ =\frac{1}{2p^2} \end{gathered}[/tex]It is a series of converges.
[tex]\begin{gathered} =\frac{1}{2p^2} \\ \\ =\frac{1}{2(2)^2} \\ \\ =\frac{1}{2\times4} \\ \\ =\frac{1}{8} \end{gathered}[/tex]32. Find the equation of the line that matches thefollowing data table:Xy491661A. y = -x + 10B. y = x +9C. y = -3x + 3D. y = 3x + 9
Answers
ANSWER
A. y = -1/4x + 10
EXPLANATION
We have to find the equation of the line in slope-intercept form,
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]In this case, only two points are given, so the slope of the line is,
[tex]m=\frac{6-9}{16-4}=\frac{-3}{12}=-\frac{1}{4}[/tex]So, for now, the equation is,
[tex]y=-\frac{1}{4}x+b[/tex]To find the y-intercept, b, replace x and y with one of the points,
[tex]9=-\frac{1}{4}(4)+b[/tex]And solve for b,
[tex]9=-1+b\text{ }\Rightarrow\text{ }b=9+1=10[/tex]Hence, the equation of the line is y = -1/4x + 10.
45 points!!!!
If triangles ABC and ADE are similar in this diagram, what is the length of the pond?
The pond is ? ft long.
Answers
Answer:
a
Step-by-step explanation:
ans. 87.25 ft
(solution shown in picture)
A research study asked 1749 homeowners how many bedrooms were in their homes. The results are shown in the table below. What is the probability that a homeowner chosen at random has 3 bedrooms? # of bedrooms # of homeowners12 or less. 4903. 5774. 4555 ot more. 227Answers:13%26%28%33%
Answers
Probability that a homeowner chosen at random has 3 bedrooms:
[tex]\begin{gathered} P(3\text{ bedrooms)=}\frac{\#homeowners\text{ with 3 bedrooms}}{\#\text{total homeowners}} \\ \\ P(3\text{ bedrooms)=}\frac{577}{490+577+455+227}=\frac{577}{1749}\approx0.33 \end{gathered}[/tex]Multiply the probability by 100 to get it in %:
[tex]0.33\cdot100=33[/tex]Then, the probability that a homeowner chosen at random has 3 bedrooms is 33%BRAINLIEST Look at the image for the problem, round to the nearest hundredth if possible.
Answers
use the elimination method to solve the system of equations write your answer as ordered pair
Answers
Solution:
Given the system of equations below;
[tex]\begin{gathered} 4x+6y=24...(1) \\ 4x-y=10...(2) \end{gathered}[/tex]Applying the elimination method
Eliminating the variable x by subtracting equation (2) from (1)
[tex]\begin{gathered} 4x+6y-(4x-y)=24-10 \\ 4x+6y-4x+y=14 \\ Collect\text{ like terms} \\ 4x-4x+6y+y=14 \\ 7y=14 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7y}{7}=\frac{14}{7} \\ y=2 \end{gathered}[/tex]Substituting 2 for y into equation (2) to find the value of x
[tex]\begin{gathered} 4x-y=10 \\ 4x-2=10 \\ Collect\text{ like terms} \\ 4x=10+2 \\ 4x=12 \\ Divide\text{ both sides by 4} \\ \frac{4x}{4}=\frac{12}{4} \\ x=3 \end{gathered}[/tex]The solution to the system of equations in ordered pair is
[tex](3,2)[/tex]To check the solution
Compute the probability of tossing a six-sided die and getting an even number
Answers
sixe sided die so number of possible outcome is=6
And a die with even number is (2,4,6)
so number of favorable outcome is:3
then probability is:
[tex]\begin{gathered} \text{probability}=\frac{favorable-outcom\text{ }}{\text{total outcom}} \\ =\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]so probability is half.
at the candy store Jackson spent $26 on 8 pounds of candy how much did he spend per pound
Answers
Money spent: $26
Pounds = 8
Divide the amount of money (26) by the pounds:
26 /8 = $3.25 per pound
A triangular prism has base edges 3 cm ,6 cm, and 7 cm long . it's lateral area is 272 cm2. what is the highest of the prism ?The height of the prism is _cm. (simplify your answer .)
Answers
ANSWER
h = 17cm
EXPLANATION
The lateral area is the sum of the areas of the non-triangular faces - which are rec
PART A: Solve both linear equations for y = mx + b form. (2 points) y = -2x + 3 2x + 2y = 4
Answers
Answer:
(1, 1)
Explanation;
Given the simultaneous equation:
y = -2x + 3 ..... 1
2x + 2y = 4 ...... 2
Substitute equation 1 into 2;
2x+2y = 4
2x+2(-2x+3) = 4
Expand
2x-4x+6 = 4
-2x + 6 = 4
-2x = 4 - 6
-2x = -2
Divide both sides by -2
-2x/-2 = -2/-2
x = 1
Substituting x = 1 into equation 1;
From 1:
y = -2x + 3
y = -2(1) + 3
y = -2 + 3
y = 1
Hence the solution to the system of equation is (1, 1)