Given:
The explicit formula is
[tex]2\times7^{(n-1)}[/tex]Required:
To find the 8th term of the sequence.
Explanation:
For n=8,
[tex]\begin{gathered} =2\times7^{(8-1)} \\ \\ =2\times7^7 \\ \\ =2\times7\times7\times7\times7\times7\times7\times7 \\ \\ =1647086 \end{gathered}[/tex]Final Answer:
The first option is correct.
[tex]1647086[/tex]What is the y-intercept in this equation: -1.5= y-12/0-4
The y-intercept in this equation: -1.5= y-12/0-4 is 18.
What is equation?
Equation: A statement stating the equality of two expressions with variables or integers. Essentially, equations are questions, and attempt to systematically find the answers to these questions have been the inspiration for the development of mathematics.
Given Equation:
-1.5 = y - 12 / 0-4
Solve the above equation, and we get,
-1.5 = y - 12 / (-4)
y -12 = 6.0
y = 18
Therefore, the y-intercept in this equation: -1.5= y-12/0-4 is 18.
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can you please help me
Answer:
15
Explanation:
The y-intercept of a line is the point where it intersects the y-axis. This happens when x = 0; therefore, the y-coordinate of the y-axis is found by putting x = 0 in the equation given. This gives
[tex]18(0)-y=-15[/tex][tex]-y=-15[/tex][tex]y=15[/tex]which is our answer!
The formula S=C(1+r) models inflation, where C = the value today, r = the annual inflation rate, and S = the inflated value t years from now. a. If the inflation rate is 6%, how much will a house now worth $465,000 be worth in 10 years? b. If the inflation rate is 3%, how much will a house now worth $510,000 be worth in 5 years?
The formula that models inflation is
[tex]S=C(1+r)^t[/tex]C= value today
r= annual inflation rate → usually this value is given as a percentage, but when you input the value in the formula, you have to express it as a decimal value.
S= the inflated value given a determined period of time (t).
a.
r=6%=6/100=0.06/year
C=$465000
t=10 years
[tex]\begin{gathered} S=465000(1+0.06)^{10} \\ S=832744.1789 \end{gathered}[/tex]The price of the house in 10 years at an inflation rate of 6% will be S=$832744.18
b.
r=3%=3/100=0.03/year
C=$510000
t=5years
[tex]\begin{gathered} S=510000(1+0.03)^5 \\ S=437954.3531 \end{gathered}[/tex]The price of the house in 5 years at an inflation rate of 3% will be S=$437954.35
The two triangles below are similar. Also, m A = 15° and m ZC - 35° as shown below Find m2P, m 2Q, and m ZR. Assume the triangles are accurately drawn
Answer
Angle R = 15°
Angle P = 130°
Angle Q = 35°
Explanation
First noting that the sum of angles in a triangle is 180°.
We first need to calculate the Angle B for the first triangle.
Angle A + Angle B + Angle C = 180°
15° + Angle B + 35° = 180°
Angle B + 50° = 180°
Angle B = 180° - 50°
Angle B = 130°
We are then told to find Angles P, Q and R.
We are told that the two triangles are similar .
Two similar triangles will have the same angle measures.
So, we just need to note the corresponding angles and equate the unknowns.
Triangle ABC is similar to Triangle RPQ
Angle R = Angle A = 15°
Angle P = Angle B = 130°
Angle Q = Angle C = 35°
Hope this Helps!!!
Can you please help me find the area? Thank you. :)))
The figure shown in the picture is a rectangular shape that is missing a triangular piece. To determine the area of the figure you have to determine the area of the rectangle and the area of the triangular piece, then you have to subtract the area of the triangle from the area of the rectangle.
The rectangular shape has a width of 12 inches and a length of 20 inches. The area of the rectangle is equal to the multiplication of the width (w) and the length (l), following the formula:
[tex]A=w\cdot l[/tex]For our rectangle w=12 in and l=20 in, the area is:
[tex]\begin{gathered} A_{\text{rectangle}}=12\cdot20 \\ A_{\text{rectangle}}=240in^2 \end{gathered}[/tex]The triangular piece has a height of 6in and its base has a length unknown. Before calculating the area of the triangle, you have to determine the length of the base, which I marked with an "x" in the sketch above.
The length of the rectangle is 20 inches, the triangular piece divides this length into three segments, two of which measure 8 inches and the third one is of unknown length.
You can determine the value of x as follows:
[tex]\begin{gathered} 20=8+8+x \\ 20=16+x \\ 20-16=x \\ 4=x \end{gathered}[/tex]x=4 in → this means that the base of the triangle is 4in long.
The area of the triangle is equal to half the product of the base by the height, following the formula:
[tex]A=\frac{b\cdot h}{2}[/tex]For our triangle, the base is b=4in and the height is h=6in, then the area is:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{4\cdot6}{2} \\ A_{\text{triangle}}=\frac{24}{2} \\ A_{\text{triangle}}=12in^2 \end{gathered}[/tex]Finally, to determine the area of the shape you have to subtract the area of the triangle from the area of the rectangle:
[tex]\begin{gathered} A_{\text{total}}=A_{\text{rectangle}}-A_{\text{triangle}} \\ A_{\text{total}}=240-12 \\ A_{\text{total}}=228in^2 \end{gathered}[/tex]The area of the figure is 228in²
Hello,Can you please help with question 33 on the photo? Thank you
With the help of the given formula, we can find the first four terms of the sequence:
[tex]\begin{gathered} a_1=30 \\ a_2=a_{2-1}-10=a_1-10=20 \\ a_3=a_{3-1}-10=a_2-10=10 \\ a_4=a_{4-1}-10=a_3-10=0 \end{gathered}[/tex]Then, the first four terms of the sequence are 30, 20, 10, 0, ...
Now, as we can see, this is an arithmetic sequence because there is a common difference between each term. The explicit formula of an arithmetic sequence is shown below:
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ \text{ Where} \\ \text{ d is the common difference} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a_1=30 \\ d=-10 \end{gathered}[/tex][tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_n=30-10(n-1) \\ \text{ Apply the distributive property} \\ a_n=30-10*n-10*-1 \\ a_n=30-10n+10 \\ a_n=-10n+40 \end{gathered}[/tex]Thus, a formula for the general term of the sequence is:
[tex]a_{n}=-10n+40[/tex]Now, we substitute n = 20 in the above formula to find the 20th term of the sequence:
[tex]\begin{gathered} a_{n}=-10n+40 \\ a_{20}=-10(20)+40 \\ a_{20}=-200+40 \\ a_{20}=-160 \end{gathered}[/tex]AnswerA formula for the general term of the sequence is:
[tex]a_{n}=-10n+40[/tex]The 20th term of the sequence is -160.
Jada bought an art kit with 50 colored pencils. She and her 3 sisters will share the pencils equally. How many pencils will each person receive? Will there be any pencils left over? If so, how many?
Each will get 16 coloured pencils and 2 will be the left over
Step-by-step explanation:
Give 10 pencil each then add 6 more for each one and the answer will be 16 each and multiple 3×16 =48 and remainder 2
Find each unknown function value or x value for f(x) = 4x - 7 and g(x) = -3x + 5
Step 1
Find f(2)
[tex]To\text{ do this we substitute for f= 2 in f(x)}[/tex][tex]\begin{gathered} f(x)\text{ = }4x-7 \\ f(2)\text{ = 4(2) -7 = 8 - 7 = 1} \end{gathered}[/tex]Step 2
Find f(0)
[tex]f(0)\text{ = 4(0) -7 = 0 - 7 = -7}[/tex]Step 3
Find f(-3)
[tex]f(-3)\text{ = 4(-3) -7 = -12 -7 = -19}[/tex]Step 4
Find x, when f(x) = -3
[tex]\begin{gathered} f(x)\text{ = -3}--------------(1) \\ f(x)\text{ =4x-7}---------------(2) \\ \text{Equate both equations} \\ -3=4x-7 \\ -3+7\text{ = 4x} \\ 4x\text{ = 4} \\ x\text{ = }\frac{4}{4}=1 \end{gathered}[/tex]Find the image of the given pointunder the given translation.
Answer: P' = (4, 4)
Explanation
As the given point is (8, –3), then the transformation is:
[tex]T(x,y)=(x-4,y+7)=(8-4,-3+7)[/tex][tex]T(x,y)=(4,4)[/tex]Step 1 Step 2 Step 3 Using the figures above, how many small squares will there be in step 4 and step 15? a. Step 4 = b. Step 15 =
Step 4 = 16 squares
Step 15 = 225 squares
1) In the 1st step we can see, 1 square. In the 2nd, 4, and on the third one 9
So there's a sequence, 1, 4, 9
2) We can write the positions and raise them to the 2nd power we can see how it grows:
position (steps) n | 1 | 2 | 3
# squares | 1 | 4 | 9
3) We can derive a formula for that sequence:
[tex]a_n=n^2[/tex]Following this rule, we can find that
Step 4 = 4² = 16 squares
Step 15 = 15² = 225 squares
fill in the blank with the correct answer. the number _______is divisibel by 2, 3, 4, 5, and 6
a)44
b)180
c)280
d)385
Answer:
b) 180
Explanation:
[tex]180 / 2 = 90\\180 / 3 = 60\\180 / 4 = 45\\180 / 5 = 36\\180 / 6 = 30[/tex]
Hope you have a nice day and a nice Thanksgiving!
A brainiliest would also be nice. thx.
Solve x2 + 5x = 0.Step 1. Factor x2 + 5x as the product of two linear expressions.
Taking common factor x:
[tex]x(x+5)=0[/tex]Equal each factor to zero, and solve for x:
[tex]x=0[/tex][tex]\begin{gathered} x+5=0 \\ x=-5 \end{gathered}[/tex]So, the solution is:
[tex]\begin{gathered} x_1=0 \\ x_2=-5 \end{gathered}[/tex]in a circle the radius is 11.5 which is the circumference??
The circumference of a circle is the perimeter or external measure.
Given a circle of radius r, the circumference is calculated as:
C=2 π r
The circle has a radius of r=11.5 units
The circumference is:
C=2 π (11.5) = 72.26 units
The circumference is 72.26 units
solve the system of linear equations by substitution 3y=-2x and y=x-5
Step 1
Given;
[tex]\begin{gathered} 3y=-2x--(1) \\ y=x-5--(2) \end{gathered}[/tex]Required; To solve the system of linear equations
Step 2
Find the value of y and x
[tex]\begin{gathered} Substitute\text{ 2 into 1} \\ 3(x-5)=-2x \\ 3x-15=-2x \\ 5x=15 \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \end{gathered}[/tex][tex]\begin{gathered} From\text{ 2, y=x-5} \\ y=3-5=-2 \end{gathered}[/tex]Answers;
[tex]x=3,\text{ y=-2}[/tex]A small publishing company is planning to publish a new book. the production cost will include one-time fix costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-timed fixed costs will total $15,756, and the variable costs will be $23.50 per book. With the other method, the one-timed costs will total $48,108, and the variable costs will be $12 per book. For how many books produced will the costs from the two methods be the same?
What we must do is equal both equations like this:
[tex]15756+23.5\cdot x=48108+12\cdot x[/tex]solving for x (numbers of books):
[tex]\begin{gathered} 23.5\cdot x-12\cdot x=48108-15756 \\ 11.5\cdot x=32352 \\ x=\frac{32352}{11.5} \\ x=2813.2=2813 \end{gathered}[/tex]In aproximately 2813 books
Simplify: 6-(-9) divided by -9/-4
Answer:
6 2/3
Explanation:
Given the expression:
[tex]\lbrack6-\mleft(-9\mright)\rbrack\div\frac{-9}{-4}[/tex]First, we simplify to obtain:
[tex]=\lbrack6+9\rbrack\div-\frac{9}{-4}[/tex]Note that -9/-4=9/4. The minus sign cancels each other out.
This gives us:
[tex]15\div\frac{9}{4}[/tex]We then change the division sign to multiplication as shown below:
[tex]\begin{gathered} =15\times\frac{4}{9} \\ =\frac{60}{9} \\ =6\frac{6}{9} \\ =6\frac{2}{3} \end{gathered}[/tex]Third-degree, with zeros of 2-i, 2+i and 3 and a leading coefficient of -4
Answer:
Step-by-step explanation:
Subtract.7x2 - 5x+3(2x2 +7x-4)A. 5x2 - 2x + 7B. 5x2 - 12x +7C. 5x2 + 12x-1D. 5x2 + 2x-1
We have to evaluate the expression 7x^2 - 5x + 3 - (2x^2 +7x-4):
[tex]\begin{gathered} 7x^2-5x+3-(2x^2+7x-4) \\ (7-2)x^2+(-5-7)x+(3-(-4)) \\ 5x^2-12x+(3+4) \\ 5x^2-12x+7 \end{gathered}[/tex]Answer: B. 5x2 - 12x +7
Inequality statement for -13,-25,-8
The inequality statement for -13,-25,-8 is -13 > -25 < -8.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
It should be noted that -13 is greater than -25 while -25 is less than -8.
In this case, -13 > -25 < -8.
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5: =3:21 its equivalent ratios
The number that makes the ratios equivalent is 35. Thus, the ratio becomes 5:35 = 3:21
Equivalent ratiosFrom the question, we are to determine the number that will make the two ratios equivalent ratios.
From the given equation,
5: = 3:21
Let the unknown number be x.
Thus,
The equation becomes
5:x = 3:21
Then,
We can write that
5/x = 3/21
Cross multiply
x × 3 = 5 × 21
3x = 105
Divide both sides by 3
3x/3 = 105/3
x = 35
Hence, the number is 35
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For any right triangle, the side lengths of the triangle can be put in the equation a^2+ b^2 = c^2 where a, b, and c are the side lengths. A triangle with the side lengths 3 inches, 4 inches, and 5 inches is a right triangle. Which way(s) can you substitute the values into the equation to make it true? Which variable has to match the longest side length? Why?
It is given that the side lengths of any right triangle can be put in the equation:
[tex]a^2+b^2=c^2[/tex]For a triangle with the side lengths 3 inches, 4 inches, and 5 inches, it can be substituted in two ways that will make the equation true:
Let a=3, b=4, and c=5:
[tex]\begin{gathered} 3^2+4^2=5^2 \\ \Rightarrow9+16=25 \\ \Rightarrow25=25 \end{gathered}[/tex]Hence, the equation is true.
You can also substitute a=4, b=3, and c=5.
This will also give the same result.
Notice that variable c has to match the longest side length.
The reason for this is that equality can only hold if the longest side is the variable at the right, if not there'll be an inequality instead.
A local bakery has determined the probability distribution for the number of cheesecake that they sell in a given day let X equal the number of cheesecake sold on a randomly selected day
1) First, from the question we see that we have a table with the probability distribution p(X) for the number of cheesecakes (X) sold on a randomly selected day. We know that the numbers in the table for P(X) should sum up to 1, that's because the total probability always sums 1. So using this fact we can see that:
[tex]P(x=15)=0.28[/tex]2) The probability of selling at least 10 cheesecakes is the sum of probabilities P(x) for x ≥ 10, using the data from the table and the probability obtained above we have:
[tex]\begin{gathered} P(x\ge10)=P(x=10)+P(x=15)+P(x=20) \\ P(x\ge10)=0.21+0.28+0.1 \\ P(x\ge10)=0.59 \end{gathered}[/tex]3) The probability of selling 5 or 15 cheesecakes is the joint probability of the events of selling 5 cheesecakes P(x = 5) or 15 cheesecakes P(x = 15) because they are independent events (i.e. P(x=5 ∩ x=15) = 0), we have:
[tex]\begin{gathered} P(x=5orx=15)=P(x=5)+P(x=15)-P(x=5andx=15) \\ P(x=5orx=15)=0.3+0.28-0 \\ P(x=5orx=15)=0.58 \end{gathered}[/tex]4) From the table we see that we don't have an assigned value for the probability of selling x = 25 cheesecakes, so the probability for this event is zero:
[tex]P(x=25)=0[/tex]5) The probability of selling at most 10 cheesecakes is the sum of the probabilities P(x) for x ≤ 10, using the data from the table we have:
[tex]\begin{gathered} P(x\leq10)=P(x=0)+P(x=5)+P(x=10) \\ P(x\leq10)=0.11+0.3+0.21 \\ P(x\leq10)=0.62 \end{gathered}[/tex]6) Finally, we must compute the expected value μ of cheesecakes sold on any given day, applying the following formula and the data of the table we get:
[tex]\begin{gathered} \mu=\sum ^{}_iX_i\cdot P(X_i) \\ \mu=0\cdot0.11+5\cdot0.3+10\cdot0.21+15\cdot0.28+20\cdot0.1 \\ \mu=9.8 \end{gathered}[/tex]Answers summary:
1) P(x = 15) = 0.28
2) P(x ≥ 10) = 0.59
3) P(x = 5 or x = 15) = 0.58
4) P(x = 25) = 0
5) P(x ≤ 10) = 0.62
6) μ = 9.8
Select all of the expressions that are less than 10103O A 103хB. 1x 10oC 103 x 2OD } x 103O E 103
Let's check every option:
[tex]10\frac{2}{3}=\frac{32}{3}\approx10.667[/tex]A.
[tex]10\frac{2}{3}\times\frac{9}{10}=9.6<10.667[/tex]This option is correct
------------------------
B.
[tex]1\times10\frac{2}{3}=10.667=10.667[/tex]This option is not correct.
----------------------
C.
[tex]10\frac{2}{3}\times2\frac{1}{3}\approx24.888>10.667[/tex]This option is not correct
-------------------
D.
[tex]\frac{1}{8}\times10\frac{2}{3}\approx1.33<10.667[/tex]This option is correct
----------------------------
E.
[tex]10\frac{2}{3}\times\frac{3}{5}=6.4<10.667[/tex]This option is correct
Answer:
A
D
E
Use my radians find the amplitude and period of each function then graph
For a function of the form:
[tex]y=acos(b\theta)[/tex]a = amplitude = 2
b = angular frequency = 1/4
The period can be calculated as follows:
[tex]\begin{gathered} T=\frac{2\pi}{b} \\ So: \\ T=\frac{2\pi}{1/4} \\ T=8\pi \end{gathered}[/tex]Now, we can graph the function easily:
Zero and negative exponentswrite in simplest for without zero or negative exponents10c -²
Explanation
remember some properties of the exponents
[tex]\begin{gathered} a^m\cdot a^n=a^{m+n} \\ (a^m)^n=a^{m\cdot n} \\ a^{-m}=\frac{1}{a^m} \end{gathered}[/tex]Hence,apply
[tex]10c^{-2}=10\cdot c^{-2}=\frac{10}{c^2}[/tex]I hope this helps you
Solve each equation by using the square root property. 2x^2–9=11
We want to solve
2x^2–9=11
First, isolate the portion of the equation that's actually being squared. That is:
2x^2 = 11 + 9
that is equivalent to:
2x^2 = 20
that is equivalent to
x^2 = 20/ 2 = 10
that is
x^2 = 10
Now square root both sides and simplify, that is:
[tex]\sqrt[]{x^2\text{ }}=\text{ }\sqrt[]{10}[/tex]we know that the square root is the inverse function of the function x^ 2, so we can cancel the square :
[tex]x\text{ = }\sqrt[]{10}[/tex]but note that there is always the possibility of two roots for every square root: one positive and one negative: so the final answer is:
[tex]x\text{ = +/- }\sqrt[]{10}[/tex]
A spinner is shown below. what is the probability that a 5 is spun?
Answer:
The probability that 5 is spun is;
[tex]\begin{gathered} P(5)=\frac{2}{9} \\ or \\ P(5)=22.22\text{\%} \end{gathered}[/tex]Explanation:
Given the figure in the attached image.
We will assume that each of the sectors are of the same size.
The probability of spinning a 5 is equal to the number of sectors with 5 divided by the total number of sectors.
[tex]\begin{gathered} n(5)=2 \\ n(\text{total)}=9 \end{gathered}[/tex]So, the probability that 5 is spun is;
[tex]\begin{gathered} P(5)=\frac{n(5)}{n(\text{total)}}=\frac{2}{9} \\ P(5)=\frac{2}{9} \\ \text{ in percentage;} \\ P(5)=\frac{2}{9}\times100\text{\%} \\ P(5)=22.22\text{\%} \end{gathered}[/tex]Therefore, the probability that 5 is spun is;
[tex]\begin{gathered} P(5)=\frac{2}{9} \\ or \\ P(5)=22.22\text{\%} \end{gathered}[/tex]A data set has these values: 6, 8, 8, 10, 10, 10, 10, 12, 12, 14. The histogram ofthe distribution is shown.Aanb542<-057 9 11 13 15Data valuesWhich statement does not describe the data set?
It has a range of [tex]$15^{\prime \prime}$[/tex] is not describe the data set.
The data set is Symmetric.
it has a mode m=10= median = mean.
[tex]$$\begin{aligned}\text { Range } &=14-6 \\&=8\end{aligned}$$[/tex]
So option (c) is correct.
"It has a range of [tex]$15^{\prime \prime}$[/tex]
A data set is, for example, each student's test scores in a specific class. A data set is the number of fish consumed by each dolphin in an aquarium.
A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.
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a vector s has the initial point (-2,-4) and terminal point (-1,3) write s in the form s = ai + bj
To write the vector s in the form s=ai + bj, we can use the next formula:
[tex]\vec{s}=(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}[/tex]Where (x1,y1) are the coordinates of the initial point and (x2,y2) are the coordinates of the terminal point, by replacing these values we have:
[tex]\begin{gathered} \vec{s}=((-1)-(-2))\vec{i}+(3-(-4))\vec{j} \\ \vec{s}=((-1)+2)\vec{i}+(3+4)\vec{j} \\ \vec{s}=(1)\vec{i}+(7)\vec{j} \end{gathered}[/tex]Then the vector s in the form s=ai+bj is: s= 1i + 7j
Daniel opened a small business. His profit for the first month was -$503. If his average profit for months 2-4 was $-421, what was the total profit for months 1-4?Please help me
If Daniel profit for the first month was -$503. If his average profit for months 2-4 was $-421, then $924 was the total profit for months 1-4
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Daniel opened a small business.
Profit for the first month was -$503 five hundred and three
Average profit for months 2-4 was $-421, four hundred and twenty one.
We need to find the total profit for months 1-4
Add profit for 1s month and 2-4 months.
$503+$421
$924
Hence $924 was the total profit for months 1-4
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