The arithmetic sequence A(n) = –3 + (n – 1)(–2.2) yields the first, fourth, and tenth terms as -3, -9.6, and -22.8 respectively when n is substituted with the corresponding term number.
Explanation:The arithmetic sequence described by the rule A(n) = –3 + (n – 1)(–2.2) can be used to find specific terms of the sequence. To find the first term, plug in n = 1 into the formula to get A(1) = -3 + (1 - 1)(-2.2) = -3. The fourth term can be found by plugging in n = 4 which yields A(4) = -3 + (4 - 1)(-2.2) = -9.6. The tenth term is calculated as A(10) = -3 + (10 - 1)(-2.2) = -22.8. Therefore, the first, fourth, and tenth terms are -3, -9.6, and -22.8 respectively.
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A dart hits the circular dartboard shown below at a random point. find the probability that the dart lands in the shaded square region. the radius of the dartboard is 11in, and each side of the shaded region is 4in.
Answer:
.13 or 13%
Step-by-step explanation:
P = area of shaded region/area of entire board
Entire area: 3.14 * (11 * 11) = 379.94
shaded area: 3.14 * (4 *4) = 50.24
p = 50.24/379.94 = .13 or 13%
Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 7? 20 POINTS
Answer with explanation:
The exponential function is
[tex]3^y=7\\\\ \text{taking log on both sides}\\\\y\log3=\log7\\\\y=\frac{\log7}{\log3}\\\\y=\log_{3}7\\\\y=\frac{0.8450}{0.477}\\\\y=1.77[/tex]
It is equation of a line, parallel to X axis.
Drawn the graph of the function , which cuts the y axis at ,(1.77,0).
None of the curve matches with the given Options.
In PQR, point S lies on QR. If PS is perpendicular to QR, which term describes PS?A. Perpendicular bisector
B. Angle bisector
C. Median
D. Altitude
George and Carmen went on a bicycle trip. They took a bus to their starting point, and then biked the rest. They traveled 275 kilometers in total, and they biked 55 kilometers more than they were bussed. Let x = kilometers traveled by bike and y = kilometers traveled by bus. Find how many kilometers they traveled by bike.
In a community fitness group, 40% of members run for exercise and 36% of members run and play a sport. What percentage of members who run for exercise also play a sport?
By dividing the percentage of community fitness group members who run and play a sport (36%) by those who run for exercise (40%), we find that 90% of the members who run for exercise also play a sport.
To determine the percentage of community fitness group members who run for exercise and also play a sport, we can use the information provided. The question states that 40% of members run for exercise and 36% of members run and play a sport. To find what percentage of members who run also play a sport, we need to find the proportion of runners who are also sport players.
To do this, we divide the percentage of members who run and play a sport by the percentage who only run:
Percentage of runners who also play a sport = (Percentage of members who run and play a sport) / (Percentage of members who run for exercise)
So,
Percentage of runners who also play a sport = 36% / 40% = 0.9
We then multiply by 100 to convert this to a percentage:
0.9 × 100 = 90%.
Therefore, 90% of the members who run for exercise also play a sport.
How would you graph a point at -5?
A: Put a point 5 units to the right of zero.
B: Put a point at zero.
C: Put a point 5 units to the left of zero.
Answer:
C: Put a point 5 units to the left of zero.
Step-by-step explanation:
Write an equation of the line that passes through (-5,-1) and is parallel to the line y=4x-6
How is the multiplication property for inequalities different from the multiplication property of equality?
what doesThe mathematical expression 2 ∈ V means
Sets that cover a range of points, including those between isolated points, and cannot be written as lists are called _______ sets.
A. mapping
B. continuous
C. finite
D. discrete
Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula
V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2
Answer:
option C is correct
[tex]8x^5+24x^3+48x^2[/tex]
Step-by-step explanation:
As per the statement:
The length(l), width(w) and height(h) of the rectangular prism are:
l = 4x
w = 2x
[tex]h = x^3+3x+6[/tex]
We have to find volume.
Use the formula:
[tex]V = lwh[/tex]
Substitute the given values we have;
[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]
⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]
Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]V = 8x^5+24x^3+48x^2[/tex]
Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]
If the volume for 3-D pyramid A is 300 cm3 and the volume for 3-D pyramid B is 900 cm3, how many times bigger is the volume of pyramid B than pyramid A?
Answer:
Volume of pyramid B is three times bigger than the volume of pyramid A
Step-by-step explanation:
We are given that:
The volume for 3-D pyramid A is 300 cm³ .
and the volume for 3-D pyramid B is 900 cm³.
We have to tell how many times bigger is volume of pyramid B than volume of pyramid A.
volume of 3-D pyramid B= 900 cm³
= 3×300 cm³
= 3×volume of 3-D pyramid A
Hence, Volume of pyramid B is three times bigger than the volume of pyramid A
Answer:
Step-by-step explanation: 3%
What methods can be used to rewrite square trinomials and difference of squares binomials as separate factors?
Final answer:
Square trinomials and difference of squares binomials can be rewritten into separate factors using methods such as completing the square, the difference of squares method, and factoring by grouping.
Explanation:
Completing the square method: Rewrite square trinomials by completing the square to factor them into separate factors. For example, [tex]x^2 + 6x + 9[/tex] can be written as (x + 3)(x + 3).
Difference of squares method: Rewrite binomials with a difference of squares by factoring them into separate factors. For instance, [tex]x^2 - 4[/tex] can be expressed as (x + 2)(x - 2).
Factoring by grouping: For more complex trinomials, you can use the method of factoring by grouping to rewrite them as separate factors.
Write an equation in point-slope form of the line having the given slope that contains the given point. m=5m=5, (4,3)
Which method(s) can be used to solve a system of equations? Select all that apply.
distributing
graphing
substitution
formulas
addition
modeling
Answer:graphong, substitution, addition
Step-by-step explanation:
What is the radius of a circle with an area of 32.1 sq ft
What is a tangent of a circle
Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.
Answer:
The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
Step-by-step explanation:
The given expression is
[tex]3n+3[/tex]
For n=1,
[tex]3(1)+3=6[/tex]
For n=2,
[tex]3(2)+3=9[/tex]
For n=3,
[tex]3(3)+3=12[/tex]
The required AP is
[tex]6, 9, 12, ...[/tex]
Here first term is 6 and common difference is 3.
The sum of n terms of an AP is
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{13}=\frac{13}{2}[2(6)+(13-1)(3)][/tex]
[tex]S_{13}=\frac{13}{2}[12+36][/tex]
[tex]S_{13}=312[/tex]
Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
Find the number of possible positive real zeros of 2x^4+14x^3-35x^2
The polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² has one possible positive real zero according to Descartes' Rule of Signs. We observe one change of sign in the coefficients. Thus, there is a maximum of one positive real root.
Determining the Number of Possible Positive Real Zeros:
To determine the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x², we can use Descartes' Rule of Signs. This rule helps us to count the number of sign changes in the polynomial and thus infer the number of positive real roots.
First, let's observe the original polynomial:
[tex]2x^{4}[/tex] + 14x³ - 35x²
We examine the coefficients: 2, 14, and -35. By running our eye across these coefficients:
From 2 to 14: No sign change (positive to positive).From 14 to -35: One sign change (positive to negative).The polynomial has one sign change. According to Descartes' Rule of Signs, there is a maximum of one positive real root.
Therefore, the number of possible positive real zeros of the polynomial [tex]2x^{4}[/tex] + 14x³ - 35x² is one.
The risk set by the researcher for rejecting a null hypothesis when it is true is called the
Mount Rushmore is a sculpture that was carved using a model with a scale of 1 in :1 ft. If the model of George Washington’s face was 5 ft tall, how tall is his face on Mount Rushmore?
The height of the face is 60 inch.
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
As 1inch = 1ft,
then to find out how many inches is George Washington’s face.
As there are 12inch in a foot
=12*5
=60inches
Thus , his face is 60ft tall.
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Please help! Geometry.
What is the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously? ≈ $5006.50 ≈ $6125.25 ≈ $4062.65 ≈ $3955.64
The total amount for the investment is approximately $4062.65.
Explanation:To calculate the total amount for an investment of $1,250 invested at 9.6% for 12 years and compounded continuously, we can use the formula A = P * e^(rt), where A is the total amount, P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate, and t is the number of years. Plugging in the values, we have A = 1250 * e^(0.096 * 12). Using a calculator, we find that A is approximately $4062.65.
The cost of fertilizing a lawn is $0.25 per square foot. find the cost to fertilize the triangular lawn whose base is left parenthesis 8 plus startroot 19 endroot right parenthesis8+19 feet and altitude is startroot 76 endroot76 feet.
Susu is solving the quadratic equation 4x2 – 8x – 13 = 0 by completing the square. Her first four steps are shown in the table.
In which step did Susu first make an error?
Step 1
Step 2
Step 3
Step 4
The given Quadratic equation is
[tex]4x^2- 8x - 13 = 0\\\\4(x^2- 2 x - \frac{13}{4}) = 0\\\\ (x-1)^2-1^2- \frac{13}{4}=0\\\\ (x-1)^2=\frac{\sqrt{17}}{4}\\\\ x-1=\pm\frac{\sqrt{17}}{4}\\\\ x=1 +\frac{\sqrt{17}}{4} \text{or} x=1-\frac{\sqrt{17}}{4}[/tex]
These are the steps to determine the roots as well as solve the quadratic equation.
You can find the mistake by looking at the procedure of solving the quadratic equation by completing the square solved above.
Answer:
step 3
Step-by-step explanation:
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The system Mx+Ny=P has the solution (1,3), where Rx+Sy=T
M,N,P,R,S and T are non zero real numbers. Which of the following system would not have (1,3) as a solution.
Answer: C.
[tex]Mx+Ny=P\\(2M-R)x+(2N-S)y=P-2[/tex]
Step-by-step explanation:
Given: The system [tex]Mx+Ny=P\\ Rx+Sy=T[/tex] has the solution (1,3), where M,N,P,R,S and T are non zero real numbers.
A.
[tex]Mx+Ny=P\\ 7Rx+7Sy=7T[/tex]
Divide 7 on both sides on the second equation , we will get
[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]
Thus, this system has solution (1,3)
B.
[tex](M+R)x+(N+S)y=P+T.......(1)\\\\ 7Rx+7Sy=7T................(2)[/tex]
Subtract equation (2) from equation (1), we get
[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]
Thus, this system has solution (1,3)
C.
[tex]Mx+Ny=P...........(1)\\\\(2M-R)x+(2N-S)y=P-2T............(2)[/tex]
We can rewrite the equation (2) as
[tex]2Mx-Rx+2Ny-Sy=P-2T............(3)[/tex]
Multiply 2 on both sides of equation (1), we get
[tex]2Mx+2Ny=2P.........(4)[/tex]
Subtract equation (3) from (4), we get
[tex]Rx+Sy=P+2T[/tex]
But [tex]Rx+Sy=T[/tex]
Thus, this system does not have solution as (1,3).
D.
[tex]\frac{M}{2}+\frac{N}{2}=\frac{P}{2}\\\\Rx+Sy=T[/tex]
Multiply 2 on both sides on the first equation , we will get
[tex]Mx+Ny=P\\ Rx+Sy=T[/tex]
Thus, this system has solution (1,3)
One person can do a certain job in fifteen minutes, and another person can do the same job in thirty minutes. How many minutes will it take them to do the job together?
A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon. It's an octagon with on side 4/3x - 1/3 and another side x+7
To find the perimeter of the regular octagon, set the expressions for the sides equal to each other to find the value of x, substitute this value into either of the expressions for the sides to find the side length, and finally multiply the side length by 8.
Explanation:In mathematics, a regular polygon is a polygon that is equilateral and equiangular. In this case, you have an octagon, which means it has 8 equal sides. If one side is defined as 4/3x - 1/3 and another side is defined as x+7, since it's a regular octagon, all sides must be equal. Therefore, to find the perimeter of the octagon, you need to set the two expressions for the sides equal to each other to find the value of x, and then substitute the value of x into either of the expressions for the sides. Multiply this side length by 8 to get the perimeter.
Here are the steps:
Set the expressions for the sides equal to each other: 4/3x - 1/3 = x + 7Solve for x.Substitute the value of x into either of the side expressions to find the side length.Multiply the side length by 8 to get the perimeter.Learn more about Perimeter of a Regular Polygon here:https://brainly.com/question/19034638
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In a regular polygon, all sides and angles are equal. Given a regular octagon with two sides expressed as 4/3x - 1/3 and x+7, the expressions should be equal since all sides are equal in a regular polygon. Having found x, you can multiply by 8 to find the perimeter of the octagon.
Explanation:Thus, If a polygon is regular, this means all of its sides have the same length. If we're given that one side of the regular octagon is 4/3x - 1/3 and another side is x+7, these two expressions should be equal to each other since it's a regular polygon. This gives us an equation:
4/3x - 1/3 = x + 7
Solving for 'x' will give us the length of one side of the regular polygon. Once you have the length of each side, you can find the perimeter of the regular octagon by multiplying this length by 8 (since an octagon has 8 sides).
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What is 10095 m/a to miles/s
The length of a rectangle is 3 ft more than twice the width, and the area of the rectangle is 77 ft2 . find the dimensions of the rectangle.