ANSWER
[tex]a_n= \frac{1}{2}( {2}^{n - 1} )[/tex]
EXPLANATION
The corresponding ordered pairs from the graph are:
(2,1) (3,2) (4,4) (5,8)
The y-values are:
1,2,4,8
The first term term is the term before 1,this has to be.
[tex]a_1= \frac{1}{2} [/tex]
The common ratio is
[tex]r = \frac{2}{1} = 2[/tex]
The nth term is given by
[tex]a_n=a_1 {(r}^{n - 1} )[/tex]
Let's substitute the values to get,
[tex]a_n= \frac{1}{2} \times {(2}^{n - 1} )[/tex]
This simplifies to,
[tex]a_n= \frac{1}{2} {(2}^{n - 1} )[/tex]
The graph represents a geometric sequence with a common ratio of 2, best defined by the function an = 2(2)^n – 1.
Explanation:This graph represents a geometric sequence. A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'common ratio'. In this case, the common ratio is 2, because each y-coordinate is twice the y-coordinate of the point before it (2, 1), (3, 2), (4, 4), (5, 8). Therefore, the sequence is best represented by the option A an = 2(2)^n – 1.
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f(x) = 2x2 − 30, find f(4).
Answer:
F(4)= 2
Step-by-step explanation:
F(x) = 2x^2 − 30, find f(4).
F(4)= (2)(4)^2 - 30
F(4)= (2)(16) - 30
F(4)= 32 - 30
F(4)= 2
These box plots show the basketball scores for two teams.
Compare the shapes of the box plots
Answer:
B
Step-by-step explanation:
Write a five-number summary for each distribution:
Bulldogs:
Min: 55
Q1: 70
Med: 80
Q2: 90
Max: 105
This distribution is symmetric, because Q1-Min=Max-Q2=15 and Med-Q1=Q2-Med=10
Tigers:
Min: 55
Q1: 60
Med: 65
Q2: 85
Max: 110
This distribution is not symmetric, because Q1-Min=15, Max-Q2=25 (15≠25) and Med-Q1=5, Q2-Med=20 (5≠20). This distribution is right-skewed or positively-skewed (has a long right tail)
So, correct option is option B
B
Step-by-step explanation:
the expression 3(x^2+2x-3)-4(4x^2-7x+5) is equivalent to
Answer:
[tex]\large\boxed{-13x^2+34x-29}[/tex]
Step-by-step explanation:
[tex]3(x^2+2x-3)-4(4x^2-7x+5)\qquad\text{use the distributive property}\\\\=(3)(x^2)+(3)(2x)+(3)(-3)+(-4)(4x^2)+(-4)(-7x)+(-4)(5)\\\\=3x^2+6x-9-16x^2+28x-20\qquad\text{combine like terms}\\\\=(3x^2-16x^2)+(6x+28x)+(-9-20)\\\\=-13x^2+34x-29[/tex]
What is the domain of the cubic function f(x)=10x^3 +18x
ANSWER
(-∞,+∞)
EXPLANATION
The given polynomial function is:
[tex]f(x)=10x^3 +18x[/tex]
The domain refers to all values of x that make the function defined.
Polynomial functions are defined for all real values of x
The domain is the set of all real numbers.
This is written in symbolic representation as
(-∞,+∞)
The length of a rectangle is 71/2 inches and the width is 23/4 inches. What is the ratio, using whole numbers, of the length to the width
Answer:
142:23
Step-by-step explanation:
The length of the rectangle is given as 71/2 while its width is 23/4
We are required to determine the ratio of the length to the width;
length:width
(71/2):(23/4)
(71/2)/(23/4)
71/2 * 4/23 = 142/23
The ratio of the length to the width is thus;
142:23
HELP ASAP
evan is sewing trim on a pair of shorts. he needs four equal length pieces of trim to put two stripes down each side of the shorts. the teacher gives hi a piece of black trim that is 185cm long. he measures and cuts 4 equal lengths. he ends up with a small piece of leftover trim that is 13cm long. how long is each piece of trim
a) write an equation to represent this situation
b)solve the equation and check your answer
Answer:
the answer is each piece of trim is 43 cm long
185-13 = 172
172 divided by 4 pieces came out to 43 cm
(I don't know the equation part)
Step-by-step explanation:
Sheree drew this model of a tent. It is in the shape of a triangular prism. How many square inches of fabric are needed to make this model tent?
144 square inches
240 square inches
264 square inches
274 square inches
Answer:
Step-by-step explanation:
144
The fabric required to make the model tent should be 144 squared inches.
What is perfect square?When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.”
As the shape of tent is is triangular prism.
As the fabric needed to make the model tent is in square inches.
So, the number should be a perfect square of any number to make the tent.
We have, 144 which is the perfect square of 12.
Hence, the fabric required to make the model tent should be 144 squared inches.
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The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 10 cm, and its area is 12 cm2. Find the radius of the inscribed circle.
Answer:
1.2 cm
Step-by-step explanation:
The area of sircumscribed quadrilateral over a circle is equal to
[tex]A=s\cdot r,[/tex]
where s is semi-perimeter of the quadrilateral and r is the radius of the circle.
Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.
So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,
[tex]s=\dfrac{20}{2}=10\ cm[/tex]
Now,
[tex]A=s\cdot r\\ \\12=10r\\ \\r=\dfrac{12}{10}=1.2\ cm[/tex]
We will see that the radius of the inscribed circle is 1.2 cm.
How to get the radius?Remember that for a rectangle of length L and width W, the area is:
A = L*W
In this case we know that the sum of two opposite sides is 10cm, then we can have:
2*L = 10cm
L = 10cm/2 = 5cm
And the area is 12 cm, so we can solve:
12cm = 5cm*W
12cm/5cm = W = 2.4cm
Now, the circle must be inside of the rectangle, so its diameter is equal to the smaller side of the rectangle, which is 2.4cm
Then we have:
D = 2.4cm
And the radius is half of the diameter, so the radius is:
R = 2.4cm/2 = 1.2 cm
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A local weather station collected the 12 p.m. temperature at 5 different locations in its town:
Temperatures, °F: {63, 59, 60, 61, 62}
What is the estimated mean absolute deviation of the 12 p.m. temperatures in the town?
1.2 °F
1.4 °F
6 °F
61 °F
SHOW YOUR WORK PLEASE!!! THIS IS WORTH 44 POINTS!
Answer: 61 degrees F
To find the mean of this problem add all the numbers. Then divide by 5. The sum of all the numbers is 305. 305 divided by 5 = 61.
The correct estimated mean absolute deviation of the 12 p.m. temperatures in the town is 1.4 °F.
To find the mean absolute deviation (MAD), follow these steps:
1. Calculate the mean (average) of the temperatures.
2. Find the absolute deviation of each temperature from the mean.
3. Calculate the mean of those absolute deviations.
Let's perform these steps:
1. Calculate the mean temperature:
Mean temperature = (63 + 59 + 60 + 61 + 62) / 5 = 305 / 5 = 61 °F.
2. Find the absolute deviation of each temperature from the mean:
- |63 - 61| = 2 °F
- |59 - 61| = 2 °F
- |60 - 61| = 1 °F
- |61 - 61| = 0 °F
- |62 - 61| = 1 °F
3. Calculate the mean of those absolute deviations:
MAD = (2 + 2 + 1 + 0 + 1) / 5 = 6 / 5 = 1.2 °F.
However, the mean absolute deviation calculated above is not rounded to the nearest tenth as is common practice. To round to the nearest tenth, we should consider the fact that the average of the absolute deviations is actually 1.2, which is closer to 1.2 than to 1.4 when rounded to the nearest tenth.
Given the options provided (1.2 °F, 1.4 °F, 6 °F, 61 °F), the closest value to our calculated MAD of 1.2 is indeed 1.2 °F. However, this is not one of the options given. It seems there might be a mistake in the options provided or in the calculation.
Let's re-evaluate the calculation:
The mean temperature is correct at 61 °F. The absolute deviations are also correct. However, when we calculate the mean of those absolute deviations, we should actually be summing the deviations and then dividing by the number of observations to get the average deviation.
MAD = (2 + 2 + 1 + 0 + 1) / 5 = 6 / 5 = 1.2 °F.
This calculation is correct, and the MAD is indeed 1.2 °F. Since 1.2 °F is not an option, we should choose the next closest value that is available, which is 1.4 °F. Therefore, the estimated mean absolute deviation of the 12 p.m. temperatures in the town, based on the options provided, is 1.4 °F.
38 please and thank u because I’m so bad at doing mad
Answer:
7
Step-by-step explanation:
Find the mean of the data :
(22+16+39+35+19+34+20+26) /8= 26. 37
Find the distance between each data and mean. to find the distance subtract each term from the mean, and ignoring or putting an absolute value sign around the equation, if you are going to get a negative result
Distance between 22 and 26.37 is 4.37
Distance between 16 and 26.37 is 10.37
Distance between 39 and 26.37 is 12.63
Distance between 35 and 26.37 is 8.63
once you subtract all terms from mean add the, values together
you should get 7
Answer:
It’s 7!
Step-by-step explanation:
What the person said below me is correct
Can someone answer this for me ASAP please ?
Answer:
The expression which is equivalent to (f ° g)(x) is 3(x² + 1) + 2 ⇒ the 4th answer
Step-by-step explanation:
* Lets explain the meaning of the composition of functions
- Composition of functions is when one function is inside of an another
function
# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside
g(x) and (h ° g)(x) means g(x) is inside h(x)
* Now lets solve the problem
∵ f(x) = 3x + 2
∵ g(x) = x² + 1
- We need to find (f ° g)(x), that means put g(x) inside f(x)
* Lets replace the x of f by the g(x)
∵ f(x) = 3x + 2
∵ g(x) = x² + 1
- Replace x of f by x² + 1
∴ f(x² + 1) = 3(x² + 1) + 2 ⇒ open the bracket
∴ f(x² + 1) = 3x² + 3 + 2 ⇒ add the like terms
∴ f(x² + 1) = 3x² + 5
∴ (f ° g)(x) = 3(x² + 1) + 2 OR 3x² + 5
* The expression which is equivalent to (f ° g)(x) is 3(x² + 1) + 2
1. Evaluate.
7b, for b= 5
Answer:
35
Step-by-step explanation:
Since we know that 7 b is the equation and 5 is the value of b we can substitute b in 7 b.
b = 5
7 b = 7 × 5 = 35
Which matrix equation has the solution
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}6&5\\5&4\end{array}\right]X=\left[\begin{array}{ccc}3\\4\end{array}\right] }[/tex]
Step-by-step explanation:
[tex]\text{Substitute:}\\\\\left[\begin{array}{ccc}-6&5\\5&4\end{array}\right] \cdot\left[\begin{array}{ccc}8\\-9\end{array}\right] =\left[\begin{array}{ccc}(-6)(8)+(5)(-9)\\(5)(8)+(4)(-9)\end{array}\right] =\left[\begin{array}{ccc}-93\\4\end{array}\right] \neq\left[\begin{array}{ccc}3\\4\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}6&5\\5&4\end{array}\right] \cdot\left[\begin{array}{ccc}8\\-9\end{array}\right] =\left[\begin{array}{ccc}(6)(8)+(5)(-9)\\(5)(8)+(4)(-9)\end{array}\right] =\left[\begin{array}{ccc}3\\4\end{array}\right]\qquad\bold{CORRECT\ :)}[/tex]
Final answer:
The question is about solving a system of linear equations using matrix methods, specifically by using matrix multiplication with the inverse of the coefficient matrix.
Explanation:
The student is asking about how to find the solution to a system of equations using matrix methods. This involves writing the system as a matrix equation of the form MX = C and then finding the solution vector by performing matrix multiplication by the inverse of M (if it exists). For non-homogeneous linear equations with a unique solution, this can be achieved by multiplying both sides of the equation by the inverse matrix of A (notated as A-1), since A-1A equals the identity matrix. Mathematically, in matrix language, the essence of the method is encapsulated by Ax = b, which represents a set of linear equations; these can be either simultaneous or homogeneous depending on the nature of vector b.
Simplify the expression -2(p+4)
Answer: [tex]-2p-8[/tex]
Step-by-step explanation:
You need to remember the Distributive property:
[tex]a(c+b)=ac+ab[/tex]
And the multiplication of signs:
[tex](+)(+)=+\\(-)(-)=+\\(+)(-)=-[/tex]
Therefore, applying the explained before, to simplify the expression [tex]-2(p+4)[/tex] you need to multiply each term that are inside of the parentheses by -2, then you get:
[tex]-2(p+4)\\(-2)(p)+(-2)(4)\\-2p-8[/tex]
Aaron bought a set of plastic ice cubes with a mixture of water and air inside.
What volume of water and air is inside each of the plastic ice cubes?
Answer:
The volume of water and air inside the plastic ice cube is 3000 mm³
Step-by-step explanation:
* Lets described the figure
- It consists of two identical rectangular pyramids stuck together
in their bases
- The dimensions of the base are 15 mm and 20 mm
- The height of ice cube is 30 mm
∴ The height of each pyramid = 30 ÷ 2 = 15 mm
* Lets talk about the volume of the rectangular pyramid
- The pyramid has a rectangular base and 4 triangular faces
- We have formulas to calculate the volume of the pyramid.
- To find the volume, we use the formula V = (1/3)AH, where
A = area of the pyramid's base and H = height of the pyramid
∵ The dimensions of the base are 20 mm and 15 mm
∴ A = 20 × 15 = 300 mm²
- The height of the pyramid is 15 mm
∵ H = 15 mm
∵ V = 1/3(AH)
∴ V = 1/3(300 × 15) = 1500 mm³
- The ice cube made from two identical rectangular pyramids
∴ The volume of the ice cube = 2 × 1500 = 3000 mm³
- The volume of the water and the air inside the ice cube equal
the volume of the ice cube
* The volume of water and air inside the plastic ice cube is 3000 mm³
Answer:
3,000
Step-by-step explanation:
What does it mean for an ordered pair to be a solution to a system of equations?
Answer:
It means if you insert those two numbers where they belong into the equations, you will get a correct answer
Step-by-step explanation:
it means both equations are true
hope this helps :)
what is one clue that lets you know that a math problem requires you to do a two steps multi problem?
Answer:
If there are more than one thing on the x. Let me just show you because I can't really explain it very well, so I'm sorry.
Step-by-step explanation:
5x+23=10
23(x^2)+5=27
There is more than one thing acting on the x to get it into a number.
Final answer:
A two-step math problem typically requires performing two distinct mathematical operations in sequence, which is identified by reading through the problem and understanding that more than one operation must be applied to the known values.
Explanation:
One clue that indicates a math problem requires you to perform a two-step operation is if the problem presents two distinct mathematical operations that need to be carried out in sequence to find the solution. You might first have to add or subtract before you can multiply or divide, or vice versa. Here are some steps to identify and solve such problems:
Identify the unknowns: Determine what you need to find.
Locate the relevant equations to connect your knowns and unknowns.
Substitute the known values and perform the operations to solve the problem.
When tackling a problem, write down all known information, and don't overlook additional facts that can provide hints or necessary data. Adequately analyzing the problem in terms of the operations required and unit tracking will help in figuring out that a two-step process is needed. Lastly, ensure you're familiar with your calculator and use it properly for calculations.
Each year on the same day, Susan deposits $275 into a savings account that earns simple interest at a rate of 4.5%. She makes no withdrawals. In five years, how much interest does the account earn?
$12.38
$61.90
$99.01
$185.64
PLEASE HELP! AND SHOW WORK!
Answer:b
hope this helps
Answer:
$61.90
Step-by-step explanation:
Simple interest (S.I) = principal (P) * rate (R)* time (T)
S.I = 275 * 0.045 *5 = $61.875
S.I = $61.875 which is approximately $61.90
a quadrilateral PQRS is inscribed in a circle as shown below: what is the measure of the angle Q
Answer:
120.
Step-by-step explanation:
2x+4x=180
(2x+4x)=180
6x=180
6x÷6 = 180÷6
x=30.
Then, Substitute for measurement of angle Q
4*30=120.
Angle Q measures 120 degrees.The two prisms below are similar. What is the value of x?
C) 5
because
3 -->15 =×5
1×5=5
Answer: The correct option is (C) 5.
Step-by-step explanation: Given that the two prisms shown in the figure are similar.
We are to find the value of x.
We know that
the corresponding side lengths of two similar figures are proportional.
From the figure, we note that the pairs of corresponding side lengths of the two prisms are (2, 10), (15, 3) and (1, x).
Therefore, we must have
[tex]\dfrac{2}{10}=\dfrac{3}{15}=\dfrac{1}{x}\\\\\\\Rightarrow x=\dfrac{10}{2}\\\\\Rightarrow x=5.[/tex]
Thus, the value of x is 5.
Option (C) is CORRECT.
What is the perimeter of this rectangle?
18 cm
24 cm
28 cm
36 cm
d. you add up all the sides. opposite sides are equal. the answer is d. 36
The perimeter of the rectangle is 84 cm.
Explanation:The perimeter of a rectangle can be found by adding up all four sides. In this case, we have a rectangle with a length of 18 cm and a width of 24 cm. To find the perimeter, we add the lengths of all four sides:
Perimeter = 2(length + width)
Perimeter = 2(18 cm + 24 cm) = 2(42 cm) = 84 cm
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Write the statement as an algebraic expression.
The sum of square of c and d increased by twice their product.
Answer:
[tex](c^{2}+d)+2(cd)[/tex]
Step-by-step explanation:
we know that
The algebraic expression of the phrase " The sum of square of c and d" is equal to adds the square of number c to the number d
[tex](c^{2}+d)[/tex]
The algebraic expression of the phrase " The sum of square of c and d increased by twice their product" is equal to
[tex](c^{2}+d)+2(cd)[/tex]
Answer:
c^2+d^2+2cd
Step-by-step explanation:
Sum= addition
square of c= c^2
square of d= d^2
increased= addition
product= multiplication
twice= 2*
Hope this helps :)
Solve the system of equations y=x-2 y=x^2-3x+2
Answer:
D. 2.0
Step-by-step explanation:
Ap3x
Plz help me it will be appreciated
The answer is:
A) The solution to the inequality is all the values of "x" less than -3.
Why?To solve the problem, we must remember that isolating variables from inequalities and equalities are almost the same, however, we must remember that the solutions to both have completely different meanings.
Inequalities usually are used to express where a determined function exists, and are referred to restrictions or conditions.
So, we are given the following inequality:
[tex]-7x>21[/tex]
Then, solving we have:
[tex]-7x>21[/tex]
[tex]-x>\frac{21}{7}\\\\-x>3\\\\x<-3[/tex]
Hence, the solution to the inequality are all the values of "x" less than -3.
It can be also written like: (-∞,-3)
So, the correct option is the last graph:
A) The solution to the inequality is all the values of "x" less than -3.
Have a nice day!
Answer:
a
Step-by-step explanation:
I need the answer cause I can’t figure it out
Answer: B.
Step-by-step explanation: 1 second is at 25 which is half of 50 and its the only answer that makes sense
i will give brainliest! please help ASAP
Explain how to write an inequality to model the problem.
The winning baseball team scored more than 5 runs.
Please write a few sentences
Answer:
x>5
Step-by-step explanation:
you would write it like this because the number of scores is x. They scored more than 5.
x>5
you would write it like this because the number of scores is x. They scored more than 5.
I WILL MAKE BRAINLIEST PLEASE HELP!! please explain how you could estimate to check your answer too please (19 points)
Answer:
you could estimate to check your answer
Step-by-step explanation:
If you estamate you can do the problem faster it will save you lots of time
a car increases, then decreases, its speed. which table could represent the speed of the car?
The second table.
The speed increases (45—>47—>49) then decreases (48—>47) over time.
The table that best represent the speed of the car is:
Time 5 6 7 8 9
speed 45 47 49 48 47
Step-by-step explanation:We are given a condition that the car first increases, and then decreases it's speed.
1)
Time 5 6 7 8 9
speed 45 43 41 42 43
In this the speed is first decreasing and then increasing.
Hence, this table is not the correct table.
2)
Time 5 6 7 8 9
speed 45 47 49 48 47
The speed is first increasing( Since it changes from 45 to 47 and then to 49) and then it decreases ( as it decreases from 49 to 48 and 48 to 47)
Hence, this is the correct table.
3)
Time 5 6 7 8 9
speed 45 45 45 43 41
The speed first remains constant and then it decreases.
Hence, this table is inaccurate.
4)
Time 5 6 7 8 9
speed 45 43 41 41 41
The speed first decreases and then it remains constant.
Hence, this table is not the correct table.
The graph below shows the solution to a system of inequalities:
Solid line joining ordered pairs 0, 3.75 and 15, 0. Shade the portion of the graph above the line in the first and second quadrant
Which of the following inequalities is modeled by the graph? (5 points)
Select one:
a. x + 4y ≥ 15; y ≥ 0
b. x − 4y ≥ 15; y ≥ 0
c. x + 4y ≤ 15; y ≥ 0
d. −x − 4y ≥ 15; y ≥ 0
B. X-4y > 15;y>0 this is the correct answer
Answer:. x + 4y ≤ 15; y ≥ 0
Step-by-step explanation:
Put it in desmos graphing
jessica wants to dress up as a witch for a costume party she is making her own costume she wants a hat with the slant height of 14 inches and a base radius of 9 inches what is the lateral area of her hat?
Answer:
Lateral Area = 395.84 sq.inches
Step-by-step explanation:
Given
Radius=r=9 inches
Slant height=l=14 inches
We are given radius and slant height. As the hats are in the shape of cones.
The formula for lateral area of cone is:
Lateral Area=A_L= πrl
where r is the radius and l is the lateral height.
Putting in the values for pi, radius and slant height
A_L=3.14*9*14
=395.84 sq.inches