Answer:
131072
Step-by-step explanation:
Let's put it into expression form and simplify as much as possible :
[tex]\frac{(2)(4)(8)(16)(32)(64)}{2^{4} }[/tex] =
[tex]\frac{2097152}{16}[/tex] =
131072
Hope this helped and have a good day
Answer: 131,072
Step-by-step explanation:
2 x 4=8
8 x 8=64
64 x 16=1024
1024 x 32=32768
32768 x 64=2097152
[tex]2^{4}[/tex]=16
2097152/16= 131072
Manuela has a piece of red ribbon 7 1/2 feet long. She cut the ribbon to have one piece 1 3/4 feet long.
How long is the piece of ribbon that is left?
Answer:
the leftover piece of ribbon is 5 3/4 feet long.
Step-by-step explanation:
if she has 7 1/2 feet of ribbon, and she removes (by cutting it off) 1 3/4 feet of ribbon.
So, if we set up this scenario like a math problem, we can write it as this:
7 1/2 feet of ribbon - 1 3/4 feet of ribbon = remaining ribbon
[ - = take away]
so, we are solving the equation:
7 1/2 - 1 3/4
To solve this, it is easiest to make the fractions have the same denominators
1 / 2 is equal to 2 / 4
However, 2/4 is less than 3/4, so we need to make this fraction a larger number.
To do this, we can take away 1 foot from the 7, and write it as if it were fourths
1 [foot] = 4/4 quarter foot
So, we can add 4/4 + 2/4 = 6/4
Now, we can re-write our situation.
6 6/4 - 1 3/4 = left over ribbon
6 6/4
- 1 3/4
__________
5 3/4
So, the leftover piece of ribbon is 5 3/4 feet long.
Hope this helps!
Solve the equation sin 79.5° = cos 2x
Answer:
x=5.24-9+180n,174.75+180n
Step-by-step explanation:
what are the solution of the quadratic equation (x-8)3-13x(x-8)+3=0? use u substitution to solve.
[tex]3(x - 8) - 13x(x - 8) + 3 = 0 \\ 3x - 24 - 13 {x}^{2} + 104x + 3 = 0 \\ - 13 {x}^{2} + 107x - 21 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ a = - 13 \\ b = 107 \\ c = - 21 \\ x = \frac{ - 107 + - \sqrt{ {107}^{2} - 4(13)( - 21)} }{2( - 13)} \\ x1 = \frac{107 - \sqrt{10357} }{26} \\ x2 = \frac{107 + \sqrt{10357} }{26} [/tex]
Hope it helps
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he graph of the function f(x) = –(x + 6)(x + 2) is shown below.
The domain of the function is all real numbers, the range of a function is y ≤ 4
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = –(x + 6)(x + 2)
If we plot this function on the coordinate plane, we will see it is a graph of a quadratic function.
Here the no other details are given.
But we can say:
The domain of the function is all real numbers.The range of a function is y ≤ 4The x-axis intercept will be at (-6, 0) and (-2, 0).Thus, the domain of the function is all real numbers, the range of a function is y ≤ 4
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The estimated distribution (in millions) of the population by age in a certain country for the year 2015 is shown in the
pie chart. Make a frequency distribution for the data. Then use the table to estimate the sample mean and the
sample standard deviation of the data set. Use 70 as the midpoint for "65 years and over."
The sample mean is x- (Round to two decimal places as needed.)
Under 4 years: 24.8
15-14 years: 422
15-19 years 194
20-24 years: 256
25-34 years 50.7
35-44 years: 35.7
45-64 years 75.2
65 years and over 54.3
The sample mean for the data is 21.38 and the sample standard deviation for the data is 56.19
The frequency distribution for the dataTo do this, we start by calculating the midpoint of each class using:
Midpoint= (Lower + Upper)/2
Using the above formula, we have:
Age (x) Frequency (f)
2 24.8
9.5 422
17 194
22 256
29.5 50.7
39.5 35.7
54.5 75.2
70 54.3
The sample mean for the dataThis is calculated using:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{2*24.8 + 9.5*422 + 17*194 + 22*256 + 29.5*50.7 + 39.5*35.7 + 54.5*75.2+70*54.3}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3}[/tex]
Evaluate
[tex]\bar x = \frac{23793.8}{1112.7}[/tex]
[tex]\bar x = 21.38[/tex]
Hence, the sample mean for the data is 21.38
The sample standard deviation for the dataThis is calculated using:
[tex]\sigma_x = \sqrt{\frac{\sum f(x- \bar x)^2}{\sum f - 1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{2*(24.8-21.38)^2 + .............+70*(54.3-21.38)^2}{24.8 + 422 + 194 + 256 + 50.7 + 35.7 + 75.2 + 54.3 - 1}}[/tex]
Evaluate
[tex]\sigma_x = \sqrt{\frac{3509508.4556}{1111.7}}[/tex]
[tex]\sigma_x = \sqrt{3156.88446128}[/tex]
[tex]\sigma_x = 56.19[/tex]
Hence, the sample standard deviation for the data is 56.19
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In isosceles triangle ABC, AC=BC=20, the measure of angle A=68, and CD is the altitude to side AB. What is CD to the nearest 10th
Answer:
Step-by-step explanation:
Comment
The way the diagram looks when it is drawn is that you are going to need the sine function to solve for the side opposite which is CD.
Formula
Sin(A) = Sin(68 = opposite / hypotenuse Substitute values.
Solution
sin(68) = altitude (side opposite) / 20 multiply both sides by 20
20*sin(68) = 20* altitude / 20 substitute for sin(68)
20* 0.9272 = altitude
altitude = 18.5
Answer: 18.5 to the nearest tenth
which table represents an exponential function of the form y=bx when 0
The table that represents an exponential function of the form y = [tex]b^{x}[/tex] when 0 < b < 1 is Table - 2. See the attached tables.
What is an exponential function?
A function is exponential when its value is a constant that is raised to the power of the argument. This is so especially when the function of the constant is e.
What is the solution?Recall that the exponential function y = [tex]b^{x}[/tex] given that 0 < b < 1. Notice that the table number 2 see to the exponential function that has the following form:
y(x) = (1/3)ˣ
substituting the values of x into the equation, we have:
y(-3) = (1/3) ⁻³ = 27
x = -2; thus
y(-2) = (1/3) ⁻³ = 9
x = -1; thus
y(-1) = (1/3) ⁻³ = 3
x = 0; thus
y(0) = (1/3) ⁻⁰ = 1
x = 1; thus
y(1) = (1/3) ¹ = 1/3
x = 2; thus
y(2) = (1/3) ⁻² = 1/9
x = 3; thus
y(3) = (1/3) ⁻³ = 1/27
Therefore, according to the obtained values, one can summarize that the table that depicts the exponential function y = bˣ is table 2.
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Triangle QRS is reflected across the x-axis. Then it is reflected across the y-axis. Finally, it is
translated according to the rule (x + 7, y + 3). What are the final coordinates of point R'?
Answer: (4,-4)
Step-by-step explanation:
Reflection across the x axis means [tex](x,y) \longrightarrow (x,-y)[/tex], so [tex](3,7) \longrightarrow (3,-7)[/tex].
Reflection across the y axis means [tex](x,y) \longrightarrow (-x,y)[/tex], so [tex](3,-7) \longrightarrow (-3,-7)[/tex].
Then, [tex](-3,-7) \longrightarrow R'\boxed{(4,-4)}[/tex]
What is the answer?
I want the explanation step by step
Help me
If 2,6 kg of potatoes cost R13,20, what will the cost of 3,3 kg be?
Answer:
[tex]\huge\boxed{\sf R. 16.75}[/tex]
Step-by-step explanation:
*Assuming commas are used for decimals.
Given that:2.6 kg potatoes = R 13.20
Using unitary methodDivide 2.6 to both sides
1 kg potatoes = R 13.20/2.6
1 kg potatoes = R 5.1
Multiply 3.3 to both sides
3.3 kg potatoes = R 5.1 × 3.3
3.3 kg potatoes = R 16.75
[tex]\rule[225]{225}{2}[/tex]
HELP!!!!!!!!!!!!!!!!!!!!
Answer:
D is the answer hope
Step-by-step explanation:
hope this helped
What is 20 divided by 1/2 inches
REPEATED SUBTRACTION TO DIVIDE
PLSSS TELL.
Answer:
40Step-by-step explanation:
What is 20 divided by 1/2 inches
20 : 1/2 =
20 * 2 =
40
I just need help with question one, but if you want to you can answer question 2 as well. I’ll give 100 points!
Explanation:
Given f(x) : (2, -3)
Translation's:f(x) + 2 then graph translates up by 2 units up = [tex]\boxed{\sf (2, -1)}[/tex]
f(x) - 3 then graph translates down 3 units down = [tex]\boxed{\sf (2, -6)}[/tex]
f(x + 5) then graph translates left 5 units = [tex]\boxed{\sf (-3, -3)}[/tex]
-f(x) then graph reflects over x axis = [tex]\sf \boxed{\sf (2, 3)}[/tex]
f(-x) then graph reflects over y axis = [tex]\sf \boxed{\sf (-2,-3)}[/tex]
f(2x) then graph has horizontal compression = (2/2, -3) = [tex]\boxed{\sf (1, -3)}[/tex]
2f(x) then graph has vertical compression = (2, (-3)2) = [tex]\boxed{\sf (2, -6)}[/tex]
-f(x - 4) then graph reflects over x axis, moves 4 units to right = [tex]\sf \boxed{\sf (6, 3)}[/tex]
Solution 2Parent function: y = x²
Graph function: f(x) = (x + 8)² - 4
After Identification:
D. The graph has a translation of 8 units left and 4 units down.
Answer:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Question 1Given: [tex]f(x)=(2,-3)[/tex]
[tex]f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)[/tex]
[tex]f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)[/tex]
[tex]f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)[/tex]
[tex]-f(x) \implies (x,-y)=(2,-(-3))=(2,3)[/tex]
[tex]f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)[/tex]
[tex]f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)[/tex]
[tex]2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)[/tex]
[tex]-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)[/tex]
[tex]\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}[/tex]
Question 2Parent function: [tex]y=x^2[/tex]
Given function: [tex]f(x)=(x+8)^2-4[/tex]
[tex]f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}[/tex]
[tex]f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}[/tex]
Therefore, a translation 8 units to the left and 4 units down.
Consider two spinners I have the colors gray orange blue and yellow to make an area model what letter combination will go in the box highlighted in yellow below GB BB BG OY
Answer:
BB
Hope that helps!
Given the graph of f(x), determine the range of f−1(x).
R
(2, infinity)
(-infinity, 2) U (2, infinity)
(-infinity, 3) U (3, infinity)
The range of a graph of a function is (-∞, 3) U (3, ∞) option (D) (-∞, 3) U (3, ∞) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The graph of a hyperbola function is given.
As we know the graph of an inverse of a function is reflections over the line y=x.
We get the same graph as given in the picture.
The range of a graph of a function:
Range: (-∞, 3) U (3, ∞)
Thus, the range of a graph of a function is (-∞, 3) U (3, ∞) option (D) (-∞, 3) U (3, ∞) is correct.
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please help i will give brainliest
A train leaves Little Rock, Arkansas, and travels north at 85 kilometers per hour. Another train leaves at the same time and travels south at 85 kilometers per hour.
How long will it take before they are 680 kilometers apart?
Answer:
4hours
Step-by-step explanation:
1hour =85+85
=170km/h
time= distance÷
speed=170km/h
680÷170=time
=4h
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Answer:
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Step-by-step explanation:
Use prime factorizations to find the GCF of 18 and 33.
Prime factorization of 18: 2 × 3 × 3
Prime factorization of 33: 3 x 11
The GCF of 18 and 33 is
Answer:
3 XD
Step-by-step explanation:
Given the function f(x) = ³x – 1, evaluate f(-12).
Evaluation:
The answe for the function is -1.
Chris and Hillary are remodeling their family room. They are deciding on the flooring, sofa and TV. How many possible combinations are shown in the tree diagram?
A. 10
B. 11
C. 12
D. 13
Answer:
its C ^^ makes more sense :D
Step-by-step explanation:
hope this helps
I need the answer please help!
2. The number of hours you study for an exam impacts your grade. What is a reasonable value of the range?
70
-8
1.75
1/6
Answer:
62.
Step-by-step explanation:
because I subtract 70 to 8 equal to 62
Answer:
I think
Step-by-step explanation:
I think 62 hope you have a good day
Use the following math quiz scores to answer the questions. 85%, 65%, 87%, 68%, 90%, 73%, 65%, 85%, 95%, 85% 17) What is the mean of these scores? 18) What is the median score? The point on the scale that divides the distribution of scores in half 19) What is the mode of these scores? The value that occurs most frequently in a set. 20) What is the range of these scores? The difference between the lowest and highest values
Answer:
79.8
Step-by-step explanation:
The sales tax for an item was $15 and it cost $500 before tax. Find the sales tax rate. Write your answer as a percentage.
4.
Solve the system of inequalities graphically. Label the solution set with an S.
Help asap
Answer:
Solution = (2,1)
Step-by-step explanation:
Make them equal each other and solve for x.
2x - 3 = 1
2x = 4
x = 2
2 * 2 - 3 = 1
Solution = (2,1)
WILL GIVE BRILLIANT
Which of the following is not true of a trapezoid that has been reflected across the x-axis?
A
The x-coordinates of the new trapezoid are the same as the x-coordinates of the
original trapezoid.
B
The new trapezoid is the same size as the original trapezoid.
C
The new trapezoid is the same shape as the original trapezoid.
D
The new trapezoid is in the same orientation as the original trapezoid.
Answer:
D
Step-by-step:
The y-coordinates will change, not the x. Size and shape will also remain the same.
D. -1 7. A weaver bought a bundle of grass for $50.00 from which he made 8 mats. If each mat was sold for $ 15.00, find the percentage profit. 10 %
Profit percentage for weaver after selling mat is equals to 140%.
What is percentage ?" Percentage is defined as the hundredth part of the whole given quantity. It is represented by symbol %."
Formula used
Profit% = [tex](\frac{Profit }{cost price} )[/tex]× 100
According to the question,
Given,
Cost price of bundle of grass = $50.00
Number of mats made = 8
Selling price of each mat = $15.00
Therefore,
Selling price of 8 mats = 15 × 8
= $120
Selling price > Cost price
Therefore,
Profit = Selling price - Cost price
= 120 - 50
= $70
Substitute the value in the formula to get profit percentage we get,
Profit% = [tex]\frac{70}{50}[/tex] ×100
= 140%
Hence, profit percentage for weaver after selling mat is equals to 140%.
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You need to make party favors for a friend's birthday. 48 people were invited, but you'll only have to make favors for those who say they will attend. Some of the favors will be yellow and the rest will be xanadu. Make a graph using paper or technology that shows all of the possible combinations of yellow or xanadu party favors you might choose to make. Let a represent the xanadu favors and y represent the yellow favors. Your graph should be labeled with x-intercept, y-intercept, shaded region, linear boundary (solid or dashed). Also include an additional point with coordinates clearly labeled in the solution region that shows me how many of each favor you choose to make after all RSVP's are received
The update of the completed graph is given in the image attached as it shows the possible combinations of Yellow or Xanadu party favors that might choose will be ( 48, 0).
What is the graph about?For this graph, we shall make Xanadu party favors as X
and yellow favors as Y
Therefore note that: X + Y = 48
In the graph of X - Intercept
Y = 0, X = 48
In the graph of Y- intercept,
Y = 48 , X = 0
Therefore, the graphical representation of the combinations is given in the image attached.
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Finding the slope from points
Answer:
m = -3
Step-by-step explanation:
The formula to find the slope of the line is :
slope = m = [tex]\frac{y_1 - y_2}{x_1-x_2}[/tex]
Given that the two coordinates of the line are :
( -1 , - 7 ) ⇒ ( x₁ , y₁ )
( 1 , -13 ) ⇒ ( x₂ , y₂ )
Let us solve now.
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
m = ( -7 - ( -13)) ÷ ( -1 - 1 )
m = ( -7 + 13 ) ÷ ( -2 )
m = 6 ÷ -2
m = -3
Answer:
m = -3
Step-by-step explanation:
Given two points:
(-1,-7) & (1,-13)To Find:
The slopeSolution:
Using slope's formulae,
[m denotes slope][tex] \boxed{ \rm{m = \cfrac{y_2 -y_1 }{x_2 - x_1} }}[/tex]
According to the question, on the formula:
(y_2,y_1) = (-13,-7)(x_2,x_1) = (1,-1)Substitute them onto the formulae:
[tex] \rm \: m = \cfrac{ - 13 - ( - 7)}{1 - ( - 1)} [/tex]
Simplify using PEMDAS:
P = ParenthesesE = exponentsM = MultiplicationD = DivisionA = additionS = subtraction[tex] \rm \: m = \cfrac{ - 13 + 7}{1 \ + 1} [/tex]
[tex] \rm \: m = \cfrac{ - \cancel6}{ \cancel2} = \boxed{ - 3}[/tex]
Hence, the slope of the line that passes through the given points in it's simplest form is -3.
Calculate the discriminant to determine the number of real roots of the equation.
y = x2 + 3x + 9
one real root
no real roots
three real roots
two real roots
find D which is the discriminant and with D < 0.
therefore the equation has an imaginary root and not a real root.