width = x
length = 3 + x
perimeter = x + x + ( 3 + x ) + (3+x)
18 = x + x + ( 3 + x ) + (3+x)
x + x + ( 3 + x ) + (3+x) = 18
6 + 4x = 18
4x = 12
x = 3
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting 2 queens and 2 kings.
The probability is ___.
(Round to six decimal places as needed.)
Answer:
1.083
Step-by-step explanation:
Exact form: 13/12
Decimal form: 1.083 (put a line above the 3)
Mixed number form: 1 1/12
Which of the following sets shows all the numbers from the set {0.5,1,2.5,3,3.5} that make the inequality 4a + 2 > 12 true
============================================================
Explanation:
Let's isolate the variable 'a' in the given inequality.
4a + 2 > 12
4a + 2-2 > 12-2
4a > 10
4a/4 > 10/4
a > 2.5
In the second step, I subtracted 2 from both sides to undo the "plus 2". In the second to last step, I divided both sides by 4 to undo the multiplication.
The solution is a > 2.5, meaning that anything larger than 2.5 will work in the original inequality.
For example, we could try a = 3 to get
4a + 2 > 12
4*3 + 2 > 12
12 + 2 > 12
14 > 12
which is true. This makes a = 3 a solution. The value a = 3.5 is a similar story, so it's also a solution.
------------
As an example of a non-solution, let's try a = 1
4a + 2 > 12
4*1 + 2 > 12
4 + 2 > 12
6 > 12
which is false. So we can see why a = 1 is not part of the solution set. You should find that a= 0.5 and a = 2.5 won't work as well for similar reasoning.
Corresponding sides of what triangles are proportional
Answer:
In a pair of similar triangles, the corresponding sides are proportional.
Step-by-step explanation:
Corresponding sides touch the same two angle pairs. When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number.
Simplify 4^-4.
please help I have 10 minutes
Answer:
1/256
Step-by-step explanation:
[tex]4^{-4}[/tex]
[tex](1/4)^{4}[/tex]
=> 1/256
Which of the following statements accurately describes the period of a trigonometric function?
Answer:
b
Step-by-step explanation:
b is correct.
A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
f (x) = sqrt(x)+ 2, g(x)=x^2+ 1
find f(g(x))
and g(f(x))
Answer:
[tex]f(x) = \sqrt{x} + 2 \\ \\ g(x) = {x}^{2} + 1 \\ \\ f{g(x)} = \sqrt{ {x}^{2} + 1 } + 2 \\ \\ g{f(x)} = {( \sqrt{x} + 2 )}^{2} + 1[/tex]
A refrigerator magnet uses five eights of an inch of magnetic tape how many refrigerator magnets can you make with 10 inches of magnetic tape
ANSWER: You can make 16 refrigerator magnets.
If you divide 10 by 5/8, you multiply by the reciprocal of 5/8 which is 8/5. You have 8/5 x 10. Cross simplify and you have 16.
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
find the surface area of prism
Answer:
114 cm²
Step-by-step explanation:
Surface area of the rectangular prism,
2(wl+hl+hw)
=2×(3×8+3×8+3×3)
=2×(24+24+9)
=2×(57)
=114 cm²
compute (-12)+(-8)+30
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Please show detailed work if possible-that will help me to better understand the questions
start with this expression:
f(x) = 2x2 − x − 10
1st- What are the x-intercepts of the graph of f(x)? Show work on how to get this
2nd- Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Show work on how to get this
Part C: What are the steps you would use to graph f(x)? show how you can use the answers obtained in Part A and Part B to draw a graph
Answer:
We are given the function:
[tex]f(x)=2x^2-x-10[/tex]
[tex]Here,\\a=2, b=-1,c=-10[/tex]
1. X-intercepts are the points at which the graph of a function intersects or cuts the x-axis. Since the x-intercept always lies on the x-axis, its ordinate or y-coordinate will always be 0. Since the function is quadratic, it will have at most 2 x-intercepts.
In order to find the x intercept, we basically solve for x at y=0:
[tex]f(x)=2x^2-x-10\\As\ y=0,\\0=2x^2-x-10\\2x^2-x-10=0\\ 2x^2-5x+4x-10=0\\x(2x-5)+2(2x-5)=0\\(x+2)(2x-5)=0\\Hence,\\Individually:\\x=-2,\ x=\frac{5}{2}[/tex]
Hence, the x-intercepts of the parabola of f(x) is (-2,0),(2.5,0)
2. The vertex of parabola is determined as maximum or minimum, solely on how it opens. This depends on the nature of the co-efficient of the x^2 term or 'a'. If a is positive the parabola opens upwards (minimum point) and downwards (maximum point) if negative. Hence, here as a=2, the parabola opens upwards and its vertex is minimum.
[tex]Vertex=(\frac{-b}{2a},\frac{-D}{4a})\\Hence,\\D=b^2-4ac\\Substituting\ a=2,b=-1,c=-10:\\D=(-1)^2-4*2*-10=1+80=81\\Hence,\\Vertex\ of\ f(x)=(\frac{-(-1)}{2*2},\frac{-81}{4*2})=(\frac{1}{4},\frac{-81}{8})[/tex]
3. [Please refer to the attachment]
From the graph, we observe that the parabola cuts the x-axis at (-2,0),(2.5,0). Also, its clear that the axis of symmetry passes through [tex](\frac{1}{4},\frac{-81}{8})[/tex], which is its minimum point.
Answer:
A chord of a circle is 9cm long if it's distance from the centre of the circle is 5cm calculate the radius of the circle
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
Assume the population of regulation basketball weights are normally distributed with a mean of 22 and a standard deviation of 1 ounce. If a sample of 100 regulation basketballs is taken, what is the probability that its sample mean will be greater than 22.2 ounces
Answer: 0.0228
Step-by-step explanation:
please check photo explanation
The probability that the sample mean will be greater than 22.2 ounces will be equal to 0.0228
What is probability?Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.
As per the given values in the question,
[tex]\mu_x[/tex] = 22
σ(x) = σ/√n
= 1/√100
σ(x) = 0.1
P(x>22.2) = 1- P(x<22.2)
= 1- P(x × μ(x))/ σ(x) < (22.2 - 22)/0.1
1 - P (z < 2.00)
1- 0.9772
= 0.0228
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Based on corresponding angles and vertical angles, which angles must always be congruent to the angles given? Complete the table.
Answer:
A and B must always be congruent
B and D
E and G
F and H
Step-by-step explanation:
I have to be honest. from the picture I cannot see the vertical angles. All I see is a straight blue line and red letters. But based on the vertical theorem
A and B must always be congruent
B and D
E and G
F and H
also if you want to make sure it's right try to include another picture.
Answer:
Step-by-step explanation:
edmentum :)
William sold tooth pick for €2 a pack.On Selling 60% of his ware he still had 200 left.How much money did he collect from his entire sales?
Answer:
.......................
Carmen Martinez
What is the slope of the line that passes through the point 4,4 and 10,7 write your answer in simplest form
[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto m\approx0.5[/tex]
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-4}{10-4}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m=\frac{1}{2}[/tex]
[tex]m=0.5[/tex]
POUILO 11. For a bivariate frequency table having (p + q) classification the total number of cells is
(a) p (b) p +q (c) q (d) pq
Answer:
g
Step-by-step explanation:
f
Intro to Translations
Acellus
Find the image of the given point
under the given translation.
P(-1,2)
T(x, y) = (x + 2, y - 4)
P' = ([?], [])
Enter the number that belongs
in the green box.
Answer:
(1,-2)
Step-by-step explanation:
P(-1,2) and (x, y) -> (x + 2, y - 4). Plugging in x and y in the transformation, the transformed points are (-1+2, 2-4) = (1,-2)
The length of two sides of triangular field are 16 m and 19m . The perimeter of rectangle is 50 cm find the third side?
50 - (16 + 19)
= 50 - 35
= 15m
help me plzzzzzzzzzzzzzzzzzzzzzzzzzz
Drag the tiles to the correct boxes to complete the pairs.
Given that x= 3 + 81 and y= 7 - 1 match the equivalent expressions.
-15 + 19
58 + 106
-&
411
-29 - 531
I. 2y
-
y
–50 ty
23 - 3y
9514 1404 393
Answer:
58 +106i-29 -53i-8 -41i-15 +19iStep-by-step explanation:
For the purpose of selecting the appropriate tile, it is only necessary to figure the real part of the sum or product.
We notice that the second product (-xy) is -1/2 times the first product (2xy). This can let you find the answers on that basis alone. The only tiles with a (-1) : (2) relationship are (-29 -53i) : (58 +106i).
__
The sum -5x +y has a real part of -5(3) +7 = -8.
The sum 2x -3y has a real part of 2(3) -3(7) = 6 -21 = -15.
Hence the sequence of answers needed on the right side is as shown above.
_____
Additional comment
You know that arithmetic operations with complex numbers (multiplication and addition) are identical to those operations performed on any polynomials. That is, "i" can be treated as a variable. The simplification comes at the end, where any instances of i² can be replaced by -1.
xy = (3 +8i)(7 -i) = 3·7 -3·i +8·7·i -8·i·i = 21 +53i -8i²
= (21 +8) +53i . . . . replaced i² with -1, so -8i² = +8
= 29 +53i
PLEASE HELP AND BE RIGHT PLEASE AND THANK YOU
Answer:
4 units
Step-by-step explanation:
A'B' = 2 × AB
8 = 2×AB
AB = 8/2 = 4
Answer:
16 units
Step-by-step explanation:
The triangle will get bigger because it has a scale factor that is greater than 1.
k=scale factor
k<1=reduction
k>1=enlargement
For a certain country, the bar graph shows the population of it’s public school students, in millions, and the amount that the country’s government spent on public education, in billions of dollars, for five selected years. Complete part A and B.
A.
Express 2007 student population in scientific notation. (Use the multiplication symbol as needed)
B.
Express the amount that the government spent on public education in 2007 in scientific notation. (Use the multiplication symbol as needed)
Answer:
B
Step-by-step explanation:
I took a test in school and this was the answer...at least for my class.
Solve each equation.
1)-9 + x = 4
14 cm 8 cm 10cm 5 cm.
find the area and the perimeter of the above figures
Perimeter = Sum of all sides
Perimeter = 14cm + 8cm + 10cm + 5cm
Perimeter = 22cm + 15cm
Perimeter = 37cm
Step-by-step explanation:
hope it helps you
...
........
The cost of producing pens with the company logo printed on them consists of a onetime setup fee of $265.00 plus $0.95 for each pen produced. This cost can be calculated using the formula C=265.00+0.95p, where p represents the number of pens produced and C is the cost. Use the formula to calculate the cost of producing 2900 pens.
A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
11 meters
Step-by-step explanation:
First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).
The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is
(√3/4)((11-4x)/3)²
= (√3/4)(11/3 - 4x/3)²
= (√3/4)(121/9 - 88x/9 + 16x²/9)
= (16√3/36)x² - (88√3/36)x + (121√3/36)
The total area is then
(16√3/36)x² - (88√3/36)x + (121√3/36) + x²
= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)
Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)
When x=0, each side of the triangle is 11/3 meters long and its area is
(√3/4)a² ≈ 5.82
When x=2.75, each side of the square is 2.75 meters long and its area is
2.75² = 7.5625
Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 11 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (11 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (11 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(11 - x)/3 = 0
2x/4 - (√3/6)(11 - x) = 0
2x / 4 = (√3/6)(11 - x)
√3x = 11 - x
√3x + x = 11
x (√3 + 1) = 11
x = 11 / (1.732 + 1)
x = 11/2.732
x = 4
Thus,
The length of the square must be 4 m in order to maximize the total area.
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Five hundred randomly selected adult residents in Sacramento are surveyed to determine whether they believe children should have limited smartphone access. Of the 500 people surveyed, 381 responded yes - they believe children should have limited smartphone access.
You wish to estimate a population mean y with a known population standard devi- ation o = 3.5. If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?
Answer:
The sample size must be of 47,059,600.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation:
[tex]\sigma = 3.5[/tex]
If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?
This is n for which M = 0.001. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.001 = 1.96\frac{3.5}{\sqrt{n}}[/tex]
[tex]0.001\sqrt{n} = 1.96*3.5[/tex]
[tex]\sqrt{n} = \frac{1.96*3.5}{0.001}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3.5}{0.001})^2[/tex]
[tex]n = 47059600[/tex]
The sample size must be of 47,059,600.
