The expression which is equivalent to the required expression (p - q)(x) is; Choice C; (x²-1)-5(x - 1).
Which expression is equivalent to (p - q)(x) given that p(x) = x² - 1 and g(x)= 5(x-1)?It follows from the task content that the premise functions as given in the task content are;
p(x) = x² - 1
g(x)= 5(x-1).
Consequently, the required expression for the function operations; (p - q)(x) is simply;
p(x) - q(x) and is equivalent to;
(x² - 1) - 5(x - 1)
Therefore, the expression which is equivalent to the required expression (p - q)(x) is Choice C; (x²-1)-5(x - 1).
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pls help will mark this brainlest
The ordered pairs (0,13) and (10, 0) are joined to best draw the line of best fit for the given scatter plot. So, option 4 is correct.
How to draw the line of best fit for a scatter plot?For the given scatter plot, to draw a line of best fit, the slope is to be calculated. The slope of the required line is calculated by
m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]
Where,
∑xy = sum of the product of x and y values
∑x = sum of x values
∑y = sum of y values
∑x² = sum of square values of x
n = total number of scatter points
And the y-intercept is calculated by
b = [∑y - m(∑x)]/n
Where m is the slope obtained above
Calculation:The given scatter plot has the coordinate points:
(0,14), (1, 11), (2, 9), (3, 10),(4, 7), (5, 7), (6, 5), (7, 5), (8, 3), (9, 1), (10, 0)
Such that n = 11
Then the required components are calculated as follows:
∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
∑y = 14 + 11 + 9 + 10 + 7 + 7 + 5 + 5 + 3 + 1 + 0 = 72
∑xy = (0 × 14) + (1 × 11) + (2 × 9) + (3 × 10) + (4 × 7) + (5 × 7) + (6 × 5) + (7 × 5) + (8 × 3) + (9 × 1) + (10 × 0) = 220
∑x² = 0² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² = 385
Then the slope is calculated as follows:
slope m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]
On substituting,
m = [11(220) - (55)(72)]/[11(385) - (55)²]
⇒ m = -14/11 = -1.2727273 ≅ -1.3
∴ m = -1.3
Then calculating the y-intercept:
we have b = [∑y - m(∑x)]/n
On substituting,
b = [72 - -1.3(55)]/11
∴ b = 13
Then the slope-intercept form of the required line is
y = -1.3x + 13
When x = 0,
y = -1.3(0) + 13 = 13
When y = 0,
0 = -1.3x + 13
⇒ 1.3x = 13
⇒ x = 13/1.3 = 10
Therefore, the coordinates (0, 13) and (10, 0) give the best draw for the line of best fit.
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You are interested in doing a content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers. your unit of analysis is:_______.
To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.
Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.
Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.
When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.
Hence the unit of analysis is objective of the section.
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help please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111
Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
Given solution of a question done by two people.
Jenna's method
5(30+4)
(5)(30)+(5)(4)
150+20=170
Mia's method
5(30+4)
5(34)=170
We are required to find why they have achieved at the same answer.
Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.
Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
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find the perimeter of the figure below, composed of a rectangle and two semicircles
.
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's consider the shape given to us:
⇒ a rectangle with two semicircles cutout on the edges
⇒ perimeter/circumference of the two semicircles can count as one
circle
Let's solve:
Circumference = circumference of two semicircle[tex]\hookrightarrow \text{Total circumference} =\frac{1}{2} *\pi *\text{ diameter} +\frac{1}{2} *\pi * \text{diameter}\\= \pi *\text{diameter}=10\pi =10 * 3.14 = 31.4[/tex]
Total Perimeter = 31.4 + 14 + 14 = 31.4 + 28 = 59.4Answer: 59.4 square units
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Jessica fills a cube shaped tank that has an edge of 70 cm with water from a tap. Water flows into the tank at a rate of 7L per minute. How long will it take to fill the tank fully?
The volume of the tank is (70 cm)³ = 343,000 cm³.
Now,
1 mL = 1 cm³
1 L = 1000 mL
so we convert the given rate to
[tex]\dfrac{7\,\rm L}{1\,\rm min} \cdot \dfrac{1000\,\rm mL}{1\,\rm L} \cdot \dfrac{1\,\mathrm{cm}^3}{1\,\rm mL} = \dfrac{7000\,\mathrm{cm}^3}{1\,\rm min}[/tex]
Then the time it will take to fill up the tank is
[tex]343,000\,\mathrm{cm}^3 \cdot \dfrac{1\,\rm min}{7000\,\mathrm{cm}^3} = \boxed{49\,\rm min}[/tex]
Towns A, B, and C lie on a straight line, as shown below. Jack and Arthur start at Town B and drive for an hour from Town B to Town C, where they stop for an hour to eat lunch. Which of the following graphs could represent their distance from Town A during these two hours?
The situation described by the distance from Town A is the first graph.
Given that cities A,B and C are on straight line.
We are required to find the graph appropriate the given situation.
Distance is basically the measurement of how far two things,places are located.It can be measurement from one point to another .
On the first hour,they leave town B to town C moving farther from Town A,hence the distance is increasing on the first hour.
On the second hour they stop for lunch,meaning that the distance remains constant at the point, it was at the end of the first hour.
Hence if towns A,B C lie on a straight line and Jack and Arthur start at town B and drive for an hour from Town B to Town C then the distance shown from Town A during these two hours is first graph.
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Find the area of the shaded region. Round the answer to the nearest
tenth decimal place.
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Area of shaded region = 2571.66 in²[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Radius of smaller circle = 25 in
Radius of larger circle = 25 + 13 = 38 in
Area of ring : Area of larger circle - Area of smaller circle
[tex]\qquad❖ \: \sf \:\pi {(38)}^{2} - \pi {(25)}^{2} [/tex]
[tex]\qquad❖ \: \sf \:\pi( {38}^{2} - 25 {}^{2} )[/tex]
[tex]\qquad❖ \: \sf \:3.14(1444 - 625)[/tex]
[tex]\qquad❖ \: \sf \:3.14(819)[/tex]
[tex]\qquad❖ \: \sf \:2571.66 \: \: in {}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Area = 2571.66 in²how many rectangles of different sizes can be formed from 36 identical rectangles
Answer:
i think answer is 5
Step-by-step explanation:
since you could think what are factors of 36
1x36
2x18
3x12
4x9 and
6x6
A figure has vertices at A(—3, 2), B(—l, —l), and C(—4, —2). After a transformation,the image of the figure has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). Draw the preimage and image. Then identify the transformation
Answer:
rotate 180° about origin
The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).
Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.
Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:
(x, y) → (-x, y)
A(-3, 2) → A'(3,2)
B(-1, -1) → B'(1, -1)
C(-4, -2) → C'(4,-2)
Hence, the transformation rule is (x, y) → (-x, y).
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A spirit shop outside the hockey stadium sells merchandise representing the three school districts that built the arena. the entrances to the arena, the spirit shop, and the parking lot form the vertices of a triangle. the planning committee has decided to erect a memorial statue and would like it to be equidistant from the entrances to the arena, the spirit shop, and the parking lot. at what point should the statue be located? explain your answer.
Point E is where the statue should be placed.
What is called a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.Triangles are three-sided shapes. The various kinds of triangles go by various names. The angles' size and the sides' length determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.The triangle is most frequently seen in our daily lives on traffic signs. The signs are triangular in shape and equilateral, which means that all three of their sides are the same length and have the same angle.At what point should the statue be:
The intersection of the doors to the arena, the spirit store, and the parking lot forms a triangle, with Point E in its center. The radius of the circumscribed circle will therefore equal the distance from the statue to each vertex, placing it at the same distance from all three landmarks.
Point E is where the statue should be placed.
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The Pyramid of Giza is shown. It has a base length of 230 meters and a height of 150 meters.
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is
m2.
The volume is
m3.
the area and volume of the Pyramid of Gaza are 139, 840 m²
and 52950 m³ respectively.
How to determine the parametersThe formula for volume and area of a square pyramid are given thus;
Volume, V= [tex]a^2\frac{h}{3}[/tex]
Area , [tex]A=a^2+2a \sqrt{\frac{a^2}{4}+ h^2 }[/tex]
Where
a is the base lengthh is the heightSubstitute the values;
Area = [tex]230^2 + 2(230) \sqrt{\frac{230^2}{4}+ 150^2 }[/tex]
Area = [tex]52900 + 460 + \sqrt{13225 + 22500}[/tex]
Area = [tex]52900 + 460(189)[/tex]
Area = 52900 + 86, 940
Area = 139, 840 m²
Volume , v = [tex]230^2 + \frac{150}{3}[/tex]
Volume = 52900 + 50
Volume = 52950 m³
Thus, the area and volume of the Pyramid of Gaza are 139, 840 m²
and 52950 m³ respectively.
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answer is in the attachment below
goodluck!!
Select the correct answer.
Graph the following system of inequalities.
y ≥x-2
y ≤-4x - 2
y
-6-5
6
0 1 2 3 4
X
9
5
2
F
6
12 RE
NUE
F
4 5 6
Answer:
I don't understand the formatting after the first two equations.
Step-by-step explanation:
See attached graph.
PLS HELP ASAP! THX
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
The value of the polynomial difference when the value of x is 2.1 is -3.51
Difference of polynomialsPolynomials are functions that has a leading degree of 3 and above. Given the following polynomial expression below;
g(x)= 2x^2+3x-9 and;
h(x)=x^2+2x-6
Take the difference
(h-g)(x) = h(x) - g(x)
Substitute
(h-g)(x) = x^2+2x-6 - (2x^2+3x-9)
(h-g)(x) = x^2+2x-6-2x^2-3x+9
(h-g)(x) = -x^2-x+3
Substitute the value of x to have;
(h-g)(2.1) = -(2.1)^2 - 2.1 + 3
(h-g)(2.1) = -4.41 + 0.9
(h-g)(2.1) = -3.51
Hence the value of the polynomial difference when the value of x is 2.1 is -3.51
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A gardener uses 1/3 of a liter of water to water 2/7 of a garden.
Answer:
[tex]\boxed{\sf 1\dfrac{1}{6}\ liters \ of \ water}[/tex]
Explanation:
Let the total water required water the entire ground be g
Equation:
[tex]\sf \dfrac{2}{7}\:g = \dfrac{1}{3} \ liters \ of \ water[/tex]
rearranging
[tex]\sf g = \dfrac{7(1)}{3(2)}[/tex]
simplify
[tex]\sf g = \dfrac{7}{6} \ liters \ of \ water[/tex]
rewrite in mixed fraction
[tex]\bf g = 1\dfrac{1}{6}\ liters \ of \ water[/tex]
The water required to water the entire ground is 1 1/6 liters.
What is the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet?
Volume=80cubic feet
Length×Width×Height =80cubic feet
Base area×Height =80cubic feet
25square feet×Height =80cubic feet
Height =80÷25
=3.2feet
The height of the rectangular prism is 3.2 feet.
To determine the height of a rectangular prism with a volume of 80 cubic feet and a base area of 25 square feet,
The volume of a rectangular prism, that is V = lwh, where l is the length, w is the width, and h is the height of the prism.
Given:
Volume (V) = 80 cubic feet
Base area (A) = 25 square feet
We know that the base area is equal to the product of the length and width:
A = lw.
Calculate the length (l) and width (w) from the given base area:
We know that A = lw, and A = 25 square feet.
If we assume the length to be greater than the width, we can express the base area as lw = 25.
We need to find two factors of 25 that have a difference as small as possible. The factors of 25 are 1, 5, and 25.
We can choose l = 5 feet and w = 5 feet.
V = lwh.
80 = 5 * 5 * h
Divide both sides of the equation by 25:
80/25 = h.
h = 16/5 = 3.2 feet.
Therefore, the height of the rectangular prism is 3.2 feet.
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for f(x) = x+1 and g(x)= 2x+3, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d.(gof)(2)
Answer:
a) 2x + 4
b) 2x + 5
c) 8
d) 9
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]
Function composition is an operation that takes two or more functions and combines them into a single function.
(f o g)(x) means find g(x) first and then substitute the result into f(x).
(g o f)(x) means find f(x) first and then substitute the result into g(x).
Part (a)
[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]
Part (b)
[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]
Part (c)
[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]
Part (d)
[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]
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(fog)(x)
f(g(x))f(2x+3)2x+3+12x+4(gof)(x)
g(f(x))g(x+1)2x+2+32x+5(fog)(2))
2(2)+48(gof)(2)
2(2)+59Find the 4 terms in the sequence given [tex]an=n^2+4[/tex]
Answer:
a₁ = 5
a₂ = 8
a₃ = 13
a₄ = 20
Step-by-step explanation:
Given sequence formula
aₙ = n² + 4
Requirement of the question
Find the 4 terms in the sequence
Substitute 4 values into the sequence formula
a₁ = (1)² + 4 = 1 + 4 = [tex]\Large\boxed{5}[/tex]
a₂ = (2)² + 4 = 4 + 4 = [tex]\Large\boxed{8}[/tex]
a₃ = (3)² + 4 = 9 + 4 = [tex]\Large\boxed{13}[/tex]
a₄ = (4)² + 4 = 16 + 4 = [tex]\Large\boxed{20}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers.
Samantha and Mia are 13 km apart from each other.
What is Pythagorean ?A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.
Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.
Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.
A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.
Hypotenuse of the triangle, which measures distance between the females
the Pythagorean theorem,
H² = P² + B²
H² = 7² + 11²
H² = 49 + 121
H = √170
H = 13.038
H = 13km
Between them, there is a 13 kilometer distance.
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(01.02 mc)matt is showing his work in simplifying (6.2 − 1.6) − 4.4 7.8. identify any error in his work or reasoning. step 1: (6.2 − 1.6) − 4.4 7.8 step 2: 6.2 (− 1.6 − 4.4) 7.8 (commutative property) step 3: 6.2 − 6 7.8 step 4: −14 − 6 = 8 (commutative property) step 5: 14 − 6 = 8 he wrote commutative instead of distributive in step 4. he wrote commutative instead of distributive in step 2. he wrote commutative instead of associative in step 4. he wrote commutative instead of associative in step 2.
The correct option is (d)
He wrote commutative instead of associative in step 2.
What is the commutative property?According to the commutative property, a mathematical principle, the product of a multiplication does not depend on the order in which the numbers are multiplied.
Commutative property: a+b = b+a
Associative property: (a+b) + = a+(b+c)
Now consider the provided expression.
(6.2 − 1.6) − 4.4 + 7.8
Step 1:
(6.2 − 1.6) − 4.4 + 7.8
Step 2 Use Associative property
6.2 + (−1.6 − 4.4) + 7.8
Step 3: Simplify
6.2 − 6 + 7.8
Step 4: Use commutative property
14 − 6
Step 5: Simplify
14 − 6 = 8
Hence, the wrong step is step 2.
He wrote commutative instead of associative in Step 2.
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I understand that the question you are looking for is:
Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning. Step 1: (6.2 − 1.6) − 4.4 + 7.8 Step 2: 6.2 + (− 1.6 − 4.4) + 7.8 (commutative property) Step 3: 6.2 − 6 + 7.8 Step 4: −14 − 6 = 8 (commutative property) Step 5: 14 − 6 = 8
(a)-He wrote commutative instead of distributive in Step 4.
(b)-He wrote commutative instead of distributive in Step 2.
(c)-He wrote commutative instead of associative in Step 4.
(d)-He wrote commutative instead of associative in Step 2.
Choose the numbers that are terminating decimals. Select all that apply.
A. 0.032
B. 0.999...
C. 0.525
D. 0.75
Answer: A, C, and D
Step-by-step explanation:
A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.
✓ A. 0.032
✗ B. 0.999...
✓ C. 0.525
✓ D. 0.75
A scientist uses a submarine to study ocean life.
She begins 86 feet below sea level.
After traveling down for 3 seconds, she's 193 feet below sea level.
Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.
Answer: 35.7 feet per second.
Step-by-step explanation: The scientist starts at -86 feet. Then she goes to -193 feet. The difference here is 193-86 = 107 feet. That means she traveled 107 ft in 3 seconds. 107/3 = 35 with a remainder of 2. 2/3 approximately equals 0.6666667. We need to round to the nearest tenth which is 0.7. So, we are left with 35.7.
A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 8y 7z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ −8 (y z = 6) ⋅ 7 (8y 7z = 1) ⋅ 7 (8y 7z = 1) ⋅ 8
Correct option for solving the system of two equation is ([tex]y\times z =6[/tex])[tex]\times -8[/tex] .
What is simultaneous linear equation?
A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. Finding values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.
Simultaneous linear equations are two linear equations in two variables put together.
The ordered pair (x, y) that satisfies both linear equations is the system of simultaneous linear equations' solution.
Given,
Equation p: [tex]y+z=6[/tex]
Equation q: [tex]8y+7z=1[/tex]
To solve the above simultaneous linear equation multiply the equation p with (-8)
[tex](y+z=6)\times -8[/tex] ...................................................... Equation (1)
Now add Equation (1) with Equation (q)
[tex]-8y-8z=-48[/tex]
+ [tex]8y+7z=1[/tex]
⇒ [tex]-z=-47[/tex]
⇒ [tex]z=47[/tex]
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The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
The length is 25 feet and the width is 135 feet
What are consecutive odd integers?
Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.
How to find the perimeter of the rectangle?
⇒Perimeter of rectangle = 2(l+w)
The perimeter of a rectangle is 320 feet
let the length of a rectangle is x
The next consecutive odd integer is x+2
width = 5(x+2)
=5x+10
2(length + width) = 320
l+w=160
x+5x+10=160
6x=150
x=25
length = 25 feet
width = 5(25+2)=135 feet
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Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). give the interval of convergence for the resulting series
The power series is
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
To deduce the power series of g(x) from the power series for f(x) and identify its radius of convergence
The power series for f(x) is just the geometric series derived from 1/1-y ,setting y=2x.
Its radius of convergence is 0.5
Let,
f(x)= 1/1-2x = 1+ (2x) + (2x)2 + .........+(2x)n......+....
The power series expansion (geometric series),
valid for I2xI < 1 , IxI < 0.5
so, radius of convergence = 0.5
The power series for g(x) is found by integrating term by term the power series of f(x) (upto a constant). The radius of converngence of g(d) is the same as that of f(x) (from general theory) =0.5
Now, g(x) = ln(1-2x)
= -2 [tex]\int\limits^a_b {(1/1-2x)} \, dx = -2 \int\limits^a_b {f(x)} \, dx[/tex]
=-2 [tex]\int\limits^a_b {[1+(2x)+ (2x)2 +........+ (2x)n+.......]} \, dx[/tex]
g(x) = -2x - (2x)2/2 - (2x)3/3 -(2x)4/4 -.......-(2x)n/n - .....
is the power series expansion for g(x).
radius of convergence =0.5
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Small numbers that are added to avoid unfair scoring of low-probability outcomes are called ___.
Small numbers that are added to avoid unfair scoring of low-probability outcomes are called pseudocodes
How to complete the blank?From the statement, we have the following highlights:
The numbers are small numbers Adding the numbers is used to avoid unfair scoring of low-probability outcomesThe term for the statements in the above highlight is pseudocodes
This is because pseudocodes are false codes or small numbers
Hence, the small numbers that are added to avoid unfair scoring of low-probability outcomes are called pseudocodes
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Dean's father, Franco, is 5 times his age. Dean is 8 years older than his sister, Helen. The sum of their ages is 62 years. How old is each person
Answer:
dean = 10
franco = 50
helen = 2
steps
you want to get the age of one of the people first
'is' means equal
'older than' means plus
'sum' means total by adding
d
f = 5d
d = 8 + h
d + f + h = 62
make sure there is 1 letter to solve for
d = 8 + h -> h = d - 8
f = 5d
d = d
d + f + h = 62
d + (5d) + (d-8)
7d - 8 = 62
7d = 70
d = 10
f = 50
h = 2
Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x 3y − z = 0.
The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].
Then the plane we want has equation
[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]f(x)=-2(x-3)^2+2[/tex]
Step-by-step explanation:
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.
x-intercept(s): (2,0),(4,0)
y-intercept(s): (0,−16)
Answer:
D f(x) = -2(x - 3)² + 2
Step-by-step explanation:
The y-intercept occurs at x = 0.
A
f(x) = 2x(x + 14) - 64
f(0) = -64 Not -16
B
f(x) = (x + 4)² + 2x
f(0) = 16 Not -16
C
f(x) = (x - 16)² + 4
f(0) = 260 Not -16
D
f(x) = -2(x - 3)² + 2
f(0) = -18 + 2 = -16 <-------------------- this is it
If a system reliability of 0. 998 is required, what reliability of two components in series is required?
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
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Refer to the figure to the right.
A. If RV RT, name two congruent angles.
B. If RSSV, name two congruent angles.
C. If LSRT LSTR, name two congruent segments.
D. If LSTV= LSVT, name two congruent segments.
R
T
Answer:
c if lsrt lstr name two congruent segments